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Revision **5896** -
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*Thu Sep 11 17:26:18 2008 UTC*
(11 years, 5 months ago)
by *dpvc*

File size: 10805 byte(s)

File size: 10805 byte(s)

Fixed a problem where if two FormulaUpToConstant objects were used in the same problem, the second would always be marked as incorrect. (Subtle interplay of variable names in the safe compartment.)

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 1.11.2.1 2008/06/24 00:44:54 gage 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 19 parserFormulaUpToConstant.pl - implements formulas "plus a constant". 20 21 =head1 DESCRIPTION 22 23 This file implements the FormulaUpToConstant object, which is 24 a formula that is only unique up to a constant (i.e., this is 25 an anti-derivative). Students must include the "+C" as part of 26 their answers, but they can use any (single-letter) constant that 27 they want, and it doesn't have to be the one the professor used. 28 29 To use FormulaWithConstat objects, load this macro file at the 30 top of your problem: 31 32 loadMacros("parserFormulaUpToConstant.pl"); 33 34 then create a formula with constant as follows: 35 36 $f = FormulaUpToConstant("sin(x)+C"); 37 38 Note that the C should NOT already be a variable in the Context; 39 the FormulaUpToConstant object will handle adding it in for 40 you. If you don't include a constant in your formula (i.e., if 41 all the variables that you used are already in your Context, 42 then the FormulaUpToConstant object will add "+C" for you. 43 44 The FormulaUpToConstant should work like any normal Formula, 45 and in particular, you use $f->cmp to get its answer checker. 46 47 ANS($f->cmp); 48 49 Note that the FormulaUpToConstant object creates its only private 50 copy of the current Context (so that it can add variables without 51 affecting the rest of the problem). You should not notice this 52 in general, but if you need to access that context, use $f->{context}. 53 E.g. 54 55 Context($f->{context}); 56 57 would make the current context the one being used by the 58 FormulaUpToConstant, while 59 60 $f->{context}->variables->names 61 62 would return a list of the variables in the private context. 63 64 To get the name of the constant in use in the formula, 65 use 66 67 $f->constant. 68 69 If you combine a FormulaUpToConstant with other formulas, 70 the result will be a new FormulaUpToConstant object, with 71 a new Context, and potentially a new + C added to it. This 72 is likely not what you want. Instead, you should convert 73 back to a Formula first, then combine with other objects, 74 then convert back to a FormulaUpToConstant, if necessary. 75 To 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); # $h will be "sin(x)+cos(x)+C" 81 82 The answer evaluator by default will give "helpful" messages 83 to the student when the "+ C" is left out. You can turn off 84 these messages using the showHints option to the cmp() method: 85 86 ANS($f->cmp(showHints => 0)); 87 88 One of the hints is about whether the student's answer is linear 89 in the arbitrary constant. This test requires differentiating 90 the student answer. Since there are times when that could be 91 problematic, you can disable that test via the showLinearityHints 92 flag. (Note: setting showHints to 0 also disables these hints.) 93 94 ANS($f->cmp(showLinearityHints => 0)); 95 96 =cut 97 98 loadMacros("MathObjects.pl"); 99 100 sub _parserFormulaUpToConstant_init {FormulaUpToConstant::Init()} 101 102 package FormulaUpToConstant; 103 @ISA = ('Value::Formula'); 104 105 sub Init { 106 main::PG_restricted_eval('sub FormulaUpToConstant {FormulaUpToConstant->new(@_)}'); 107 } 108 109 # 110 # Create an instance of a FormulaUpToConstant. If no constant 111 # is supplied, we add C ourselves. 112 # 113 sub new { 114 my $self = shift; my $class = ref($self) || $self; 115 # 116 # Copy the context (so we can modify it) and 117 # replace the usual Variable object with our own. 118 # 119 my $context = (Value::isContext($_[0]) ? shift : $self->context)->copy; 120 $context->{parser}{Variable} = 'FormulaUpToConstant::Variable'; 121 # 122 # Create a formula from the user's input. 123 # 124 my $f = main::Formula($context,@_); 125 # 126 # If it doesn't have a constant already, add one. 127 # (should check that C isn't already in use, and look 128 # up the first free name, but we'll cross our fingers 129 # for now. Could look through the defined variables 130 # to see if there is already an arbitraryConstant 131 # and use that.) 132 # 133 unless ($f->{constant}) {$f = $f + "C", $f->{constant} = "C"} 134 # 135 # Check that the formula is linear in C. 136 # 137 my $n = $f->D($f->{constant}); 138 Value->Error("Your formula isn't linear in the arbitrary constant '%s'",$f->{constant}) 139 unless $n->isConstant; 140 # 141 # Make a version with adaptive parameters for use in the 142 # comparison later on. We could like n0*C, but already have $n 143 # copies of C, so remove them. That way, n0 will be 0 when there 144 # are no C's in the student answer during the adaptive comparison. 