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| 1 : | sh002i | 2558 | #! /usr/local/bin/perl |
| 2 : | |||
| 3 : | package PowerPolynomial; | ||
| 4 : | |||
| 5 : | #@ISA = qw(Function); | ||
| 6 : | |||
| 7 : | |||
| 8 : | sub givenVariableAndHash { # Give anonymous hash of coefficients | ||
| 9 : | my ($class, $variable, $hash) = @_; | ||
| 10 : | my $terms = {}; | ||
| 11 : | my @exponents = keys(%{$hash}); | ||
| 12 : | my $p; | ||
| 13 : | my $q; | ||
| 14 : | my $cp; | ||
| 15 : | my $cq; | ||
| 16 : | foreach my $ith (@exponents) { | ||
| 17 : | $cp = $hash -> {$ith} -> [0] -> [0]; | ||
| 18 : | $cq = $hash -> {$ith} -> [0] -> [1]; | ||
| 19 : | $cq = (!defined($cq)) ? 1 : $cq ; | ||
| 20 : | $terms ->{$ith} -> {'coef'} = new Fraction($cp, $cq); | ||
| 21 : | $p = $hash -> {$ith} -> [1] -> [0]; | ||
| 22 : | $q = $hash -> {$ith} -> [1] -> [1]; | ||
| 23 : | $q = (!defined($q)) ? 1 : $q ; | ||
| 24 : | $terms ->{$ith} -> {'exp'} = new Fraction($p, $q); | ||
| 25 : | } | ||
| 26 : | my $self = { 'variable' => $variable, | ||
| 27 : | 'terms' => $terms, | ||
| 28 : | }; | ||
| 29 : | bless $self, $class; | ||
| 30 : | return($self); | ||
| 31 : | } | ||
| 32 : | |||
| 33 : | sub givenVariableAndTerms { # Give reference to hash of Fraction coefficients and exponents | ||
| 34 : | my ($class, $variable, $hash) = @_; | ||
| 35 : | my $terms = {}; | ||
| 36 : | my @exponents = keys(%{$hash}); | ||
| 37 : | foreach my $ith (@exponents) { | ||
| 38 : | $terms ->{$ith} -> {'coef'} = $hash -> {$ith} -> {'coef'} -> copy ; | ||
| 39 : | $terms ->{$ith} -> {'exp'} = $hash -> {$ith} -> {'exp'} -> copy ; | ||
| 40 : | } | ||
| 41 : | my $self = { 'variable' => $variable, | ||
| 42 : | 'terms' => $terms, | ||
| 43 : | }; | ||
| 44 : | bless $self, $class; | ||
| 45 : | return($self); | ||
| 46 : | } | ||
| 47 : | |||
| 48 : | |||
| 49 : | |||
| 50 : | |||
| 51 : | sub terms { | ||
| 52 : | my $self = shift; | ||
| 53 : | if (@_) {$self -> {'terms'} = shift;} | ||
| 54 : | return ($self -> {'terms'}); | ||
| 55 : | } | ||
| 56 : | |||
| 57 : | sub variable { | ||
| 58 : | my $self = shift; | ||
| 59 : | if (@_) {$self->{'variable'} = shift;} | ||
| 60 : | return($self ->{'variable'}); | ||
| 61 : | } | ||
| 62 : | |||
| 63 : | sub printSelf { | ||
| 64 : | my $self = shift; | ||
| 65 : | my $variable = $self->variable(); | ||
| 66 : | my $terms = $self -> terms(); | ||
| 67 : | my @exponents = keys(%{$terms}); | ||
| 68 : | my $string = ""; | ||
| 69 : | my $numTerms = scalar(@exponents); | ||
| 70 : | my $jth; | ||
| 71 : | my $coef; | ||
| 72 : | my $exp; | ||
| 73 : | my $p; | ||
| 74 : | my $q; | ||
| 75 : | foreach my $i (0..$numTerms-1) { | ||
| 76 : | $jth = $exponents[$i]; | ||
| 77 : | $coef = $terms -> {$jth} -> [0]; | ||
| 78 : | $p = $terms -> {$jth} -> [1] -> [0]; | ||
