Annotation of /trunk/webwork/system/courseScripts/PGanswermacros.pl

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1 :	gage	28	#!/usr/local/bin/webwork-perl
2 :	sam	2
3 :			# This file is PGanswermacros.pl
4 :			# This includes the subroutines for the ANS macros, that
5 :			# is, macros allowing a more flexible answer checking
6 :			####################################################################
7 :			# Copyright @ 1995-2000 University of Rochester
8 :			# All Rights Reserved
9 :			####################################################################
10 :	gage	32	#$Id$
11 :	sam	2
12 :			=head1 NAME
13 :
14 :			PGanswermacros.pl -- located in the courseScripts directory
15 :
16 :			=head1 SYNPOSIS
17 :
18 :			Number Answer Evaluators:
19 :			num_cmp() -- uses an input hash to determine parameters
20 :			std_num_cmp(), std_num_cmp_list(), std_num_cmp_abs, std_num_cmp_abs_list()
21 :			frac_num_cmp(), frac_num_cmp_list(), frac_num_cmp_abs, frac_num_cmp_abs_list()
22 :			arith_num_cmp(), arith_num_cmp_list(), arith_num_cmp_abs, arith_num_cmp_abs_list()
23 :			strict_num_cmp(), strict_num_cmp_list(), strict_num_cmp_abs, strict_num_cmp_abs_list()
24 :			numerical_compare_with_units() -- requires units as part of the answer
25 :			std_num_str_cmp() -- also accepts a set of strings as possible answers
26 :
27 :			Function Answer Evaluators:
28 :			fun_cmp() -- uses an input hash to determine parameters
29 :			function_cmp(), function_cmp_abs()
30 :			function_cmp_up_to_constant(), function_cmp_up_to_constant_abs()
31 :			multivar_function_cmp()
32 :
33 :			String Answer Evaluators:
34 :			str_cmp() -- uses an input hash to determine parameters
35 :			std_str_cmp(), std_str_cmp_list(), std_cs_str_cmp(), std_cs_str_cmp_list()
36 :			strict_str_cmp(), strict_str_cmp_list()
37 :			ordered_str_cmp(), ordered_str_cmp_list(), ordered_cs_str_cmp(), ordered_cs_str_cmp_list()
38 :			unordered_str_cmp(), unordered_str_cmp_list(), unordered_cs_str_cmp(), unordered_cs_str_cmp_list()
39 :
40 :			Miscellaneous Answer Evaluators:
41 :			checkbox_cmp()
42 :			radio_cmp()
43 :
44 :			=cut
45 :
46 :			=head1 DESCRIPTION
47 :
48 :			This file adds subroutines which create "answer evaluators" for checking
49 :			answers. Each answer evaluator accepts a single input from a student answer,
50 :			checks it and creates an output hash %ans_hash with seven or eight entries
51 :			(the preview_latex_string is optional). The output hash is now being created
52 :			with the AnswerHash package "class", which is located at the end of this file.
53 :			This class is currently just a wrapper for the hash, but this might change in
54 :			the future as new capabilities are added.
55 :
56 :	chris	54	score => $correctQ,
57 :			correct_ans => $originalCorrEqn,
58 :			student_ans => $modified_student_ans
59 :	sam	2	original_student_ans => $original_student_answer,
60 :	chris	54	ans_message => $PGanswerMessage,
61 :			type => 'typeString',
62 :			preview_text_string => $preview_text_string,
63 :	sam	2	preview_latex_string => $preview_latex_string
64 :
65 :
66 :	chris	81	$ans_hash{score} -- a number between 0 and 1 indicating
67 :	sam	2	whether the answer is correct. Fractions
68 :			allow the implementation of partial
69 :			credit for incorrect answers.
70 :			$ans_hash{correct_ans} -- The correct answer, as supplied by the
71 :			instructor and then formatted. This can
72 :			be viewed by the student after the answer date.
73 :			$ans_hash{student_ans} -- This is the student answer, after reformatting;
74 :			for example the answer might be forced
75 :			to capital letters for comparison with
76 :			the instructors answer. For a numerical
77 :			answer, it gives the evaluated answer.
78 :			This is displayed in the section reporting
79 :			the results of checking the student answers.
80 :	chris	81	$ans_hash{original_student_ans} -- This is the original student answer. This is displayed
81 :	sam	2	on the preview page and may be used for sticky answers.
82 :			$ans_hash{ans_message} -- Any error message, or hint provided by the answer evaluator.
83 :			This is also displayed in the section reporting
84 :			the results of checking the student answers.
85 :	chris	81	$ans_hash{type} -- A string indicating the type of answer evaluator. This
86 :	sam	2	helps in preprocessing the student answer for errors.
87 :			Some examples:
88 :			'number_with_units'
89 :			'function'
90 :			'frac_number'
91 :			'arith_number'
92 :	chris	81	$ans_hash{preview_text_string} -- This typically shows how the student answer was parsed. It is
93 :	sam	2	displayed on the preview page. For a student answer of 2sin(3x)
94 :			this would be 2sin(3x). For string answers it is typically the
95 :			same as $ans_hash{student_ans}.
96 :	chris	81	$ans_hash{preview_latex_string -- THIS IS OPTIONAL. This is latex version of the student answer
97 :	sam	2	which is used to show a typeset view on the answer on the preview
98 :			page. For a student answer of 2/3, this would be \frac{2}{3}.
99 :
100 :			Technical note: the routines in this file are not actually answer evaluators. Instead, they create
101 :			answer evaluators. An answer evaluator is an anonymous subroutine, referenced by a named scalar. The
102 :			routines in this file build the subroutine and return a reference to it. Later, when the student
103 :			actually enters an answer, the problem processor feeds that answer to the referenced subroutine, which
104 :			evaluates it and returns a score (usually 0 or 1). For most users, this distinction is unimportant, but
105 :			if you plan on writing your own answer evaluators, you should understand this point.
106 :
107 :			=cut
108 :
109 :			BEGIN {
110 :			be_strict(); # an alias for use strict. This means that all global variable must contain main:: as a prefix.
111 :			}
112 :	gage	33
113 :
114 :	chris	81	my ($BR , # convenient localizations.
115 :			$PAR ,
116 :	gage	36	$numRelPercentTolDefault ,
117 :			$numZeroLevelDefault ,
118 :			$numZeroLevelTolDefault ,
119 :	chris	81	$numAbsTolDefault ,
120 :			$numFormatDefault ,
121 :	gage	36	$functRelPercentTolDefault ,
122 :			$functZeroLevelDefault ,
123 :			$functZeroLevelTolDefault ,
124 :	chris	81	$functAbsTolDefault ,
125 :			$functNumOfPoints ,
126 :			$functVarDefault ,
127 :			$functLLimitDefault ,
128 :			$functULimitDefault ,
129 :			$functMaxConstantOfIntegration ,
130 :			$CA
131 :	gage	36	);
132 :
133 :	gage	32	sub _PGanswermacros_init {
134 :	gage	34
135 :	gage	32	$BR = $main::BR; # convenient localizations.
136 :			$PAR = $main::PAR;
137 :
138 :			# import defaults
139 :			# these are now imported from the %envir variable
140 :	gage	36	$numRelPercentTolDefault = $main::numRelPercentTolDefault;
141 :			$numZeroLevelDefault = $main::numZeroLevelDefault;
142 :			$numZeroLevelTolDefault = $main::numZeroLevelTolDefault;
143 :	chris	54	$numAbsTolDefault = $main::numAbsTolDefault;
144 :			$numFormatDefault = $main::numFormatDefault;
145 :	gage	36	$functRelPercentTolDefault = $main::functRelPercentTolDefault;
146 :			$functZeroLevelDefault = $main::functZeroLevelDefault;
147 :			$functZeroLevelTolDefault = $main::functZeroLevelTolDefault;
148 :			$functAbsTolDefault = $main::functAbsTolDefault;
149 :	chris	54	$functNumOfPoints = $main::functNumOfPoints;
150 :			$functVarDefault = $main::functVarDefault;
151 :	gage	36	$functLLimitDefault = $main::functLLimitDefault;
152 :			$functULimitDefault = $main::functULimitDefault;
153 :	chris	54	$functMaxConstantOfIntegration = $main::functMaxConstantOfIntegration;
154 :	gage	32
155 :	gage	34
156 :
157 :	gage	32	}
158 :	sam	2
159 :			##########################################################################
160 :			##########################################################################
161 :			## Number answer evaluators
162 :
163 :			=head2 Number Answer Evaluators
164 :
165 :			Number answer evaluators take in a numerical answer, compare it to the correct answer,
166 :			and return a score. In addition, they can choose to accept or reject an answer based on
167 :			its format, closeness to the correct answer, and other criteria. There are two types
168 :			of numerical answer evaluators: num_cmp(), which takes a hash of named options as parameters,
169 :			and the "mode"_num_cmp() variety, which use different functions to access different sets of
170 :			options. In addition, there is the special case of std_num_str_cmp(), which can evaluate
171 :			both numbers and strings.
172 :
173 :			Numerical Comparison Options
174 :
175 :	chris	81	correctAnswer -- This is the correct answer that the student answer will
176 :	sam	2	be compared to. However, this does not mean that the
177 :			student answer must match this exactly. How close the
178 :			student answer must be is determined by the other
179 :			options, especially tolerance and format.
180 :
181 :			tolerance -- These options determine how close the student answer
182 :			must be to the correct answer to qualify. There are two
183 :			types of tolerance: relative and absolute. Relative
184 :			tolerances are given in percentages. A relative
185 :			tolerance of 1 indicates that the student answer must
186 :			be within 1% of the correct answer to qualify as correct.
187 :			In other words, a student answer is correct when
188 :			abs(studentAnswer - correctAnswer) <= abs(.01relpercentTolcorrectAnswer)
189 :			Using absolute tolerance, the student answer must be a
190 :			fixed distance from the correct answer to qualify.
191 :			For example, an absolute tolerance of 5 means that any
192 :			number which is +-5 of the correct answer qualifies as correct.
193 :			Final (rarely used) tolerance options are zeroLevel
194 :			and zeroLevelTol, used in conjunction with relative
195 :			tolerance. if correctAnswer has absolute value less than
196 :			or equal to zeroLevel, then the student answer must be,
197 :			in absolute terms, within zeroLevelTol of correctAnswer, i.e.,
198 :			abs(studentAnswer - correctAnswer) <= zeroLevelTol.
199 :			In other words, if the correct answer is very near zero,
200 :			an absolute tolerance will be used. One must do this to
201 :			handle floating point answers very near zero, because of
202 :			the inaccuracy of floating point arithmetic. However, the
203 :			default values are almost always adequate.
204 :
205 :			mode -- This determines the allowable methods for entering an
206 :			answer. Answers which do not meet this requirement will
207 :			be graded as incorrect, regardless of their numerical
208 :			value. The recognized modes are:
209 :			'std' (default) -- allows any expression which evaluates
210 :			to a number, including those using
211 :			elementary functions like sin() and
212 :			exp(), as well as the operations of
213 :			arithmetic (+, -, *, /, ^)
214 :	chris	81	'strict' -- only decimal numbers are allowed
215 :			'frac' -- whole numbers and fractions are allowed
216 :			'arith' -- arithmetic expressions are allowed, but
217 :	sam	2	no functions
218 :			Note that all modes allow the use of "pi" and "e" as
219 :			constants, and also the use of "E" to represent scientific
220 :			notation.
221 :
222 :			format -- The format to use when displaying the correct and
223 :			submitted answers. This has no effect on how answers are
224 :			evaluated; it is only for cosmetic purposes. The
225 :			formatting syntax is the same as Perl uses for the sprintf()
226 :			function. Format strings are of the form '%m.nx' or '%m.nx#',
227 :			where m and n are described below, and x is a formatter.
228 :			Esentially, m is the minimum length of the field
229 :			(make this negative to left-justify). Note that the decimal
230 :			point counts as a character when determining the field width.
231 :			If m begins with a zero, the number will be padded with zeros
232 :			instead of spaces to fit the field.
233 :			The precision specifier (n) works differently, depending
234 :			on which formatter you are using. For d, i, o, u, x and X
235 :			formatters (non-floating point formatters), n is the minimum
236 :			number of digits to display. For e and f, it is the number of
237 :			digits that appear after the decimal point (extra digits will
238 :			be rounded; insufficient digits will be padded with spaces--see
239 :			'#' below). For g, it is the number of significant digits to
240 :			display.
241 :			The full list of formatters can be found in the manpage
242 :			for printf(3), or by typing "perldoc -f sprintf" at a
243 :			terminal prompt. The following is a brief summary of the
244 :			most frequent formatters:
245 :			d -- decimal number
246 :			ld -- long decimal number
247 :			u -- unsigned decimal number
248 :			lu -- long unsigned decimal number
249 :			x -- hexadecimal number
250 :			o -- octal number
251 :			e -- floating point number in scientific notation
252 :			f -- floating point number
253 :			g -- either e or f, whichever takes less space
254 :			Technically, g will use e if the exponent is less than -4 or
255 :			greater than or equal to the precision. Trailing zeros are
256 :			removed in this mode.
257 :			If the format string ends in '#', trailing zeros will be
258 :			removed in the decimal part. Note that this is not a standard
259 :			syntax; it is handled internally by WeBWorK and not by Perl
260 :			(although this should not be a concern to end users).
261 :			The default format is '%0.5f#', which displays as a floating
262 :			point number with 5 digits of precision and no trailing zeros.
263 :			Other useful format strings might be '%0.2f' for displaying
264 :			dollar amounts, or '%010d' to display an integer with leading
265 :			zeros. Setting format to an empty string ( '' ) means no
266 :			formatting will be used; this will show 'arbitrary' precision
267 :			floating points.
268 :
269 :			Default Values (As of 7/24/2000) (Option -- Variable Name -- Value)
270 :
271 :	chris	54	Format -- $numFormatDefault -- "%0.5f#"
272 :			Relative Tolerance -- $numRelPercentTolDefault -- .1
273 :			Absolute Tolerance -- $numAbsTolDefault -- .001
274 :			Zero Level -- $numZeroLevelDefault -- 1E-14
275 :	sam	2	Zero Level Tolerance -- $numZeroLevelTolDefault -- 1E-12
276 :
277 :			=cut
278 :
279 :			=head3 "mode"_num_cmp() functions
280 :
281 :			There are 16 functions total, 4 for each mode (std, frac, strict, arith). Each mode has
282 :			one "normal" function, one which accepts a list of answers, one which uses absolute
283 :			rather than relative tolerance, and one which uses absolute tolerance and accepts a list.
284 :			The "std" family is documented below; all others work precisely the same.
285 :
286 :			std_num_cmp($correctAnswer) OR
287 :			std_num_cmp($correctAnswer, $relPercentTol) OR
288 :			std_num_cmp($correctAnswer, $relPercentTol, $format) OR
289 :			std_num_cmp($correctAnswer, $relPercentTol, $format, $zeroLevel) OR
290 :			std_num_cmp($correctAnswer, $relPercentTol, $format, $zeroLevel, $zeroLevelTol)
291 :
292 :			$correctAnswer -- the correct answer
293 :			$relPercentTol -- the tolerance, as a percentage (optional)
294 :	chris	54	$format -- the format of the displayed answer (optional)
295 :			$zeroLevel -- if the correct answer is this close to zero, then zeroLevelTol applies (optional)
296 :	sam	2	$zeroLevelTol -- absolute tolerance to allow when correct answer is close to zero (optional)
297 :
298 :			std_num_cmp() uses standard mode (arithmetic operations and elementary
299 :			functions allowed) and relative tolerance. Options are specified by
300 :			one or more parameters. Note that if you wish to set an option which
301 :			is later in the parameter list, you must set all previous options.
302 :
303 :			std_num_cmp_abs($correctAnswer) OR
304 :			std_num_cmp_abs($correctAnswer, $absTol) OR
305 :			std_num_cmp_abs($correctAnswer, $absTol, $format)
306 :
307 :	chris	54	$correctAnswer -- the correct answer
308 :	sam	2	$absTol -- an absolute tolerance (optional)
309 :			$format -- the format of the displayed answer (optional)
310 :
311 :			std_num_cmp_abs() uses standard mode and absolute tolerance. Options
312 :			are set as with std_num_cmp(). Note that $zeroLevel and $zeroLevelTol
313 :			do not apply with absolute tolerance.
314 :
315 :			std_num_cmp_list($relPercentTol, $format, @answerList)
316 :
317 :	chris	54	$relPercentTol -- the tolerance, as a percentage
318 :	sam	2	$format -- the format of the displayed answer(s)
319 :			@answerList -- a list of one or more correct answers
320 :
321 :			std_num_cmp_list() uses standard mode and relative tolerance. There
322 :			is no way to set $zeroLevel or $zeroLevelTol. Note that no
323 :			parameters are optional. All answers in the list will be
324 :			evaluated with the same set of parameters.
325 :
326 :			std_num_cmp_abs_list($absTol, $format, @answerList)
327 :
328 :			$absTol -- an absolute tolerance
329 :			$format -- the format of the displayed answer(s)
330 :			@answerList -- a list of one or more correct answers
331 :
332 :			std_num_cmp_abs_list() uses standard mode and absolute tolerance.
333 :			Note that no parameters are optional. All answers in the list will be
334 :			evaluated with the same set of parameters.
335 :
336 :			arith_num_cmp(), arith_num_cmp_list(), arith_num_cmp_abs(), arith_num_cmp_abs_list()
337 :			strict_num_cmp(), strict_num_cmp_list(), strict_num_cmp_abs(), strict_num_cmp_abs_list()
338 :			frac_num_cmp(), frac_num_cmp_list(), frac_num_cmp_abs(), frac_num_cmp_abs_list()
339 :
340 :			Examples:
341 :
342 :			ANS( strict_num_cmp( 3.14159 ) ) -- The student answer must be a number
343 :			in decimal or scientific notation which is within .1 percent of 3.14159.
344 :			This assumes $numRelPercentTolDefault has been set to .1.
345 :			ANS( strict_num_cmp( $answer, .01 ) ) -- The student answer must be a
346 :			number within .01 percent of $answer (e.g. 3.14159 if $answer is 3.14159
347 :			or $answer is "pi" or $answer is 4*atan(1)).
348 :			ANS( frac_num_cmp( $answer) ) or ANS( frac_num_cmp( $answer,.01 )) --
349 :			The student answer can be a number or fraction, e.g. 2/3.
350 :			ANS( arith_num_cmp( $answer) ) or ANS( arith_num_cmp( $answer,.01 )) --
351 :			The student answer can be an arithmetic expression, e.g. (2+3)/7-2^.5 .
352 :			ANS( std_num_cmp( $answer) ) or ANS( std_num_cmp( $answer,.01 )) --
353 :			The student answer can contain elementary functions, e.g. sin(.3+pi/2)
354 :
355 :			=cut
356 :
357 :	chris	54	sub std_num_cmp { # compare numbers allowing use of elementary functions
358 :	chris	22	my ( $correctAnswer, $relPercentTol, $format, $zeroLevel, $zeroLevelTol ) = @_;
359 :	sam	2
360 :	chris	22	my %options = ( 'tolerance' => $relPercentTol,
361 :			'format' => $format,
362 :			'zeroLevel' => $zeroLevel,
363 :			'zeroLevelTol' => $zeroLevelTol
364 :	chris	81	);
365 :	chris	22
366 :			set_default_options( \%options,
367 :			'tolType' => 'relative',
368 :			'tolerance' => $numRelPercentTolDefault,
369 :	chris	54	'mode' => 'std',
370 :			'format' => $numFormatDefault,
371 :			'relTol' => $numRelPercentTolDefault,
372 :	chris	22	'zeroLevel' => $numZeroLevelDefault,
373 :			'zeroLevelTol' => $numZeroLevelTolDefault,
374 :			'debug' => 0,
375 :	chris	81	);
376 :	gage	34
377 :	chris	22	num_cmp([$correctAnswer], %options);
378 :	sam	2	}
379 :
380 :			## Similar to std_num_cmp but accepts a list of numbers in the form
381 :			## std_num_cmp_list(relpercentTol,format,ans1,ans2,ans3,...)
