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

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