[35aab3] | 1 | // ---------------------------------------------------------------------------- |
---|
| 2 | // npolygon.cc |
---|
| 3 | // begin of file |
---|
| 4 | // Stephan Endrass, endrass@mathematik.uni-mainz.de |
---|
| 5 | // 23.7.99 |
---|
| 6 | // ---------------------------------------------------------------------------- |
---|
| 7 | |
---|
| 8 | #define NPOLYGON_CC |
---|
| 9 | |
---|
[599326] | 10 | #include <kernel/mod2.h> |
---|
[35aab3] | 11 | |
---|
| 12 | #ifdef HAVE_SPECTRUM |
---|
| 13 | |
---|
| 14 | #ifdef NPOLYGON_PRINT |
---|
| 15 | #include <iostream.h> |
---|
| 16 | #ifndef NPOLYGON_IOSTREAM |
---|
| 17 | #include <stdio.h> |
---|
| 18 | #endif |
---|
| 19 | #endif |
---|
| 20 | |
---|
[b938f4] | 21 | //#include <polys/polys.h> |
---|
| 22 | #include <polys/monomials/p_polys.h> |
---|
| 23 | #include <polys/monomials/ring.h> |
---|
| 24 | |
---|
[599326] | 25 | #include <kernel/GMPrat.h> |
---|
| 26 | #include <kernel/kmatrix.h> |
---|
| 27 | #include <kernel/npolygon.h> |
---|
[b938f4] | 28 | #include <kernel/structs.h> |
---|
[35aab3] | 29 | |
---|
| 30 | // ---------------------------------------------------------------------------- |
---|
| 31 | // Allocate memory for a linear form of k terms |
---|
| 32 | // ---------------------------------------------------------------------------- |
---|
| 33 | |
---|
| 34 | void linearForm::copy_new( int k ) |
---|
| 35 | { |
---|
| 36 | if( k > 0 ) |
---|
| 37 | { |
---|
| 38 | c = new Rational[k]; |
---|
| 39 | |
---|
| 40 | #ifndef NBDEBUG |
---|
| 41 | if( c == (Rational*)NULL ) |
---|
| 42 | { |
---|
| 43 | #ifdef NPOLYGON_PRINT |
---|
| 44 | #ifdef NPOLYGON_IOSTREAM |
---|
| 45 | cerr << |
---|
| 46 | "void linearForm::copy_new( int k ): no memory left ...\n" ; |
---|
| 47 | #else |
---|
| 48 | fprintf( stderr, |
---|
| 49 | "void linearForm::copy_new( int k ): no memory left ...\n"); |
---|
| 50 | #endif |
---|
| 51 | #endif |
---|
| 52 | HALT(); |
---|
| 53 | } |
---|
| 54 | #endif |
---|
| 55 | } |
---|
| 56 | else if( k == 0 ) |
---|
| 57 | { |
---|
| 58 | c = (Rational*)NULL; |
---|
| 59 | } |
---|
| 60 | else if( k < 0 ) |
---|
| 61 | { |
---|
| 62 | #ifdef NPOLYGON_PRINT |
---|
| 63 | #ifdef NPOLYGON_IOSTREAM |
---|
| 64 | cerr << |
---|
| 65 | "void linearForm::copy_new( int k ): k < 0 ...\n"; |
---|
| 66 | #else |
---|
| 67 | fprintf( stderr, |
---|
| 68 | "void linearForm::copy_new( int k ): k < 0 ...\n" ); |
---|
| 69 | #endif |
---|
| 70 | #endif |
---|
| 71 | |
---|
| 72 | HALT(); |
---|
| 73 | } |
---|
| 74 | } |
---|
| 75 | |
---|
| 76 | // ---------------------------------------------------------------------------- |
---|
| 77 | // Delete the memory of a linear form |
---|
| 78 | // ---------------------------------------------------------------------------- |
---|
| 79 | |
---|
| 80 | void linearForm::copy_delete( void ) |
---|
| 81 | { |
---|
| 82 | if( c != (Rational*)NULL && N > 0 ) |
---|
| 83 | delete [] c; |
---|
| 84 | copy_zero( ); |
---|
| 85 | } |
---|
| 86 | |
---|
| 87 | // ---------------------------------------------------------------------------- |
---|
| 88 | // Initialize deep from another linear form |
---|
| 89 | // ---------------------------------------------------------------------------- |
---|
| 90 | |
---|
| 91 | void linearForm::copy_deep( const linearForm &l ) |
---|
| 92 | { |
---|
| 93 | copy_new( l.N ); |
---|
| 94 | for( int i=l.N-1; i>=0; i-- ) |
---|
| 95 | { |
---|
| 96 | c[i] = l.c[i]; |
---|
| 97 | } |
---|
| 98 | N = l.N; |
---|
| 99 | } |
---|
| 100 | |