382 :			## format is of the form "%10.3g" or "", i.e., a format suitable for sprintf(). Use "" for default
383 :			## You must enter a format and tolerance
384 :	chris	81
385 :	chris	54	sub std_num_cmp_list {
386 :	sam	2	my ( $relPercentTol, $format, @answerList) = @_;
387 :
388 :	chris	54	my %options = ( 'tolerance' => $relPercentTol,
389 :			'format' => $format,
390 :	chris	81	);
391 :	chris	22
392 :			set_default_options( \%options,
393 :			'tolType' => 'relative',
394 :			'tolerance' => $numRelPercentTolDefault,
395 :			'mode' => 'std',
396 :			'format' => $numFormatDefault,
397 :			'relTol' => $numRelPercentTolDefault,
398 :			'zeroLevel' => $numZeroLevelDefault,
399 :			'zeroLevelTol' => $numZeroLevelTolDefault,
400 :			'debug' => 0,
401 :			);
402 :
403 :			num_cmp(\@answerList, %options);
404 :
405 :	sam	2	}
406 :
407 :	chris	54	sub std_num_cmp_abs { # compare numbers allowing use of elementary functions with absolute tolerance
408 :	sam	2	my ( $correctAnswer, $absTol, $format) = @_;
409 :	chris	22	my %options = ( 'tolerance' => $absTol,
410 :	chris	54	'format' => $format
411 :	chris	81	);
412 :	chris	22
413 :			set_default_options (\%options,
414 :			'tolType' => 'absolute',
415 :			'tolerance' => $absTol,
416 :			'mode' => 'std',
417 :			'format' => $numFormatDefault,
418 :			'zeroLevel' => 0,
419 :			'zeroLevelTol' => 0,
420 :			'debug' => 0,
421 :	chris	81	);
422 :	sam	2
423 :	chris	22	num_cmp([$correctAnswer], %options);
424 :	sam	2	}
425 :
426 :			## See std_num_cmp_list for usage
427 :	chris	22
428 :	chris	54	sub std_num_cmp_abs_list {
429 :	sam	2	my ( $absTol, $format, @answerList ) = @_;
430 :
431 :	chris	22	my %options = ( 'tolerance' => $absTol,
432 :			'format' => $format,
433 :	chris	81	);
434 :	chris	22
435 :			set_default_options( \%options,
436 :			'tolType' => 'absolute',
437 :			'tolerance' => $absTol,
438 :			'mode' => 'std',
439 :			'format' => $numFormatDefault,
440 :			'zeroLevel' => 0,
441 :			'zeroLevelTol' => 0,
442 :			'debug' => 0,
443 :	chris	81	);
444 :	chris	22
445 :			num_cmp(\@answerList, %options);
446 :	sam	2	}
447 :
448 :	chris	54	sub frac_num_cmp { # only allow fractions and numbers as submitted answer
449 :	sam	2
450 :	chris	22	my ( $correctAnswer, $relPercentTol, $format, $zeroLevel, $zeroLevelTol ) = @_;
451 :
452 :			my %options = ( 'tolerance' => $relPercentTol,
453 :			'format' => $format,
454 :			'zeroLevel' => $zeroLevel,
455 :			'zeroLevelTol' => $zeroLevelTol
456 :	chris	81	);
457 :	chris	22
458 :			set_default_options( \%options,
459 :			'tolType' => 'relative',
460 :			'tolerance' => $relPercentTol,
461 :			'mode' => 'frac',
462 :			'format' => $numFormatDefault,
463 :			'zeroLevel' => $numZeroLevelDefault,
464 :			'zeroLevelTol' => $numZeroLevelTolDefault,
465 :			'relTol' => $numRelPercentTolDefault,
466 :			'debug' => 0,
467 :	chris	81	);
468 :	chris	22
469 :			num_cmp([$correctAnswer], %options);
470 :	sam	2	}
471 :
472 :			## See std_num_cmp_list for usage
473 :	chris	54	sub frac_num_cmp_list {
474 :	chris	22	my ( $relPercentTol, $format, @answerList ) = @_;
475 :
476 :			my %options = ( 'tolerance' => $relPercentTol,
477 :			'format' => $format
478 :	chris	81	);
479 :	chris	22
480 :			set_default_options( \%options,
481 :			'tolType' => 'relative',
482 :			'tolerance' => $relPercentTol,
483 :			'mode' => 'frac',
484 :			'format' => $numFormatDefault,
485 :			'zeroLevel' => $numZeroLevelDefault,
486 :			'zeroLevelTol' => $numZeroLevelTolDefault,
487 :			'relTol' => $numRelPercentTolDefault,
488 :			'debug' => 0,
489 :	chris	81	);
490 :	chris	22
491 :			num_cmp(\@answerList, %options);
492 :	sam	2	}
493 :
494 :	chris	54	sub frac_num_cmp_abs { # only allow fraction expressions as submitted answer with absolute tolerance
495 :	chris	22	my ( $correctAnswer, $absTol, $format ) = @_;
496 :
497 :	chris	54	my %options = ( 'tolerance' => $absTol,
498 :			'format' => $format
499 :	chris	81	);
500 :	chris	22
501 :			set_default_options (\%options,
502 :	chris	54	'tolType' => 'absolute',
503 :			'tolerance' => $absTol,
504 :			'mode' => 'frac',
505 :			'format' => $numFormatDefault,
506 :			'zeroLevel' => 0,
507 :			'zeroLevelTol' => 0,
508 :			'debug' => 0,
509 :	chris	81	);
510 :	gage	32
511 :	chris	54	num_cmp([$correctAnswer], %options);
512 :	sam	2	}
513 :	chris	22
514 :	sam	2	## See std_num_cmp_list for usage
515 :	chris	81
516 :	chris	54	sub frac_num_cmp_abs_list {
517 :	chris	22	my ( $absTol, $format, @answerList ) = @_;
518 :
519 :	chris	54	my %options = ( 'tolerance' => $absTol,
520 :			'format' => $format
521 :	chris	81	);
522 :	chris	22
523 :			set_default_options (\%options,
524 :			'tolType' => 'absolute',
525 :			'tolerance' => $absTol,
526 :			'mode' => 'frac',
527 :			'format' => $numFormatDefault,
528 :			'zeroLevel' => 0,
529 :			'zeroLevelTol' => 0,
530 :			'debug' => 0,
531 :	chris	81	);
532 :	chris	22
533 :			num_cmp(\@answerList, %options);
534 :	sam	2	}
535 :
536 :
537 :	chris	54	sub arith_num_cmp { # only allow arithmetic expressions as submitted answer
538 :	chris	22
539 :			my ( $correctAnswer, $relPercentTol, $format, $zeroLevel, $zeroLevelTol ) = @_;
540 :
541 :	chris	54	my %options = ( 'tolerance' => $relPercentTol,
542 :			'format' => $format,
543 :			'zeroLevel' => $zeroLevel,
544 :			'zeroLevelTol' => $zeroLevelTol
545 :	chris	81	);
546 :	chris	22
547 :			set_default_options( \%options,
548 :	chris	54	'tolType' => 'relative',
549 :			'tolerance' => $relPercentTol,
550 :			'mode' => 'arith',
551 :			'format' => $numFormatDefault,
552 :			'zeroLevel' => $numZeroLevelDefault,
553 :			'zeroLevelTol' => $numZeroLevelTolDefault,
554 :			'relTol' => $numRelPercentTolDefault,
555 :			'debug' => 0,
556 :	chris	81	);
557 :	sam	2
558 :	chris	22	num_cmp([$correctAnswer], %options);
559 :	sam	2	}
560 :
561 :			## See std_num_cmp_list for usage
562 :	chris	54	sub arith_num_cmp_list {
563 :	chris	22	my ( $relPercentTol, $format, @answerList ) = @_;
564 :	sam	2
565 :	chris	54	my %options = ( 'tolerance' => $relPercentTol,
566 :			'format' => $format,
567 :	chris	81	);
568 :	chris	22
569 :			set_default_options( \%options,
570 :			'tolType' => 'relative',
571 :			'tolerance' => $relPercentTol,
572 :			'mode' => 'arith',
573 :			'format' => $numFormatDefault,
574 :			'zeroLevel' => $numZeroLevelDefault,
575 :			'zeroLevelTol' => $numZeroLevelTolDefault,
576 :			'relTol' => $numRelPercentTolDefault,
577 :			'debug' => 0,
578 :	chris	81	);
579 :
580 :	chris	22	num_cmp(\@answerList, %options);
581 :	sam	2	}
582 :
583 :	chris	54	sub arith_num_cmp_abs { # only allow arithmetic expressions as submitted answer with absolute tolerance
584 :	chris	22	my ( $correctAnswer, $absTol, $format ) = @_;
585 :
586 :	chris	54	my %options = ( 'tolerance' => $absTol,
587 :			'format' => $format
588 :	chris	81	);
589 :	chris	22
590 :			set_default_options (\%options,
591 :			'tolType' => 'absolute',
592 :			'tolerance' => $absTol,
593 :			'mode' => 'arith',
594 :			'format' => $numFormatDefault,
595 :			'zeroLevel' => 0,
596 :			'zeroLevelTol' => 0,
597 :			'debug' => 0,
598 :	chris	81	);
599 :
600 :	chris	22	num_cmp([$correctAnswer], %options);
601 :	sam	2	}
602 :
603 :			## See std_num_cmp_list for usage
604 :	chris	54	sub arith_num_cmp_abs_list {
605 :	chris	22	my ( $absTol, $format, @answerList ) = @_;
606 :
607 :	chris	54	my %options = ( 'tolerance' => $absTol,
608 :			'format' => $format
609 :	chris	81	);
610 :	chris	22
611 :			set_default_options (\%options,
612 :			'tolType' => 'absolute',
613 :			'tolerance' => $absTol,
614 :			'mode' => 'arith',
615 :			'format' => $numFormatDefault,
616 :			'zeroLevel' => 0,
617 :			'zeroLevelTol' => 0,
618 :			'debug' => 0,
619 :			);
620 :
621 :	chris	81	num_cmp(\@answerList, %options);
622 :	sam	2	}
623 :
624 :	chris	54	sub strict_num_cmp { # only allow numbers as submitted answer
625 :	chris	22	my ( $correctAnswer, $relPercentTol, $format, $zeroLevel, $zeroLevelTol ) = @_;
626 :
627 :	chris	54	my %options = ( 'tolerance' => $relPercentTol,
628 :			'format' => $format,
629 :			'zeroLevel' => $zeroLevel,
630 :			'zeroLevelTol' => $zeroLevelTol
631 :	chris	22	);
632 :
633 :			set_default_options( \%options,
634 :			'tolType' => 'relative',
635 :			'tolerance' => $relPercentTol,
636 :			'mode' => 'strict',
637 :			'format' => $numFormatDefault,
638 :			'zeroLevel' => $numZeroLevelDefault,
639 :			'zeroLevelTol' => $numZeroLevelTolDefault,
640 :			'relTol' => $numRelPercentTolDefault,
641 :			'debug' => 0,
642 :			);
643 :			num_cmp([$correctAnswer], %options);
644 :	chris	81
645 :	sam	2	}
646 :
647 :			## See std_num_cmp_list for usage
648 :	chris	54	sub strict_num_cmp_list { # compare numbers
649 :	chris	81	my ( $relPercentTol, $format, @answerList ) = @_;
650 :	chris	22
651 :	chris	81	my %options = ( 'tolerance' => $relPercentTol,
652 :	chris	54	'format' => $format,
653 :	chris	81	);
654 :	chris	22
655 :	chris	81	set_default_options( \%options,
656 :	chris	22	'tolType' => 'relative',
657 :			'tolerance' => $relPercentTol,
658 :			'mode' => 'strict',
659 :			'format' => $numFormatDefault,
660 :			'zeroLevel' => $numZeroLevelDefault,
661 :			'zeroLevelTol' => $numZeroLevelTolDefault,
662 :			'relTol' => $numRelPercentTolDefault,
663 :			'debug' => 0,
664 :	chris	81	);
665 :
666 :			num_cmp(\@answerList, %options);
667 :			}
668 :	sam	2
669 :	chris	22
670 :	chris	54	sub strict_num_cmp_abs { # only allow numbers as submitted answer with absolute tolerance
671 :	chris	22	my ( $correctAnswer, $absTol, $format ) = @_;
672 :
673 :	chris	54	my %options = ( 'tolerance' => $absTol,
674 :			'format' => $format
675 :	chris	81	);
676 :	chris	22
677 :			set_default_options (\%options,
678 :			'tolType' => 'absolute',
679 :			'tolerance' => $absTol,
680 :			'mode' => 'strict',
681 :			'format' => $numFormatDefault,
682 :			'zeroLevel' => 0,
683 :			'zeroLevelTol' => 0,
684 :			'debug' => 0,
685 :	chris	81	);
686 :	chris	22	num_cmp([$correctAnswer], %options);
687 :
688 :	sam	2	}
689 :
690 :			## See std_num_cmp_list for usage
691 :	chris	54	sub strict_num_cmp_abs_list { # compare numbers
692 :	chris	22	my ( $absTol, $format, @answerList ) = @_;
693 :	chris	81
694 :	chris	54	my %options = ( 'tolerance' => $absTol,
695 :			'format' => $format
696 :	chris	81	);
697 :	sam	2
698 :	chris	22	set_default_options (\%options,
699 :			'tolType' => 'absolute',
700 :			'tolerance' => $absTol,
701 :			'mode' => 'strict',
702 :			'format' => $numFormatDefault,
703 :			'zeroLevel' => 0,
704 :			'zeroLevelTol' => 0,
705 :			'debug' => 0,
706 :	chris	81	);
707 :	chris	22
708 :			num_cmp(\@answerList, %options);
709 :	sam	2	}
710 :
711 :	chris	81	## sub numerical_compare_with_units
712 :	sam	2	## Compares a number with units
713 :			## Deprecated; use num_cmp()
714 :			##
715 :			## IN: a string which includes the numerical answer and the units
716 :			## a hash with the following keys (all optional):
717 :	chris	81	## mode -- 'std', 'frac', 'arith', or 'strict'
718 :			## format -- the format to use when displaying the answer
719 :			## tol -- an absolute tolerance, or
720 :			## relTol -- a relative tolerance
721 :			## zeroLevel -- if the correct answer is this close to zero, then zeroLevelTol applies
722 :	sam	2	## zeroLevelTol -- absolute tolerance to allow when correct answer is close to zero
723 :
724 :	chris	35	# This mode is depricated. send input through num_cmp -- it can handle units.
725 :	chris	54
726 :			sub numerical_compare_with_units {
727 :	chris	81	my $correct_answer = shift; # the answer is a string which includes both the numerical answer and the units.
728 :	chris	22	my %options = @_; # all of the other inputs are (key value) pairs
729 :	sam	2
730 :	chris	22	# Prepare the correct answer
731 :			$correct_answer = str_filters( $correct_answer, 'trim_whitespace' );
732 :	sam	2
733 :	chris	22	# it surprises me that the match below works since the first .* is greedy.
734 :			my ($correct_num_answer, $correct_units) = $correct_answer =~ /^(.)\s+([^\s])$/;
735 :			$options{units} = $correct_units;
736 :
737 :			num_cmp($correct_num_answer, %options);
738 :	sam	2	}
739 :	chris	22
740 :	sam	2
741 :			=head3 std_num_str_cmp()
742 :	chris	22
743 :	sam	2	NOTE: This function is maintained for compatibility. num_cmp() with the
744 :			'strings' parameter is slightly preferred.
745 :
746 :			std_num_str_cmp() is used when the correct answer could be either a number or a
747 :			string. For example, if you wanted the student to evaluate a function at number
748 :			of points, but write "Inf" or "Minf" if the function is unbounded. This routine
749 :			will provide error messages that do not give a hint as to whether the correct
750 :			answer is a string or a number. For numerical comparisons, std_num_cmp() is
751 :			used internally; for string comparisons, std_str_cmp() is used.
752 :
753 :			std_num_str_cmp( $correctAnswer ) OR
754 :			std_num_str_cmp( $correctAnswer, $ra_legalStrings ) OR
755 :			std_num_str_cmp( $correctAnswer, $ra_legalStrings, $relPercentTol ) OR
756 :			std_num_str_cmp( $correctAnswer, $ra_legalStrings, $relPercentTol, $format ) OR
757 :			std_num_str_cmp( $correctAnswer, $ra_legalStrings, $relPercentTol, $format, $zeroLevel ) OR
758 :			std_num_str_cmp( $correctAnswer, $ra_legalStrings, $relPercentTol, $format,
759 :			$zeroLevel, $zeroLevelTol )
760 :
761 :			$correctAnswer -- the correct answer
762 :			$ra_legalStrings -- a reference to an array of legal strings, e.g. ["str1", "str2"]
763 :			$relPercentTol -- the error tolerance as a percentage
764 :	chris	54	$format -- the display format
765 :			$zeroLevel -- if the correct answer is this close to zero, then zeroLevelTol applies
766 :	sam	2	$zeroLevelTol -- absolute tolerance to allow when correct answer is close to zero
767 :
768 :			Example:
769 :			ANS( std_num_str_cmp( $ans, ["Inf", "Minf", "NaN"] ) );
770 :
771 :			=cut
772 :
773 :	chris	54	sub std_num_str_cmp {
774 :	sam	2	my ( $correctAnswer, $ra_legalStrings, $relpercentTol, $format, $zeroLevel, $zeroLevelTol ) = @_;
775 :	chris	35	# warn ('This method is depreciated. Use num_cmp instead.');
776 :			return num_cmp ($correctAnswer, strings=>$ra_legalStrings, relTol=>$relpercentTol, format=>$format,
777 :			zeroLevel=>$zeroLevel, zeroLevelTol=>$zeroLevelTol);
778 :			}
779 :	sam	2
780 :			=head3 num_cmp()
781 :
782 :			Compares a number or a list of numbers, using a named hash of options to set
783 :			parameters. This can make for more readable code than using the "mode"_num_cmp()
784 :			style, but some people find one or the other easier to remember.
785 :
786 :			ANS( num_cmp( answer or answer_array_ref, options_hash ) );
787 :
788 :			1. the correct answer, or a reference to an array of correct answers
789 :			2. a hash with the following keys (all optional):
790 :	chris	81	mode -- 'std' (default) (allows any expression evaluating to a number)
791 :	sam	2	'strict' (only numbers are allowed)
792 :			'frac' (fractions are allowed)
793 :	chris	81	'arith' (arithmetic expressions allowed)
794 :	sam	2	format -- '%0.5f#' (default); defines formatting for the correct answer
795 :	chris	54	tol -- an absolute tolerance, or
796 :	sam	2	relTol -- a relative tolerance
797 :			units -- the units to use for the answer(s)
798 :			strings -- a reference to an array of strings which are valid
799 :			answers (works like std_num_str_cmp() )
800 :			zeroLevel -- if the correct answer is this close to zero, then zeroLevelTol applies
801 :	chris	54	zeroLevelTol -- absolute tolerance to allow when answer is close to zero
802 :	chris	81
803 :			debug -- if set to 1, provides verbose listing of hash entries throughout fliters.
804 :	sam	2
805 :			Returns an answer evaluator, or (if given a reference to an array of
806 :			answers), a list of answer evaluators. Note that a reference to an array of
807 :			answers results is just a shortcut to writing a separate cum_cmp() for each
808 :			answer. It does not mean that any of those answers are considered correct
809 :			for one question.
810 :
811 :			EXAMPLES:
812 :
813 :	chris	54	num_cmp( 5 ) -- correct answer is 5, using defaults for all options
814 :			num_cmp( [5,6,7] ) -- correct answers are 5, 6, and 7, using defaults for all options
815 :	sam	2	num_cmp( 5, mode => 'strict' ) -- correct answer is 5, mode is strict
816 :			num_cmp( [5,6], relTol => 5 ) -- correct answers are 5 and 6, both with 5% relative tolerance
817 :			num_cmp( 6, strings => ["Inf", "Minf", "NaN"] ) -- correct answer is 6, "Inf", "Minf", and "NaN"
818 :			recognized as valid answers
819 :
820 :			=cut
821 :
822 :	chris	54	sub num_cmp {
823 :	chris	81	my $correctAnswer = shift @_;
824 :			$CA = $correctAnswer;
825 :	sam	2	my @opt = @_;
826 :	chris	22	my %out_options;
827 :	sam	2
828 :	chris	22	#########################################################################
829 :			# Retain this first check for backword compatibility. Allows input of the form
830 :			# num_cmp($ans, 1, '%0.5f') but warns against it
831 :			#########################################################################
832 :	sam	2	my %known_options = ( 'mode' => 'std',
833 :	chris	22	'format' => $numFormatDefault,
834 :			'tol' => $numAbsTolDefault,
835 :			'relTol' => $numRelPercentTolDefault,
836 :			'units' => undef,
837 :			'strings' => undef,
838 :			'zeroLevel' => $numZeroLevelDefault,
839 :			'zeroLevelTol' => $numZeroLevelTolDefault,
840 :			'tolType' => 'relative',
841 :			'tolerance' => 1,
842 :			'reltol' => undef, #alternate spelling
843 :	gage	40	'unit' => undef, #alternate spelling
844 :			'debug' => 0
845 :	chris	81	);
846 :	chris	22
847 :	sam	2	my @output_list;
848 :	gage	32	my( $relPercentTol, $format, $zeroLevel, $zeroLevelTol) = @opt;
849 :	chris	22
850 :	sam	2	unless( ref($correctAnswer) eq 'ARRAY' \|\| scalar( @opt ) == 0 \|\|
851 :			( defined($opt[0]) and exists $known_options{$opt[0]} ) ) {
852 :			# unless the first parameter is a list of arrays
853 :			# or the second parameter is a known option or
854 :			# no options were used,
855 :	chris	81	# use the old num_cmp which does not use options, but has inputs
856 :	sam	2	# $relPercentTol,$format,$zeroLevel,$zeroLevelTol
857 :			warn "This method of using num_cmp() is deprecated. Please rewrite this" .
858 :			" problem using the options style of parameter passing (or" .
859 :			" check that your first option is spelled correctly).";
860 :	gage	32
861 :			%out_options = ( 'relTol' => $relPercentTol,
862 :	chris	54	'format' => $format,
863 :			'zeroLevel' => $zeroLevel,
864 :			'zeroLevelTol' => $zeroLevelTol,
865 :			'mode' => 'std'
866 :	chris	81	);
867 :	gage	32	}
868 :	chris	54
869 :	chris	22	#########################################################################
870 :			# Now handle the options assuming they are entered in the form
871 :			# num_cmp($ans, relTol=>1, format=>'%0.5f')
872 :			#########################################################################
873 :			%out_options = @opt;
874 :			assign_option_aliases( \%out_options,
875 :	chris	54	'reltol' => 'relTol',
876 :			'unit' => 'units',
877 :			);
878 :	sam	2
879 :	chris	22	set_default_options( \%out_options,
880 :			'tolType' => (defined($out_options{tol}) ) ? 'absolute' : 'relative',
881 :			'tolerance' => (defined($out_options{tol}) ) ? $numAbsTolDefault : $numRelPercentTolDefault,
882 :			'mode' => 'std',
883 :			'format' => $numFormatDefault,
884 :	chris	35	'tol' => $numAbsTolDefault,
885 :	chris	22	'relTol' => $numRelPercentTolDefault,
886 :			'units' => undef,
887 :			'strings' => undef,
888 :			'zeroLevel' => $numZeroLevelDefault,
889 :			'zeroLevelTol' => $numZeroLevelTolDefault,
890 :			'debug' => 0,
891 :	chris	81	);
892 :	sam	2
893 :	chris	22	# can't use both units and strings
894 :			if( defined( $out_options{'units'} ) && defined( $out_options{'strings'} ) ) {
895 :			warn "Can't use both 'units' and 'strings' in the same problem " .
896 :			"(check your parameters to num_cmp() )";
897 :	sam	2	}
898 :
899 :	chris	22	# my ($tolType, $tol);
900 :			if ($out_options{tolType} eq 'absolute') {
901 :			$out_options{'tolerance'}=$out_options{'tol'};
902 :			delete($out_options{'relTol'}) if exists( $out_options{'relTol'} );
903 :			} else {
904 :			$out_options{'tolerance'}=$out_options{'relTol'};
905 :			# delete($out_options{'tol'}) if exists( $out_options{'tol'} );
906 :	sam	2	}
907 :
908 :			# thread over lists
909 :			my @ans_list = ();
910 :
911 :			if ( ref($correctAnswer) eq 'ARRAY' ) {
912 :			@ans_list = @{$correctAnswer};
913 :			}
914 :	chris	54	else { push( @ans_list, $correctAnswer );
915 :	sam	2	}
916 :	chris	22
917 :	sam	2	# produce answer evaluators
918 :	chris	81	foreach my $ans (@ans_list) {
919 :	chris	22	if( defined( $out_options{'units'} ) ) {
920 :			$ans = "$ans $out_options{'units'}";
921 :
922 :			push( @output_list, NUM_CMP( 'correctAnswer' => $ans,
923 :			'tolerance' => $out_options{tolerance},
924 :			'tolType' => $out_options{tolType},
925 :			'format' => $out_options{'format'},
926 :			'mode' => $out_options{'mode'},
927 :			'zeroLevel' => $out_options{'zeroLevel'},
928 :			'zeroLevelTol' => $out_options{'zeroLevelTol'},
929 :			'debug' => $out_options{'debug'},
930 :			'units' => $out_options{'units'},
931 :	chris	81	)
932 :			);
933 :			}
934 :	chris	22	elsif( defined( $out_options{'strings'} ) ) {
935 :	chris	35	#if( defined $out_options{'tol'} ) {
936 :			# warn "You are using 'tol' (for absolute tolerance) with a num/str " .
937 :			# "compare, which currently only uses relative tolerance. The default " .
