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| 3 | ## This file is PGpolynomialmacros.pl ## |
3 | ## This file is PGpolynomialmacros.pl ## |
| 4 | ## It contains rountines used to create and manipulate ## |
4 | ## It contains rountines used to create and manipulate ## |
| 5 | ## polynomials for WeBWorK ## |
5 | ## polynomials for WeBWorK ## |
| 6 | ## ## |
6 | ## ## |
| 7 | ## Copyright 2002 Mark Schmitt ## |
7 | ## Copyright 2002 Mark Schmitt ## |
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|
8 | ## Version 1.1.2 ## |
| 8 | ########################################################## |
9 | ########################################################## |
| 9 | |
10 | |
| 10 | ## In the current version, there is no attempt to verify that correct arrays are being passed to the routines. |
11 | ## In the current version, there is no attempt to verify that correct arrays are being passed to the routines. |
| 11 | ## This ought to be changed in the next incarnation. |
12 | ## This ought to be changed in the next incarnation. |
| 12 | ## It is assumed that arrays passed to the routines have no leading zeros, and represent the coefficients of |
13 | ## It is assumed that arrays passed to the routines have no leading zeros, and represent the coefficients of |
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| 24 | ## Stringification : converting an array of coefficients into a properly formatted polynomial string |
25 | ## Stringification : converting an array of coefficients into a properly formatted polynomial string |
| 25 | ## Polynomial Addition |
26 | ## Polynomial Addition |
| 26 | ## Polynomial Subtraction |
27 | ## Polynomial Subtraction |
| 27 | |
28 | |
| 28 | |
29 | |
| 29 | |
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|
| 30 | ## |
30 | ## |
| 31 | ## @sum = PolyAdd(~~@x,~~@y); |
31 | ## ValidPoly |
| 32 | ## Returns the sum of polynomials x and y |
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|
| 33 | ## |
32 | ## |
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33 | sub ValidPoly { |
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34 | my $xref = @_; |
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35 | if (${$xref}[0] != 0) {return 1;} |
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36 | else {return 0;} |
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37 | } |
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38 | |
| 34 | sub PolyAdd{ |
39 | sub PolyAdd{ |
| 35 | my ($xref,$yref) = @_; |
40 | my ($xref,$yref) = @_; |
| 36 | @local_x = @{$xref}; |
41 | @local_x = @{$xref}; |
| 37 | @local_y = @{$yref}; |
42 | @local_y = @{$yref}; |
| 38 | if ($#local_x < $#local_y) { |
43 | if ($#local_x < $#local_y) { |
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| 44 | foreach $i (0..$#local_x) { |
49 | foreach $i (0..$#local_x) { |
| 45 | $sum[$i] = $local_x[$i] + $local_y[$i]; |
50 | $sum[$i] = $local_x[$i] + $local_y[$i]; |
| 46 | } |
51 | } |
| 47 | return @sum; |
52 | return @sum; |
| 48 | } |
53 | } |
| 49 | ## |
54 | |
| 50 | ## @diff = PolySub(~~@x,~~@y); |
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|
| 51 | ## Returns the polynomial x-y |
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|
| 52 | ## |
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|
| 53 | sub PolySub{ |
55 | sub PolySub{ |
| 54 | my ($xref,$yref) = @_; |
56 | my ($xref,$yref) = @_; |
| 55 | @local_x = @{$xref}; |
57 | @local_x = @{$xref}; |
| 56 | @local_y = @{$yref}; |
58 | @local_y = @{$yref}; |
| 57 | if ($#local_x < $#local_y) { |
59 | if ($#local_x < $#local_y) { |
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| 65 | } |
67 | } |
| 66 | return @diff; |
68 | return @diff; |
| 67 | } |
69 | } |
| 68 | |
70 | |
| 69 | ## |
71 | ## |
| 70 | ## @product = PolyMult(~~@coefficientArray1,~~@coefficientArray2); |
72 | ## @newPoly = PolyMult(~~@coefficientArray1,~~@coefficientArray2); |
| 71 | ## |
73 | ## |
| 72 | ## accepts two arrays containing coefficients in descending order |
74 | ## accepts two arrays containing coefficients in descending order |
| 73 | ## returns an array with the coefficients of the product |
75 | ## returns an array with the coefficients of the product |
| 74 | ## |
76 | ## |
| 75 | |
77 | |