---|
| 101 | // ---------------------------------------------------------------------------- |
---|
| 102 | // Copy constructor |
---|
| 103 | // ---------------------------------------------------------------------------- |
---|
| 104 | |
---|
| 105 | linearForm::linearForm( const linearForm &l ) |
---|
| 106 | { |
---|
| 107 | copy_deep( l ); |
---|
| 108 | } |
---|
| 109 | |
---|
| 110 | // ---------------------------------------------------------------------------- |
---|
| 111 | // Destructor |
---|
| 112 | // ---------------------------------------------------------------------------- |
---|
| 113 | |
---|
| 114 | linearForm::~linearForm( ) |
---|
| 115 | { |
---|
| 116 | copy_delete( ); |
---|
| 117 | } |
---|
| 118 | |
---|
| 119 | // ---------------------------------------------------------------------------- |
---|
| 120 | // Define `=` to be a deep copy |
---|
| 121 | // ---------------------------------------------------------------------------- |
---|
| 122 | |
---|
| 123 | linearForm & linearForm::operator = ( const linearForm &l ) |
---|
| 124 | { |
---|
| 125 | copy_delete( ); |
---|
| 126 | copy_deep( l ); |
---|
| 127 | |
---|
| 128 | return *this; |
---|
| 129 | } |
---|
| 130 | |
---|
| 131 | // ---------------------------------------------------------------------------- |
---|
| 132 | // ostream for linear form |
---|
| 133 | // ---------------------------------------------------------------------------- |
---|
| 134 | |
---|
| 135 | #ifdef NPOLYGON_PRINT |
---|
| 136 | |
---|
| 137 | ostream & operator << ( ostream &s,const linearForm &l ) |
---|
| 138 | { |
---|
| 139 | for( int i=0; i<l.N; i++ ) |
---|
| 140 | { |
---|
| 141 | if( l.c[i] != (Rational)0 ) |
---|
| 142 | { |
---|
| 143 | if( i > 0 && l.c[i] >= (Rational)0 ) |
---|
| 144 | { |
---|
| 145 | #ifdef NPOLYGON_IOSTREAM |
---|
| 146 | s << "+"; |
---|
| 147 | #else |
---|
| 148 | fprintf( stdout,"+" ); |
---|
| 149 | #endif |
---|
| 150 | } |
---|
| 151 | |
---|
| 152 | s << l.c[i]; |
---|
| 153 | |
---|
| 154 | #ifdef NPOLYGON_IOSTREAM |
---|
| 155 | s << "*x" << i+1; |
---|
| 156 | #else |
---|
| 157 | fprintf( stdout,"*x%d",i+1 ); |
---|
| 158 | #endif |
---|
| 159 | } |
---|
| 160 | } |
---|
| 161 | return s; |
---|
| 162 | } |
---|
| 163 | |
---|
| 164 | #endif |
---|
| 165 | |
---|
| 166 | // ---------------------------------------------------------------------------- |
---|
| 167 | // Equality of linear forms |
---|
| 168 | // ---------------------------------------------------------------------------- |
---|
| 169 | |
---|
| 170 | int operator == ( const linearForm &l1,const linearForm &l2 ) |
---|
| 171 | { |
---|
| 172 | if( l1.N!=l2.N ) |
---|
| 173 | return FALSE; |
---|
| 174 | for( int i=l1.N-1; i >=0 ; i-- ) |
---|
| 175 | { |
---|
| 176 | if( l1.c[i]!=l2.c[i] ) |
---|
| 177 | return FALSE; |
---|
| 178 | } |
---|
| 179 | return TRUE; |
---|
| 180 | } |
---|
| 181 | |
---|
| 182 | |
---|
| 183 | // ---------------------------------------------------------------------------- |
---|
| 184 | // Newton weight of a monomial |
---|
| 185 | // ---------------------------------------------------------------------------- |
---|
| 186 | |
---|
[b938f4] | 187 | Rational linearForm::weight( poly m, const ring r ) const |
---|
[35aab3] | 188 | { |
---|
| 189 | Rational ret=(Rational)0; |
---|
| 190 | |
---|
| 191 | for( int i=0,j=1; i<N; i++,j++ ) |
---|
| 192 | { |
---|
[b938f4] | 193 | ret += c[i]*(Rational)p_GetExp( m,j,r ); |
---|
[35aab3] | 194 | } |
---|
| 195 | |
---|
| 196 | return ret; |