938 :			# "tolerance will be used.";
939 :			#}
940 :	chris	22
941 :	chris	35	push( @output_list, NUM_CMP( 'correctAnswer' => $ans,
942 :			'tolerance' => $out_options{tolerance},
943 :			'tolType' => $out_options{tolType},
944 :			'format' => $out_options{'format'},
945 :			'mode' => $out_options{'mode'},
946 :			'zeroLevel' => $out_options{'zeroLevel'},
947 :			'zeroLevelTol' => $out_options{'zeroLevelTol'},
948 :			'debug' => $out_options{'debug'},
949 :			'strings' => $out_options{'strings'},
950 :	chris	81	)
951 :			);
952 :			} else { push(@output_list,
953 :	chris	22	NUM_CMP( 'correctAnswer' => $ans,
954 :			'tolerance' => $out_options{tolerance},
955 :			'tolType' => $out_options{tolType},
956 :			'format' => $out_options{'format'},
957 :			'mode' => $out_options{'mode'},
958 :			'zeroLevel' => $out_options{'zeroLevel'},
959 :			'zeroLevelTol' => $out_options{'zeroLevelTol'},
960 :	chris	35	'debug' => $out_options{'debug'},
961 :	chris	81	),
962 :			);
963 :	chris	22	}
964 :	sam	2	}
965 :	chris	22
966 :	sam	2	return @output_list;
967 :	chris	22	}
968 :	sam	2
969 :			#legacy code for compatability purposes
970 :	chris	54	sub num_rel_cmp { # compare numbers
971 :	chris	22	std_num_cmp( @_ );
972 :	sam	2	}
973 :
974 :	chris	54	sub NUM_CMP { # low level numeric compare
975 :	chris	22	my %num_params = @_;
976 :	gage	34
977 :	chris	22	my @keys = qw ( correctAnswer tolerance tolType format mode zeroLevel zeroLevelTol debug );
978 :			foreach my $key (@keys) {
979 :			warn "$key must be defined in options when calling NUM_CMP" unless defined ($num_params{$key});
980 :			}
981 :	sam	2
982 :	chris	22	my $correctAnswer = $num_params{'correctAnswer'};
983 :			my $format = $num_params{'format'};
984 :			my $mode = $num_params{'mode'};
985 :
986 :			if( $num_params{tolType} eq 'relative' ) {
987 :			$num_params{'tolerance'} = .01*$num_params{'tolerance'};
988 :			}
989 :
990 :			my $formattedCorrectAnswer;
991 :			my $correct_units;
992 :			my $correct_num_answer;
993 :			my %correct_units;
994 :	chris	35	my $corrAnswerIsString = 0;
995 :
996 :	sam	2
997 :	chris	22	if (defined($num_params{units}) && $num_params{units}) {
998 :			$correctAnswer = str_filters( $correctAnswer, 'trim_whitespace' );
999 :			# units are in form stuff space units where units contains no spaces.
1000 :
1001 :			($correct_num_answer, $correct_units) = $correctAnswer =~ /^(.)\s+([^\s])$/;
1002 :			%correct_units = Units::evaluate_units($correct_units);
1003 :			if ( defined( $correct_units{'ERROR'} ) ) {
1004 :			warn ("ERROR: The answer \"$correctAnswer\" in the problem definition cannot be parsed:\n" .
1005 :			"$correct_units{'ERROR'}\n");
1006 :	sam	2	}
1007 :	chris	22	# $formattedCorrectAnswer = spf($correct_num_answer,$num_params{'format'}) . " $correct_units";
1008 :	chris	35	$formattedCorrectAnswer = prfmt($correct_num_answer,$num_params{'format'}) . " $correct_units";
1009 :	chris	22
1010 :	chris	35	} elsif (defined($num_params{strings}) && $num_params{strings}) {
1011 :			my $legalString = '';
1012 :			my @legalStrings = @{$num_params{strings}};
1013 :			$correct_num_answer = $correctAnswer;
1014 :			$formattedCorrectAnswer = $correctAnswer;
1015 :			foreach $legalString (@legalStrings) {
1016 :			if ( uc($correctAnswer) eq uc($legalString) ) {
1017 :			$corrAnswerIsString = 1;
1018 :			last;
1019 :			}
1020 :			} ## at this point $corrAnswerIsString = 0 iff correct answer is numeric
1021 :	chris	22	} else {
1022 :			$correct_num_answer = $correctAnswer;
1023 :			$formattedCorrectAnswer = prfmt( $correctAnswer, $num_params{'format'} );
1024 :			}
1025 :	sam	2
1026 :	chris	22	$correct_num_answer = math_constants($correct_num_answer);
1027 :
1028 :			my $PGanswerMessage = '';
1029 :
1030 :			my ($inVal,$correctVal,$PG_eval_errors,$PG_full_error_report);
1031 :
1032 :	chris	35	if (defined($correct_num_answer) && $correct_num_answer =~ /\S/ && $corrAnswerIsString == 0 ) {
1033 :	chris	49	($correctVal, $PG_eval_errors,$PG_full_error_report) = PG_answer_eval($correct_num_answer);
1034 :	chris	22	}
1035 :	chris	54	else { $PG_eval_errors = ' ';
1036 :	chris	22	}
1037 :	sam	2
1038 :	chris	35	if ( ($PG_eval_errors && $corrAnswerIsString == 0) or ((not is_a_number($correctVal)) && $corrAnswerIsString == 0)) {
1039 :			##error message from eval or above
1040 :	chris	22	warn "Error in 'correct' answer: $PG_eval_errors<br>
1041 :			The answer $correctAnswer evaluates to $correctVal,
1042 :			which cannot be interpreted as a number. ";
1043 :
1044 :			}
1045 :			#########################################################################
1046 :	sam	2
1047 :	chris	22	#construct the answer evaluator
1048 :			my $answer_evaluator = new AnswerEvaluator;
1049 :			$answer_evaluator->{debug} = $num_params{debug};
1050 :			$answer_evaluator->ans_hash( correct_ans => $correct_num_answer,
1051 :			type => "${mode}_number",
1052 :			tolerance => $num_params{tolerance},
1053 :			tolType => $num_params{tolType},
1054 :			units => $correct_units,
1055 :			original_correct_ans => $formattedCorrectAnswer,
1056 :			rh_correct_units => \%correct_units,
1057 :	chris	35	answerIsString => $corrAnswerIsString,
1058 :	chris	22	);
1059 :			my ($in, $formattedSubmittedAnswer);
1060 :			$answer_evaluator->install_pre_filter(sub {my $rh_ans = shift;
1061 :			$rh_ans->{original_student_ans} = $rh_ans->{student_ans}; $rh_ans;}
1062 :			);
1063 :			if (defined($num_params{units}) && $num_params{units}) {
1064 :			$answer_evaluator->install_pre_filter(\&check_units);
1065 :			}
1066 :	chris	35	if (defined($num_params{strings}) && $num_params{strings}) {
1067 :			$answer_evaluator->install_pre_filter(\&check_strings, %num_params);
1068 :			}
1069 :
1070 :	chris	22	$answer_evaluator->install_pre_filter(\&check_syntax);
1071 :
1072 :			$answer_evaluator->install_pre_filter(\&math_constants);
1073 :	chris	44
1074 :	chris	22	if ($mode eq 'std') {
1075 :			# do nothing
1076 :			} elsif ($mode eq 'strict') {
1077 :			$answer_evaluator->install_pre_filter(\&is_a_number);
1078 :			} elsif ($mode eq 'arith') {
1079 :			$answer_evaluator->install_pre_filter(\&is_an_arithmetic_expression);
1080 :			} elsif ($mode eq 'frac') {
1081 :			$answer_evaluator->install_pre_filter(\&is_a_fraction);
1082 :	sam	2
1083 :	chris	22	} else {
1084 :			$PGanswerMessage = 'Tell your professor that there is an error in his or her answer mechanism. No mode was specified.';
1085 :			$formattedSubmittedAnswer = $in;
1086 :	sam	2	}
1087 :	chris	44
1088 :	chris	35	if ($corrAnswerIsString == 0 ){ # avoiding running compare_numbers when correct answer is a string.
1089 :			$answer_evaluator->install_evaluator(\&compare_numbers, %num_params);
1090 :	chris	49	}
1091 :
1092 :
1093 :	gage	40	###############################################################################
1094 :			# We'll leave these next lines out for now, so that the evaluated versions of the student's and professor's
1095 :			# can be displayed in the answer message. This may still cause a few anomolies when strings are used
1096 :			#
1097 :			###############################################################################
1098 :	sam	2
1099 :	chris	41	$answer_evaluator->install_post_filter(\&fix_answers_for_display);
1100 :	sam	2
1101 :	chris	81	$answer_evaluator->install_post_filter(sub {my $rh_ans = shift;
1102 :	chris	22	return $rh_ans unless $rh_ans->catch_error('EVAL');
1103 :			$rh_ans->{student_ans} = $rh_ans->{original_student_ans}. ' '. $rh_ans->{error_message};
1104 :			$rh_ans->clear_error('EVAL'); } );
1105 :			$answer_evaluator->install_post_filter(sub {my $rh_ans = shift; $rh_ans->clear_error('SYNTAX'); } );
1106 :			$answer_evaluator->install_post_filter(sub {my $rh_ans = shift; $rh_ans->clear_error('UNITS'); } );
1107 :			$answer_evaluator->install_post_filter(sub {my $rh_ans = shift; $rh_ans->clear_error('NUMBER'); } );
1108 :	chris	35	$answer_evaluator->install_post_filter(sub {my $rh_ans = shift; $rh_ans->clear_error('STRING'); } );
1109 :	chris	22	$answer_evaluator;
1110 :	sam	2	}
1111 :
1112 :	chris	54	sub fix_answers_for_display {
1113 :	chris	41	my ($rh_ans, %options) = @_;
1114 :	chris	49	if ( $rh_ans->{answerIsString} ==1) {
1115 :			$rh_ans = evaluatesToNumber ($rh_ans, %options);
1116 :			}
1117 :	chris	41	if (defined ($rh_ans->{student_units})) {
1118 :			$rh_ans->{student_ans} = $rh_ans->{student_ans}. ' '. $rh_ans->{student_units};
1119 :			}
1120 :			$rh_ans->{correct_ans} = $rh_ans->{original_correct_ans};
1121 :	chris	81
1122 :	chris	41	$rh_ans;
1123 :			}
1124 :	sam	2
1125 :	chris	54	sub evaluatesToNumber {
1126 :	chris	49	my ($rh_ans, %options) = @_;
1127 :	chris	50	if (is_a_numeric_expression($rh_ans->{student_ans})) {
1128 :	chris	81	my ($inVal,$PG_eval_errors,$PG_full_error_report) = PG_answer_eval($rh_ans->{student_ans});
1129 :			if ($PG_eval_errors) { # this if statement should never be run
1130 :	chris	50	# change nothing
1131 :	chris	81	} else {
1132 :	chris	50	# change this
1133 :			$rh_ans->{student_ans} = prfmt($inVal,$options{format});
1134 :			}
1135 :			}
1136 :			$rh_ans;
1137 :			}
1138 :
1139 :	chris	54	sub is_a_numeric_expression {
1140 :	chris	50	my $testString = shift;
1141 :			my $is_a_numeric_expression = 0;
1142 :			my ($inVal,$PG_eval_errors,$PG_full_error_report) = PG_answer_eval($testString);
1143 :	chris	49	if ($PG_eval_errors) {
1144 :	chris	50	$is_a_numeric_expression = 0;
1145 :	chris	49	} else {
1146 :	chris	50	$is_a_numeric_expression = 1;
1147 :	chris	49	}
1148 :	chris	50	$is_a_numeric_expression;
1149 :	chris	49	}
1150 :
1151 :	sam	2	##########################################################################
1152 :			##########################################################################
1153 :			## Function answer evaluators
1154 :
1155 :			=head2 Function Answer Evaluators
1156 :
1157 :			Function answer evaluators take in a function, compare it numerically to a
1158 :			correct function, and return a score. They can require an exactly equivalent
1159 :			function, or one that is equal up to a constant. They can accept or reject an
1160 :			answer based on specified tolerances for numerical deviation.
1161 :
1162 :			Function Comparison Options
1163 :
1164 :			correctEqn -- The correct equation, specified as a string. It may include
1165 :			all basic arithmetic operations, as well as elementary
1166 :			functions. Variable usage is described below.
1167 :
1168 :			Variables -- The independent variable(s). When comparing the correct
1169 :			equation to the student equation, each variable will be
1170 :			replaced by a certain number of numerical values. If
1171 :			the student equation agrees numerically with the correct
1172 :			equation, they are considered equal. Note that all
1173 :			comparison is numeric; it is possible (although highly
1174 :			unlikely and never a practical concern) for two unequal
1175 :			functions to yield the same numerical results.
1176 :
1177 :			Limits -- The limits of evaluation for the independent variables.
1178 :			Each variable is evaluated only in the half-open interval
1179 :			[lower_limit, upper_limit). This is useful if the function
1180 :			has a singularity or is not defined in a certain range.
1181 :			For example, the function "sqrt(-1-x)" could be evaluated
1182 :			in [-2,-1).
1183 :
1184 :			Tolerance -- Tolerance in function comparisons works exactly as in
1185 :			numerical comparisons; see the numerical comparison
1186 :			documentation for a complete description. Note that the
1187 :			tolerance does applies to the function as a whole, not
1188 :			each point individually.
1189 :
1190 :			Number of -- Specifies how many points to evaluate each variable at. This
1191 :			Points is typically 3, but can be set higher if it is felt that
1192 :			there is a strong possibility of "false positives."
1193 :
1194 :			Maximum -- Sets the maximum size of the constant of integration. For
1195 :			Constant of technical reasons concerning floating point arithmetic, if
1196 :			Integration the additive constant, i.e., the constant of integration, is
1197 :			greater (in absolute value) than maxConstantOfIntegration
1198 :			AND is greater than maxConstantOfIntegration times the
1199 :			correct value, WeBWorK will give an error message saying
1200 :			that it can not handle such a large constant of integration.
1201 :			This is to prevent e.g. cos(x) + 1E20 or even 1E20 as being
1202 :			accepted as a correct antiderivatives of sin(x) since
1203 :			floating point arithmetic cannot tell the difference
1204 :			between cos(x) + 1E20, 1E20, and -cos(x) + 1E20.
1205 :
1206 :			Technical note: if you examine the code for the function routines, you will see
1207 :			that most subroutines are simply doing some basic error-checking and then
1208 :			passing the parameters on to the low-level FUNCTION_CMP(). Because this routine
1209 :			is set up to handle multivariable functions, with single-variable functions as
1210 :			a special case, it is possible to pass multivariable parameters to single-
1211 :			variable functions. This usage is strongly discouraged as unnecessarily
1212 :			confusing. Avoid it.
1213 :
1214 :			Default Values (As of 7/24/2000) (Option -- Variable Name -- Value)
1215 :
1216 :	chris	81	Variable -- $functVarDefault -- 'x'
1217 :	sam	2	Relative Tolerance -- $functRelPercentTolDefault -- .1
1218 :	chris	81	Absolute Tolerance -- $functAbsTolDefault -- .001
1219 :			Lower Limit -- $functLLimitDefault -- .0000001
1220 :			Upper Limit -- $functULimitDefault -- 1
1221 :			Number of Points -- $functNumOfPoints -- 3
1222 :			Zero Level -- $functZeroLevelDefault -- 1E-14
1223 :			Zero Level Tolerance -- $functZeroLevelTolDefault -- 1E-12
1224 :			Maximum Constant -- $functMaxConstantOfIntegration -- 1E8
1225 :	sam	2	of Integration
1226 :
1227 :			=cut
1228 :
1229 :			=head3 Single-variable Function Comparisons
1230 :
1231 :			There are four single-variable function answer evaluators: "normal," absolute
1232 :			tolerance, antiderivative, and antiderivative with absolute tolerance. All
1233 :			parameters (other than the correct equation) are optional.
1234 :
1235 :			function_cmp( $correctEqn ) OR
1236 :			function_cmp( $correctEqn, $var ) OR
1237 :			function_cmp( $correctEqn, $var, $llimit, $ulimit ) OR
1238 :			function_cmp( $correctEqn, $var, $llimit, $ulimit, $relPercentTol ) OR
1239 :			function_cmp( $correctEqn, $var, $llimit, $ulimit,
1240 :			$relPercentTol, $numPoints ) OR
1241 :			function_cmp( $correctEqn, $var, $llimit, $ulimit,
1242 :			$relPercentTol, $numPoints, $zeroLevel ) OR
1243 :			function_cmp( $correctEqn, $var, $llimit, $ulimit, $relPercentTol, $numPoints,
1244 :			$zeroLevel,$zeroLevelTol )
1245 :
1246 :			$correctEqn -- the correct equation, as a string
1247 :			$var -- the string representing the variable (optional)
1248 :			$llimit -- the lower limit of the interval to evaluate the
1249 :			variable in (optional)
1250 :			$ulimit -- the upper limit of the interval to evaluate the
1251 :			variable in (optional)
1252 :			$relPercentTol -- the error tolerance as a percentage (optional)
1253 :			$numPoints -- the number of points at which to evaluate the
1254 :			variable (optional)
1255 :			$zeroLevel -- if the correct answer is this close to zero, then
1256 :			zeroLevelTol applies (optional)
1257 :			$zeroLevelTol -- absolute tolerance to allow when answer is close to zero
1258 :
1259 :			function_cmp() uses standard comparison and relative tolerance. It takes a
1260 :			string representing a single-variable function and compares the student
1261 :			answer to that function numerically.
1262 :
1263 :			function_cmp_up_to_constant( $correctEqn ) OR
1264 :			function_cmp_up_to_constant( $correctEqn, $var ) OR
1265 :			function_cmp_up_to_constant( $correctEqn, $var, $llimit, $ulimit ) OR
1266 :			function_cmp_up_to_constant( $correctEqn, $var, $llimit, $ulimit,
1267 :			$relpercentTol ) OR
1268 :			function_cmp_up_to_constant( $correctEqn, $var, $llimit, $ulimit,
1269 :			$relpercentTol, $numOfPoints ) OR
1270 :			function_cmp_up_to_constant( $correctEqn, $var, $llimit, $ulimit,
1271 :			$relpercentTol, $numOfPoints,
1272 :			$maxConstantOfIntegration ) OR
1273 :			function_cmp_up_to_constant( $correctEqn, $var, $llimit, $ulimit,
1274 :			$relpercentTol, $numOfPoints,
1275 :			$maxConstantOfIntegration, $zeroLevel) OR
1276 :			function_cmp_up_to_constant( $correctEqn, $var, $llimit, $ulimit,
1277 :			$relpercentTol, $numOfPoints,
1278 :			$maxConstantOfIntegration,
1279 :			$zeroLevel, $zeroLevelTol )
1280 :
1281 :			$maxConstantOfIntegration -- the maximum size of the constant of
1282 :			integration
1283 :
1284 :			function_cmp_up_to_constant() uses antiderivative compare and relative
1285 :			tolerance. All options work exactly like function_cmp(), except of course
1286 :			$maxConstantOfIntegration. It will accept as correct any function which
1287 :			differs from $correctEqn by at most a constant; that is, if
1288 :			$studentEqn = $correctEqn + C
1289 :			the answer is correct.
1290 :
1291 :			function_cmp_abs( $correctFunction ) OR
1292 :			function_cmp_abs( $correctFunction, $var ) OR
1293 :			function_cmp_abs( $correctFunction, $var, $llimit, $ulimit ) OR
1294 :			function_cmp_abs( $correctFunction, $var, $llimit, $ulimit, $absTol ) OR
1295 :			function_cmp_abs( $correctFunction, $var, $llimit, $ulimit, $absTol,
1296 :			$numOfPoints )
1297 :
1298 :			$absTol -- the tolerance as an absolute value
1299 :
1300 :			function_cmp_abs() uses standard compare and absolute tolerance. All
1301 :			other options work exactly as for function_cmp().
1302 :
1303 :			function_cmp_up_to_constant_abs( $correctFunction ) OR
1304 :			function_cmp_up_to_constant_abs( $correctFunction, $var ) OR
1305 :			function_cmp_up_to_constant_abs( $correctFunction, $var, $llimit, $ulimit ) OR
1306 :			function_cmp_up_to_constant_abs( $correctFunction, $var, $llimit, $ulimit,
1307 :			$absTol ) OR
1308 :			function_cmp_up_to_constant_abs( $correctFunction, $var, $llimit, $ulimit,
1309 :			$absTol, $numOfPoints ) OR
1310 :			function_cmp_up_to_constant_abs( $correctFunction, $var, $llimit, $ulimit,
1311 :			$absTol, $numOfPoints,
1312 :			$maxConstantOfIntegration )
1313 :
1314 :			function_cmp_up_to_constant_abs() uses antiderivative compare
1315 :			and absolute tolerance. All other options work exactly as with
1316 :			function_cmp_up_to_constant().
1317 :
1318 :			Examples:
1319 :
1320 :			ANS( function_cmp( "cos(x)" ) ) -- Accepts cos(x), sin(x+pi/2),
1321 :			sin(x)^2 + cos(x) + cos(x)^2 -1, etc. This assumes
1322 :			$functVarDefault has been set to "x".
1323 :			ANS( function_cmp( $answer, "t" ) ) -- Assuming $answer is "cos(t)",
1324 :			accepts cos(t), etc.
1325 :			ANS( function_cmp_up_to_constant( "cos(x)" ) ) -- Accepts any
1326 :			antiderivative of sin(x), e.g. cos(x) + 5.
1327 :			ANS( function_cmp_up_to_constant( "cos(z)", "z" ) ) -- Accepts any
1328 :			antiderivative of sin(z), e.g. sin(z+pi/2) + 5.
