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1################################################################################
2# WeBWorK Online Homework Delivery System
3# Copyright 2000-2007 The WeBWorK Project, http://openwebwork.sf.net/
4# $CVSHeader: pg/macros/parserFormulaUpToConstant.pl,v 1.17 2008/09/16 03:01:17 dpvc Exp $
5#
6# This program is free software; you can redistribute it and/or modify it under
7# the terms of either: (a) the GNU General Public License as published by the
8# Free Software Foundation; either version 2, or (at your option) any later
9# version, or (b) the "Artistic License" which comes with this package.
10#
11# This program is distributed in the hope that it will be useful, but WITHOUT
12# ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
13# FOR A PARTICULAR PURPOSE. See either the GNU General Public License or the
14# Artistic License for more details.
15################################################################################
16
17=head1 NAME
18
19parserFormulaUpToConstant.pl - implements formulas "plus a constant".
20
21=head1 DESCRIPTION
22
23This file implements the FormulaUpToConstant object, which is
24a formula that is only unique up to a constant (i.e., this is
25an anti-derivative). Students must include the "+C" as part of
26their answers, but they can use any (single-letter) constant that
27they want, and it doesn't have to be the one the professor used.
28
29To use FormulaWithConstat objects, load this macro file at the
30top of your problem:
31
32 loadMacros("parserFormulaUpToConstant.pl");
33
34then create a formula with constant as follows:
35
36 $f = FormulaUpToConstant("sin(x)+C");
37
38Note that the C should NOT already be a variable in the Context;
39the FormulaUpToConstant object will handle adding it in for
40you. If you don't include a constant in your formula (i.e., if
41all the variables that you used are already in your Context,
42then the FormulaUpToConstant object will add "+C" for you.
43
44The FormulaUpToConstant should work like any normal Formula,
45and in particular, you use $f->cmp to get its answer checker.
46
47 ANS($f->cmp);
48
49Note that the FormulaUpToConstant object creates its only private
50copy of the current Context (so that it can add variables without
51affecting the rest of the problem). You should not notice this
52in general, but if you need to access that context, use $f->{context}.
53E.g.
54
55 Context($f->{context});
56
57would make the current context the one being used by the
58FormulaUpToConstant, while
59
60 $f->{context}->variables->names
61
62would return a list of the variables in the private context.
63
64To get the name of the constant in use in the formula,
65use
66
67 $f->constant.
68
69If you combine a FormulaUpToConstant with other formulas,
70the result will be a new FormulaUpToConstant object, with
71a new Context, and potentially a new + C added to it. This
72is likely not what you want. Instead, you should convert
73back to a Formula first, then combine with other objects,
74then convert back to a FormulaUpToConstant, if necessary.
75To do this, use the removeConstant() method:
76
77 $f = FormulaUpToConstant("sin(x)+C");
78 $g = Formula("cos(x)");
79 $h = $f->removeConstant + $g; # $h will be "sin(x)+cos(x)"
80 $h = FormulaUpToConstant($h); # $h will be "sin(x)+cos(x)+C"
81
82The answer evaluator by default will give "helpful" messages
83to the student when the "+ C" is left out. You can turn off
84these messages using the showHints option to the cmp() method:
85
86 ANS($f->cmp(showHints => 0));
87
88One of the hints is about whether the student's answer is linear
89in the arbitrary constant. This test requires differentiating
90the student answer. Since there are times when that could be
91problematic, you can disable that test via the showLinearityHints
92flag. (Note: setting showHints to 0 also disables these hints.)
93
94 ANS($f->cmp(showLinearityHints => 0));
95
96=cut
97
1loadMacros("MathObjects.pl"); 98loadMacros("MathObjects.pl");
2 99
3sub _parserFormulaUpToConstant_init {FormulaUpToConstant::Init()} 100sub _parserFormulaUpToConstant_init {FormulaUpToConstant::Init()}
4
5=head1 FormulaUpToConstant();
6
7 ######################################################################
8 #
9 # This file implements the FormulaUpToConstant object, which is
10 # a formula that is only unique up to a constant (i.e., this is
11 # an anti-derivative). Students must include the "+C" as part of
12 # their answers, but they can use any (single-letter) constant that
13 # they want, and it doesn't have to be the one the professor used.