---|
| 197 | } |
---|
| 198 | |
---|
| 199 | // ---------------------------------------------------------------------------- |
---|
| 200 | // Newton weight of a polynomial |
---|
| 201 | // ---------------------------------------------------------------------------- |
---|
| 202 | |
---|
[b938f4] | 203 | Rational linearForm::pweight( poly m, const ring r ) const |
---|
[35aab3] | 204 | { |
---|
| 205 | if( m==(poly)NULL ) |
---|
| 206 | return (Rational)0; |
---|
| 207 | |
---|
[b938f4] | 208 | Rational ret = weight( m, r ); |
---|
[35aab3] | 209 | Rational tmp; |
---|
| 210 | |
---|
| 211 | for( m=pNext(m); m!=(poly)NULL; pIter(m) ) |
---|
| 212 | { |
---|
[b938f4] | 213 | tmp = weight( m, r ); |
---|
[35aab3] | 214 | if( tmp<ret ) |
---|
| 215 | { |
---|
| 216 | ret = tmp; |
---|
| 217 | } |
---|
| 218 | } |
---|
| 219 | |
---|
| 220 | return ret; |
---|
| 221 | } |
---|
| 222 | |
---|
| 223 | // ---------------------------------------------------------------------------- |
---|
| 224 | // Newton weight of a monomial shifted by the product of the variables |
---|
| 225 | // ---------------------------------------------------------------------------- |
---|
| 226 | |
---|
[b938f4] | 227 | Rational linearForm::weight_shift( poly m, const ring r ) const |
---|
[35aab3] | 228 | { |
---|
| 229 | Rational ret=(Rational)0; |
---|
| 230 | |
---|
| 231 | for( int i=0,j=1; i<N; i++,j++ ) |
---|
| 232 | { |
---|
[b938f4] | 233 | ret += c[i]*(Rational)( p_GetExp( m,j,r ) + 1 ); |
---|
[35aab3] | 234 | } |
---|
| 235 | |
---|
| 236 | return ret; |
---|
| 237 | } |
---|
| 238 | |
---|
| 239 | // ---------------------------------------------------------------------------- |
---|
| 240 | // Newton weight of a monomial (forgetting the first variable) |
---|
| 241 | // ---------------------------------------------------------------------------- |
---|
| 242 | |
---|
[b938f4] | 243 | Rational linearForm::weight1( poly m, const ring r ) const |
---|
[35aab3] | 244 | { |
---|
| 245 | Rational ret=(Rational)0; |
---|
| 246 | |
---|
| 247 | for( int i=0,j=2; i<N; i++,j++ ) |
---|
| 248 | { |
---|
[b938f4] | 249 | ret += c[i]*(Rational)p_GetExp( m,j,r ); |
---|
[35aab3] | 250 | } |
---|
| 251 | |
---|
| 252 | return ret; |
---|
| 253 | } |
---|
| 254 | |
---|
| 255 | // ---------------------------------------------------------------------------- |
---|
| 256 | // Newton weight of a monomial shifted by the product of the variables |
---|
| 257 | // (forgetting the first variable) |
---|
| 258 | // ---------------------------------------------------------------------------- |
---|
| 259 | |
---|
[b938f4] | 260 | Rational linearForm::weight_shift1( poly m, const ring r ) const |
---|
[35aab3] | 261 | { |
---|
| 262 | Rational ret=(Rational)0; |
---|
| 263 | |
---|
| 264 | for( int i=0,j=2; i<N; i++,j++ ) |
---|
| 265 | { |
---|
[b938f4] | 266 | ret += c[i]*(Rational)( p_GetExp( m,j,r ) + 1 ); |
---|
[35aab3] | 267 | } |
---|
| 268 | |
---|
| 269 | return ret; |
---|
| 270 | } |
---|
| 271 | |
---|
| 272 | |
---|
| 273 | // ---------------------------------------------------------------------------- |
---|
| 274 | // Test if all coefficients of a linear form are positive |
---|
| 275 | // ---------------------------------------------------------------------------- |
---|
| 276 | |
---|
| 277 | int linearForm::positive( void ) |
---|
| 278 | { |
---|
| 279 | for( int i=0; i<N; i++ ) |
---|
| 280 | { |
---|
| 281 | if( c[i] <= (Rational)0 ) |
---|
| 282 | { |
---|
| 283 | return FALSE; |
---|
| 284 | } |
