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1 | =head1 NAME |
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2 | |
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3 | parserFormulaUpToConstant.pl - implements formulas "plus a constant". |
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4 | |
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5 | =head1 DESCRIPTION |
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6 | |
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7 | This file implements the FormulaUpToConstant object, which is |
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8 | a formula that is only unique up to a constant (i.e., this is |
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9 | an anti-derivative). Students must include the "+C" as part of |
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10 | their answers, but they can use any (single-letter) constant that |
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11 | they want, and it doesn't have to be the one the professor used. |
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12 | |
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13 | To use FormulaWithConstat objects, load this macro file at the |
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14 | top of your problem: |
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15 | |
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16 | loadMacros("parserFormulaUpToConstant.pl"); |
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17 | |
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18 | then create a formula with constant as follows: |
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19 | |
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20 | $f = FormulaUpToConstant("sin(x)+C"); |
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21 | |
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22 | Note that the C should NOT already be a variable in the Context; |
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23 | the FormulaUpToConstant object will handle adding it in for |
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24 | you. If you don't include a constant in your formula (i.e., if |
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25 | all the variables that you used are already in your Context, |
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26 | then the FormulaUpToConstant object will add "+C" for you. |
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27 | |
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28 | The FormulaUpToConstant should work like any normal Formula, |
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29 | and in particular, you use $f->cmp to get its answer checker. |
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30 | |
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31 | ANS($f->cmp); |
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32 | |
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33 | Note that the FormulaUpToConstant object creates its only private |
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34 | copy of the current Context (so that it can add variables without |
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35 | affecting the rest of the problem). You should not notice this |
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36 | in general, but if you need to access that context, use $f->{context}. |
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37 | E.g. |
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38 | |
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39 | Context($f->{context}); |
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40 | |
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41 | would make the current context the one being used by the |
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42 | FormulaUpToConstant, while |
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43 | |
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44 | $f->{context}->variables->names |
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45 | |
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46 | would return a list of the variables in the private context. |
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47 | |
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48 | To get the name of the constant in use in the formula, |
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49 | use |
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50 | |
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51 | $f->constant. |
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52 | |
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53 | If you combine a FormulaUpToConstant with other formulas, |
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54 | the result will be a new FormulaUpToConstant object, with |
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55 | a new Context, and potentially a new + C added to it. This |
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56 | is likely not what you want. Instead, you should convert |
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57 | back to a Formula first, then combine with other objects, |
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58 | then convert back to a FormulaUpToConstant, if necessary. |
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59 | To do this, use the removeConstant() method: |
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60 | |
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61 | $f = FormulaUpToConstant("sin(x)+C"); |
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62 | $g = Formula("cos(x)"); |
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63 | $h = $f->removeConstant + $g; # $h will be "sin(x)+cos(x)" |
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64 | $h = FormulaUpToConstant($h); # $h will be "sin(x)+cos(x)+C" |
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65 | |
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66 | The answer evaluator by default will give "helpful" messages |
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67 | to the student when the "+ C" is left out. You can turn off |
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68 | these messages using the showHints option to the cmp() method: |
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69 | |
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70 | ANS($f->cmp(showHints => 0)); |
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71 | |
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72 | One of the hints is about whether the student's answer is linear |
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73 | in the arbitrary constant. This test requires differentiating |
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74 | the student answer. Since there are times when that could be |
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75 | problematic, you can disable that test via the showLinearityHints |
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76 | flag. (Note: setting showHints to 0 also disables these hints.) |
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77 | |
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78 | ANS($f->cmp(showLinearityHints => 0)); |
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79 | |
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80 | =cut |
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81 | |
| 1 | loadMacros("MathObjects.pl"); |
82 | loadMacros("MathObjects.pl"); |
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83 | |
| 3 | sub _parserFormulaUpToConstant_init {FormulaUpToConstant::Init()} |
84 | sub _parserFormulaUpToConstant_init {FormulaUpToConstant::Init()} |
| 4 | |
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| 5 | =head1 FormulaUpToConstant(); |
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| 6 | |
