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*Tue Oct 2 20:48:05 2007 UTC*
(12 years, 2 months ago)
by *sh002i*

File size: 9595 byte(s)

File size: 9595 byte(s)

improved formatting for docs -- these were in pod sections but were all formatted as verbatim sections, and i moved them into normal paragraphs, lists, etc. should make things more readable from the web.

1 =head1 NAME 2 3 parserFormulaUpToConstant.pl - implements formulas "plus a constant". 4 5 =head1 DESCRIPTION 6 7 This file implements the FormulaUpToConstant object, which is 8 a formula that is only unique up to a constant (i.e., this is 9 an anti-derivative). Students must include the "+C" as part of 10 their answers, but they can use any (single-letter) constant that 11 they want, and it doesn't have to be the one the professor used. 12 13 To use FormulaWithConstat objects, load this macro file at the 14 top of your problem: 15 16 loadMacros("parserFormulaUpToConstant.pl"); 17 18 then create a formula with constant as follows: 19 20 $f = FormulaUpToConstant("sin(x)+C"); 21 22 Note that the C should NOT already be a variable in the Context; 23 the FormulaUpToConstant object will handle adding it in for 24 you. If you don't include a constant in your formula (i.e., if 25 all the variables that you used are already in your Context, 26 then the FormulaUpToConstant object will add "+C" for you. 27 28 The FormulaUpToConstant should work like any normal Formula, 29 and in particular, you use $f->cmp to get its answer checker. 30 31 ANS($f->cmp); 32 33 Note that the FormulaUpToConstant object creates its only private 34 copy of the current Context (so that it can add variables without 35 affecting the rest of the problem). You should not notice this 36 in general, but if you need to access that context, use $f->{context}. 37 E.g. 38 39 Context($f->{context}); 40 41 would make the current context the one being used by the 42 FormulaUpToConstant, while 43 44 $f->{context}->variables->names 45 46 would return a list of the variables in the private context. 47 48 To get the name of the constant in use in the formula, 49 use 50 51 $f->constant. 52 53 If you combine a FormulaUpToConstant with other formulas, 54 the result will be a new FormulaUpToConstant object, with 55 a new Context, and potentially a new + C added to it. This 56 is likely not what you want. Instead, you should convert 57 back to a Formula first, then combine with other objects, 58 then convert back to a FormulaUpToConstant, if necessary. 59 To do this, use the removeConstant() method: 60 61 $f = FormulaUpToConstant("sin(x)+C"); 62 $g = Formula("cos(x)"); 63 $h = $f->removeConstant + $g; # $h will be "sin(x)+cos(x)" 64 $h = FormulaUpToConstant($h); # $h will be "sin(x)+cos(x)+C" 65 66 The answer evaluator by default will give "helpful" messages 67 to the student when the "+ C" is left out. You can turn off 68 these messages using the showHints option to the cmp() method: 69 70 ANS($f->cmp(showHints => 0)); 71 72 One of the hints is about whether the student's answer is linear 73 in the arbitrary constant. This test requires differentiating 74 the student answer. Since there are times when that could be 75 problematic, you can disable that test via the showLinearityHints 76 flag. (Note: setting showHints to 0 also disables these hints.) 77 78 ANS($f->cmp(showLinearityHints => 0)); 79 80 =cut 81 82 loadMacros("MathObjects.pl"); 83 84 sub _parserFormulaUpToConstant_init {FormulaUpToConstant::Init()} 85 86 package FormulaUpToConstant; 87 @ISA = ('Value::Formula'); 88 89 sub Init { 90 main::PG_restricted_eval('sub FormulaUpToConstant {FormulaUpToConstant->new(@_)}'); 91 } 92 93 # 94 # Create an instance of a FormulaUpToConstant. If no constant 95 # is supplied, we add C ourselves. 96 # 97 sub new { 98 my $self = shift; my $class = ref($self) || $self; 99 # 100 # Copy the context (so we can modify it) and 101 # replace the usual Variable object with our own. 102 # 103 my $context = (Value::isContext($_[0]) ? shift : $self->context)->copy; 104 $context->{parser}{Variable} = 'FormulaUpToConstant::Variable'; 105 # 106 # Create a formula from the user's input. 107 # 108 my $f = main::Formula($context,@_); 109 # 110 # If it doesn't have a constant already, add one. 111 # (should check that C isn't already in use, and look 112 # up the first free name, but we'll cross our fingers 113 # for now. Could look through the defined variables 114 # to see if there is already an arbitraryConstant 115 # and use that.) 116 # 117 unless ($f->{constant}) {$f = $f + "C", $f->{constant} = "C"} 118 # 119 # Check that the formula is linear in C. 120 # 121 my $n = $f->D($f->{constant}); 122 Value->Error("Your formula isn't linear in the arbitrary constant '%s'",$f->{constant}) 123 unless $n->isConstant; 124 # 125 # Make a version with adaptive parameters for use in the 126 # comparison later on. We could like n0*C, but already have $n 127 # copies of C, so remove them. That way, n0 will be 0 when there 128 # are no C's in the student answer during the adaptive comparison. 