| 79 : | $q = $terms -> {$jth} -> [1] -> [1]; | ||
| 80 : | $exp = ( !defined($q) or $q==1) ? "$p" : "$p/$q"; | ||
| 81 : | $string .= " + " . $coef ." x^{" . $jth ."}"; | ||
| 82 : | } | ||
| 83 : | return($string); | ||
| 84 : | } | ||
| 85 : | |||
| 86 : | sub TeXizeHighFirst { | ||
| 87 : | my $self = shift; | ||
| 88 : | my $variable = $self->variable(); | ||
| 89 : | my $terms = $self->terms(); | ||
| 90 : | my @exponents =keys(%{$terms}); | ||
| 91 : | my @sorted_exponents = &PGtranslator::PGsort(sub {$_[0] <=> $_[1]}, @exponents); | ||
| 92 : | my $numTerms = scalar(@sorted_exponents); | ||
| 93 : | my $string = ""; | ||
| 94 : | my $found = 0; | ||
| 95 : | my $coef; | ||
| 96 : | my $jth; | ||
| 97 : | my $p; | ||
| 98 : | my $q; | ||
| 99 : | my $exp; | ||
| 100 : | my $numer; | ||
| 101 : | my $denom; | ||
| 102 : | foreach my $i (0..$numTerms-1) { | ||
| 103 : | $jth = $sorted_exponents[$numTerms -1 -$i]; | ||
| 104 : | if ($jth != 0) { | ||
| 105 : | $exp = $terms -> {$jth} -> {'exp'}; | ||
| 106 : | $exp -> reduce(); | ||
| 107 : | $numer = $exp -> numerator; | ||
| 108 : | $numerAbs = ($numer < 0) ? -$numer : $numer; | ||
| 109 : | $denom = $exp -> denominator; | ||
| 110 : | $expStr = $exp -> TeXize; | ||
| 111 : | $vterm = ($jth == 1) ? "$variable" : | ||
| 112 : | ( $denom == 1 and $numer >0 ) ? "$variable^{$expStr}" | ||
| 113 : | : ($denom == 1 and $numer == -1) ? "\\frac{1}{$variable}" | ||
| 114 : | : ($denom == 1 and $numer < 0) ? "\\frac{1}{$variable^{$numerAbs}}" | ||
| 115 : | : ($denom == 2 and $numer == 1) ? "\\sqrt{$variable}" | ||
| 116 : | : ($denom == 2 and $numer > 0) ? "\\sqrt{$variable^{$numer}}" | ||
| 117 : | : ($denom == 2 and $numer == -1) ? "\\frac{1}{\\sqrt{$variable}}" | ||
| 118 : | : ($denom == 2 and $numer < 0) ? "\\frac{1}{\\sqrt{$variable^{$numerAbs}}}" | ||
| 119 : | : ($denom != 1 and $numer == 1) ? "\\sqrt[$denom]{$variable}" | ||
| 120 : | : ($denom != 1 and $numer > 0) ? "\\sqrt[$denom]{$variable^{$numer}}" | ||
| 121 : | : ($denom != 1 and $numer == -1) ? "\\frac{1}{\\sqrt[$denom]{$variable}}" | ||
| 122 : | : ($denom != 1 and $numer < 0) ? "\\frac{1}{\\sqrt[$denom]{$variable^{$numerAbs}}}" | ||
| 123 : | : "$variable^{$expStr}"; | ||
| 124 : | if (($coef = $terms -> {$jth} -> {'coef'} ->scalar) != 0) | ||
| 125 : | {$coefStr = $terms -> {$jth} -> {'coef'} -> TeXize; | ||
| 126 : | if ($found) { | ||
| 127 : | $string .= | ||
| 128 : | ($coef == 1) ? " + $vterm" | ||
| 129 : | : ($coef > 0) ? " + $coefStr $vterm" | ||
| 130 : | : ($coef == -1) ? " - $vterm" | ||
| 131 : | : " $coefStr $vterm"; | ||
| 132 : | } | ||
| 133 : | else { | ||
| 134 : | $found=1; | ||
| 135 : | $string .= | ||
| 136 : | ($coef == 1) ? " $vterm" | ||
| 137 : | : ($coef > 0) ? " $coefStr $vterm" | ||