14 #
15 # To use FormulaWithConstat objects, load this macro file at the
16 # top of your problem:
17 #
18 # loadMacros("parserFormulaUpToConstant");
19 #
20 # then create a formula with constant as follows:
21 #
22 # $f = FormulaUpToConstant("sin(x)+C");
23 #
24 # Note that the C should NOT already be a variable in the Context;
25 # the FormulaUpToConstant object will handle adding it in for
26 # you. If you don't include a constant in your formula (i.e., if
27 # all the variables that you used are already in your Context,
28 # then the FormulaUpToConstant object will add "+C" for you.
29 #
30 # The FormulaUpToConstant should work like any normal Formula,
31 # and in particular, you use $f->cmp to get its answer checker.
32 #
33 # ANS($f->cmp);
34 #
35 # Note that the FormulaUpToConstant object creates its only private
36 # copy of the current Context (so that it can add variables without
37 # affecting the rest of the problem). You should not notice this
38 # in general, but if you need to access that context, use $f->{context}.
39 # E.g.
40 #
41 # Context($f->{context});
42 #
43 # would make the current context the one being used by the
44 # FormulaUpToConstant, while
45 #
46 # $f->{context}->variables->names
47 #
48 # would return a list of the variables in the private context.
49 #
50 # To get the name of the constant in use in the formula,
51 # use
52 #
53 # $f->constant.
54 #
55 # If you combine a FormulaUpToConstant with other formulas,
56 # the result will be a new FormulaUpToConstant object, with
57 # a new Context, and potentially a new + C added to it. This
58 # is likely not what you want. Instead, you should convert
59 # back to a Formula first, then combine with other objects,
60 # then convert back to a FormulaUpToConstant, if necessary.
61 # To do this, use the removeConstant() method:
62 #
63 # $f = FormulaUpToConstant("sin(x)+C");
64 # $g = Formula("cos(x)");
65 # $h = $f->removeConstant + $g; # $h will be "sin(x)+cos(x)"
66 # $h = FormulaUpToConstant($h); # $h will be "sin(x)+cos(x)+C"
67 #
68 ######################################################################
69
70=cut
71 101
72package FormulaUpToConstant; 102package FormulaUpToConstant;
73@ISA = ('Value::Formula'); 103@ISA = ('Value::Formula');
74 104
75sub Init { 105sub Init {
106 # 136 #
107 my $n = $f->D($f->{constant}); 137 my $n = $f->D($f->{constant});
108 Value->Error("Your formula isn't linear in the arbitrary constant '%s'",$f->{constant}) 138 Value->Error("Your formula isn't linear in the arbitrary constant '%s'",$f->{constant})
109 unless $n->isConstant; 139 unless $n->isConstant;
110 # 140 #
111 # Make a version with an adaptive parameter for use in the 141 # Make a version with adaptive parameters for use in the
112 # comparison later on. We could like n0*C, but already have $n 142 # comparison later on. We could like n0*C, but already have $n
113 # copies of C, so remove them. That way, n0 will be 0 when there 143 # copies of C, so remove them. That way, n0 will be 0 when there
114 # are no C's in the student answer during the adaptive comparison. 144 # are no C's in the student answer during the adaptive comparison.
115 # (Again, should really check that n0 is not in use already) 145 # (Again, should really check that n0 is not in use already)
116 # 146 #
117 my $n0 = $context->variables->get("n0"); 147 my $n00 = $context->variables->get("n00");
118 $context->variables->add(n0=>'Parameter') unless $n0 and $n0->{parameter}; 148 $context->variables->add(n00=>'Parameter') unless $n00 and $n00->{parameter};
149 my $n01 = $context->variables->get("n01");
150 $context->variables->add(n01=>'Parameter') unless $n01 and $n01->{parameter};
119 $f->{adapt} = $f + "(n0-$n)$f->{constant}"; 151 $f->{adapt} = $f + "(n00-$n)$f->{constant} + n01";
152
120 return bless $f, $class; 153 return bless $f, $class;
121} 154}
122 155
123################################################## 156##################################################
124# 157#
141 # 174 #
142 $r = $r->substitute($r->{constant}=>$l->{constant}) unless $r->{constant} eq $l->{constant}; 175 $r = $r->substitute($r->{constant}=>$l->{constant}) unless $r->{constant} eq $l->{constant};
143 # 176 #
144 # Compare with adaptive parameters to see if $l + n0 C = $r for some n0. 177 # Compare with adaptive parameters to see if $l + n0 C = $r for some n0.