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| 7 | ###################################################################### |
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| 8 | # |
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| 9 | # This file implements the FormulaUpToConstant object, which is |
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| 10 | # a formula that is only unique up to a constant (i.e., this is |
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| 11 | # an anti-derivative). Students must include the "+C" as part of |
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| 12 | # their answers, but they can use any (single-letter) constant that |
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| 13 | # they want, and it doesn't have to be the one the professor used. |
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| 14 | # |
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| 15 | # To use FormulaWithConstat objects, load this macro file at the |
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| 16 | # top of your problem: |
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| 17 | # |
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| 18 | # loadMacros("parserFormulaUpToConstant.pl"); |
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| 19 | # |
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| 20 | # then create a formula with constant as follows: |
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| 21 | # |
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| 22 | # $f = FormulaUpToConstant("sin(x)+C"); |
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| 23 | # |
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| 24 | # Note that the C should NOT already be a variable in the Context; |
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| 25 | # the FormulaUpToConstant object will handle adding it in for |
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| 26 | # you. If you don't include a constant in your formula (i.e., if |
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| 27 | # all the variables that you used are already in your Context, |
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| 28 | # then the FormulaUpToConstant object will add "+C" for you. |
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| 29 | # |
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| 30 | # The FormulaUpToConstant should work like any normal Formula, |
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| 31 | # and in particular, you use $f->cmp to get its answer checker. |
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| 32 | # |
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| 33 | # ANS($f->cmp); |
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| 34 | # |
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| 35 | # Note that the FormulaUpToConstant object creates its only private |
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| 36 | # copy of the current Context (so that it can add variables without |
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| 37 | # affecting the rest of the problem). You should not notice this |
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| 38 | # in general, but if you need to access that context, use $f->{context}. |
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| 39 | # E.g. |
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| 40 | # |
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| 41 | # Context($f->{context}); |
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| 42 | # |
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| 43 | # would make the current context the one being used by the |
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| 44 | # FormulaUpToConstant, while |
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| 45 | # |
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| 46 | # $f->{context}->variables->names |
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| 47 | # |
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| 48 | # would return a list of the variables in the private context. |
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| 49 | # |
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| 50 | # To get the name of the constant in use in the formula, |
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| 51 | # use |
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| 52 | # |
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| 53 | # $f->constant. |
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| 54 | # |
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| 55 | # If you combine a FormulaUpToConstant with other formulas, |
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| 56 | # the result will be a new FormulaUpToConstant object, with |
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| 57 | # a new Context, and potentially a new + C added to it. This |
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| 58 | # is likely not what you want. Instead, you should convert |
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| 59 | # back to a Formula first, then combine with other objects, |
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| 60 | # then convert back to a FormulaUpToConstant, if necessary. |
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| 61 | # To do this, use the removeConstant() method: |
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| 62 | # |
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| 63 | # $f = FormulaUpToConstant("sin(x)+C"); |
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| 64 | # $g = Formula("cos(x)"); |
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| 65 | # $h = $f->removeConstant + $g; # $h will be "sin(x)+cos(x)" |
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| 66 | # $h = FormulaUpToConstant($h); # $h will be "sin(x)+cos(x)+C" |
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| 67 | # |
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| 68 | # The answer evaluator by default will give "helpful" messages |
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| 69 | # to the student when the "+ C" is left out. You can turn off |
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| 70 | # these messages using the showHints option to the cmp() method: |
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| 71 | # |
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| 72 | # ANS($f->cmp(showHints => 0)); |
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| 73 | # |
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| 74 | # One of the hints is about whether the student's answer is linear |
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| 75 | # in the arbitrary constant. This test requires differentiating |
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| 76 | # the student answer. Since there are times when that could be |
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| 77 | # problematic, you can disable that test via the showLinearityHints |
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| 78 | # flag. (Note: setting showHints to 0 also disables these hints.) |
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| 79 | # |
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| 80 | # ANS($f->cmp(showLinearityHints => 0)); |
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| 81 | # |
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| 82 | ###################################################################### |
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| 83 | |
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| 84 | =cut |
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| 85 | |
85 | |
| 86 | package FormulaUpToConstant; |
86 | package FormulaUpToConstant; |
| 87 | @ISA = ('Value::Formula'); |
87 | @ISA = ('Value::Formula'); |
| 88 | |
88 | |
| 89 | sub Init { |
89 | sub Init { |
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