| 138 : | : ($coef == -1) ? " - $vterm" | ||
| 139 : | : " $coefStr $vterm"; | ||
| 140 : | } | ||
| 141 : | } | ||
| 142 : | } | ||
| 143 : | else { | ||
| 144 : | if (($coef = $terms -> {$jth} -> {'coef'} ->scalar) != 0) | ||
| 145 : | {$coefStr = $terms -> {$jth} -> {'coef'} -> TeXize; | ||
| 146 : | if ($found) { | ||
| 147 : | $string .= ($coef > 0) ? " + $coefStr " | ||
| 148 : | : " $coefStr " ; | ||
| 149 : | } | ||
| 150 : | else { | ||
| 151 : | $found=1; | ||
| 152 : | $string .= ($coef > 0) ? " $coefStr " | ||
| 153 : | : " $coefStr " ; | ||
| 154 : | } | ||
| 155 : | } | ||
| 156 : | } | ||
| 157 : | } | ||
| 158 : | return($string); | ||
| 159 : | } | ||
| 160 : | |||
| 161 : | sub TeXizeHighFirstAt { | ||
| 162 : | my ($self, $at, @rest) = @_; | ||
| 163 : | my $variable = $self->variable(); | ||
| 164 : | if (defined($at)) { | ||
| 165 : | if (ref($at) ne '') { | ||
| 166 : | $variable = $at -> TeXizeHighFirstAt(@rest); } | ||
| 167 : | else { | ||
| 168 : | $variable = $at; | ||
| 169 : | } | ||
| 170 : | $variable = '\left(' . $variable . '\right)'; | ||
| 171 : | } | ||
| 172 : | my $terms = $self->terms(); | ||
| 173 : | my @exponents =keys(%{$terms}); | ||
| 174 : | my @sorted_exponents = &PGtranslator::PGsort(sub {$_[0] <=> $_[1]}, @exponents); | ||
| 175 : | my $numTerms = scalar(@sorted_exponents); | ||
| 176 : | my $string = ""; | ||
| 177 : | my $found = 0; | ||
| 178 : | my $coef; | ||
| 179 : | my $jth; | ||
| 180 : | my $p; | ||
| 181 : | my $q; | ||
| 182 : | my $exp; | ||
| 183 : | my $numer; | ||
| 184 : | my $denom; | ||
| 185 : | foreach my $i (0..$numTerms-1) { | ||
| 186 : | $jth = $sorted_exponents[$numTerms -1 -$i]; | ||
| 187 : | if ($jth != 0) { | ||
| 188 : | $exp = $terms -> {$jth} -> {'exp'}; | ||
| 189 : | $exp -> reduce(); | ||
| 190 : | $numer = $exp -> numerator; | ||
| 191 : | $numerAbs = ($numer < 0) ? -$numer : $numer; | ||
| 192 : | $denom = $exp -> denominator; | ||
| 193 : | $expStr = $exp -> TeXize; | ||
| 194 : | $vterm = ($jth == 1) ? "$variable" : | ||
| 195 : | ( $denom == 1 and $numer >0 ) ? "$variable^{$expStr}" | ||
| 196 : | : ($denom == 1 and $numer == -1) ? "\\frac{1}{$variable}" | ||
| 197 : | : ($denom == 1 and $numer < 0) ? "\\frac{1}{$variable^{$numerAbs}}" | ||
| 198 : | : ($denom == 2 and $numer == 1) ? "\\sqrt{$variable}" | ||
| 199 : | : ($denom == 2 and $numer > 0) ? "\\sqrt{$variable^{$numer}}" | ||
| 200 : | : ($denom == 2 and $numer == -1) ? "\\frac{1}{\\sqrt{$variable}}" | ||
| 201 : | : ($denom == 2 and $numer < 0) ? "\\frac{1}{\\sqrt{$variable^{$numerAbs}}}" | ||
| 202 : | : ($denom != 1 and $numer == 1) ? "\\sqrt[$denom]{$variable}" | ||
| 203 : | : ($denom != 1 and $numer > 0) ? "\\sqrt[$denom]{$variable^{$numer}}" | ||
| 204 : | : ($denom != 1 and $numer == -1) ? "\\frac{1}{\\sqrt[$denom]{$variable}}" | ||