1329 :
1330 :			=cut
1331 :			sub adaptive_function_cmp {
1332 :			my $correctEqn = shift;
1333 :			my %options = @_;
1334 :			set_default_options( \%options,
1335 :	chris	81	'vars' => [qw( x y )],
1336 :	sam	2	'params' => [],
1337 :			'limits' => [ [0,1], [0,1]],
1338 :			'reltol' => $main::functRelPercentTolDefault,
1339 :			'numPoints' => $main::functNumOfPoints,
1340 :			'zeroLevel' => $main::functZeroLevelDefault,
1341 :	chris	22	'zeroLevelTol' => $main::functZeroLevelTolDefault,
1342 :	sam	2	'debug' => 0,
1343 :			);
1344 :
1345 :	chris	81	my $var_ref = $options{'vars'};
1346 :	sam	2	my $ra_params = $options{ 'params'};
1347 :			my $limit_ref = $options{'limits'};
1348 :			my $relPercentTol= $options{'reltol'};
1349 :			my $numPoints = $options{'numPoints'};
1350 :			my $zeroLevel = $options{'zeroLevel'};
1351 :			my $zeroLevelTol = $options{'zeroLevelTol'};
1352 :
1353 :	chris	22	FUNCTION_CMP( 'correctEqn' => $correctEqn,
1354 :			'var' => $var_ref,
1355 :			'limits' => $limit_ref,
1356 :			'tolerance' => $relPercentTol,
1357 :			'tolType' => 'relative',
1358 :			'numPoints' => $numPoints,
1359 :			'mode' => 'std',
1360 :			'maxConstantOfIntegration' => 10**100,
1361 :			'zeroLevel' => $zeroLevel,
1362 :			'zeroLevelTol' => $zeroLevelTol,
1363 :			'scale_norm' => 1,
1364 :			'params' => $ra_params,
1365 :			'debug' => $options{debug} ,
1366 :	chris	81	);
1367 :	sam	2	}
1368 :
1369 :	chris	54	sub function_cmp {
1370 :	sam	2	my ($correctEqn,$var,$llimit,$ulimit,$relPercentTol,$numPoints,$zeroLevel,$zeroLevelTol) = @_;
1371 :
1372 :			if ( (scalar(@_) == 3) or (scalar(@_) > 8) or (scalar(@_) == 0) ) {
1373 :			function_invalid_params( $correctEqn );
1374 :			}
1375 :			else {
1376 :	chris	22	FUNCTION_CMP( 'correctEqn' => $correctEqn,
1377 :			'var' => $var,
1378 :			'limits' => [$llimit, $ulimit],
1379 :			'tolerance' => $relPercentTol,
1380 :			'tolType' => 'relative',
1381 :			'numPoints' => $numPoints,
1382 :			'mode' => 'std',
1383 :			'maxConstantOfIntegration' => 0,
1384 :			'zeroLevel' => $zeroLevel,
1385 :			'zeroLevelTol' => $zeroLevelTol
1386 :	sam	2	);
1387 :			}
1388 :			}
1389 :
1390 :	chris	54	sub function_cmp_up_to_constant { ## for antiderivative problems
1391 :	sam	2	my ($correctEqn,$var,$llimit,$ulimit,$relPercentTol,$numPoints,$maxConstantOfIntegration,$zeroLevel,$zeroLevelTol) = @_;
1392 :
1393 :			if ( (scalar(@_) == 3) or (scalar(@_) > 9) or (scalar(@_) == 0) ) {
1394 :			function_invalid_params( $correctEqn );
1395 :			}
1396 :			else {
1397 :	chris	22	FUNCTION_CMP( 'correctEqn' => $correctEqn,
1398 :			'var' => $var,
1399 :			'limits' => [$llimit, $ulimit],
1400 :			'tolerance' => $relPercentTol,
1401 :			'tolType' => 'relative',
1402 :			'numPoints' => $numPoints,
1403 :			'mode' => 'antider',
1404 :			'maxConstantOfIntegration' => $maxConstantOfIntegration,
1405 :			'zeroLevel' => $zeroLevel,
1406 :			'zeroLevelTol' => $zeroLevelTol
1407 :	chris	81	);
1408 :	sam	2	}
1409 :			}
1410 :
1411 :	chris	54	sub function_cmp_abs { ## similar to function_cmp but uses absolute tolerance
1412 :	sam	2	my ($correctEqn,$var,$llimit,$ulimit,$absTol,$numPoints) = @_;
1413 :
1414 :			if ( (scalar(@_) == 3) or (scalar(@_) > 6) or (scalar(@_) == 0) ) {
1415 :			function_invalid_params( $correctEqn );
1416 :			}
1417 :			else {
1418 :	chris	54	FUNCTION_CMP( 'correctEqn' => $correctEqn,
1419 :			'var' => $var,
1420 :			'limits' => [$llimit, $ulimit],
1421 :			'tolerance' => $absTol,
1422 :			'tolType' => 'absolute',
1423 :			'numPoints' => $numPoints,
1424 :			'mode' => 'std',
1425 :			'maxConstantOfIntegration' => 0,
1426 :			'zeroLevel' => 0,
1427 :			'zeroLevelTol' => 0
1428 :	chris	81	);
1429 :	sam	2	}
1430 :			}
1431 :
1432 :
1433 :	chris	54	sub function_cmp_up_to_constant_abs { ## for antiderivative problems
1434 :	sam	2	## similar to function_cmp_up_to_constant
1435 :			## but uses absolute tolerance
1436 :			my ($correctEqn,$var,$llimit,$ulimit,$absTol,$numPoints,$maxConstantOfIntegration) = @_;
1437 :
1438 :			if ( (scalar(@_) == 3) or (scalar(@_) > 7) or (scalar(@_) == 0) ) {
1439 :			function_invalid_params( $correctEqn );
1440 :			}
1441 :
1442 :			else {
1443 :	chris	22	FUNCTION_CMP( 'correctEqn' => $correctEqn,
1444 :			'var' => $var,
1445 :			'limits' => [$llimit, $ulimit],
1446 :			'tolerance' => $absTol,
1447 :			'tolType' => 'absolute',
1448 :			'numPoints' => $numPoints,
1449 :			'mode' => 'antider',
1450 :			'maxConstantOfIntegration' => $maxConstantOfIntegration,
1451 :			'zeroLevel' => 0,
1452 :			'zeroLevelTol' => 0
1453 :	chris	81	);
1454 :	sam	2	}
1455 :			}
1456 :
1457 :			## The following answer evaluator for comparing multivarable functions was
1458 :			## contributed by Professor William K. Ziemer
1459 :			## (Note: most of the multivariable functionality provided by Professor Ziemer
1460 :			## has now been integrated into fun_cmp and FUNCTION_CMP)
1461 :			############################
1462 :			# W.K. Ziemer, Sep. 1999
1463 :			# Math Dept. CSULB
1464 :			# email: wziemer@csulb.edu
1465 :			############################
1466 :
1467 :			=head3 multivar_function_cmp
1468 :
1469 :			NOTE: this function is maintained for compatibility. fun_cmp() is
1470 :			slightly preferred.
1471 :
1472 :			usage:
1473 :
1474 :			multivar_function_cmp( $answer, $var_reference, options)
1475 :			$answer -- string, represents function of several variables
1476 :			$var_reference -- number (of variables), or list reference (e.g. ["var1","var2"] )
1477 :			options:
1478 :			$limit_reference -- reference to list of lists (e.g. [[1,2],[3,4]])
1479 :			$relPercentTol -- relative percent tolerance in answer
1480 :			$numPoints -- number of points to sample in for each variable
1481 :			$zeroLevel -- if the correct answer is this close to zero, then zeroLevelTol applies
1482 :			$zeroLevelTol -- absolute tolerance to allow when answer is close to zero
1483 :
1484 :			=cut
1485 :
1486 :			sub multivar_function_cmp {
1487 :			my ($correctEqn,$var_ref,$limit_ref,$relPercentTol,$numPoints,$zeroLevel,$zeroLevelTol) = @_;
1488 :
1489 :			if ( (scalar(@_) > 7) or (scalar(@_) < 2) ) {
1490 :			function_invalid_params( $correctEqn );
1491 :			}
1492 :
1493 :	chris	81	FUNCTION_CMP( 'correctEqn' => $correctEqn,
1494 :			'var' => $var_ref,
1495 :			'limits' => $limit_ref,
1496 :			'tolerance' => $relPercentTol,
1497 :			'tolType' => 'relative',
1498 :			'numPoints' => $numPoints,
1499 :			'mode' => 'std',
1500 :			'maxConstantOfIntegration' => 0,
1501 :			'zeroLevel' => $zeroLevel,
1502 :			'zeroLevelTol' => $zeroLevelTol
1503 :			);
1504 :	sam	2	}
1505 :
1506 :			=head3 fun_cmp()
1507 :
1508 :			Compares a function or a list of functions, using a named hash of options to set
1509 :			parameters. This can make for more readable code than using the function_cmp()
1510 :			style, but some people find one or the other easier to remember.
1511 :
1512 :			ANS( fun_cmp( answer or answer_array_ref, options_hash ) );
1513 :
1514 :			1. a string containing the correct function, or a reference to an
1515 :			array of correct functions
1516 :			2. a hash containing the following items (all optional):
1517 :	chris	81	var -- either the number of variables or a reference to an
1518 :	sam	2	array of variable names (see below)
1519 :			limits -- reference to an array of arrays of limits (see below), or:
1520 :			mode -- 'std' (default) (function must match exactly), or:
1521 :			'antider' (function must match up to a constant)
1522 :			relTol -- (default) a relative tolerance (as a percentage), or:
1523 :	chris	81	tol -- an absolute tolerance for error
1524 :	sam	2	numPoints -- the number of points to evaluate the function at
1525 :	chris	81	maxConstantOfIntegration -- maximum size of the constant of integration
1526 :	sam	2	zeroLevel -- if the correct answer is this close to zero, then
1527 :			zeroLevelTol applies
1528 :	chris	81	zeroLevelTol -- absolute tolerance to allow when answer is close to zero
1529 :			params an array of "free" parameters which can be used to adapt
1530 :			the correct answer to the submitted answer. (e.g. ['c'] for
1531 :			a constant of integration in the answer x^3/3 + c.
1532 :			debug -- when set to 1 this provides extra information while checking the
1533 :			the answer.
1534 :	sam	2
1535 :			Returns an answer evaluator, or (if given a reference to an array
1536 :			of answers), a list of answer evaluators
1537 :
1538 :			ANSWER:
1539 :
1540 :			The answer must be in the form of a string. The answer can contain
1541 :			functions, pi, e, and arithmetic operations. However, the correct answer
1542 :			string follows a slightly stricter syntax than student answers; specifically,
1543 :			there is no implicit multiplication. So the correct answer must be "3*x" rather
1544 :			than "3 x". Students can still enter "3 x".
1545 :
1546 :			VARIABLES:
1547 :
1548 :			The var parameter can contain either a number or a reference to an array of
1549 :			variable names. If it contains a number, the variables are named automatically
1550 :			as follows: 1 variable -- x
1551 :	chris	81	2 variables -- x, y
1552 :			3 variables -- x, y, z
1553 :			4 or more -- x_1, x_2, x_3, etc.
1554 :	sam	2	If the var parameter contains a reference to an array of variable names, then
1555 :			the number of variables is determined by the number of items in the array. A
1556 :			reference to an array is created with brackets, e.g. "var => ['r', 's', 't']".
1557 :			If only one variable is being used, you can write either "var => ['t']" for
1558 :			consistency or "var => 't'" as a shortcut. The default is one variable, x.
1559 :
1560 :			LIMITS:
1561 :
1562 :			Limits are specified with the limits parameter. You may NOT use llimit/ulimit.
1563 :			If you specify limits for one variable, you must specify them for all variables.
1564 :			The limit parameter must be a reference to an array of arrays of the form
1565 :			[lower_limit. upper_limit], each array corresponding to the lower and upper
1566 :			endpoints of the (half-open) domain of one variable. For example,
1567 :			"vars => 2, limits => [[0,2], [-3,8]]" would cause x to be evaluated in [0,2) and
1568 :			y to be evaluated in [-3,8). If only one variable is being used, you can write
1569 :			either "limits => [[0,3]]" for consistency or "limits => [0,3]" as a shortcut.
1570 :
1571 :			EXAMPLES:
1572 :
1573 :			fun_cmp( "3*x" ) -- standard compare, variable is x
1574 :			fun_cmp( ["3x", "4x+3", "3x*2"] ) -- standard compare, defaults used for all three functions
1575 :			fun_cmp( "3*t", var => 't' ) -- standard compare, variable is t
1576 :			fun_cmp( "5xy*z", var => 3 ) -- x, y and z are the variables
1577 :			fun_cmp( "5*x", mode => 'antider' ) -- student answer must match up to constant (i.e., 5x+C)
1578 :			fun_cmp( ["3xy", "4xy"], limits => [[0,2], [5,7]] ) -- x evaluated in [0,2)
1579 :			y evaluated in [5,7)
1580 :
1581 :			=cut
1582 :
1583 :			sub fun_cmp {
1584 :			my $correctAnswer = shift @_;
1585 :			my %opt = @_;
1586 :
1587 :			assign_option_aliases( \%opt,
1588 :	chris	81	'vars' => 'var', # set the standard option 'var' to the one specified as vars
1589 :			'domain' => 'limits', # set the standard option 'limits' to the one specified as domain
1590 :			'reltol' => 'relTol',
1591 :			'param' => 'params',
1592 :	sam	2	);
1593 :
1594 :			set_default_options( \%opt,
1595 :	chris	81	'var' => $functVarDefault,
1596 :			'params' => [],
1597 :			'limits' => [[$functLLimitDefault, $functULimitDefault]],
1598 :			'mode' => 'std',
1599 :			'tolType' => (defined($opt{tol}) ) ? 'absolute' : 'relative',
1600 :			'tol' => .01, # default mode should be relative, to obtain this tol must not be defined
1601 :			'relTol' => $functRelPercentTolDefault,
1602 :			'numPoints' => $functNumOfPoints,
1603 :			'maxConstantOfIntegration' => $functMaxConstantOfIntegration,
1604 :			'zeroLevel' => $functZeroLevelDefault,
1605 :			'zeroLevelTol' => $functZeroLevelTolDefault,
1606 :			'debug' => 0,
1607 :			);
1608 :	sam	2
1609 :
1610 :
1611 :			# allow var => 'x' as an abbreviation for var => ['x']
1612 :			my %out_options = %opt;
1613 :			unless ( ref($out_options{var}) eq 'ARRAY' ) {
1614 :			$out_options{var} = [$out_options{var}];
1615 :			}
1616 :			# allow params => 'c' as an abbreviation for params => ['c']
1617 :			unless ( ref($out_options{params}) eq 'ARRAY' ) {
1618 :			$out_options{params} = [$out_options{params}];
1619 :			}
1620 :			my ($tolType, $tol);
1621 :			if ($out_options{tolType} eq 'absolute') {
1622 :			$tolType = 'absolute';
1623 :			$tol = $out_options{'tol'};
1624 :			delete($out_options{'relTol'}) if exists( $out_options{'relTol'} );
1625 :			} else {
1626 :			$tolType = 'relative';
1627 :			$tol = $out_options{'relTol'};
1628 :			delete($out_options{'tol'}) if exists( $out_options{'tol'} );
1629 :			}
1630 :
1631 :			my @output_list = ();
1632 :			# thread over lists
1633 :			my @ans_list = ();
1634 :
1635 :			if ( ref($correctAnswer) eq 'ARRAY' ) {
1636 :			@ans_list = @{$correctAnswer};
1637 :			}
1638 :			else {
1639 :			push( @ans_list, $correctAnswer );
1640 :			}
1641 :
1642 :			# produce answer evaluators
1643 :			foreach my $ans (@ans_list) {
1644 :			push(@output_list,
1645 :	chris	22	FUNCTION_CMP( 'correctEqn' => $ans,
1646 :			'var' => $out_options{'var'},
1647 :			'limits' => $out_options{'limits'},
1648 :			'tolerance' => $tol,
1649 :			'tolType' => $tolType,
1650 :			'numPoints' => $out_options{'numPoints'},
1651 :			'mode' => $out_options{'mode'},
1652 :			'maxConstantOfIntegration' => $out_options{'maxConstantOfIntegration'},
1653 :			'zeroLevel' => $out_options{'zeroLevel'},
1654 :			'zeroLevelTol' => $out_options{'zeroLevelTol'},
1655 :			'params' => $out_options{'params'},
1656 :			'debug' => $out_options{'debug'},
1657 :	sam	2	),
1658 :			);
1659 :			}
1660 :
1661 :			return @output_list;
1662 :			}
1663 :
1664 :			## LOW-LEVEL ROUTINE -- NOT NORMALLY FOR END USERS -- USE WITH CAUTION
1665 :			## NOTE: PG_answer_eval is used instead of PG_restricted_eval in order to insure that the answer
1666 :			## evaluated within the context of the package the problem was originally defined in.
1667 :			## Includes multivariable modifications contributed by Professor William K. Ziemer
1668 :			##
1669 :			## IN: a hash consisting of the following keys (error checking to be added later?)
1670 :	chris	81	## correctEqn -- the correct equation as a string
1671 :			## var -- the variable name as a string,
1672 :			## or a reference to an array of variables
1673 :			## limits -- reference to an array of arrays of type [lower,upper]
1674 :			## tolerance -- the allowable margin of error
1675 :			## tolType -- 'relative' or 'absolute'
1676 :			## numPoints -- the number of points to evaluate the function at
1677 :			## mode -- 'std' or 'antider'
1678 :	sam	2	## maxConstantOfIntegration -- maximum size of the constant of integration
1679 :	chris	81	## zeroLevel -- if the correct answer is this close to zero,
1680 :	sam	2	## then zeroLevelTol applies
1681 :	chris	81	## zeroLevelTol -- absolute tolerance to allow when answer is close to zero
1682 :	sam	2
1683 :
1684 :	chris	54	sub FUNCTION_CMP {
1685 :	sam	2	my %func_params = @_;
1686 :
1687 :			my $correctEqn = $func_params{'correctEqn'};
1688 :	chris	22	my $var = $func_params{'var'};
1689 :	sam	2	my $ra_limits = $func_params{'limits'};
1690 :	chris	22	my $tol = $func_params{'tolerance'};
1691 :			my $tolType = $func_params{'tolType'};
1692 :	sam	2	my $numPoints = $func_params{'numPoints'};
1693 :	chris	22	my $mode = $func_params{'mode'};
1694 :			my $maxConstantOfIntegration = $func_params{'maxConstantOfIntegration'};
1695 :	sam	2	my $zeroLevel = $func_params{'zeroLevel'};
1696 :			my $zeroLevelTol = $func_params{'zeroLevelTol'};
1697 :
1698 :
1699 :			# Check that everything is defined:
1700 :			$func_params{debug} = 0 unless defined($func_params{debug});
1701 :			$mode = 'std' unless defined($mode);
1702 :			my @VARS = get_var_array( $var );
1703 :			my @limits = get_limits_array( $ra_limits );
1704 :			my @PARAMS = ();
1705 :			@PARAMS = @{$func_params{'params'}} if defined($func_params{'params'});
1706 :
1707 :			if ($mode eq 'antider' ) {
1708 :			# doctor the equation to allow addition of a constant
1709 :			my $CONSTANT_PARAM = 'Q'; # unfortunately parameters must be single letters.
1710 :			# There is the possibility of conflict here.
1711 :			# 'Q' seemed less dangerous than 'C'.
1712 :			$correctEqn = "( $correctEqn ) + $CONSTANT_PARAM";
1713 :			push(@PARAMS, $CONSTANT_PARAM);
1714 :			}
1715 :			my $dim_of_param_space = @PARAMS; # dimension of equivalence space
1716 :
1717 :			if( $tolType eq 'relative' ) {
1718 :	chris	81	$tol = $functRelPercentTolDefault unless defined $tol;
1719 :	sam	2	$tol *= .01;
1720 :			}
1721 :			else {
1722 :	chris	81	$tol = $functAbsTolDefault unless defined $tol;
1723 :	sam	2	}
1724 :
1725 :			#loop ensures that number of limits matches number of variables
1726 :			for( my $i = 0; $i < scalar(@VARS); $i++ ) {
1727 :	chris	81	$limits[$i][0] = $functLLimitDefault unless defined $limits[$i][0];
1728 :			$limits[$i][1] = $functULimitDefault unless defined $limits[$i][1];
1729 :	sam	2	}
1730 :	chris	81	$numPoints = $functNumOfPoints unless defined $numPoints;
1731 :	sam	2	$maxConstantOfIntegration = $functMaxConstantOfIntegration unless defined $maxConstantOfIntegration;
1732 :	chris	81	$zeroLevel = $functZeroLevelDefault unless defined $zeroLevel;
1733 :			$zeroLevelTol = $functZeroLevelTolDefault unless defined $zeroLevelTol;
1734 :	sam	2
1735 :	chris	22	$func_params{'var'} = $var;
1736 :			$func_params{'limits'} = \@limits;
1737 :			$func_params{'tolerance'} = $tol;
1738 :			$func_params{'tolType'} = $tolType;
1739 :			$func_params{'numPoints'} = $numPoints;
1740 :			$func_params{'mode'} = $mode;
1741 :			$func_params{'maxConstantOfIntegration'} = $maxConstantOfIntegration;
1742 :			$func_params{'zeroLevel'} = $zeroLevel;
1743 :			$func_params{'zeroLevelTol'} = $zeroLevelTol;
1744 :
1745 :	gage	5	########################################################
1746 :			# End of cleanup of calling parameters
1747 :			########################################################
1748 :	sam	2	my $i; #for use with loops
1749 :			my $PGanswerMessage = "";
1750 :			my $originalCorrEqn = $correctEqn;
1751 :
1752 :			#prepare the correct answer and check it's syntax
1753 :	chris	22	my $rh_correct_ans = new AnswerHash;
1754 :	sam	2	$rh_correct_ans->input($correctEqn);
1755 :			$rh_correct_ans = check_syntax($rh_correct_ans);
1756 :			warn $rh_correct_ans->{error_message} if $rh_correct_ans->{error_flag};
1757 :			$rh_correct_ans->clear_error();
1758 :			$rh_correct_ans = function_from_string2($rh_correct_ans, ra_vars => [ @VARS, @PARAMS ],
1759 :			store_in =>'rf_correct_ans',
1760 :			debug => $func_params{debug});
1761 :			my $correct_eqn_sub = $rh_correct_ans->{rf_correct_ans};
1762 :			warn $rh_correct_ans->{error_message} if $rh_correct_ans->{error_flag};
1763 :
1764 :			#create the evaluation points
1765 :			my $random_for_answers = new PGrandom($main::PG_original_problemSeed);
1766 :	chris	22	my $NUMBER_OF_STEPS_IN_RANDOM = 1000; # determines the granularity of the random_for_answers number generator
1767 :	sam	2	my (@evaluation_points);
1768 :			for( my $count = 0; $count < @PARAMS+1+$numPoints; $count++ ) {
1769 :			my (@vars,$iteration_limit);
1770 :			for( my $i = 0; $i < @VARS; $i++ ) {
1771 :			my $iteration_limit = 10;
1772 :			while ( 0 < --$iteration_limit ) { # make sure that the endpoints of the interval are not included
1773 :			$vars[$i] = $random_for_answers->random($limits[$i][0], $limits[$i][1], abs($limits[$i][1] - $limits[$i][0])/$NUMBER_OF_STEPS_IN_RANDOM );
1774 :			last if $vars[$i]!=$limits[$i][0] and $vars[$i]!=$limits[$i][1];
1775 :			}
1776 :			warn "Unable to properly choose evaluation points for this function in the interval ( $limits[$i][0] , $limits[$i][1] )"
1777 :			if $iteration_limit == 0;
1778 :			};
1779 :
1780 :			push(@evaluation_points,\@vars);
1781 :			}
1782 :			my $evaluation_points = Matrix->new_from_array_ref(\@evaluation_points);
1783 :
1784 :			#my $COEFFS = determine_param_coeffs($correct_eqn_sub,$evaluation_points[0],$numOfParameters);
1785 :	chris	22	#warn "coeff", join(" \| ", @{$COEFFS});
1786 :	sam	2
1787 :			#construct the answer evaluator
1788 :			my $answer_evaluator = new AnswerEvaluator;
1789 :			$answer_evaluator->{debug} = $func_params{debug};
1790 :			$answer_evaluator->ans_hash( correct_ans => $originalCorrEqn,
1791 :	chris	54	rf_correct_ans => $rh_correct_ans->{rf_correct_ans},
1792 :			evaluation_points => \@evaluation_points,
1793 :			ra_param_vars => \@PARAMS,
1794 :			ra_vars => \@VARS,
1795 :			type => 'function',
1796 :	sam	2	);
1797 :
1798 :			$answer_evaluator->install_pre_filter(\&check_syntax);
1799 :			$answer_evaluator->install_pre_filter(\&function_from_string2, ra_vars => \@VARS,debug=>$func_params{debug},); # @VARS has been guaranteed to be an array, $var might be a single string.
