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merged changes from rel-2-1-a1 -- stop using that branch.
1 #! /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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