---|
| 285 | } |
---|
| 286 | return TRUE; |
---|
| 287 | } |
---|
| 288 | |
---|
| 289 | |
---|
| 290 | // ---------------------------------------------------------------------------- |
---|
| 291 | // Allocate memory for a newton polygon of k linear forms |
---|
| 292 | // ---------------------------------------------------------------------------- |
---|
| 293 | |
---|
| 294 | void newtonPolygon::copy_new( int k ) |
---|
| 295 | { |
---|
| 296 | if( k > 0 ) |
---|
| 297 | { |
---|
| 298 | l = new linearForm[k]; |
---|
| 299 | |
---|
| 300 | #ifndef NDEBUG |
---|
| 301 | if( l == (linearForm*)NULL ) |
---|
| 302 | { |
---|
| 303 | #ifdef NPOLYGON_PRINT |
---|
| 304 | #ifdef NPOLYGON_IOSTREAM |
---|
| 305 | cerr << |
---|
| 306 | "void newtonPolygon::copy_new( int k ): no memory left ...\n"; |
---|
| 307 | #else |
---|
| 308 | fprintf( stderr, |
---|
| 309 | "void newtonPolygon::copy_new( int k ): no memory left ...\n" ); |
---|
| 310 | #endif |
---|
| 311 | #endif |
---|
| 312 | |
---|
| 313 | HALT(); |
---|
| 314 | } |
---|
| 315 | #endif |
---|
| 316 | } |
---|
| 317 | else if( k == 0 ) |
---|
| 318 | { |
---|
| 319 | l = (linearForm*)NULL; |
---|
| 320 | } |
---|
| 321 | else if( k < 0 ) |
---|
| 322 | { |
---|
| 323 | #ifdef NPOLYGON_PRINT |
---|
| 324 | #ifdef NPOLYGON_IOSTREAM |
---|
| 325 | cerr << "void newtonPolygon::copy_new( int k ): k < 0 ...\n"; |
---|
| 326 | #else |
---|
| 327 | fprintf( stderr, |
---|
| 328 | "void newtonPolygon::copy_new( int k ): k < 0 ...\n" ); |
---|
| 329 | #endif |
---|
| 330 | #endif |
---|
| 331 | |
---|
| 332 | HALT(); |
---|
| 333 | } |
---|
| 334 | } |
---|
| 335 | |
---|
| 336 | // ---------------------------------------------------------------------------- |
---|
| 337 | // Delete the memory of a Newton polygon |
---|
| 338 | // ---------------------------------------------------------------------------- |
---|
| 339 | |
---|
| 340 | void newtonPolygon::copy_delete( void ) |
---|
| 341 | { |
---|
| 342 | if( l != (linearForm*)NULL && N > 0 ) |
---|
| 343 | delete [] l; |
---|
| 344 | copy_zero( ); |
---|
| 345 | } |
---|
| 346 | |
---|
| 347 | // ---------------------------------------------------------------------------- |
---|
| 348 | // Initialize deep from another Newton polygon |
---|
| 349 | // ---------------------------------------------------------------------------- |
---|
| 350 | |
---|
| 351 | void newtonPolygon::copy_deep( const newtonPolygon &np ) |
---|
| 352 | { |
---|
| 353 | copy_new( np.N ); |
---|
| 354 | for( int i=0; i<np.N; i++ ) |
---|
| 355 | { |
---|
| 356 | l[i] = np.l[i]; |
---|
| 357 | } |
---|
| 358 | N = np.N; |
---|
| 359 | } |
---|
| 360 | |
---|
| 361 | // ---------------------------------------------------------------------------- |
---|
| 362 | // Copy constructor |
---|
| 363 | // ---------------------------------------------------------------------------- |
---|
| 364 | |
---|
| 365 | newtonPolygon::newtonPolygon( const newtonPolygon &np ) |
---|
| 366 | { |
---|
| 367 | copy_deep( np ); |
---|
| 368 | } |
---|
| 369 | |
---|
| 370 | // ---------------------------------------------------------------------------- |
---|
| 371 | // Destructor |
---|
| 372 | // ---------------------------------------------------------------------------- |
---|
| 373 | |
---|
| 374 | newtonPolygon::~newtonPolygon( ) |
---|
| 375 | { |
---|
| 376 | copy_delete( ); |
---|
| 377 | } |
---|
| 378 | |
---|
| 379 | // ---------------------------------------------------------------------------- |
---|
| 380 | // We define `=` to be a deep copy |