1800 :			$answer_evaluator->install_pre_filter(\&best_approx_parameters, %func_params, param_vars => \@PARAMS);
1801 :			$answer_evaluator->install_evaluator(\&calculate_difference_vector, %func_params);
1802 :			$answer_evaluator->install_evaluator(\&is_zero_array, tol => $tol );
1803 :			$answer_evaluator->install_post_filter(sub {my $rh_ans = shift; $rh_ans->clear_error('SYNTAX'); $rh_ans;} );
1804 :			$answer_evaluator->install_post_filter(sub {my $rh_ans = shift;
1805 :	chris	81	if ($rh_ans->catch_error('EVAL') ) {
1806 :			$rh_ans->{ans_message} = $rh_ans->{error_message};
1807 :			$rh_ans->clear_error('EVAL');
1808 :			}
1809 :			$rh_ans;});
1810 :	sam	2	$answer_evaluator;
1811 :			}
1812 :
1813 :			=head4 Filters
1814 :
1815 :			=pod
1816 :
1817 :			is_array($rh_ans)
1818 :	chris	81	returns: $rh_ans. Throws error "NOTARRAY" if this is not an array
1819 :	sam	2
1820 :			=cut
1821 :
1822 :	chris	54	sub is_array {
1823 :	sam	2	my $rh_ans = shift;
1824 :			# return if the result is an array
1825 :			return($rh_ans) if ref($rh_ans->{student_ans}) eq 'ARRAY' ;
1826 :			$rh_ans->throw_error("NOTARRAY","The answer is not an array");
1827 :			$rh_ans;
1828 :			}
1829 :
1830 :			=pod
1831 :
1832 :			check_syntax( $rh_ans, %options)
1833 :			returns an answer hash.
1834 :
1835 :			latex2html preview code are installed in the answer hash.
1836 :			The input has been transformed, changing 7pi to 7pi or 7x to 7x.
1837 :			Syntax error messages may be generated and stored in student_ans
1838 :			Additional syntax error messages are stored in {ans_message} and duplicated in {error_message}
1839 :
1840 :
1841 :			=cut
1842 :
1843 :			sub check_syntax {
1844 :			my $rh_ans = shift;
1845 :			my %options = @_;
1846 :			unless ( defined( $rh_ans->{student_ans} ) ) {
1847 :			warn "Check_syntax requires an equation in the field {student_ans} or input";
1848 :			$rh_ans->throw_error("1","{student_ans} field not defined");
1849 :			return $rh_ans;
1850 :			}
1851 :			my $in = $rh_ans->{student_ans};
1852 :			my $parser = new AlgParserWithImplicitExpand;
1853 :	chris	81	my $ret = $parser -> parse($in); #for use with loops
1854 :	sam	2
1855 :			if ( ref($ret) ) { ## parsed successfully
1856 :			$parser -> tostring();
1857 :			$parser -> normalize();
1858 :			$rh_ans->input( $parser -> tostring() );
1859 :			$rh_ans->{preview_text_string} = $in;
1860 :			$rh_ans->{preview_latex_string} = $parser -> tolatex();
1861 :
1862 :			} else { ## error in parsing
1863 :
1864 :			$rh_ans->{'student_ans'} = 'syntax error:'. $parser->{htmlerror},
1865 :			$rh_ans->{'ans_message'} = $parser -> {error_msg},
1866 :			$rh_ans->{'preview_text_string'} = '',
1867 :			$rh_ans->{'preview_latex_string'} = '',
1868 :			$rh_ans->throw_error('SYNTAX', 'syntax error in answer:'. $parser->{htmlerror} . "$BR" .$parser -> {error_msg});
1869 :			}
1870 :			$rh_ans;
1871 :
1872 :			}
1873 :
1874 :			=pod
1875 :
1876 :	chris	54	check_strings ($rh_ans, %options)
1877 :	chris	81	returns $rh_ans
1878 :	chris	54
1879 :			=cut
1880 :
1881 :			sub check_strings {
1882 :			my ($rh_ans, %options) = @_;
1883 :
1884 :			# if the student's answer is a number, simply return the answer hash (unchanged).
1885 :
1886 :			if ( $rh_ans->{student_ans} =~ m/[\d+\-\/^(){}\[\]]\|^\se\s$\|^\spi\s*$/) {
1887 :			if ( $rh_ans->{answerIsString} == 1) {
1888 :			#$rh_ans->throw_error('STRING','Incorrect Answer'); # student's answer is a number
1889 :			}
1890 :			return $rh_ans;
1891 :			}
1892 :			# the student's answer is recognized as a string
1893 :			my $ans = $rh_ans->{student_ans};
1894 :	chris	81
1895 :	chris	54	# OVERVIEW of remindar of function:
1896 :			# if answer is correct, return correct. (adjust score to 1)
1897 :			# if answer is incorect:
1898 :			# 1) determine if the answer is sensible. if it is, return incorrect.
1899 :			# 2) if the answer is not sensible (and incorrect), then return an error message indicating so.
1900 :			# no matter what: throw a 'STRING' error to skip numerical evaluations. (error flag skips remainder of pre_filters and evaluators)
1901 :			# last: 'STRING' post_filter will clear the error (avoiding pink screen.)
1902 :	chris	81
1903 :	chris	54	my $sensibleAnswer = 0;
1904 :			$ans = str_filters( $ans, 'compress_whitespace' ); # remove trailing, leading, and double spaces.
1905 :			my ($ans_eval) = str_cmp($rh_ans->{correct_ans});
1906 :			my $temp_ans_hash = &$ans_eval($ans);
1907 :			$rh_ans->{test} = $temp_ans_hash;
1908 :			if ($temp_ans_hash->{score} ==1 ) { # students answer matches the correct answer.
1909 :			$rh_ans->{score} = 1;
1910 :			$sensibleAnswer = 1;
1911 :			} else { # students answer does not match the correct answer.
1912 :	chris	81	my $legalString = ''; # find out if string makes sense
1913 :	chris	54	my @legalStrings = @{$options{strings}};
1914 :			foreach $legalString (@legalStrings) {
1915 :			if ( uc($ans) eq uc($legalString) ) {
1916 :			$sensibleAnswer = 1;
1917 :			last;
1918 :			}
1919 :			}
1920 :			$sensibleAnswer = 1 unless $ans =~ /\S/; ## empty answers are sensible
1921 :	chris	81	$rh_ans->throw_error('EVAL', "Your answer is not a recognized answer") unless ($sensibleAnswer);
1922 :	chris	54	# $temp_ans_hash -> setKeys( 'ans_message' => 'Your answer is not a recognized answer' ) unless ($sensibleAnswer);
1923 :			# $temp_ans_hash -> setKeys( 'student_ans' => uc($ans) );
1924 :			}
1925 :			$rh_ans->{student_ans} = $ans;
1926 :			if ($sensibleAnswer) {
1927 :			$rh_ans->throw_error('STRING', "The student's answer $rh_ans->{student_ans} is interpreted as a string.");
1928 :			}
1929 :			# warn ("\$rh_ans->{answerIsString} = $rh_ans->{answerIsString}");
1930 :			$rh_ans;
1931 :			}
1932 :
1933 :			=pod
1934 :
1935 :			check_strings ($rh_ans, %options)
1936 :	chris	81	returns $rh_ans
1937 :	chris	54
1938 :
1939 :			=cut
1940 :
1941 :			sub check_units {
1942 :			my ($rh_ans, %options) = @_;
1943 :			my %correct_units = %{$rh_ans-> {rh_correct_units}};
1944 :			my $ans = $rh_ans->{student_ans};
1945 :			# $ans = '' unless defined ($ans);
1946 :			$ans = str_filters ($ans, 'trim_whitespace');
1947 :			my $original_student_ans = $ans;
1948 :			$rh_ans->{original_student_ans} = $original_student_ans;
1949 :
1950 :			# it surprises me that the match below works since the first .* is greedy.
1951 :			my ($num_answer, $units) = $ans =~ /^(.)\s+([^\s])$/;
1952 :
1953 :			unless ( defined($num_answer) && $units ) {
1954 :			# there is an error reading the input
1955 :			if ( $ans =~ /\S/ ) { # the answer is not blank
1956 :			$rh_ans -> setKeys( 'ans_message' => "The answer \"$ans\" could not be interpreted " .
1957 :			"as a number or an arithmetic expression followed by a unit specification. " .
1958 :			"Your answer must contain units." );
1959 :			$rh_ans->throw_error('UNITS', "The answer \"$ans\" could not be interpreted " .
1960 :			"as a number or an arithmetic expression followed by a unit specification. " .
1961 :			"Your answer must contain units." );
1962 :			}
1963 :			return $rh_ans;
1964 :			}
1965 :
1966 :			# we have been able to parse the answer into a numerical part and a unit part
1967 :
1968 :			# $num_answer = $1; #$1 and $2 from the regular expression above
1969 :			# $units = $2;
1970 :
1971 :			my %units = Units::evaluate_units($units);
1972 :			if ( defined( $units{'ERROR'} ) ) {
1973 :			# handle error condition
1974 :			$units{'ERROR'} = clean_up_error_msg($units{'ERROR'});
1975 :			$rh_ans -> setKeys( 'ans_message' => "$units{'ERROR'}" );
1976 :			$rh_ans -> throw_error('UNITS', "$units{'ERROR'}");
1977 :			return $rh_ans;
1978 :			}
1979 :
1980 :			my $units_match = 1;
1981 :			my $fund_unit;
1982 :			foreach $fund_unit (keys %correct_units) {
1983 :			next if $fund_unit eq 'factor';
1984 :			$units_match = 0 unless $correct_units{$fund_unit} == $units{$fund_unit};
1985 :			}
1986 :
1987 :			if ( $units_match ) {
1988 :			# units are ok. Evaluate the numerical part of the answer
1989 :			$rh_ans->{'tolerance'} = $rh_ans->{'tolerance'}* $correct_units{'factor'}/$units{'factor'} if
1990 :			$rh_ans->{'tolType'} eq 'absolute'; # the tolerance is in the units specified by the instructor.
1991 :			$rh_ans->{correct_ans} = prfmt($rh_ans->{correct_ans}*$correct_units{'factor'}/$units{'factor'});
1992 :			$rh_ans->{student_units} = $units;
1993 :			$rh_ans->{student_ans} = $num_answer;
1994 :
1995 :			} else {
1996 :			$rh_ans -> setKeys( ans_message => 'There is an error in the units for this answer.' );
1997 :			$rh_ans -> throw_error ( 'UNITS', 'There is an error in the units for this answer.' );
1998 :			}
1999 :
2000 :			return $rh_ans;
2001 :			}
2002 :
2003 :			## LOW-LEVEL ROUTINE -- NOT NORMALLY FOR END USERS -- USE WITH CAUTION
2004 :			##
2005 :			## IN: a hash containing the following items (error-checking to be added later?):
2006 :			## correctAnswer -- the correct answer
2007 :			## tolerance -- the allowable margin of error
2008 :			## tolType -- 'relative' or 'absolute'
2009 :			## format -- the display format of the answer
2010 :			## mode -- one of 'std', 'strict', 'arith', or 'frac';
2011 :			## determines allowable formats for the input
2012 :			## zeroLevel -- if the correct answer is this close to zero, then zeroLevelTol applies
2013 :			## zeroLevelTol -- absolute tolerance to allow when answer is close to zero
2014 :
2015 :			sub compare_numbers {
2016 :			my ($rh_ans, %options) = @_;
2017 :			my ($inVal,$PG_eval_errors,$PG_full_error_report) = PG_answer_eval($rh_ans->{student_ans});
2018 :			if ($PG_eval_errors) {
2019 :			$rh_ans->throw_error('EVAL','There is a syntax error in your answer');
2020 :			$rh_ans->{ans_message} = clean_up_error_msg($PG_eval_errors);
2021 :	chris	81	# return $rh_ans;
2022 :	chris	54	} else {
2023 :			$rh_ans->{student_ans} = prfmt($inVal,$options{format});
2024 :			}
2025 :
2026 :			my $permitted_error;
2027 :
2028 :			if ($rh_ans->{tolType} eq 'absolute') {
2029 :			$permitted_error = $rh_ans->{tolerance};
2030 :			}
2031 :			elsif ( abs($rh_ans->{correct_ans}) <= $options{zeroLevel}) {
2032 :			$permitted_error = $options{zeroLevelTol}; ## want $tol to be non zero
2033 :			}
2034 :			else {
2035 :			$permitted_error = abs($rh_ans->{tolerance}*$rh_ans->{correct_ans});
2036 :			}
2037 :
2038 :			my $is_a_number = is_a_number($inVal);
2039 :			$rh_ans->{score} = 1 if ( ($is_a_number) and
2040 :			(abs( $inVal - $rh_ans->{correct_ans} ) <= $permitted_error) );
2041 :			if (not $is_a_number) {
2042 :	chris	81	$rh_ans->{error_message} = "$rh_ans->{error_message}". 'Your answer does not evaluate to a number ';
2043 :	chris	54	}
2044 :
2045 :			$rh_ans;
2046 :			}
2047 :
2048 :			=pod
2049 :
2050 :	sam	2	std_num_filter($rh_ans, %options)
2051 :			returns $rh_ans
2052 :
2053 :			Replaces some constants using math_constants, then evaluates a perl expression.
2054 :
2055 :
2056 :			=cut
2057 :
2058 :			sub std_num_filter {
2059 :			my $rh_ans = shift;
2060 :			my %options = @_;
2061 :			my $in = $rh_ans->input();
2062 :			$in = math_constants($in);
2063 :			$rh_ans->{type} = 'std_number';
2064 :			my ($inVal,$PG_eval_errors,$PG_full_error_report);
2065 :			if ($in =~ /\S/) {
2066 :			($inVal,$PG_eval_errors,$PG_full_error_report) = PG_answer_eval($in);
2067 :	chris	81	} else {
2068 :			$PG_eval_errors = '';
2069 :	sam	2	}
2070 :
2071 :			if ($PG_eval_errors) { ##error message from eval or above
2072 :			$rh_ans->{ans_message} = 'There is a syntax error in your answer';
2073 :			$rh_ans->{student_ans} = clean_up_error_msg($PG_eval_errors);
2074 :			} else {
2075 :			$rh_ans->{student_ans} = $inVal;
2076 :			}
2077 :			$rh_ans;
2078 :			}
2079 :
2080 :			=pod
2081 :
2082 :			std_num_array_filter($rh_ans, %options)
2083 :			returns $rh_ans
2084 :
2085 :			Assumes the {student_ans} field is a numerical array, and applies BOTH check_syntax and std_num_filter
2086 :			to each element of the array. Does it's best to generate sensible error messages for syntax errors.
2087 :			A typical error message displayed in {studnet_ans} might be ( 56, error message, -4).
2088 :
2089 :			=cut
2090 :
2091 :	chris	54	sub std_num_array_filter {
2092 :	sam	2	my $rh_ans= shift;
2093 :			my %options = @_;
2094 :			my @in = @{$rh_ans->{student_ans}};
2095 :			my $temp_hash = new AnswerHash;
2096 :			my @out=();
2097 :			my $PGanswerMessage = '';
2098 :			foreach my $item (@in) { # evaluate each number in the vector
2099 :			$temp_hash->input($item);
2100 :			$temp_hash = check_syntax($temp_hash);
2101 :			if (defined($temp_hash->{error_flag}) and $temp_hash->{error_flag} eq 'SYNTAX') {
2102 :			$PGanswerMessage .= $temp_hash->{ans_message};
2103 :			$temp_hash->{ans_message} = undef;
2104 :			} else {
2105 :			#continue processing
2106 :			$temp_hash = std_num_filter($temp_hash);
2107 :			if (defined($temp_hash->{ans_message}) and $temp_hash->{ans_message} ) {
2108 :			$PGanswerMessage .= $temp_hash->{ans_message};
2109 :			$temp_hash->{ans_message} = undef;
2110 :			}
2111 :			}
2112 :			push(@out, $temp_hash->input());
2113 :
2114 :			}
2115 :			if ($PGanswerMessage) {
2116 :			$rh_ans->input( "( " . join(", ", @out ) . " )" );
2117 :	chris	81	$rh_ans->throw_error('SYNTAX', 'There is a syntax error in your answer.');
2118 :	sam	2	} else {
2119 :			$rh_ans->input( [@out] );
2120 :			}
2121 :			$rh_ans;
2122 :			}
2123 :
2124 :			sub function_from_string2 {
2125 :			my $rh_ans = shift;
2126 :			my %options = @_;
2127 :			my $eqn = $rh_ans->{student_ans};
2128 :			set_default_options( \%options,
2129 :	chris	54	'store_in' => 'rf_student_ans',
2130 :			'ra_vars' => [qw( x y )],
2131 :			'debug' => 0,
2132 :			);
2133 :	sam	2	my @VARS = @{ $options{ 'ra_vars'}};
2134 :			warn "VARS = ", join("<>", @VARS) if defined($options{debug}) and $options{debug} ==1;
2135 :			my $originalEqn = $eqn;
2136 :	chris	54	$eqn = &math_constants($eqn);
2137 :	sam	2	for( my $i = 0; $i < @VARS; $i++ ) {
2138 :	gage	36	# This next line is a hack required for 5.6.0 -- it doesn't appear to be needed in 5.6.1
2139 :			my ($temp,$er1,$er2) = PG_restricted_eval('"'. $VARS[$i] . '"');
2140 :	chris	54	#$eqn =~ s/\b$VARS[$i]\b/\$VARS[$i]/g;
2141 :	gage	36	$eqn =~ s/\b$temp\b/\$VARS[$i]/g;
2142 :
2143 :	sam	2	}
2144 :			warn "equation evaluated = $eqn",$rh_ans->pretty_print(), "<br>\noptions<br>\n",
2145 :			pretty_print(\%options)
2146 :			if defined($options{debug}) and $options{debug} ==1;
2147 :			my ($function_sub,$PG_eval_errors, $PG_full_errors) = PG_answer_eval( q!
2148 :			sub {
2149 :			my @VARS = @_;
2150 :			my $input_str = '';
2151 :			for( my $i=0; $i<@VARS; $i++ ) {
2152 :			$input_str .= "\$VARS[$i] = $VARS[$i]; ";
2153 :			}
2154 :			my $PGanswerMessage;
2155 :			$input_str .= '! . $eqn . q!'; # need the single quotes to keep the contents of $eqn from being
2156 :			# evaluated when it is assigned to $input_str;
2157 :			my ($out, $PG_eval_errors, $PG_full_errors) = PG_answer_eval($input_str); #Finally evaluated
2158 :
2159 :			if ( defined($PG_eval_errors) and $PG_eval_errors =~ /\S/ ) {
2160 :			$PGanswerMessage = clean_up_error_msg($PG_eval_errors);
2161 :			# This message seemed too verbose, but it does give extra information, we'll see if it is needed.
2162 :			# "<br> There was an error in evaluating your function <br>
2163 :			# !. $originalEqn . q! <br>
2164 :			# at ( " . join(', ', @VARS) . " ) <br>
2165 :			# $PG_eval_errors
2166 :			# "; # this message appears in the answer section which is not process by Latex2HTML so it must
2167 :			# # be in HTML. That is why $BR is NOT used.
2168 :
2169 :			}
2170 :			(wantarray) ? ($out, $PGanswerMessage): $out; # PGanswerMessage may be undefined.
2171 :			};
2172 :			!);
2173 :
2174 :			if (defined($PG_eval_errors) and $PG_eval_errors =~/\S/ ) {
2175 :			$PG_eval_errors = clean_up_error_msg($PG_eval_errors);
2176 :
2177 :			my $PGanswerMessage = "There was an error in converting the expression
2178 :			$main::BR $originalEqn $main::BR into a function.
2179 :			$main::BR $PG_eval_errors.";
2180 :			$rh_ans->{rf_student_ans} = $function_sub;
2181 :			$rh_ans->{ans_message} = $PGanswerMessage;
2182 :			$rh_ans->{error_message} = $PGanswerMessage;
2183 :			$rh_ans->{error_flag} = 1;
2184 :			# we couldn't compile the equation, we'll return an error message.
2185 :			} else {
2186 :			# if (defined($options{store_in} )) {
2187 :			# $rh_ans ->{$options{store_in}} = $function_sub;
2188 :			# } else {
2189 :			# $rh_ans->{rf_student_ans} = $function_sub;
2190 :			# }
2191 :			$rh_ans ->{$options{store_in}} = $function_sub;
2192 :			}
2193 :
2194 :			$rh_ans;
2195 :			}
2196 :
2197 :
2198 :	chris	54	sub is_zero_array {
2199 :	sam	2	my $rh_ans = shift;
2200 :			my %options = @_;
2201 :			my $array = $rh_ans -> {ra_differences};
2202 :			my $num = @$array;
2203 :			my $i;
2204 :			my $max = 0; my $mm;
2205 :			for ($i=0; $i< $num; $i++) {
2206 :			$mm = $array->[$i] ;
2207 :			if (not is_a_number($mm) ) {
2208 :			$max = $mm; # break out if one of the elements is not a number
2209 :			last;
2210 :			}
2211 :			$max = abs($mm) if abs($mm) > $max;
2212 :			}
2213 :			if (not is_a_number($max)) {
2214 :			$rh_ans->{score} = 0;
2215 :			my $error = "WeBWorK was unable evaluate your function. Please check that your
2216 :			expression doesn't take roots of negative numbers, or divide by zero.";
2217 :			$rh_ans->throw_error('EVAL',$error);
2218 :			} else {
2219 :	chris	81	my $tol = $options{tol} if defined($options{tol});
2220 :			#$tol = 0.01*$options{reltol} if defined($options{reltol});
2221 :			$tol = .000001 unless defined($tol);
2222 :	sam	2
2223 :			$rh_ans->{score} = ($max <$tol) ? 1: 0; # 1 if the array is close to 0;
2224 :			}
2225 :			$rh_ans;
2226 :			}
2227 :	chris	54
2228 :	sam	2	=pod
2229 :
2230 :			best_approx_parameters($rh_ans,%options);
2231 :	chris	54	{rf_student_ans} # reference to the test answer
2232 :			{rf_correct_ans} # reference to the comparison answer
2233 :			{evaluation_points}, # an array of row vectors indicating the points
2234 :			# to evaluate when comparing the functions
2235 :			%options # debug => 1 gives more error answers
2236 :			# param_vars => [''] additional parameters used to adapt to function
2237 :	sam	2	)
2238 :			returns $rh_ans;
2239 :			The parameters for the comparison function which best approximates the test_function are stored
2240 :			in the field {ra_parameters}.
2241 :
2242 :			The last $dim_of_parms_space variables are assumed to be parameters, and it is also
2243 :			assumed that the function \&comparison_fun
2244 :			depends linearly on these variables. This function finds the values for these parameters which minimizes the
2245 :			Euclidean distance (L2 distance) between the test function and the comparison function and the test points specified
2246 :			by the array reference \@rows_of_test_points. This is assumed to be an array of arrays, with the inner arrays
2247 :			determining a test point.