145 # 178 #
146 return -1 unless $l->{adapt} == $r; 179 my $adapt = $l->adapt;
180 $main::{_cmp_} = sub {return $adapt == $r}; # a closure to access local variables
181 my $equal = main::PG_restricted_eval('&{$main::{_cmp_}}'); # prevents errors with large adaptive parameters
182 delete $main::{_cmp_}; # remove temprary function
183 $self->{adapt} = $self->{adapt}->inherit($adapt); # save the adapted value's flags
184 return -1 unless $equal;
147 # 185 #
148 # Check that n0 is non-zero (i.e., there is a multiple of C in the student answer) 186 # Check that n0 is non-zero (i.e., there is a multiple of C in the student answer)
149 # (remember: return value of 0 is equal, and non-zero is unequal) 187 # (remember: return value of 0 is equal, and non-zero is unequal)
150 # 188 #
151 return abs($context->variables->get("n0")->{value}) < $context->flag("zeroLevelTol"); 189 return abs($context->variables->get("n00")->{value}) < $context->flag("zeroLevelTol");
152} 190}
191
192#
193# Return the {adapt} formula with test points adjusted
194#
195sub adapt {
196 my $self = shift;
197 my $adapt = $self->{adapt}->inherit($self); delete $adapt->{adapt};
198 return $self->adjustInherit($self->{adapt});
199}
200
201#
202# Inherit from the main FormulaUpToConstant, but
203# adjust the test points to include the constants
204#
205sub adjustInherit {
206 my $self = shift;
207 my $f = shift->inherit($self);
208 delete $f->{adapt}; delete $f->{constant};
209 foreach my $id ('test_points','test_at') {
210 if (defined $f->{$id}) {
211 $f->{$id} = $f->{$id}->value if Value::isValue($f->{$id});
212 $f->{$id} = [$f->{$id}] unless ref($f->{$id}) eq 'ARRAY';
213 $f->{$id} = [map {[$_]} @{$f->{$id}}] unless ref($f->{$id}[0]) eq 'ARRAY';
214 $f->{$id} = $self->addConstants($f->{$id});
215 }
216 }
217 return $f;
218}
219
220#
221# Insert dummy values for the constants for the test points
222# (These are supposed to be +C, so the value shouldn't matter?)
223#
224sub addConstants {
225 my $self = shift; my $points = shift;
226 my @names = $self->context->variables->variables;
227 my $variables = $self->context->{variables};
228 my $Points = [];
229 foreach my $p (@{$points}) {
230 my @P = (.1) x scalar(@names); my $j = 0;
231 foreach my $i (0..scalar(@names)-1) {
232 if (!$variables->{$names[$i]}{arbitraryConstant}) {
233 $P[$i] = $p->[$j] if defined $p->[$j]; $j++;
234 }
235 }
236 push (@{$Points}, \@P);
237 }
238 return $Points;
239}
240
241##################################################
242#
243# Here we override part of the answer comparison
244# routines in order to be able to generate
245# helpful error messages for students when
246# they leave off the + C.
247#
153 248
154# 249#
155# Show hints by default 250# Show hints by default
156# 251#
157sub cmp_defaults {((shift)->SUPER::cmp_defaults,showHints => 1)}; 252sub cmp_defaults {((shift)->SUPER::cmp_defaults,showHints => 1, showLinearityHints => 1)};
253
254#
255# Provide diagnostics based on the adapted function used to check
256# the student's answer
257#
258sub cmp_diagnostics {
259 my $self = shift;
260 $self->inherit($self->{adapt})->SUPER::cmp_diagnostics(@_);
261}
262
263#
264# Make it possible to graph single-variable formulas by setting
265# the arbitrary constants to 0 first.