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| 86 | return @result; |
88 | return @result; |
| 87 | } |
89 | } |
| 88 | |
90 | |
| 89 | ## |
91 | ## |
| 90 | ## (@quotient,$remainder) = SynDiv(~~@dividend,~~@divisor); |
92 | ## (@quotient,$remainder) = SynDiv(~~@dividend,~~@divisor); |
| 91 | ## Returns the quotient in an array and the remainder in a scalar |
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| 92 | ## |
93 | ## |
| 93 | |
94 | |
| 94 | sub SynDiv{ |
95 | sub SynDiv{ |
| 95 | my ($dividendref,$divisorref)=@_; |
96 | my ($dividendref,$divisorref)=@_; |
| 96 | my @dividend = @{$dividendref}; |
97 | my @dividend = @{$dividendref}; |
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| 102 | } |
103 | } |
| 103 | return @quotient; |
104 | return @quotient; |
| 104 | } |
105 | } |
| 105 | |
106 | |
| 106 | ## |
107 | ## |
| 107 | ## ($quotient,$remainder) = LongDiv(~~@dividend,~~@divisor); |
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| 108 | ## |
108 | ## |
| 109 | ## Returns references to the arrays that store the quotient and remainder |
109 | ## |
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|
110 | ## |
| 110 | ## |
111 | ## |
| 111 | |
112 | |
| 112 | sub LongDiv{ |
113 | sub LongDiv{ |
| 113 | my ($dividendref,$divisorref)=@_; |
114 | my ($dividendref,$divisorref)=@_; |
| 114 | my @dividend = @{$dividendref}; |
115 | my @dividend = @{$dividendref}; |
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| 213 | } |
214 | } |
| 214 | elsif ($j > 0 && $j!=1) { |
215 | elsif ($j > 0 && $j!=1) { |
| 215 | if ($poly[$i] >0) { |
216 | if ($poly[$i] >0) { |
| 216 | if ($poly[$i]!=1){ |
217 | if ($poly[$i]!=1){ |
| 217 | $string = $string."+$poly[$i] x^{$j}";} |
218 | $string = $string."+$poly[$i] x^{$j}";} |
| 218 | else {$string = $string."x^{$j}";}} |
219 | else {$string = $string."+x^{$j}";}} |
| 219 | elsif ($poly[$i] == 0) {} |
220 | elsif ($poly[$i] == 0) {} |
| 220 | elsif ($poly[$i] == -1) {$string=$string."-x^{$j}";} |
221 | elsif ($poly[$i] == -1) {$string=$string."-x^{$j}";} |
| 221 | else {$string = $string."$poly[$i] x^{$j}";} |
222 | else {$string = $string."$poly[$i] x^{$j}";} |
| 222 | } |
223 | } |
| 223 | elsif ($j == 1) { |
224 | elsif ($j == 1) { |
| 224 | if ($poly[$i] > 0){ |
225 | if ($poly[$i] > 0){ |
| 225 | if ($poly[$i]!=1){ |
226 | if ($poly[$i]!=1){ |
| 226 | $string = $string."+$poly[$i] x";} |
227 | $string = $string."+$poly[$i] x";} |
| 227 | else {$string = $string."x";}} |
228 | else {$string = $string."+x";}} |
| 228 | elsif ($poly[$i] == 0) {} |
229 | elsif ($poly[$i] == 0) {} |
| 229 | elsif ($poly[$i] == -1){$string=$string."-x";} |
230 | elsif ($poly[$i] == -1){$string=$string."-x";} |
| 230 | else {$string=$string."$poly[$i] x";} |
231 | else {$string=$string."$poly[$i] x";} |
| 231 | } |
232 | } |
| 232 | else { |
233 | else { |
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| 237 | } |
238 | } |
| 238 | } |
239 | } |
| 239 | return $string; |
240 | return $string; |
| 240 | } |
241 | } |
| 241 | |
242 | |
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243 | sub PolyFunc { |
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244 | my $temp = $_[0]; |
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245 | my @poly = @{$temp}; |
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246 | $func = ""; |
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247 | foreach $i (0..$#poly) { |
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248 | $j = $#poly-$i; |
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249 | if ($poly[$i] > 0) {$func = $func."+$poly[$i]*x**($j)";} |
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250 | else {$func = $func."$poly[$i]*x**($j)";} |
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251 | } |
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252 | return $func; |
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253 | } |
| 242 | |
254 | |
| 243 | ## |
255 | ## |
| 244 | ## ($maxpos,$maxneg) = Descartes(~~@poly); |
256 | ## ($maxpos,$maxneg) = Descartes(~~@poly); |
| 245 | ## |
257 | ## |
| 246 | ## accepts an array containing the coefficients, in descending order, of a |
258 | ## accepts an array containing the coefficients, in descending order, of a |
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