2248 :
2249 :			The comparison function should have $dim_of_params_space more input variables than the test function.
2250 :
2251 :			=cut
2252 :
2253 :	chris	54	=pod
2254 :	sam	2
2255 :	chris	54	Used internally:
2256 :
2257 :			&$determine_param_coeff( $rf_comparison_function # a reference to the correct answer function
2258 :			$ra_variables # an array of the active input variables to the functions
2259 :			$dim_of_params_space # indicates the number of parameters upon which the
2260 :			# the comparison function depends linearly. These are assumed to
2261 :			# be the last group of inputs to the comparison function.
2262 :
2263 :			%options # $options{debug} gives more error messages
2264 :
2265 :			# A typical function might look like
2266 :			# f(x,y,z,a,b) = x^2+acos(xz) + bsin(x) with a parameter
2267 :			# space of dimension 2 and a variable space of dimension 3.
2268 :			)
2269 :			# returns a list of coefficients
2270 :
2271 :			=cut
2272 :	sam	2
2273 :	chris	54	sub best_approx_parameters {
2274 :	sam	2	my $rh_ans = shift;
2275 :			my %options = @_;
2276 :			my $errors = undef;
2277 :			# This subroutine for the determining the coefficents of the parameters at a given point
2278 :			# is pretty specialized, so it is included here as a sub-subroutine.
2279 :			my $determine_param_coeffs = sub {
2280 :	chris	81	my ($rf_fun, $ra_variables, $dim_of_params_space, %options) =@_;
2281 :			my @zero_params=();
2282 :			for(my $i=1;$i<=$dim_of_params_space;$i++){push(@zero_params,0); }
2283 :			my @vars = @$ra_variables;
2284 :			my @coeff = ();
2285 :			my @inputs = (@vars,@zero_params);
2286 :			my ($f0, $f1, $err);
2287 :			($f0, $err) = &{$rf_fun}(@inputs);
2288 :			if (defined($err) ) {
2289 :			$errors .= "$err ";
2290 :			} else {
2291 :			for (my $i=@vars;$i<@inputs;$i++) {
2292 :			$inputs[$i]=1; # set one parameter to 1;
2293 :			my($f1,$err) = &$rf_fun(@inputs);
2294 :			if (defined($err) ) {
2295 :			$errors .= " $err ";
2296 :			} else {
2297 :			push(@coeff, $f1-$f0);
2298 :	sam	2	}
2299 :	chris	81	$inputs[$i]=0; # set it back
2300 :	sam	2	}
2301 :			}
2302 :	chris	81	(\@coeff, $errors);
2303 :			};
2304 :			my $rf_fun = $rh_ans->{rf_student_ans};
2305 :			my $rf_correct_fun = $rh_ans->{rf_correct_ans};
2306 :			my $ra_vars_matrix = $rh_ans->{evaluation_points};
2307 :			my $dim_of_param_space = @{$options{param_vars}};
2308 :			# Short cut. Bail if there are no param_vars
2309 :			unless ($dim_of_param_space >0) {
2310 :			$rh_ans ->{ra_parameters} = [];
2311 :			return $rh_ans;
2312 :			}
2313 :			# inputs are row arrays in this case.
2314 :			my @zero_params=();
2315 :	sam	2
2316 :	chris	81	for(my $i=1;$i<=$dim_of_param_space;$i++){push(@zero_params,0); }
2317 :			my @rows_of_vars = @$ra_vars_matrix;
2318 :			warn "input rows ", pretty_print(\@rows_of_vars) if defined($options{debug}) and $options{debug};
2319 :			my $rows = @rows_of_vars;
2320 :			my $matrix =new Matrix($rows,$dim_of_param_space);
2321 :			my $rhs_vec = new Matrix($rows, 1);
2322 :			my $row_num = 1;
2323 :			my ($ra_coeff,$val2, $val1, $err1,$err2,@inputs,@vars);
2324 :			my $number_of_data_points = $dim_of_param_space +2;
2325 :			while (@rows_of_vars and $row_num <= $number_of_data_points) {
2326 :	sam	2	# get one set of data points from the test function;
2327 :	chris	81	@vars = @{ shift(@rows_of_vars) };
2328 :	sam	2	($val2, $err1) = &{$rf_fun}(@vars);
2329 :			$errors .= " $err1 " if defined($err1);
2330 :			@inputs = (@vars,@zero_params);
2331 :			($val1, $err2) = &{$rf_correct_fun}(@inputs);
2332 :			$errors .= " $err2 " if defined($err2);
2333 :
2334 :			unless (defined($err1) or defined($err2) ) {
2335 :			$rhs_vec->assign($row_num,1, $val2-$val1 );
2336 :
2337 :			# warn "rhs data val1=$val1, val2=$val2, val2 - val1 = ", $val2 - $val1 if $options{debug};
2338 :			# warn "vars ", join(" \| ", @vars) if $options{debug};
2339 :
2340 :			($ra_coeff, $err1) = &{$determine_param_coeffs}($rf_correct_fun,\@vars,$dim_of_param_space,%options);
2341 :			if (defined($err1) ) {
2342 :			$errors .= " $err1 ";
2343 :			} else {
2344 :			my @coeff = @$ra_coeff;
2345 :			my $col_num=1;
2346 :			while(@coeff) {
2347 :			$matrix->assign($row_num,$col_num, shift(@coeff) );
2348 :			$col_num++;
2349 :			}
2350 :			}
2351 :			}
2352 :			$row_num++;
2353 :			last if $errors; # break if there are any errors.
2354 :			# This cuts down on the size of error messages.
2355 :			# However it impossible to check for equivalence at 95% of points
2356 :	gage	5	# which might be useful for functions that are not defined at some points.
2357 :	sam	2	}
2358 :			warn "<br> best_approx_parameters: matrix1 <br> ", " $matrix " if $options{debug};
2359 :			warn "<br> best_approx_parameters: vector <br> ", " $rhs_vec " if $options{debug};
2360 :
2361 :			# we have Matrix * parameter = data_vec + perpendicular vector
2362 :			# where the matrix has column vectors defining the span of the parameter space
2363 :			# multiply both sides by Matrix_transpose and solve for the parameters
2364 :			# This is exactly what the method proj_coeff method does.
2365 :			my @array;
2366 :			if (defined($errors) ) {
2367 :			@array = (); # new Matrix($dim_of_param_space,1);
2368 :			} else {
2369 :			@array = $matrix->proj_coeff($rhs_vec)->list();
2370 :			}
2371 :			# check size (hack)
2372 :			my $max = 0;
2373 :			foreach my $val (@array ) {
2374 :			$max = abs($val) if $max < abs($val);
2375 :			if (not is_a_number($val) ) {
2376 :			$max = "NaN: $val";
2377 :			last;
2378 :			}
2379 :			}
2380 :			if ($max =~/NaN/) {
2381 :			$errors .= "WeBWorK was unable evaluate your function. Please check that your
2382 :			expression doesn't take roots of negative numbers, or divide by zero.";
2383 :			} elsif ($max > $options{maxConstantOfIntegration} ) {
2384 :			$errors .= "At least one of the adapting parameters
2385 :			(perhaps the constant of integration) is too large: $max,
2386 :			( the maximum allowed is $options{maxConstantOfIntegration} )";
2387 :			}
2388 :
2389 :			$rh_ans->{ra_parameters} = \@array;
2390 :			$rh_ans->throw_error('EVAL', $errors) if defined($errors);
2391 :	chris	81	$rh_ans;
2392 :	sam	2	}
2393 :
2394 :			=pod
2395 :
2396 :			calculate_difference_vector( $ans_hash, %options);
2397 :
2398 :	chris	81	{rf_student_ans}, # a reference to the test function
2399 :	sam	2	{rf_correct_ans}, # a reference to the correct answer function
2400 :			{evaluation_points}, # an array of row vectors indicating the points
2401 :	chris	81	# to evaluate when comparing the functions
2402 :	sam	2	{ra_parameters} # these are the (optional) additional inputs to
2403 :	chris	81	# the comparison function which adapt it properly
2404 :			# to the problem at hand.
2405 :	sam	2
2406 :	chris	81	%options # mode => 'rel' specifies that each element in the
2407 :			# difference matrix is divided by the correct answer.
2408 :			# unless the correct answer is nearly 0.
2409 :	sam	2	)
2410 :
2411 :			=cut
2412 :
2413 :			sub calculate_difference_vector {
2414 :			my $rh_ans = shift;
2415 :			my %options = @_;
2416 :			# initialize
2417 :			my $rf_fun = $rh_ans -> {rf_student_ans};
2418 :			my $rf_correct_fun = $rh_ans -> {rf_correct_ans};
2419 :			my $ra_parameters = $rh_ans ->{ra_parameters};
2420 :			my @evaluation_points = @{$rh_ans->{evaluation_points} };
2421 :			my @parameters = ();
2422 :			@parameters = @$ra_parameters if defined($ra_parameters) and ref($ra_parameters) eq 'ARRAY';
2423 :			my $errors = undef;
2424 :	gage	5	my @zero_params=();
2425 :			for(my $i=1;$i<=@{$ra_parameters};$i++){push(@zero_params,0); }
2426 :	sam	2	my @differences = ();
2427 :	gage	5	my @student_values;
2428 :			my @correct_values;
2429 :			my @tol_values;
2430 :			my ($diff,$tol_val);
2431 :	sam	2	# calculate the vector of differences between the test function and the comparison function.
2432 :			while (@evaluation_points) {
2433 :	gage	5	my ($err1, $err2,$err3);
2434 :	sam	2	my @vars = @{ shift(@evaluation_points) };
2435 :			my @inputs = (@vars, @parameters);
2436 :			my ($inVal, $correctVal);
2437 :			($inVal, $err1) = &{$rf_fun}(@vars);
2438 :			$errors .= " $err1 " if defined($err1);
2439 :	gage	5	$errors .= " Error detected evaluating student input at (".join(' , ',@vars) ." ) " if defined($options{debug}) and $options{debug}=1 and defined($err1);
2440 :	sam	2	($correctVal, $err2) =&{$rf_correct_fun}(@inputs);
2441 :			$errors .= " There is an error in WeBWorK's answer to this problem, please alert your instructor.<br> $err2 " if defined($err2);
2442 :	gage	5	$errors .= " Error detected evaluating correct answer at (".join(' , ',@inputs) ." ) " if defined($options{debug}) and $options{debug}=1 and defined($err2);
2443 :			($tol_val,$err3)= &$rf_correct_fun(@vars, @zero_params);
2444 :			$errors .= " There is an error in WeBWorK's answer to this problem, please alert your instructor.<br> $err3 " if defined($err3);
2445 :			$errors .= " Error detected evaluating correct answer at (".join(' , ',@vars, @zero_params) ." ) " if defined($options{debug}) and $options{debug}=1 and defined($err3);
2446 :			unless (defined($err1) or defined($err2) or defined($err3) ) {
2447 :			$diff = ( $inVal - ($correctVal -$tol_val ) ) - $tol_val; #prevents entering too high a number?
2448 :	sam	2	#warn "taking the difference of ", $inVal, " and ", $correctVal, " is ", $diff;
2449 :			if (defined($options{tolType}) and $options{tolType} eq 'relative' ) { #relative tolerance
2450 :	gage	5	#warn "diff = $diff";
2451 :	chris	22	$diff = ( $inVal - ($correctVal-$tol_val ) )/abs($tol_val) -1 if abs($tol_val) > $options{zeroLevel};
2452 :	gage	5	#$diff = ( $inVal - ($correctVal-$tol_val- $tol_val ) )/abs($tol_val) if abs($tol_val) > $options{zeroLevel};
2453 :			#warn "diff = $diff, ", abs( &$rf_correct_fun(@inputs) ) , "-- $correctVal";
2454 :	sam	2	}
2455 :			}
2456 :			last if $errors; # break if there are any errors.
2457 :			# This cuts down on the size of error messages.
2458 :			# However it impossible to check for equivalence at 95% of points
2459 :	gage	5	# which might be useful for functions that are not defined at some points.
2460 :			push(@student_values,$inVal);
2461 :			push(@correct_values,( $inVal - ($correctVal-$tol_val ) ));
2462 :	sam	2	push(@differences, $diff);
2463 :	gage	5	push(@tol_values,$tol_val);
2464 :	sam	2	}
2465 :			$rh_ans ->{ra_differences} = \@differences;
2466 :	chris	22	$rh_ans ->{ra_student_values} = \@student_values;
2467 :			$rh_ans ->{ra_adjusted_student_values} = \@correct_values;
2468 :			$rh_ans->{ra_tol_values}=\@tol_values;
2469 :	sam	2	$rh_ans->throw_error('EVAL', $errors) if defined($errors);
2470 :			$rh_ans;
2471 :			}
2472 :
2473 :			##########################################################################
2474 :			##########################################################################
2475 :			## String answer evaluators
2476 :
2477 :			=head2 String Answer Evaluators
2478 :
2479 :			String answer evaluators compare a student string to the correct string.
2480 :			Different filters can be applied to allow various degrees of variation.
2481 :			Both the student and correct answers are subject to the same filters, to
2482 :			ensure that there are no unexpected matches or rejections.
2483 :
2484 :			String Filters
2485 :
2486 :			remove_whitespace -- Removes all whitespace from the string.
2487 :	chris	81	It applies the following substitution
2488 :			to the string:
2489 :			$filteredAnswer =~ s/\s+//g;
2490 :	sam	2
2491 :			compress_whitespace -- Removes leading and trailing whitespace, and
2492 :	chris	81	replaces all other blocks of whitespace by a
2493 :			single space. Applies the following substitutions:
2494 :			$filteredAnswer =~ s/^\s*//;
2495 :			$filteredAnswer =~ s/\s*$//;
2496 :			$filteredAnswer =~ s/\s+/ /g;
2497 :	sam	2
2498 :			trim_whitespace -- Removes leading and trailing whitespace.
2499 :	chris	81	Applies the following substitutions:
2500 :			$filteredAnswer =~ s/^\s*//;
2501 :			$filteredAnswer =~ s/\s*$//;
2502 :	sam	2
2503 :			ignore_case -- Ignores the case of the string. More accurately,
2504 :	chris	81	it converts the string to uppercase (by convention).
2505 :			Applies the following function:
2506 :			$filteredAnswer = uc $filteredAnswer;
2507 :	sam	2
2508 :			ignore_order -- Ignores the order of the letters in the string.
2509 :	chris	81	This is used for problems of the form "Choose all
2510 :			that apply." Specifically, it removes all
2511 :			whitespace and lexically sorts the letters in
2512 :			ascending alphabetical order. Applies the following
2513 :			functions:
2514 :			$filteredAnswer = join( "", lex_sort(
2515 :			split( /\s*/, $filteredAnswer ) ) );
2516 :	sam	2
2517 :			=cut
2518 :
2519 :			################################
2520 :			## STRING ANSWER FILTERS
2521 :
2522 :			## IN: --the string to be filtered
2523 :			## --a list of the filters to use
2524 :			##
2525 :			## OUT: --the modified string
2526 :			##
2527 :			## Use this subroutine instead of the
2528 :			## individual filters below it
2529 :	chris	81
2530 :	sam	2	sub str_filters {
2531 :			my $stringToFilter = shift @_;
2532 :			my @filters_to_use = @_;
2533 :			my %known_filters = ( 'remove_whitespace' => undef,
2534 :	chris	35	'compress_whitespace' => undef,
2535 :			'trim_whitespace' => undef,
2536 :			'ignore_case' => undef,
2537 :			'ignore_order' => undef
2538 :	chris	81	);
2539 :	sam	2
2540 :			#test for unknown filters
2541 :			my $filter;
2542 :			foreach $filter (@filters_to_use) {
2543 :			die "Unknown string filter $filter (try checking the parameters to str_cmp() )"
2544 :	chris	81	unless exists $known_filters{$filter};
2545 :	sam	2	}
2546 :
2547 :			if( grep( /remove_whitespace/i, @filters_to_use ) ) {
2548 :			$stringToFilter = remove_whitespace( $stringToFilter );
2549 :			}
2550 :			if( grep( /compress_whitespace/i, @filters_to_use ) ) {
2551 :			$stringToFilter = compress_whitespace( $stringToFilter );
2552 :			}
2553 :			if( grep( /trim_whitespace/i, @filters_to_use ) ) {
2554 :			$stringToFilter = trim_whitespace( $stringToFilter );
2555 :			}
2556 :			if( grep( /ignore_case/i, @filters_to_use ) ) {
2557 :			$stringToFilter = ignore_case( $stringToFilter );
2558 :			}
2559 :			if( grep( /ignore_order/i, @filters_to_use ) ) {
2560 :			$stringToFilter = ignore_order( $stringToFilter );
2561 :			}
2562 :
2563 :			return $stringToFilter;
2564 :			}
2565 :
2566 :			sub remove_whitespace {
2567 :			my $filteredAnswer = shift;
2568 :
2569 :			$filteredAnswer =~ s/\s+//g; # remove all whitespace
2570 :
2571 :			return $filteredAnswer;
2572 :			}
2573 :
2574 :	chris	54	sub compress_whitespace {
2575 :	sam	2	my $filteredAnswer = shift;
2576 :
2577 :			$filteredAnswer =~ s/^\s*//; # remove initial whitespace
2578 :			$filteredAnswer =~ s/\s*$//; # remove trailing whitespace
2579 :			$filteredAnswer =~ s/\s+/ /g; # replace spaces by single space
2580 :
2581 :			return $filteredAnswer;
2582 :			}
2583 :
2584 :			sub trim_whitespace {
2585 :			my $filteredAnswer = shift;
2586 :
2587 :			$filteredAnswer =~ s/^\s*//; # remove initial whitespace
2588 :			$filteredAnswer =~ s/\s*$//; # remove trailing whitespace
2589 :
2590 :			return $filteredAnswer;
2591 :			}
2592 :
2593 :			sub ignore_case {
2594 :			my $filteredAnswer = shift;
2595 :
2596 :			$filteredAnswer = uc $filteredAnswer;
2597 :
2598 :			return $filteredAnswer;
2599 :			}
2600 :
2601 :			sub ignore_order {
2602 :			my $filteredAnswer = shift;
2603 :
2604 :			$filteredAnswer = join( "", lex_sort( split( /\s*/, $filteredAnswer ) ) );
2605 :
2606 :			return $filteredAnswer;
2607 :			}
2608 :			################################
2609 :			## END STRING ANSWER FILTERS
2610 :
2611 :			=head3 "mode"_str_cmp functions
2612 :
2613 :			The functions of the the form "mode"_str_cmp() use different functions to
2614 :			specify which filters to apply. They take no options except the correct
2615 :			string. There are also versions which accept a list of strings.
2616 :
2617 :			std_str_cmp( $correctString )
2618 :			std_str_cmp_list( @correctStringList )
2619 :			Filters: compress_whitespace, ignore_case
2620 :
2621 :			std_cs_str_cmp( $correctString )
2622 :			std_cs_str_cmp_list( @correctStringList )
2623 :			Filters: compress_whitespace
2624 :
2625 :			strict_str_cmp( $correctString )
2626 :			strict_str_cmp_list( @correctStringList )
2627 :			Filters: trim_whitespace
2628 :
2629 :			unordered_str_cmp( $correctString )
2630 :			unordered_str_cmp_list( @correctStringList )
2631 :			Filters: ignore_order, ignore_case
2632 :
2633 :			unordered_cs_str_cmp( $correctString )
2634 :			unordered_cs_str_cmp_list( @correctStringList )
2635 :			Filters: ignore_order
2636 :
2637 :			ordered_str_cmp( $correctString )
2638 :			ordered_str_cmp_list( @correctStringList )
2639 :			Filters: remove_whitespace, ignore_case
2640 :
2641 :			ordered_cs_str_cmp( $correctString )
2642 :			ordered_cs_str_cmp_list( @correctStringList )
2643 :			Filters: remove_whitespace
2644 :
2645 :			Examples
2646 :
2647 :			ANS( std_str_cmp( "W. Mozart" ) ) -- Accepts "W. Mozart", "W. MOZarT",
2648 :			and so forth. Case insensitive. All internal spaces treated
2649 :			as single spaces.
2650 :			ANS( std_cs_str_cmp( "Mozart" ) ) -- Rejects "mozart". Same as
2651 :			std_str_cmp() but case sensitive.
2652 :			ANS( strict_str_cmp( "W. Mozart" ) ) -- Accepts only the exact string.
2653 :			ANS( unordered_str_cmp( "ABC" ) ) -- Accepts "a c B", "CBA" and so forth.
2654 :			Unordered, case insensitive, spaces ignored.
2655 :			ANS( unordered_cs_str_cmp( "ABC" ) ) -- Rejects "abc". Same as
2656 :			unordered_str_cmp() but case sensitive.
2657 :			ANS( ordered_str_cmp( "ABC" ) ) -- Accepts "a b C", "A B C" and so forth.
2658 :			Ordered, case insensitive, spaces ignored.
2659 :			ANS( ordered_cs_str_cmp( "ABC" ) ) -- Rejects "abc", accepts "A BC" and
2660 :			so forth. Same as ordered_str_cmp() but case sensitive.