129 # (Again, should really check that n0 is not in use already) 130 # 131 my $n00 = $context->variables->get("n00"); 132 $context->variables->add(n00=>'Parameter') unless $n00 and $n00->{parameter}; 133 my $n01 = $context->variables->get("n01"); 134 $context->variables->add(n01=>'Parameter') unless $n01 and $n01->{parameter}; 135 $f->{adapt} = $f + "(n00-$n)$f->{constant} + n01"; 136 return bless $f, $class; 137 } 138 139 ################################################## 140 # 141 # Remember that compare implements the overloaded perl <=> operator, 142 # and $a <=> $b is -1 when $a < $b, 0 when $a == $b and 1 when $a > $b. 143 # In our case, we only care about equality, so we will return 0 when 144 # equal and other numbers to indicate the reason they are not equal 145 # (this can be used by the answer checker to print helpful messages) 146 # 147 sub compare { 148 my ($l,$r) = @_; my $self = $l; my $context = $self->context; 149 $r = Value::makeValue($r,context=>$context); 150 # 151 # Not equal if the student value is constant or has no + C 152 # 153 return 2 if !Value::isFormula($r); 154 return 3 if !defined($r->{constant}); 155 # 156 # If constants aren't the same, substitute the professor's in the student answer. 157 # 158 $r = $r->substitute($r->{constant}=>$l->{constant}) unless $r->{constant} eq $l->{constant}; 159 # 160 # Compare with adaptive parameters to see if $l + n0 C = $r for some n0. 161 # 162 return -1 unless $l->{adapt} == $r; 163 # 164 # Check that n0 is non-zero (i.e., there is a multiple of C in the student answer) 165 # (remember: return value of 0 is equal, and non-zero is unequal) 166 # 167 return abs($context->variables->get("n00")->{value}) < $context->flag("zeroLevelTol"); 168 } 169 170 ################################################## 171 # 172 # Here we override part of the answer comparison 173 # routines in order to be able to generate 174 # helpful error messages for students when 175 # they leave off the + C. 176 # 177 178 # 179 # Show hints by default 180 # 181 sub cmp_defaults {((shift)->SUPER::cmp_defaults,showHints => 1, showLinearityHints => 1)}; 182 183 # 184 # Add useful messages, if the author requested them 185 # 186 sub cmp_postprocess { 187 my $self = shift; my $ans = shift; 188 $self->SUPER::cmp_postprocess($ans); 189 return unless $ans->{score} == 0 && !$ans->{isPreview}; 190 return if $ans->{ans_message} || !$self->getFlag("showHints"); 191 my $student = $ans->{student_value}; 192 my $result = $ans->{correct_value} <=> $student; # compare encodes the reason in the result 193 $self->cmp_Error($ans,"Note: there is always more than one posibility") if $result == 2 || $result == 3; 194 if ($result == 3) { 195 my $context = $self->context; 196 $context->flags->set(no_parameters=>0); 197 $context->variables->add(x00=>'Real'); 198 $result = 1 if $self->removeConstant+"n01+n00x00" == $student+"x00"; # must use both parameters 199 $context->variables->remove('x00'); 200 $context->flags->set(no_parameters=>1); 201 } 202 $self->cmp_Error($ans,"Your answer is not the most general solution") if $result == 1; 203 $self->cmp_Error($ans,"Your formula should be linear in the constant '$student->{constant}'") 204 if $result == -1 && $self->getFlag("showLinearityHints") && !$student->D($student->{constant})->isConstant; 205 } 206 207 ################################################## 208 # 209 # Get the name of the constant 210 # 211 sub constant {(shift)->{constant}} 212 213 # 214 # Remove the constant and return a Formula object 215 # 216 sub removeConstant { 217 my $self = shift; 218 main::Formula($self->substitute($self->{constant}=>0))->reduce; 219 } 220 221 # 222 # Override the differentiation so that we always return 223 # a Formula, not a FormulaUpToConstant (we don't want to 224 # add the C in again). 225 # 226 sub D { 227 my $self = shift; 228 $self->removeConstant->D(@_); 229 } 230 231 ###################################################################### 232 # 233 # This class repalces the Parser::Variable class, and its job 234 # is to look for new constants that aren't in the context, 235 # and add them in. This allows students to use ANY constant 236 # they want, and a different one from the professor. We check 237 # that the student only used ONE arbitrary constant, however. 238 # 239 package FormulaUpToConstant::Variable; 240 our @ISA = ('Parser::Variable'); 241 242 sub new { 243 my $self = shift; my $class = ref($self) || $self; 244 my $equation = shift; my $variables = $equation->{context}{variables}; 245 my ($name,$ref) = @_; my $def = $variables->{$name}; 246 # 247 # If the variable is not already in the context, add it 248 # and mark it as an arbitrary constant (for later reference) 249 # 250 if (!defined($def) && length($name) eq 1) { 251 $equation->{context}->variables->add($name => 'Real'); 252 $equation->{context}->variables->set($name => {arbitraryConstant => 1}); 253 $def = $variables->{$name}; 254 } 255 # 256 # If the variable is an arbitrary constant 257 # Error if we already have a constant and it's not this one. 258 # Save the constant so we can check with it later. 259 # 260 if ($def && $def->{arbitraryConstant}) { 261 $equation->Error(["Your formula shouldn't have two arbitrary constants"],$ref) 262 if $equation->{constant} and $name ne $equation->{constant}; 263 $equation->{constant} = $name; 264 } 265 # 266 # Do the usual Variable stuff. 267 # 268 $self->SUPER::new($equation,$name,$ref); 269 } 270 271 1;

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