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| 201 | ## returns a sting containing the polynomial with variable v |
201 | ## returns a sting containing the polynomial with variable v |
| 202 | ## default variable is x |
202 | ## default variable is x |
| 203 | ## |
203 | ## |
| 204 | |
204 | |
| 205 | sub PolyString{ |
205 | sub PolyString{ |
| 206 | my $temp = $_[0]; |
206 | my $temp = $_[0]; |
| 207 | my @poly = @{$temp}; |
207 | my @poly = @{$temp}; |
| 208 | $string = ""; |
208 | my $string = ''; |
| 209 | foreach $i (0..$#poly) { |
209 | foreach my $i (0..$#poly) { |
| 210 | $j = $#poly-$i; |
210 | my $j = $#poly-$i; |
| 211 | if ($j == $#poly) {if ($poly[$i]!=1){ |
211 | if ($j == $#poly) { |
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212 | if ($poly[$i] >0) { |
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213 | if ($poly[$i]!=1){ |
| 212 | $string = $string."$poly[$i] x^{$j}";} |
214 | $string = $string."$poly[$i] x^{$j}"; |
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215 | } |
| 213 | else {$string=$string."x^{$j}";} |
216 | else {$string=$string."x^{$j}";} |
| 214 | } |
217 | } |
| 215 | elsif ($j > 0 && $j!=1) { |
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| 216 | if ($poly[$i] >0) { |
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| 217 | if ($poly[$i]!=1){ |
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| 218 | $string = $string."+$poly[$i] x^{$j}";} |
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| 219 | else {$string = $string."+x^{$j}";}} |
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| 220 | elsif ($poly[$i] == 0) {} |
218 | elsif ($poly[$i] == 0) {} |
| 221 | elsif ($poly[$i] == -1) {$string=$string."-x^{$j}";} |
219 | elsif ($poly[$i] == -1) {$string=$string."-x^{$j}";} |
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220 | else {$string = $string."$poly[$i] x^{$j}";} |
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221 | } |
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222 | elsif ($j > 0 && $j!=1) { |
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223 | if ($poly[$i] >0) { |
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224 | if ($poly[$i]!=1){ |
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225 | $string = $string."+$poly[$i] x^{$j}"; |
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226 | } |
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227 | else {$string = $string."+x^{$j}";}} |
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228 | elsif ($poly[$i] == 0) {} |
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229 | elsif ($poly[$i] == -1) {$string=$string."-x^{$j}";} |
| 222 | else {$string = $string."$poly[$i] x^{$j}";} |
230 | else {$string = $string."$poly[$i] x^{$j}";} |
| 223 | } |
231 | } |
| 224 | elsif ($j == 1) { |
232 | elsif ($j == 1) { |
| 225 | if ($poly[$i] > 0){ |
233 | if ($poly[$i] > 0){ |
| 226 | if ($poly[$i]!=1){ |
234 | if ($poly[$i]!=1){ |
| 227 | $string = $string."+$poly[$i] x";} |
235 | $string = $string."+$poly[$i] x"; |
| 228 | else {$string = $string."+x";}} |
236 | } |
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237 | else {$string = $string."+x";} |
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238 | } |
| 229 | elsif ($poly[$i] == 0) {} |
239 | elsif ($poly[$i] == 0) {} |
| 230 | elsif ($poly[$i] == -1){$string=$string."-x";} |
240 | elsif ($poly[$i] == -1){$string=$string."-x";} |
| 231 | else {$string=$string."$poly[$i] x";} |
241 | else {$string=$string."$poly[$i] x";} |
| 232 | } |
242 | } |
| 233 | else { |
243 | else { |
| 234 | if ($poly[$i] > 0){ |
244 | if ($poly[$i] > 0){ |
| 235 | $string = $string."+$poly[$i] ";} |
245 | $string = $string."+$poly[$i] "; |
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246 | } |
| 236 | elsif ($poly[$i] == 0) {} |
247 | elsif ($poly[$i] == 0) {} |
| 237 | else {$string=$string."$poly[$i] ";} |
248 | else {$string=$string."$poly[$i] ";} |
| 238 | } |
249 | } |
| 239 | } |
250 | } |
| 240 | return $string; |
251 | return $string; |
| 241 | } |
252 | } |
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253 | |
| 242 | |
254 | |
| 243 | sub PolyFunc { |
255 | sub PolyFunc { |
| 244 | my $temp = $_[0]; |
256 | my $temp = $_[0]; |
| 245 | my @poly = @{$temp}; |
257 | my @poly = @{$temp}; |
| 246 | $func = ""; |
258 | $func = ""; |
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