| 205 : | : ($denom != 1 and $numer < 0) ? "\\frac{1}{\\sqrt[$denom]{$variable^{$numerAbs}}}" | ||
| 206 : | : "$variable^{$expStr}"; | ||
| 207 : | if (($coef = $terms -> {$jth} -> {'coef'} ->scalar) != 0) | ||
| 208 : | {$coefStr = $terms -> {$jth} -> {'coef'} -> TeXize; | ||
| 209 : | if ($found) { | ||
| 210 : | $string .= | ||
| 211 : | ($coef == 1) ? " + $vterm" | ||
| 212 : | : ($coef > 0) ? " + $coefStr $vterm" | ||
| 213 : | : ($coef == -1) ? " - $vterm" | ||
| 214 : | : " $coefStr $vterm"; | ||
| 215 : | } | ||
| 216 : | else { | ||
| 217 : | $found=1; | ||
| 218 : | $string .= | ||
| 219 : | ($coef == 1) ? " $vterm" | ||
| 220 : | : ($coef > 0) ? " $coefStr $vterm" | ||
| 221 : | : ($coef == -1) ? " - $vterm" | ||
| 222 : | : " $coefStr $vterm"; | ||
| 223 : | } | ||
| 224 : | } | ||
| 225 : | } | ||
| 226 : | else { | ||
| 227 : | if (($coef = $terms -> {$jth} -> {'coef'} ->scalar) != 0) | ||
| 228 : | {$coefStr = $terms -> {$jth} -> {'coef'} -> TeXize; | ||
| 229 : | if ($found) { | ||
| 230 : | $string .= ($coef > 0) ? " + $coefStr " | ||
| 231 : | : " $coefStr " ; | ||
| 232 : | } | ||
| 233 : | else { | ||
| 234 : | $found=1; | ||
| 235 : | $string .= ($coef > 0) ? " $coefStr " | ||
| 236 : | : " $coefStr " ; | ||
| 237 : | } | ||
| 238 : | } | ||
| 239 : | } | ||
| 240 : | } | ||
| 241 : | return($string); | ||
| 242 : | } | ||
| 243 : | |||
| 244 : | sub TeXizeLowFirst { | ||
| 245 : | my $self = shift; | ||
| 246 : | my $variable = $self->variable(); | ||
| 247 : | my $terms = $self->terms(); | ||
| 248 : | my @exponents =keys(%{$terms}); | ||
| 249 : | my @sorted_exponents = &PGtranslator::PGsort(sub {$_[1] <=> $_[2]}, @exponents); | ||
| 250 : | my $numTerms = scalar(@sorted_exponents); | ||
| 251 : | my $string = ""; | ||
| 252 : | my $found = 0; | ||
| 253 : | my $coef; | ||
| 254 : | my $jth; | ||
| 255 : | my $p; | ||
| 256 : | my $q; | ||
| 257 : | my $exp; | ||
| 258 : | foreach my $i (0..$numTerms-1) { | ||
| 259 : | $jth = $sorted_exponents[$numTerms -1 -$i]; | ||
| 260 : | if ($jth != 0) { | ||
| 261 : | $exp = $terms -> {$jth} -> {'exp'}; | ||
| 262 : | $expStr = $exp -> TeXize; | ||
| 263 : | $vterm = ($jth == 1) ? "$variable" : "$variable^{$expStr}"; | ||
| 264 : | if (($coef = $terms -> {$jth} -> {'coef'} ->scalar) != 0) | ||
| 265 : | {$coefStr = $terms -> {$jth} -> {'coef'} -> TeXize; | ||
| 266 : | if ($found) { | ||
| 267 : | $string .= | ||
| 268 : | ($coef == 1) ? " + $vterm" | ||
| 269 : | : ($coef > 0) ? " + $coefStr $vterm" | ||
| 270 : | : ($coef == -1) ? " - $vterm" | ||
| 271 : | : " $coefStr $vterm"; | ||
| 272 : | } | ||
| 273 : | else { | ||
| 274 : | $found=1; | ||
| 275 : | $string .= | ||
| 276 : | ($coef == 1) ? " $vterm" | ||
| 277 : | : ($coef > 0) ? " $coefStr $vterm" | ||
| 278 : | : ($coef == -1) ? " - $vterm" | ||