2661 :
2662 :			=cut
2663 :
2664 :	chris	54	sub std_str_cmp { # compare strings
2665 :	sam	2	my $correctAnswer = shift @_;
2666 :			my @filters = ( 'compress_whitespace', 'ignore_case' );
2667 :			my $type = 'std_str_cmp';
2668 :			STR_CMP( 'correctAnswer' => $correctAnswer,
2669 :	chris	35	'filters' => \@filters,
2670 :			'type' => $type
2671 :	sam	2	);
2672 :			}
2673 :
2674 :	chris	54	sub std_str_cmp_list { # alias for std_str_cmp
2675 :	sam	2	my @answerList = @_;
2676 :			my @output;
2677 :			while (@answerList) {
2678 :			push( @output, std_str_cmp(shift @answerList) );
2679 :			}
2680 :			@output;
2681 :			}
2682 :
2683 :	chris	54	sub std_cs_str_cmp { # compare strings case sensitive
2684 :	sam	2	my $correctAnswer = shift @_;
2685 :			my @filters = ( 'compress_whitespace' );
2686 :			my $type = 'std_cs_str_cmp';
2687 :			STR_CMP( 'correctAnswer' => $correctAnswer,
2688 :	chris	54	'filters' => \@filters,
2689 :			'type' => $type
2690 :	sam	2	);
2691 :			}
2692 :
2693 :	chris	54	sub std_cs_str_cmp_list { # alias for std_cs_str_cmp
2694 :	sam	2	my @answerList = @_;
2695 :			my @output;
2696 :			while (@answerList) {
2697 :			push( @output, std_cs_str_cmp(shift @answerList) );
2698 :			}
2699 :			@output;
2700 :			}
2701 :
2702 :	chris	54	sub strict_str_cmp { # strict string compare
2703 :	sam	2	my $correctAnswer = shift @_;
2704 :			my @filters = ( 'trim_whitespace' );
2705 :			my $type = 'strict_str_cmp';
2706 :			STR_CMP( 'correctAnswer' => $correctAnswer,
2707 :	chris	54	'filters' => \@filters,
2708 :			'type' => $type
2709 :	sam	2	);
2710 :			}
2711 :
2712 :	chris	54	sub strict_str_cmp_list { # alias for strict_str_cmp
2713 :	sam	2	my @answerList = @_;
2714 :			my @output;
2715 :			while (@answerList) {
2716 :			push( @output, strict_str_cmp(shift @answerList) );
2717 :			}
2718 :			@output;
2719 :			}
2720 :
2721 :	chris	54	sub unordered_str_cmp { # unordered, case insensitive, spaces ignored
2722 :	sam	2	my $correctAnswer = shift @_;
2723 :			my @filters = ( 'ignore_order', 'ignore_case' );
2724 :			my $type = 'unordered_str_cmp';
2725 :	chris	81	STR_CMP( 'correctAnswer' => $correctAnswer,
2726 :			'filters' => \@filters,
2727 :			'type' => $type
2728 :	sam	2	);
2729 :			}
2730 :
2731 :	chris	54	sub unordered_str_cmp_list { # alias for unordered_str_cmp
2732 :	sam	2	my @answerList = @_;
2733 :			my @output;
2734 :			while (@answerList) {
2735 :			push( @output, unordered_str_cmp(shift @answerList) );
2736 :			}
2737 :			@output;
2738 :			}
2739 :
2740 :	chris	54	sub unordered_cs_str_cmp { # unordered, case sensitive, spaces ignored
2741 :	sam	2	my $correctAnswer = shift @_;
2742 :			my @filters = ( 'ignore_order' );
2743 :			my $type = 'unordered_cs_str_cmp';
2744 :	chris	81	STR_CMP( 'correctAnswer' => $correctAnswer,
2745 :			'filters' => \@filters,
2746 :			'type' => $type
2747 :	sam	2	);
2748 :			}
2749 :
2750 :	chris	54	sub unordered_cs_str_cmp_list { # alias for unordered_cs_str_cmp
2751 :	sam	2	my @answerList = @_;
2752 :			my @output;
2753 :			while (@answerList) {
2754 :			push( @output, unordered_cs_str_cmp(shift @answerList) );
2755 :			}
2756 :			@output;
2757 :			}
2758 :
2759 :	chris	54	sub ordered_str_cmp { # ordered, case insensitive, spaces ignored
2760 :	sam	2	my $correctAnswer = shift @_;
2761 :			my @filters = ( 'remove_whitespace', 'ignore_case' );
2762 :			my $type = 'ordered_str_cmp';
2763 :			STR_CMP( 'correctAnswer' => $correctAnswer,
2764 :	chris	54	'filters' => \@filters,
2765 :			'type' => $type
2766 :	sam	2	);
2767 :			}
2768 :
2769 :	chris	54	sub ordered_str_cmp_list { # alias for ordered_str_cmp
2770 :	sam	2	my @answerList = @_;
2771 :			my @output;
2772 :			while (@answerList) {
2773 :			push( @output, ordered_str_cmp(shift @answerList) );
2774 :			}
2775 :			@output;
2776 :			}
2777 :
2778 :	chris	54	sub ordered_cs_str_cmp { # ordered, case sensitive, spaces ignored
2779 :	sam	2	my $correctAnswer = shift @_;
2780 :			my @filters = ( 'remove_whitespace' );
2781 :			my $type = 'ordered_cs_str_cmp';
2782 :			STR_CMP( 'correctAnswer' => $correctAnswer,
2783 :	chris	54	'filters' => \@filters,
2784 :			'type' => $type
2785 :	sam	2	);
2786 :			}
2787 :
2788 :	chris	54	sub ordered_cs_str_cmp_list { # alias for ordered_cs_str_cmp
2789 :	sam	2	my @answerList = @_;
2790 :			my @output;
2791 :			while (@answerList) {
2792 :			push( @output, ordered_cs_str_cmp(shift @answerList) );
2793 :			}
2794 :			@output;
2795 :			}
2796 :
2797 :			=head3 str_cmp()
2798 :
2799 :			Compares a string or a list of strings, using a named hash of options to set
2800 :			parameters. This can make for more readable code than using the "mode"_str_cmp()
2801 :			style, but some people find one or the other easier to remember.
2802 :
2803 :			ANS( str_cmp( answer or answer_array_ref, options_hash ) );
2804 :
2805 :			1. the correct answer or a reference to an array of answers
2806 :			2. either a list of filters, or:
2807 :			a hash consisting of
2808 :			filters - a reference to an array of filters
2809 :
2810 :			Returns an answer evaluator, or (if given a reference to an array of answers),
2811 :			a list of answer evaluators
2812 :
2813 :			FILTERS:
2814 :
2815 :			remove_whitespace -- removes all whitespace
2816 :			compress_whitespace -- removes whitespace from the beginning and end of the string,
2817 :			and treats one or more whitespace characters in a row as a
2818 :			single space (true by default)
2819 :			trim_whitespace -- removes whitespace from the beginning and end of the string
2820 :	chris	81	ignore_case -- ignores the case of the letters (true by default)
2821 :	sam	2	ignore_order -- ignores the order in which letters are entered
2822 :
2823 :			EXAMPLES:
2824 :
2825 :			str_cmp( "Hello" ) -- matches "Hello", " hello" (same as std_str_cmp() )
2826 :			str_cmp( ["Hello", "Goodbye"] ) -- same as std_str_cmp_list()
2827 :			str_cmp( " hello ", trim_whitespace ) -- matches "hello", " hello "
2828 :			str_cmp( "ABC", filters => 'ignore_order' ) -- matches "ACB", "A B C", but not "abc"
2829 :			str_cmp( "D E F", remove_whitespace, ignore_case ) -- matches "def" and "d e f" but not "fed"
2830 :
2831 :			=cut
2832 :
2833 :	chris	54	sub str_cmp {
2834 :	sam	2	my $correctAnswer = shift @_;
2835 :			$correctAnswer = '' unless defined($correctAnswer);
2836 :			my @options = @_;
2837 :			my $ra_filters;
2838 :
2839 :			# error-checking for filters occurs in the filters() subroutine
2840 :			if( not defined( $options[0] ) ) { # used with no filters as alias for std_str_cmp()
2841 :			@options = ( 'compress_whitespace', 'ignore_case' );
2842 :			}
2843 :
2844 :			if( $options[0] eq 'filters' ) { # using filters => [f1, f2, ...] notation
2845 :			$ra_filters = $options[1];
2846 :			}
2847 :	chris	54	else { # using a list of filters
2848 :	sam	2	$ra_filters = \@options;
2849 :			}
2850 :
2851 :			# thread over lists
2852 :			my @ans_list = ();
2853 :
2854 :			if ( ref($correctAnswer) eq 'ARRAY' ) {
2855 :			@ans_list = @{$correctAnswer};
2856 :			}
2857 :			else {
2858 :			push( @ans_list, $correctAnswer );
2859 :			}
2860 :
2861 :			# final_answer;
2862 :			my @output_list = ();
2863 :
2864 :			foreach my $ans (@ans_list) {
2865 :			push(@output_list, STR_CMP( 'correctAnswer' => $ans,
2866 :	chris	81	'filters' => $ra_filters,
2867 :			'type' => 'str_cmp'
2868 :			)
2869 :			);
2870 :	sam	2	}
2871 :
2872 :			return @output_list;
2873 :			}
2874 :
2875 :			## LOW-LEVEL ROUTINE -- NOT NORMALLY FOR END USERS -- USE WITH CAUTION
2876 :			##
2877 :			## IN: a hashtable with the following entries (error-checking to be added later?):
2878 :			## correctAnswer -- the correct answer, before filtering
2879 :			## filters -- reference to an array containing the filters to be applied
2880 :			## type -- a string containing the type of answer evaluator in use
2881 :			## OUT: a reference to an answer evaluator subroutine
2882 :	chris	35
2883 :	chris	54	sub STR_CMP {
2884 :	sam	2	my %str_params = @_;
2885 :			$str_params{'correctAnswer'} = str_filters( $str_params{'correctAnswer'}, @{$str_params{'filters'}} );
2886 :			my $answer_evaluator = sub {
2887 :			my $in = shift @_;
2888 :			$in = '' unless defined $in;
2889 :			my $original_student_ans = $in;
2890 :			$in = str_filters( $in, @{$str_params{'filters'}} );
2891 :			my $correctQ = ( $in eq $str_params{'correctAnswer'} ) ? 1: 0;
2892 :	chris	35	my $ans_hash = new AnswerHash( 'score' => $correctQ,
2893 :	sam	2	'correct_ans' => $str_params{'correctAnswer'},
2894 :			'student_ans' => $in,
2895 :			'ans_message' => '',
2896 :	chris	35	'type' => $str_params{'type'},
2897 :			'preview_text_string' => $in,
2898 :			'preview_latex_string' => $in,
2899 :			'original_student_ans' => $original_student_ans
2900 :	sam	2	);
2901 :			return $ans_hash;
2902 :			};
2903 :			return $answer_evaluator;
2904 :			}
2905 :
2906 :			##########################################################################
2907 :			##########################################################################
2908 :			## Miscellaneous answer evaluators
2909 :
2910 :			=head2 Miscellaneous Answer Evaluators (Checkboxes and Radio Buttons)
2911 :
2912 :			These evaluators do not fit any of the other categories.
2913 :
2914 :			checkbox_cmp( $correctAnswer )
2915 :
2916 :			$correctAnswer -- a string containing the names of the correct boxes,
2917 :			e.g. "ACD". Note that this means that individual
2918 :			checkbox names can only be one character. Internally,
2919 :			this is largely the same as unordered_cs_str_cmp().
2920 :
2921 :			radio_cmp( $correctAnswer )
2922 :
2923 :			$correctAnswer -- a string containing the name of the correct radio
2924 :			button, e.g. "Choice1". This is case sensitive and
2925 :			whitespace sensitive, so the correct answer must match
2926 :			the name of the radio button exactly.
2927 :
2928 :			=cut
2929 :
2930 :			# added 6/14/2000 by David Etlinger
2931 :			# because of the conversion of the answer
2932 :			# string to an array, I thought it better not
2933 :			# to force STR_CMP() to work with this
2934 :	chris	54	sub checkbox_cmp {
2935 :	sam	2	my $correctAnswer = shift @_;
2936 :			$correctAnswer = str_filters( $correctAnswer, 'ignore_order' );
2937 :
2938 :			my $answer_evaluator = sub {
2939 :			my $in = shift @_;
2940 :			$in = '' unless defined $in; #in case no boxes checked
2941 :
2942 :			my @temp = split( "\0", $in ); #convert "\0"-delimited string to array...
2943 :			$in = join( "", @temp ); #and then to a single no-delimiter string
2944 :
2945 :			my $original_student_ans = $in; #well, almost original
2946 :			$in = str_filters( $in, 'ignore_order' );
2947 :
2948 :			my $correctQ = ($in eq $correctAnswer) ? 1: 0;
2949 :
2950 :			my $ans_hash = new AnswerHash(
2951 :	chris	81	'score' => $correctQ,
2952 :			'correct_ans' => $correctAnswer,
2953 :			'student_ans' => $in,
2954 :			'ans_message' => "",
2955 :			'type' => "checkbox_cmp",
2956 :	sam	2	'preview_text_string' => $in,
2957 :			'original_student_ans' => $original_student_ans
2958 :			);
2959 :			return $ans_hash;
2960 :
2961 :			};
2962 :			return $answer_evaluator;
2963 :			}
2964 :
2965 :			#added 6/28/2000 by David Etlinger
2966 :			#exactly the same as strict_str_cmp,
2967 :			#but more intuitive to the user
2968 :			sub radio_cmp {
2969 :			strict_str_cmp( @_ );
2970 :			}
2971 :
2972 :			##########################################################################
2973 :			##########################################################################
2974 :			## Text and e-mail routines
2975 :
2976 :	chris	54	sub store_ans_at {
2977 :	sam	2	my $answerStringRef = shift;
2978 :			my %options = @_;
2979 :			my $ans_eval= '';
2980 :			if ( ref($answerStringRef) eq 'SCALAR' ) {
2981 :			$ans_eval= sub {
2982 :			my $text = shift;
2983 :			$text = '' unless defined($text);
2984 :			$$answerStringRef = $$answerStringRef . $text;
2985 :			my $ans_hash = new AnswerHash(
2986 :	chris	81	'score' => 1,
2987 :	sam	2	'correct_ans' => '',
2988 :			'student_ans' => $text,
2989 :			'ans_message' => '',
2990 :	chris	81	'type' => 'store_ans_at',
2991 :			'original_student_ans' => $text,
2992 :			'preview_text_string' => ''
2993 :	sam	2	);
2994 :
2995 :	chris	81	return $ans_hash;
2996 :	sam	2	};
2997 :			}
2998 :			else {
2999 :			die "Syntax error: \n The argument to store_ans_at() must be a pointer to a scalar.\n(e.g. store_ans_at(~~\$MSG) )\n\n";
3000 :			}
3001 :
3002 :			return $ans_eval;
3003 :			}
3004 :
3005 :			#### subroutines used in producing a questionnaire
3006 :			#### these are at least good models for other answers of this type
3007 :
3008 :			my $QUESTIONNAIRE_ANSWERS=''; # stores the answers until it is time to send them
3009 :			# this must be initialized before the answer evaluators are run
3010 :			# but that happens long after all of the text in the problem is
3011 :			# evaluated.
3012 :			# this is a utility script for cleaning up the answer output for display in
3013 :			#the answers.
3014 :
3015 :	chris	54	sub DUMMY_ANSWER {
3016 :	sam	2	my $num = shift;
3017 :			qq{<INPUT TYPE="HIDDEN" NAME="answer$num" VALUE="">}
3018 :			}
3019 :
3020 :	chris	54	sub escapeHTML {
3021 :	sam	2	my $string = shift;
3022 :			$string =~ s/\n/$BR/ge;
3023 :			$string;
3024 :			}
3025 :
3026 :			# these next two subroutines show how to modify the "store_and_at()" answer
3027 :			# evaluator to add extra information before storing the info
3028 :			# They provide a good model for how to tweak answer evaluators in special cases.
3029 :	chris	81
3030 :	chris	54	sub anstext {
3031 :	sam	2	my $num = shift;
3032 :			my $ans_eval_template = store_ans_at(\$QUESTIONNAIRE_ANSWERS);
3033 :			my $ans_eval = sub {
3034 :	chris	81	my $text = shift;
3035 :			$text = '' unless defined($text);
3036 :			my $new_text = "\n$main::psvnNumber-Problem-$main::probNum-Question-$num:\n $text "; # modify entered text
3037 :			my $out = &$ans_eval_template($new_text); # standard evaluator
3038 :			#warn "$QUESTIONNAIRE_ANSWERS";
3039 :			$out->{student_ans} = escapeHTML($text); # restore original entered text
3040 :			$out->{correct_ans} = "Question $num answered";
3041 :			$out->{original_student_ans} = escapeHTML($text);
3042 :			$out;
3043 :			};
3044 :	sam	2	$ans_eval;
3045 :			}
3046 :
3047 :	chris	54	sub ansradio {
3048 :	sam	2	my $num = shift;
3049 :			my $ans_eval_template = store_ans_at(\$QUESTIONNAIRE_ANSWERS);
3050 :			my $ans_eval = sub {
3051 :	chris	81	my $text = shift;
3052 :			$text = '' unless defined($text);
3053 :			my $new_text = "\n$main::psvnNumber-Problem-$main::probNum-RADIO-$num:\n $text "; # modify entered text
3054 :			my $out = $ans_eval_template->($new_text); # standard evaluator
3055 :			$out->{student_ans} =escapeHTML($text); # restore original entered text
3056 :			$out->{original_student_ans} = escapeHTML($text);
3057 :			$out;
3058 :	sam	2	};
3059 :
3060 :			$ans_eval;
3061 :			}
3062 :
3063 :			# This is another example of how to modify an answer evaluator to obtain
3064 :			# the desired behavior in a special case. Here the object is to have
3065 :			# have the last answer trigger the send_mail_to subroutine which mails
3066 :			# all of the answers to the designated address.
3067 :			# (This address must be listed in PG_environment{'ALLOW_MAIL_TO'} or an error occurs.)
3068 :
3069 :	chris	54	sub mail_answers_to { #accepts the last answer and mails off the result
3070 :	sam	2	my $user_address = shift;
3071 :			my $ans_eval = sub {
3072 :
3073 :	chris	81	# then mail out all of the answers, including this last one.
3074 :	sam	2
3075 :			send_mail_to( $user_address,
3076 :	chris	81	'subject' => "$main::courseName WeBWorK questionnaire",
3077 :			'body' => $QUESTIONNAIRE_ANSWERS,
3078 :			'ALLOW_MAIL_TO' => $main::ALLOW_MAIL_TO
3079 :			);
3080 :	sam	2
3081 :	chris	81	my $ans_hash = new AnswerHash( 'score' => 1,
3082 :			'correct_ans' => '',
3083 :			'student_ans' => 'Answer recorded',
3084 :			'ans_message' => '',
3085 :			'type' => 'send_mail_to',
3086 :			);
3087 :	sam	2
3088 :			return $ans_hash;
3089 :			};
3090 :
3091 :			return $ans_eval;
3092 :			}
3093 :	chris	54	sub mail_answers_to2 { #accepts the last answer and mails off the result
3094 :	sam	2	my $user_address = shift;
3095 :			my $subject = shift;
3096 :			$subject = "$main::courseName WeBWorK questionnaire" unless defined $subject;
3097 :
3098 :			send_mail_to($user_address,
3099 :			'subject' => $subject,
3100 :			'body' => $QUESTIONNAIRE_ANSWERS,
3101 :			'ALLOW_MAIL_TO' => $main::ALLOW_MAIL_TO
3102 :			);
3103 :			}
3104 :
3105 :			##########################################################################
3106 :			##########################################################################
3107 :			## Problem Grader Subroutines
3108 :
3109 :			#####################################
3110 :			# This is a model for plug-in problem graders
3111 :			#####################################
3112 :	chris	54	sub install_problem_grader {
3113 :	sam	2	my $rf_problem_grader = shift;
3114 :			$main::PG_FLAGS{PROBLEM_GRADER_TO_USE} = $rf_problem_grader;
3115 :			}
3116 :
3117 :			#this is called std only for compatability purposes;
3118 :			#almost everyone uses avg_problem_grader
3119 :	chris	54	sub std_problem_grader {
3120 :	sam	2	my $rh_evaluated_answers = shift;
3121 :			my $rh_problem_state = shift;
3122 :			my %form_options = @_;
3123 :			my %evaluated_answers = %{$rh_evaluated_answers};
3124 :			# The hash $rh_evaluated_answers typically contains:
3125 :			# 'answer1' => 34, 'answer2'=> 'Mozart', etc.
3126 :
3127 :			# By default the old problem state is simply passed back out again.
3128 :			my %problem_state = %$rh_problem_state;
3129 :
3130 :			# %form_options might include
3131 :			# The user login name
3132 :			# The permission level of the user
3133 :			# The studentLogin name for this psvn.
3134 :			# Whether the form is asking for a refresh or is submitting a new answer.
3135 :
3136 :			# initial setup of the answer
3137 :	chris	81	my %problem_result = ( score => 0,
3138 :			errors => '',
3139 :			type => 'std_problem_grader',
3140 :			msg => '',
3141 :			);
3142 :	sam	2	# Checks
3143 :
3144 :			my $ansCount = keys %evaluated_answers; # get the number of answers
3145 :			unless ($ansCount > 0 ) {
3146 :			$problem_result{msg} = "This problem did not ask any questions.";
3147 :			return(\%problem_result,\%problem_state);
3148 :			}
3149 :
3150 :			if ($ansCount > 1 ) {
3151 :			$problem_result{msg} = 'In order to get credit for this problem all answers must be correct.' ;
3152 :			}
3153 :
3154 :			unless ($form_options{answers_submitted} == 1) {
3155 :			return(\%problem_result,\%problem_state);
3156 :			}
3157 :
3158 :	chris	81	my $allAnswersCorrectQ=1;
3159 :	sam	2	foreach my $ans_name (keys %evaluated_answers) {
3160 :			# I'm not sure if this check is really useful.
3161 :			if ( ( ref($evaluated_answers{$ans_name} ) eq 'HASH' ) or ( ref($evaluated_answers{$ans_name}) eq 'AnswerHash' ) ) {
3162 :			$allAnswersCorrectQ = 0 unless( 1 == $evaluated_answers{$ans_name}->{score} );
3163 :			}
3164 :			else {
3165 :			die "Error at file ",__FILE__,"line ", __LINE__,": Answer \|$ans_name\| is not a hash reference\n".
3166 :			$evaluated_answers{$ans_name} .
3167 :			"This probably means that the answer evaluator for this answer\n" .
3168 :			"is not working correctly.";
3169 :			$problem_result{error} = "Error: Answer $ans_name is not a hash: $evaluated_answers{$ans_name}";
3170 :			}
3171 :			}
3172 :			# report the results
3173 :			$problem_result{score} = $allAnswersCorrectQ;
3174 :
3175 :			# I don't like to put in this bit of code.
3176 :			# It makes it hard to construct error free problem graders
3177 :			# I would prefer to know that the problem score was numeric.
3178 :	gage	36	unless (defined($problem_state{recorded_score}) and $problem_state{recorded_score} =~ /^([+-]?)(?=\d\|\.\d)\d(\.\d)?([Ee]([+-]?\d+))?$/ ) {
3179 :	chris	81	$problem_state{recorded_score} = 0; # This gets rid of non-numeric scores
3180 :	sam	2	}
3181 :			#
3182 :			if ($allAnswersCorrectQ == 1 or $problem_state{recorded_score} == 1) {
3183 :			$problem_state{recorded_score} = 1;
3184 :			}
3185 :			else {
3186 :			$problem_state{recorded_score} = 0;
3187 :			}
3188 :
3189 :			$problem_state{num_of_correct_ans}++ if $allAnswersCorrectQ == 1;
3190 :			$problem_state{num_of_incorrect_ans}++ if $allAnswersCorrectQ == 0;
3191 :			(\%problem_result, \%problem_state);
3192 :			}
3193 :
3194 :			#the only difference between the two versions
3195 :			#is at the end of the subroutine, where std_problem_grader2
3196 :			#records the attempt only if there have been no syntax errors,
3197 :			#whereas std_problem_grader records it regardless
3198 :	chris	54	sub std_problem_grader2 {
3199 :	sam	2	my $rh_evaluated_answers = shift;
3200 :			my $rh_problem_state = shift;
3201 :			my %form_options = @_;
3202 :			my %evaluated_answers = %{$rh_evaluated_answers};
3203 :			# The hash $rh_evaluated_answers typically contains:
3204 :			# 'answer1' => 34, 'answer2'=> 'Mozart', etc.
3205 :
3206 :			# By default the old problem state is simply passed back out again.
3207 :			my %problem_state = %$rh_problem_state;
3208 :
3209 :			# %form_options might include
3210 :			# The user login name
3211 :			# The permission level of the user
3212 :			# The studentLogin name for this psvn.
3213 :			# Whether the form is asking for a refresh or is submitting a new answer.
