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

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