| 279 : | : " $coefStr $vterm"; | ||
| 280 : | } | ||
| 281 : | } | ||
| 282 : | } | ||
| 283 : | else { | ||
| 284 : | if (($coef = $terms -> {$jth} -> {'coef'} ->scalar) != 0) | ||
| 285 : | {$coefStr = $terms -> {$jth} -> {'coef'} -> TeXize; | ||
| 286 : | if ($found) { | ||
| 287 : | $string .= ($coef > 0) ? " + $coefStr " | ||
| 288 : | : " $coefStr " ; | ||
| 289 : | } | ||
| 290 : | else { | ||
| 291 : | $found=1; | ||
| 292 : | $string .= ($coef > 0) ? " $coefStr " | ||
| 293 : | : " $coefStr " ; | ||
| 294 : | } | ||
| 295 : | } | ||
| 296 : | } | ||
| 297 : | } | ||
| 298 : | return($string); | ||
| 299 : | } | ||
| 300 : | |||
| 301 : | |||
| 302 : | sub perlizeHighFirst { | ||
| 303 : | my $self = shift; | ||
| 304 : | my $variable = $self->variable(); | ||
| 305 : | my $terms = $self->terms(); | ||
| 306 : | my @exponents =keys(%{$terms}); | ||
| 307 : | my @sorted_exponents = &PGtranslator::PGsort(sub {$_[0] <=> $_[1]}, @exponents); | ||
| 308 : | my $numTerms = scalar(@sorted_exponents); | ||
| 309 : | my $string = ""; | ||
| 310 : | my $found = 0; | ||
| 311 : | my $coef; | ||
| 312 : | my $jth; | ||
| 313 : | my $p; | ||
| 314 : | my $q; | ||
| 315 : | my $exp; | ||
| 316 : | foreach my $i (0..$numTerms-1) { | ||
| 317 : | $jth = $sorted_exponents[$numTerms -1 -$i]; | ||
| 318 : | if ($jth != 0) { | ||
| 319 : | $exp = $terms -> {$jth} -> {'exp'}; | ||
| 320 : | $expStr = $exp -> perlize; | ||
| 321 : | $vterm = ($jth == 1) ? "$variable" : "$variable**($expStr)"; | ||
| 322 : | if (($coef = $terms -> {$jth} -> {'coef'} -> scalar) != 0) | ||
| 323 : | {$coefStr = $terms -> {$jth} -> {'coef'} -> perlize; | ||
| 324 : | if ($found) { | ||
| 325 : | $string .= | ||
| 326 : | ($coef == 1) ? " + $vterm" | ||
| 327 : | : ($coef > 0) ? " + $coefStr * $vterm" | ||
| 328 : | : ($coef == -1) ? " - $vterm" | ||
| 329 : | # : " - $coefStr * $vterm"; | ||
| 330 : | : " - " . ($terms ->{$jth} -> {'coef'} -> times(-1)) -> perlize | ||
| 331 : | . $vterm; | ||
| 332 : | } | ||
| 333 : | else { | ||
| 334 : | $found=1; | ||
| 335 : | $string .= | ||
| 336 : | ($coef == 1) ? " $vterm" | ||
| 337 : | : ($coef > 0) ? " $coefStr * $vterm" | ||
| 338 : | : ($coef == -1) ? " - $vterm" | ||
| 339 : | # : " - $coefStr * $vterm"; | ||
| 340 : | : " - " . ($terms ->{$jth} -> {'coef'} -> times(-1)) -> perlize | ||
| 341 : | . $vterm; | ||
| 342 : | } | ||
| 343 : | } | ||
| 344 : | } | ||
| 345 : | else { | ||
| 346 : | if (($coef = $terms -> {$jth} -> {'coef'}) != 0) | ||
| 347 : | {$coefStr = $terms -> {$jth} -> {'coef'} -> perlize; | ||
| 348 : | if ($found) { | ||
| 349 : | $string .= ($coef > 0) ? " + $coefStr " | ||
| 350 : | # : " - $coefStr " ; | ||
| 351 : | : " - " . ($terms ->{$jth} -> {'coef'} -> times(-1)) -> perlize; | ||
| 352 : | } | ||