145 # (Again, should really check that n0 is not in use already) 146 # 147 my $n00 = $context->variables->get("n00"); 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}; 151 $f->{adapt} = $f + "(n00-$n)$f->{constant} + n01"; 152 return bless $f, $class; 153 } 154 155 ################################################## 156 # 157 # Remember that compare implements the overloaded perl <=> operator, 158 # and $a <=> $b is -1 when $a < $b, 0 when $a == $b and 1 when $a > $b. 159 # In our case, we only care about equality, so we will return 0 when 160 # equal and other numbers to indicate the reason they are not equal 161 # (this can be used by the answer checker to print helpful messages) 162 # 163 sub compare { 164 my ($l,$r) = @_; my $self = $l; my $context = $self->context; 165 $r = Value::makeValue($r,context=>$context); 166 # 167 # Not equal if the student value is constant or has no + C 168 # 169 return 2 if !Value::isFormula($r); 170 return 3 if !defined($r->{constant}); 171 # 172 # If constants aren't the same, substitute the professor's in the student answer. 173 # 174 $r = $r->substitute($r->{constant}=>$l->{constant}) unless $r->{constant} eq $l->{constant}; 175 # 176 # Compare with adaptive parameters to see if $l + n0 C = $r for some n0. 177 # 178 $main::{_cmp_} = sub {return $l->{adapt} == $r}; # a closure to access local variables 179 my $equal = main::PG_restricted_eval('&{$main::{_cmp_}}'); # prevents errors with large adaptive parameters 180 delete $main::{_cmp_}; # remove temprary function 181 return -1 unless $equal; 182 # 183 # Check that n0 is non-zero (i.e., there is a multiple of C in the student answer) 184 # (remember: return value of 0 is equal, and non-zero is unequal) 185 # 186 return abs($context->variables->get("n00")->{value}) < $context->flag("zeroLevelTol"); 187 } 188 189 ################################################## 190 # 191 # Here we override part of the answer comparison 192 # routines in order to be able to generate 193 # helpful error messages for students when 194 # they leave off the + C. 195 # 196 197 # 198 # Show hints by default 199 # 200 sub cmp_defaults {((shift)->SUPER::cmp_defaults,showHints => 1, showLinearityHints => 1)}; 201 202 # 203 # Add useful messages, if the author requested them 204 # 205 sub cmp_postprocess { 206 my $self = shift; my $ans = shift; 207 $self->SUPER::cmp_postprocess($ans); 208 return unless $ans->{score} == 0 && !$ans->{isPreview}; 209 return if $ans->{ans_message} || !$self->getFlag("showHints"); 210 my $student = $ans->{student_value}; 211 my $result = $ans->{correct_value} <=> $student; # compare encodes the reason in the result 212 $self->cmp_Error($ans,"Note: there is always more than one posibility") if $result == 2 || $result == 3; 213 if ($result == 3) { 214 my $context = $self->context; 215 $context->flags->set(no_parameters=>0); 216 $context->variables->add(x00=>'Real'); 217 $result = 1 if $self->removeConstant+"n01+n00x00" == $student+"x00"; # must use both parameters 218 $context->variables->remove('x00'); 219 $context->flags->set(no_parameters=>1); 220 } 221 $self->cmp_Error($ans,"Your answer is not the most general solution") if $result == 1; 222 $self->cmp_Error($ans,"Your formula should be linear in the constant '$student->{constant}'") 223 if $result == -1 && $self->getFlag("showLinearityHints") && !$student->D($student->{constant})->isConstant; 224 } 225 226 ################################################## 227 # 228 # Get the name of the constant 229 # 230 sub constant {(shift)->{constant}} 231 232 # 233 # Remove the constant and return a Formula object 234 # 235 sub removeConstant { 236 my $self = shift; 237 main::Formula($self->substitute($self->{constant}=>0))->reduce; 238 } 239 240 # 241 # Override the differentiation so that we always return 242 # a Formula, not a FormulaUpToConstant (we don't want to 243 # add the C in again). 244 # 245 sub D { 246 my $self = shift; 247 $self->removeConstant->D(@_); 248 } 249 250 ###################################################################### 251 # 252 # This class repalces the Parser::Variable class, and its job 253 # is to look for new constants that aren't in the context, 254 # and add them in. This allows students to use ANY constant 255 # they want, and a different one from the professor. We check 256 # that the student only used ONE arbitrary constant, however. 257 # 258 package FormulaUpToConstant::Variable; 259 our @ISA = ('Parser::Variable'); 260 261 sub new { 262 my $self = shift; my $class = ref($self) || $self; 263 my $equation = shift; my $variables = $equation->{context}{variables}; 264 my ($name,$ref) = @_; my $def = $variables->{$name}; 265 # 266 # If the variable is not already in the context, add it 267 # and mark it as an arbitrary constant (for later reference) 268 # 269 if (!defined($def) && length($name) eq 1) { 270 $equation->{context}->variables->add($name => 'Real'); 271 $equation->{context}->variables->set($name => {arbitraryConstant => 1}); 272 $def = $variables->{$name}; 273 } 274 # 275 # If the variable is an arbitrary constant 276 # Error if we already have a constant and it's not this one. 277 # Save the constant so we can check with it later. 278 # 279 if ($def && $def->{arbitraryConstant}) { 280 $equation->Error(["Your formula shouldn't have two arbitrary constants"],$ref) 281 if $equation->{constant} and $name ne $equation->{constant}; 282 $equation->{constant} = $name; 283 } 284 # 285 # Do the usual Variable stuff. 286 # 287 $self->SUPER::new($equation,$name,$ref); 288 } 289 290 1;

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