266#
267sub cmp_graph {
268 my $self = shift; my $diagnostics = shift;
269 my $F1 = shift; my $F2; ($F1,$F2) = @{$F1} if (ref($F1) eq 'ARRAY');
270 my %subs; my $context = $self->context;
271 foreach my $v ($context->variables->variables)
272 {$subs{$v} = 0 if ($context->variables->get($v)->{arbitraryConstant})}
273 $F1 = $F1->inherit($F1->{adapt})->substitute(%subs)->reduce;
274 $F2 = $F2->inherit($F2->{adapt})->substitute(%subs)->reduce;
275 $self->SUPER::cmp_graph($diagnostics,[$F1,$F2]);
276}
158 277
159# 278#
160# Add useful messages, if the author requested them 279# Add useful messages, if the author requested them
161# 280#
162sub cmp_postprocess { 281sub cmp_postprocess {
163 my $self = shift; my $ans = shift; 282 my $self = shift; my $ans = shift;
164 $self->SUPER::cmp_postprocess($ans); 283 $self->SUPER::cmp_postprocess($ans);
165 return unless $ans->{score} == 0 && !$ans->{isPreview}; 284 return unless $ans->{score} == 0 && !$ans->{isPreview};
166 return if $ans->{ans_message} || !$self->getFlag("showHints"); 285 return if $ans->{ans_message} || !$self->getFlag("showHints");
286 my $student = $ans->{student_value};
167 my $result = $ans->{correct_value} <=> $ans->{student_value}; # compare encodes the reason in the result 287 my $result = $ans->{correct_value} <=> $student; # compare encodes the reason in the result
168 $self->cmp_Error($ans,"Note: there is always more than one posibility") if $result == 2 || $result == 3; 288 $self->cmp_Error($ans,"Note: there is always more than one posibility") if $result == 2 || $result == 3;
289 if ($result == 3) {
290 my $context = $self->context;
291 $context->flags->set(no_parameters=>0);
292 $context->variables->add(x00=>'Real');
293 my $correct = $self->removeConstant+"n01+n00x00"; # must use both parameters
294 $main::{_cmp_} = sub {return $correct == $student+"x00"}; # a closure to access local variables
295 $result = 1 if main::PG_restricted_eval('&{$main::{_cmp_}}'); # prevents domain errors (and other errors)
296 delete $main::{_cmp_}; # remove temprary function
297 $context->variables->remove('x00');
298 $context->flags->set(no_parameters=>1);
299 }
169 $self->cmp_Error($ans,"Your answer is not the most general solution") 300 $self->cmp_Error($ans,"Your answer is not the most general solution") if $result == 1;
170 if $result == 1 || ($result == 3 && $self->removeConstant == $ans->{student_value}); 301 $self->cmp_Error($ans,"Your formula should be linear in the constant '$student->{constant}'")
302 if $result == -1 && $self->getFlag("showLinearityHints") && !$student->D($student->{constant})->isConstant;
171} 303}
172 304
305##################################################
173# 306#
174# Get the name of the constant 307# Get the name of the constant
175# 308#
176sub constant {(shift)->{constant}} 309sub constant {(shift)->{constant}}
177 310
178# 311#
179# Remove the constant and return a Formula object 312# Remove the constant and return a Formula object
180# 313#
181sub removeConstant { 314sub removeConstant {
182 my $self = shift; 315 my $self = shift;
183 main::Formula($self->substitute($self->{constant}=>0))->reduce; 316 return $self->adjustInherit(main::Formula($self->substitute($self->{constant}=>0))->reduce);
184} 317}
185 318
186# 319#
187# Override the differentiation so that we always return 320# Override the differentiation so that we always return
188# a Formula, not a FormulaUpToConstant (we don't want to 321# a Formula, not a FormulaUpToConstant (we don't want to
231 # Do the usual Variable stuff. 364 # Do the usual Variable stuff.
232 # 365 #
233 $self->SUPER::new($equation,$name,$ref); 366 $self->SUPER::new($equation,$name,$ref);
234} 367}
235 368
236
2371; 3691;

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