| 353 : | else { | ||
| 354 : | $found=1; | ||
| 355 : | $string .= ($coef > 0) ? " $coefStr " | ||
| 356 : | # : " - $coefStr " ; | ||
| 357 : | : " - " . ($terms ->{$jth} -> {'coef'} -> times(-1)) -> perlize; | ||
| 358 : | } | ||
| 359 : | } | ||
| 360 : | } | ||
| 361 : | } | ||
| 362 : | return($string); | ||
| 363 : | } | ||
| 364 : | |||
| 365 : | sub perlizeHighFirstAt { | ||
| 366 : | my ($self, $at, @rest) = @_; | ||
| 367 : | my $variable = $self->variable(); | ||
| 368 : | if (defined($at)) { | ||
| 369 : | if (ref($at) ne '') { | ||
| 370 : | $variable = $at -> perlizeHighFirstAt(@rest); } | ||
| 371 : | else { | ||
| 372 : | $variable = $at; | ||
| 373 : | } | ||
| 374 : | $variable = '(' . $variable . ')'; | ||
| 375 : | } | ||
| 376 : | my $terms = $self->terms(); | ||
| 377 : | my @exponents =keys(%{$terms}); | ||
| 378 : | my @sorted_exponents = &PGtranslator::PGsort(sub {$_[0] <=> $_[1]}, @exponents); | ||
| 379 : | my $numTerms = scalar(@sorted_exponents); | ||
| 380 : | my $string = ""; | ||
| 381 : | my $found = 0; | ||
| 382 : | my $coef; | ||
| 383 : | my $jth; | ||
| 384 : | my $p; | ||
| 385 : | my $q; | ||
| 386 : | my $exp; | ||
| 387 : | foreach my $i (0..$numTerms-1) { | ||
| 388 : | $jth = $sorted_exponents[$numTerms -1 -$i]; | ||
| 389 : | if ($jth != 0) { | ||
| 390 : | $exp = $terms -> {$jth} -> {'exp'}; | ||
| 391 : | $expStr = $exp -> perlize; | ||
| 392 : | $vterm = ($jth == 1) ? "$variable" : "$variable**($expStr)"; | ||
| 393 : | if (($coef = $terms -> {$jth} -> {'coef'} ->scalar) != 0) | ||
| 394 : | {$coefStr = $terms -> {$jth} -> {'coef'} -> perlize; | ||
| 395 : | if ($found) { | ||
| 396 : | $string .= | ||
| 397 : | ($coef == 1) ? " + $vterm" | ||
| 398 : | : ($coef > 0) ? " + $coefStr * $vterm" | ||
| 399 : | : ($coef == -1) ? " - $vterm" | ||
| 400 : | : " $coefStr * $vterm"; | ||
| 401 : | } | ||
| 402 : | else { | ||
| 403 : | $found=1; | ||
| 404 : | $string .= | ||
| 405 : | ($coef == 1) ? " $vterm" | ||
| 406 : | : ($coef > 0) ? " $coefStr * $vterm" | ||
| 407 : | : ($coef == -1) ? " - $vterm" | ||
| 408 : | : " $coefStr * $vterm"; | ||
| 409 : | } | ||
| 410 : | } | ||
| 411 : | } | ||
| 412 : | else { | ||
| 413 : | if (($coef = $terms -> {$jth} -> {'coef'}) != 0) | ||
| 414 : | {$coefStr = $terms -> {$jth} -> {'coef'} -> perlize; | ||
| 415 : | if ($found) { | ||
| 416 : | $string .= ($coef > 0) ? " + $coefStr " | ||
| 417 : | : " $coefStr " ; | ||
| 418 : | } | ||
| 419 : | else { | ||
| 420 : | $found=1; | ||
| 421 : | $string .= ($coef > 0) ? " $coefStr " | ||
| 422 : | : " $coefStr " ; | ||
| 423 : | } | ||
| 424 : | } | ||
| 425 : | } | ||
| 426 : | } | ||
| 427 : | return($string); | ||
| 428 : | } | ||
| 429 : | |||
| 430 : | |||
| 431 : | sub scalarMult { | ||
| 432 : | my $self = shift; | ||