3214 :
3215 :			# initial setup of the answer
3216 :			my %problem_result = ( score => 0,
3217 :	chris	81	errors => '',
3218 :			type => 'std_problem_grader',
3219 :			msg => '',
3220 :			);
3221 :	sam	2
3222 :			# syntax errors are not counted.
3223 :			my $record_problem_attempt = 1;
3224 :			# Checks
3225 :
3226 :			my $ansCount = keys %evaluated_answers; # get the number of answers
3227 :			unless ($ansCount > 0 ) {
3228 :			$problem_result{msg} = "This problem did not ask any questions.";
3229 :			return(\%problem_result,\%problem_state);
3230 :			}
3231 :
3232 :			if ($ansCount > 1 ) {
3233 :			$problem_result{msg} = 'In order to get credit for this problem all answers must be correct.' ;
3234 :			}
3235 :
3236 :			unless ($form_options{answers_submitted} == 1) {
3237 :			return(\%problem_result,\%problem_state);
3238 :			}
3239 :
3240 :			my $allAnswersCorrectQ=1;
3241 :			foreach my $ans_name (keys %evaluated_answers) {
3242 :			# I'm not sure if this check is really useful.
3243 :			if ( ( ref($evaluated_answers{$ans_name} ) eq 'HASH' ) or ( ref($evaluated_answers{$ans_name}) eq 'AnswerHash' ) ) {
3244 :			$allAnswersCorrectQ = 0 unless( 1 == $evaluated_answers{$ans_name}->{score} );
3245 :			}
3246 :			else {
3247 :			die "Error at file ",__FILE__,"line ", __LINE__,": Answer \|$ans_name\| is not a hash reference\n".
3248 :			$evaluated_answers{$ans_name} .
3249 :			"This probably means that the answer evaluator for this answer\n" .
3250 :			"is not working correctly.";
3251 :			$problem_result{error} = "Error: Answer $ans_name is not a hash: $evaluated_answers{$ans_name}";
3252 :			}
3253 :			}
3254 :			# report the results
3255 :			$problem_result{score} = $allAnswersCorrectQ;
3256 :
3257 :			# I don't like to put in this bit of code.
3258 :			# It makes it hard to construct error free problem graders
3259 :			# I would prefer to know that the problem score was numeric.
3260 :			unless ($problem_state{recorded_score} =~ /^([+-]?)(?=\d\|\.\d)\d(\.\d)?([Ee]([+-]?\d+))?$/ ) {
3261 :			$problem_state{recorded_score} = 0; # This gets rid of non-numeric scores
3262 :			}
3263 :			#
3264 :			if ($allAnswersCorrectQ == 1 or $problem_state{recorded_score} == 1) {
3265 :			$problem_state{recorded_score} = 1;
3266 :			}
3267 :			else {
3268 :			$problem_state{recorded_score} = 0;
3269 :			}
3270 :			# record attempt only if there have been no syntax errors.
3271 :
3272 :			if ($record_problem_attempt == 1) {
3273 :			$problem_state{num_of_correct_ans}++ if $allAnswersCorrectQ == 1;
3274 :			$problem_state{num_of_incorrect_ans}++ if $allAnswersCorrectQ == 0;
3275 :			}
3276 :			else {
3277 :			$problem_result{show_partial_correct_answers} = 0 ; # prevent partial correct answers from being shown for syntax errors.
3278 :			}
3279 :			(\%problem_result, \%problem_state);
3280 :			}
3281 :
3282 :	chris	54	sub avg_problem_grader {
3283 :	sam	2	my $rh_evaluated_answers = shift;
3284 :			my $rh_problem_state = shift;
3285 :			my %form_options = @_;
3286 :			my %evaluated_answers = %{$rh_evaluated_answers};
3287 :			# The hash $rh_evaluated_answers typically contains:
3288 :			# 'answer1' => 34, 'answer2'=> 'Mozart', etc.
3289 :
3290 :			# By default the old problem state is simply passed back out again.
3291 :			my %problem_state = %$rh_problem_state;
3292 :
3293 :
3294 :			# %form_options might include
3295 :			# The user login name
3296 :			# The permission level of the user
3297 :			# The studentLogin name for this psvn.
3298 :			# Whether the form is asking for a refresh or is submitting a new answer.
3299 :
3300 :			# initial setup of the answer
3301 :			my $total=0;
3302 :			my %problem_result = ( score => 0,
3303 :	chris	81	errors => '',
3304 :			type => 'avg_problem_grader',
3305 :			msg => '',
3306 :			);
3307 :	sam	2	my $count = keys %evaluated_answers;
3308 :			$problem_result{msg} = 'You can earn partial credit on this problem.' if $count >1;
3309 :			# Return unless answers have been submitted
3310 :			unless ($form_options{answers_submitted} == 1) {
3311 :			return(\%problem_result,\%problem_state);
3312 :			}
3313 :
3314 :			# Answers have been submitted -- process them.
3315 :			foreach my $ans_name (keys %evaluated_answers) {
3316 :			# I'm not sure if this check is really useful.
3317 :			if ( ( ref($evaluated_answers{$ans_name} ) eq 'HASH' ) or ( ref($evaluated_answers{$ans_name}) eq 'AnswerHash' ) ) {
3318 :			$total += $evaluated_answers{$ans_name}->{score};
3319 :			}
3320 :			else {
3321 :			die "Error: Answer \|$ans_name\| is not a hash reference\n".
3322 :			$evaluated_answers{$ans_name} .
3323 :			"This probably means that the answer evaluator for this answer\n" .
3324 :			"is not working correctly.";
3325 :			$problem_result{error} = "Error: Answer $ans_name is not a hash: $evaluated_answers{$ans_name}";
3326 :			}
3327 :			}
3328 :			# Calculate score rounded to three places to avoid roundoff problems
3329 :			$problem_result{score} = $total/$count if $count;
3330 :			# increase recorded score if the current score is greater.
3331 :			$problem_state{recorded_score} = $problem_result{score} if $problem_result{score} > $problem_state{recorded_score};
3332 :
3333 :
3334 :			$problem_state{num_of_correct_ans}++ if $total == $count;
3335 :			$problem_state{num_of_incorrect_ans}++ if $total < $count ;
3336 :			warn "Error in grading this problem the total $total is larger than $count" if $total > $count;
3337 :			(\%problem_result, \%problem_state);
3338 :			}
3339 :
3340 :			###########################################################################
3341 :			### THE FOLLOWING ARE LOCAL SUBROUTINES THAT ARE MEANT TO BE CALLED ONLY FROM THIS SCRIPT.
3342 :
3343 :			## Internal routine that converts variables into the standard array format
3344 :			##
3345 :			## IN: one of the following:
3346 :			## an undefined value (i.e., no variable was specified)
3347 :			## a reference to an array of variable names -- [var1, var2]
3348 :			## a number (the number of variables desired) -- 3
3349 :			## one or more variable names -- (var1, var2)
3350 :			## OUT: an array of variable names
3351 :	chris	54
3352 :	sam	2	sub get_var_array {
3353 :			my $in = shift @_;
3354 :			my @out;
3355 :
3356 :			if( not defined($in) ) { #if nothing defined, build default array and return
3357 :			@out = ( $functVarDefault );
3358 :			return @out;
3359 :			}
3360 :			elsif( ref( $in ) eq 'ARRAY' ) { #if given an array ref, dereference and return
3361 :			return @{$in};
3362 :			}
3363 :			elsif( $in =~ /^\d+/ ) { #if given a number, set up the array and return
3364 :			if( $in == 1 ) {
3365 :			$out[0] = 'x';
3366 :			}
3367 :			elsif( $in == 2 ) {
3368 :			$out[0] = 'x';
3369 :			$out[1] = 'y';
3370 :			}
3371 :			elsif( $in == 3 ) {
3372 :			$out[0] = 'x';
3373 :			$out[1] = 'y';
3374 :			$out[2] = 'z';
3375 :			}
3376 :			else { #default to the x_1, x_2, ... convention
3377 :			my ($i, $tag);
3378 :			for( $i=0; $i < $in; $i++ ) {
3379 :	chris	54	## akp the above seems to be off by one 1/4/00
3380 :	sam	2	$tag = $i + 1; ## akp 1/4/00
3381 :			$out[$i] = "${functVarDefault}_" . $tag; ## akp 1/4/00
3382 :			}
3383 :			}
3384 :			return @out;
3385 :			}
3386 :	chris	54	else { #if given one or more names, return as an array
3387 :	sam	2	unshift( @_, $in );
3388 :			return @_;
3389 :			}
3390 :			}
3391 :
3392 :			## Internal routine that converts limits into the standard array of arrays format
3393 :			## Some of the cases are probably unneccessary, but better safe than sorry
3394 :			##
3395 :			## IN: one of the following:
3396 :			## an undefined value (i.e., no limits were specified)
3397 :			## a reference to an array of arrays of limits -- [[llim,ulim], [llim,ulim]]
3398 :			## a reference to an array of limits -- [llim, ulim]
3399 :			## an array of array references -- ([llim,ulim], [llim,ulim])
3400 :			## an array of limits -- (llim,ulim)
3401 :			## OUT: an array of array references -- ([llim,ulim], [llim,ulim]) or ([llim,ulim])
3402 :	chris	22
3403 :	sam	2	sub get_limits_array {
3404 :			my $in = shift @_;
3405 :			my @out;
3406 :
3407 :	chris	54	if( not defined($in) ) { #if nothing defined, build default array and return
3408 :	sam	2	@out = ( [$functLLimitDefault, $functULimitDefault] );
3409 :			return @out;
3410 :			}
3411 :	chris	54	elsif( ref($in) eq 'ARRAY' ) { #$in is either ref to array, or ref to array of refs
3412 :	sam	2	my @deref = @{$in};
3413 :
3414 :	chris	54	if( ref( $in->[0] ) eq 'ARRAY' ) { #$in is a ref to an array of array refs
3415 :	sam	2	return @deref;
3416 :			}
3417 :	chris	54	else { #$in was just a ref to an array of numbers
3418 :	sam	2	@out = ( $in );
3419 :			return @out;
3420 :			}
3421 :			}
3422 :	chris	54	else { #$in was an array of references or numbers
3423 :	sam	2	unshift( @_, $in );
3424 :
3425 :	chris	54	if( ref($_[0]) eq 'ARRAY' ) { #$in was an array of references, so just return it
3426 :	sam	2	return @_;
3427 :			}
3428 :	chris	54	else { #$in was an array of numbers
3429 :	sam	2	@out = ( \@_ );
3430 :			return @out;
3431 :			}
3432 :			}
3433 :			}
3434 :
3435 :	chris	54	sub check_option_list {
3436 :	sam	2	my $size = scalar(@_);
3437 :			if( ( $size % 2 ) != 0 ) {
3438 :			warn "ERROR in answer evaluator generator:\n" .
3439 :			"Usage: <CODE>str_cmp([\$ans1, \$ans2],%options)</CODE>
3440 :			or <CODE> num_cmp([\$num1, \$num2], %options)</CODE><BR>
3441 :			A list of inputs must be inclosed in square brackets <CODE>[\$ans1, \$ans2]</CODE>";
3442 :			}
3443 :			}
3444 :
3445 :			# simple subroutine to display an error message when
3446 :			# function compares are called with invalid parameters
3447 :			sub function_invalid_params {
3448 :			my $correctEqn = shift @_;
3449 :			my $error_response = sub {
3450 :	chris	54	my $PGanswerMessage = "Tell your professor that there is an error with the parameters " .
3451 :			"to the function answer evaluator";
3452 :	sam	2	return ( 0, $correctEqn, "", $PGanswerMessage );
3453 :			};
3454 :			return $error_response;
3455 :			}
3456 :
3457 :	chris	22	#########################################################################
3458 :			# Filters for answer evaluators
3459 :			#########################################################################
3460 :
3461 :	chris	54	sub is_a_number {
3462 :	chris	22	my ($num,%options) = @_;
3463 :			my $process_ans_hash = ( ref( $num ) eq 'AnswerHash' ) ? 1 : 0 ;
3464 :			my ($rh_ans);
3465 :			if ($process_ans_hash) {
3466 :			$rh_ans = $num;
3467 :			$num = $rh_ans->{student_ans};
3468 :			}
3469 :
3470 :	sam	2	my $is_a_number = 0;
3471 :			return $is_a_number unless defined($num);
3472 :			$num =~ s/^\s*//; ## remove initial spaces
3473 :			$num =~ s/\s*$//; ## remove trailing spaces
3474 :
3475 :			## the following is copied from the online perl manual
3476 :			if ($num =~ /^([+-]?)(?=\d\|\.\d)\d(\.\d)?([Ee]([+-]?\d+))?$/){
3477 :			$is_a_number = 1;
3478 :			}
3479 :	chris	22
3480 :			if ($process_ans_hash) {
3481 :			if ($is_a_number == 1 ) {
3482 :			$rh_ans->{student_ans}=$num;
3483 :			return $rh_ans;
3484 :			} else {
3485 :			$rh_ans->{student_ans} = "Incorrect number format: You must enter a number, e.g. -6, 5.3, or 6.12E-3";
3486 :			$rh_ans->throw_error('NUMBER', 'You must enter a number, e.g. -6, 5.3, or 6.12E-3');
3487 :			return $rh_ans;
3488 :			}
3489 :			} else {
3490 :			return $is_a_number;
3491 :			}
3492 :	sam	2	}
3493 :
3494 :	chris	54	sub is_a_fraction {
3495 :	chris	22	my ($num,%options) = @_;
3496 :			my $process_ans_hash = ( ref( $num ) eq 'AnswerHash' ) ? 1 : 0 ;
3497 :			my ($rh_ans);
3498 :			if ($process_ans_hash) {
3499 :			$rh_ans = $num;
3500 :			$num = $rh_ans->{student_ans};
3501 :			}
3502 :
3503 :			my $is_a_fraction = 0;
3504 :			return $is_a_fraction unless defined($num);
3505 :			$num =~ s/^\s*//; ## remove initial spaces
3506 :			$num =~ s/\s*$//; ## remove trailing spaces
3507 :
3508 :			if ($num =~ /^\s\-?\s[\/\d\.Ee\s]*$/) {
3509 :	sam	2	$is_a_fraction = 1;
3510 :			}
3511 :	chris	22
3512 :			if ($process_ans_hash) {
3513 :			if ($is_a_fraction == 1 ) {
3514 :			$rh_ans->{student_ans}=$num;
3515 :			return $rh_ans;
3516 :			} else {
3517 :			$rh_ans->{student_ans} = "Not a number of fraction: You must enter a number or fraction, e.g. -6 or 7/13";
3518 :			$rh_ans->throw_error('NUMBER', 'You must enter a number, e.g. -6, 5.3, or 6.12E-3');
3519 :			return $rh_ans;
3520 :			}
3521 :
3522 :			} else {
3523 :			return $is_a_fraction;
3524 :			}
3525 :	sam	2	}
3526 :
3527 :	chris	22
3528 :	chris	54	sub is_an_arithmetic_expression {
3529 :	chris	22	my ($num,%options) = @_;
3530 :			my $process_ans_hash = ( ref( $num ) eq 'AnswerHash' ) ? 1 : 0 ;
3531 :			my ($rh_ans);
3532 :			if ($process_ans_hash) {
3533 :			$rh_ans = $num;
3534 :			$num = $rh_ans->{student_ans};
3535 :			}
3536 :
3537 :			my $is_an_arithmetic_expression = 0;
3538 :			return $is_an_arithmetic_expression unless defined($num);
3539 :			$num =~ s/^\s*//; ## remove initial spaces
3540 :			$num =~ s/\s*$//; ## remove trailing spaces
3541 :
3542 :			if ($num =~ /^[+\-\/\^\[\]\{\}\s\d\.Ee]$/) {
3543 :	sam	2	$is_an_arithmetic_expression = 1;
3544 :			}
3545 :	chris	22
3546 :			if ($process_ans_hash) {
3547 :			if ($is_an_arithmetic_expression == 1 ) {
3548 :			$rh_ans->{student_ans}=$num;
3549 :			return $rh_ans;
3550 :			} else {
3551 :
3552 :			$rh_ans->{student_ans} = "Not an arithmetic expression: You must enter an arithmetic expression, e.g. -6 or (2.3*4+5/3)^2";
3553 :			$rh_ans->throw_error('NUMBER', 'You must enter an arithmetic expression, e.g. -6 or (2.3*4+5/3)^2');
3554 :			return $rh_ans;
3555 :			}
3556 :
3557 :			} else {
3558 :			return $is_an_arithmetic_expression;
3559 :			}
3560 :	sam	2	}
3561 :
3562 :			#replaces pi, e, and ^ with their Perl equivalents
3563 :	chris	54	sub math_constants {
3564 :	chris	22	my($in,%options) = @_;
3565 :			my $rh_ans;
3566 :			my $process_ans_hash = ( ref( $in ) eq 'AnswerHash' ) ? 1 : 0 ;
3567 :			if ($process_ans_hash) {
3568 :			$rh_ans = $in;
3569 :			$in = $rh_ans->{student_ans};
3570 :			}
3571 :
3572 :	sam	2	$in =~s/\bpi\b/(4*atan2(1,1))/ge;
3573 :			$in =~s/\be\b/(exp(1))/ge;
3574 :			$in =~s/\^/**/g;
3575 :	chris	22
3576 :			if ($process_ans_hash) {
3577 :			$rh_ans->{student_ans}=$in;
3578 :			return $rh_ans;
3579 :			} else {
3580 :			return $in;
3581 :			}
3582 :	sam	2	}
3583 :
3584 :	chris	54	sub clean_up_error_msg {
3585 :	sam	2	my $msg = $_[0];
3586 :			$msg =~ s/^\[[^\]]\][^:]://;
3587 :			$msg =~ s/Unquoted string//g;
3588 :			$msg =~ s/may\s+clash.*/does not make sense here/;
3589 :			$msg =~ s/\sat.line [\d]//g;
3590 :			$msg = 'error: '. $msg;
3591 :
3592 :			return $msg;
3593 :			}
3594 :
3595 :			#formats the student and correct answer as specified
3596 :			#format must be of a form suitable for sprintf (e.g. '%0.5g'),
3597 :			#with the exception that a '#' at the end of the string
3598 :			#will cause trailing zeros in the decimal part to be removed
3599 :	chris	54	sub prfmt {
3600 :	sam	2	my($number,$format) = @_; # attention, the order of format and number are reversed
3601 :			my $out;
3602 :			if ($format) {
3603 :			warn "Incorrect format used: $format. <BR> Format should look something like %4.5g<BR>"
3604 :	chris	54	unless $format =~ /^\s%\d\.?\d\w#?\s$/;
3605 :	sam	2
3606 :			if( $format =~ s/#\s*$// ) { # remove trailing zeros in the decimal
3607 :			$out = sprintf( $format, $number );
3608 :			$out =~ s/(\.\d*?)0+$/$1/;
3609 :			$out =~ s/\.$//; # in case all decimal digits were zero, remove the decimal
3610 :			}
3611 :			else {
3612 :			$out = sprintf( $format, $number );
3613 :			}
3614 :			$out =~ s/e/E/g; # only use capital E's for exponents. Little e is for 2.71828...
3615 :			}
3616 :			else {
3617 :			$out = $number;
3618 :	apizer	84	$out =~ s/e/E/g; # only use capital E's for exponents. Little e is for 2.71828...
3619 :
3620 :	sam	2	}
3621 :			return $out;
3622 :			}
3623 :
3624 :			=head4
3625 :
3626 :			pretty_print()
3627 :
3628 :
3629 :			=cut
3630 :
3631 :			sub pretty_print {
3632 :			my $r_input = shift;
3633 :			my $out = '';
3634 :			if ( not ref($r_input) ) {
3635 :			$out = $r_input; # not a reference
3636 :			} elsif ("$r_input" =~/hash/i) { # this will pick up objects whose '$self' is hash and so works better than ref($r_iput).
3637 :			local($^W) = 0;
3638 :			$out .= "$r_input " ."<TABLE border = \"2\" cellpadding = \"3\" BGCOLOR = \"#FFFFFF\">";
3639 :			foreach my $key (lex_sort( keys %$r_input )) {
3640 :			$out .= "<tr><TD> $key</TD><TD>=></td><td> ".pretty_print($r_input->{$key}) . "</td></tr>";
3641 :			}
3642 :			$out .="</table>";
3643 :			} elsif (ref($r_input) eq 'ARRAY' ) {
3644 :			my @array = @$r_input;
3645 :			$out .= "( " ;
3646 :			while (@array) {
3647 :			$out .= pretty_print(shift @array) . " , ";
3648 :			}
3649 :			$out .= " )";
3650 :			} elsif (ref($r_input) eq 'CODE') {
3651 :			$out = "$r_input";
3652 :			} else {
3653 :			$out = $r_input;
3654 :			}
3655 :			$out;
3656 :			}
3657 :
3658 :			# Use this to set default options
3659 :			sub set_default_options {
3660 :			my $rh_options = shift;
3661 :			warn "The first entry to set_default_options must be a reference to the option hash" unless ref($rh_options) eq 'HASH';
3662 :			my %default_options = @_;
3663 :	gage	5	unless ( defined($default_options{allow_unknown_options}) and $default_options{allow_unknown_options} == 1 ) {
3664 :			foreach my $key1 (keys %$rh_options) {
3665 :			warn "This option \|$key1\| is not recognized in this subroutine<br> ", pretty_print($rh_options) unless exists($default_options{$key1});
3666 :			}
3667 :	sam	2	}
3668 :			foreach my $key (keys %default_options) {
3669 :			if ( not defined($rh_options->{$key} ) and defined( $default_options{$key} ) ) {
3670 :	chris	22	$rh_options->{$key} = $default_options{$key}; #this allows tol => undef to allow the tol option, but doesn't define
3671 :	sam	2	# this key unless tol is explicitly defined.
3672 :			}
3673 :			}
3674 :			}
3675 :			# Use this to assign aliases for the standard options
3676 :			sub assign_option_aliases {
3677 :			my $rh_options = shift;
3678 :			warn "The first entry to set_default_options must be a reference to the option hash" unless ref($rh_options) eq 'HASH';
3679 :			my @option_aliases = @_;
3680 :			while (@option_aliases) {
3681 :			my $alias = shift @option_aliases;
3682 :			my $option_key = shift @option_aliases;
3683 :
3684 :			if (defined($rh_options->{$alias} )) { # if the alias appears in the option list
3685 :			if (not defined($rh_options->{$option_key}) ) { # and the option itself is not defined,
3686 :			$rh_options->{$option_key} = $rh_options->{$alias}; # insert the value defined by the alias into the option value
3687 :			# the FIRST alias for a given option takes precedence
3688 :			# (after the option itself)
3689 :			} else {
3690 :			warn "option $option_key is already defined as", $rh_options->{$option_key}, "<br>\n",
3691 :			"The attempt to override this option with the alias $alias with value ", $rh_options->{$alias},
3692 :			" was ignored.";
3693 :			}
3694 :			}
3695 :			delete($rh_options->{$alias}); # remove the alias from the initial list
3696 :			}
3697 :
3698 :			}
3699 :
3700 :
3701 :			1;

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