| 433 : | my $scalar = shift; | ||
| 434 : | if (!(defined($scalar))) {return(undef());} | ||
| 435 : | my $variable = $self -> variable; | ||
| 436 : | my $terms = $self -> terms; | ||
| 437 : | my @exponents = keys(%{$terms}); | ||
| 438 : | foreach my $ith (@exponents) { | ||
| 439 : | $terms ->{$ith} -> {'coef'} = $terms -> {$ith} -> {'coef'} -> times($scalar); | ||
| 440 : | } | ||
| 441 : | my $scalarM = givenVariableAndTerms PowerPolynomial($variable, $terms); | ||
| 442 : | return($scalarM); | ||
| 443 : | } | ||
| 444 : | |||
| 445 : | |||
| 446 : | |||
| 447 : | sub derivative { | ||
| 448 : | my $self = shift; | ||
| 449 : | my $class = ref($self); | ||
| 450 : | my $variable = shift; | ||
| 451 : | if (!(defined($variable))) { $variable = $self -> variable;} | ||
| 452 : | my $terms = $self->terms(); | ||
| 453 : | my @exponents =keys(%{$terms}); | ||
| 454 : | my $derTerms = {}; | ||
| 455 : | my ($derExp, $derCoef, $derExponent); | ||
| 456 : | foreach my $exp (@exponents) { | ||
| 457 : | if ($exp != 0) { | ||
| 458 : | $derExp = $exp - 1; | ||
| 459 : | $derCoef = $terms->{$exp}->{'coef'} -> times($terms -> {$exp} -> {'exp'}); | ||
| 460 : | $derExponent = $terms -> {$exp} -> {'exp'} -> minus(1); | ||
| 461 : | $derTerms -> {$derExp} -> {'coef'} = $derCoef; | ||
| 462 : | $derTerms -> {$derExp} -> {'exp'} = $derExponent; | ||
| 463 : | } | ||
| 464 : | } | ||
| 465 : | my $derivative = {'variable' => $variable, | ||
| 466 : | 'terms' => $derTerms, | ||
| 467 : | }; | ||
| 468 : | bless $derivative, $class; | ||
| 469 : | return($derivative); | ||
| 470 : | } | ||
| 471 : | |||
| 472 : | sub antiDerivative { | ||
| 473 : | my $self = shift; | ||
| 474 : | my $class = ref($self); | ||
| 475 : | my $variable = shift; | ||
| 476 : | if (!(defined($variable))) { $variable = $self -> variable;} | ||
| 477 : | my $terms = $self->terms(); | ||
| 478 : | my @exponents =keys(%{$terms}); | ||
| 479 : | my $antiDerTerms = {}; | ||
| 480 : | my ($antiDerExp, $antiDerCoef, $antiDerExponent); | ||
| 481 : | foreach my $exp (@exponents) { | ||
| 482 : | if ($exp != -1) { | ||
| 483 : | $antiDerExp = $exp + 1; | ||
| 484 : | $antiDerCoef = $terms->{$exp}->{'coef'} -> divBy($terms->{$exp}->{'exp'}->plus(1)); | ||
| 485 : | $antiDerExponent = $terms -> {$exp} -> {'exp'} -> plus(1); | ||
| 486 : | $antiDerTerms -> {$antiDerExp} -> {'coef'} = $antiDerCoef; | ||
| 487 : | $antiDerTerms -> {$antiDerExp} -> {'exp'} = $antiDerExponent; | ||
| 488 : | } | ||
| 489 : | } | ||
| 490 : | my $antiDerivative = {'variable' => $variable, | ||
| 491 : | 'terms' => $antiDerTerms, | ||
| 492 : | }; | ||
| 493 : | bless $antiDerivative, $class; | ||
| 494 : | return($antiDerivative); | ||
| 495 : | } | ||
| 496 : | |||
| 497 : | 1; | ||
| 498 : |
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