---|
| 381 | // ---------------------------------------------------------------------------- |
---|
| 382 | |
---|
| 383 | newtonPolygon & newtonPolygon::operator = ( const newtonPolygon &np ) |
---|
| 384 | { |
---|
| 385 | copy_delete( ); |
---|
| 386 | copy_deep( np ); |
---|
| 387 | |
---|
| 388 | return *this; |
---|
| 389 | } |
---|
| 390 | |
---|
| 391 | // ---------------------------------------------------------------------------- |
---|
| 392 | // Initialize a Newton polygon from a polynomial |
---|
| 393 | // ---------------------------------------------------------------------------- |
---|
| 394 | |
---|
[b938f4] | 395 | newtonPolygon::newtonPolygon( poly f, const ring s ) |
---|
[35aab3] | 396 | { |
---|
| 397 | copy_zero( ); |
---|
| 398 | |
---|
[b938f4] | 399 | int *r=new int[s->N]; |
---|
| 400 | poly *m=new poly[s->N]; |
---|
[35aab3] | 401 | |
---|
| 402 | |
---|
[b938f4] | 403 | KMatrix<Rational> mat(s->N,s->N+1 ); |
---|
[35aab3] | 404 | |
---|
| 405 | int i,j,stop=FALSE; |
---|
| 406 | linearForm sol; |
---|
| 407 | |
---|
| 408 | // --------------- |
---|
| 409 | // init counters |
---|
| 410 | // --------------- |
---|
| 411 | |
---|
[b938f4] | 412 | for( i=0; i<s->N; i++ ) |
---|
[35aab3] | 413 | { |
---|
| 414 | r[i] = i; |
---|
| 415 | } |
---|
| 416 | |
---|
| 417 | m[0] = f; |
---|
| 418 | |
---|
[b938f4] | 419 | for( i=1; i<s->N; i++ ) |
---|
[35aab3] | 420 | { |
---|
| 421 | m[i] = pNext(m[i-1]); |
---|
| 422 | } |
---|
| 423 | |
---|
| 424 | // ----------------------------- |
---|
| 425 | // find faces (= linear forms) |
---|
| 426 | // ----------------------------- |
---|
| 427 | |
---|
| 428 | do |
---|
| 429 | { |
---|
| 430 | // --------------------------------------------------- |
---|
| 431 | // test if monomials p.m[r[0]]m,...,p.m[r[p.vars-1]] |
---|
| 432 | // are linearely independent |
---|
| 433 | // --------------------------------------------------- |
---|
| 434 | |
---|
[b938f4] | 435 | for( i=0; i<s->N; i++ ) |
---|
[35aab3] | 436 | { |
---|
[b938f4] | 437 | for( j=0; j<s->N; j++ ) |
---|
[35aab3] | 438 | { |
---|
| 439 | // mat.set( i,j,pGetExp( m[r[i]],j+1 ) ); |
---|
[b938f4] | 440 | mat.set( i,j,p_GetExp( m[i],j+1,s ) ); |
---|
[35aab3] | 441 | } |
---|
| 442 | mat.set( i,j,1 ); |
---|
| 443 | } |
---|
| 444 | |
---|
[b938f4] | 445 | if( mat.solve( &(sol.c),&(sol.N) ) == s->N ) |
---|
[35aab3] | 446 | { |
---|
| 447 | // --------------------------------- |
---|
| 448 | // check if linearForm is positive |
---|
| 449 | // check if linearForm is extremal |
---|
| 450 | // --------------------------------- |
---|
| 451 | |
---|
[b938f4] | 452 | if( sol.positive( ) && sol.pweight( f,s ) >= (Rational)1 ) |
---|
[35aab3] | 453 | { |
---|
| 454 | // ---------------------------------- |
---|
| 455 | // this is a face or the polyhedron |
---|
| 456 | // ---------------------------------- |
---|
| 457 | |
---|
| 458 | add_linearForm( sol ); |
---|
| 459 | sol.c = (Rational*)NULL; |
---|
| 460 | sol.N = 0; |
---|
| 461 | } |
---|
| 462 | } |
---|
| 463 | |
---|
| 464 | // -------------------- |
---|
| 465 | // increment counters |
---|
| 466 | // -------------------- |
---|
| 467 | |
---|
[b938f4] | 468 | for( i=1; r[i-1] + 1 == r[i] && i < s->N; i++ ); |
---|
[35aab3] | 469 | |
---|
| 470 | for( j=0; j<i-1; j++ ) |
---|
| 471 | { |
---|
| 472 | r[j]=j; |
---|
| 473 | } |
---|
| 474 | |
---|
| 475 | if( i>1 ) |
---|
| 476 | { |
---|
| 477 | m[0]=f; |
---|
| 478 | for( j=1; j<i-1; j++ ) |
---|
| 479 | { |
---|
| 480 | m[j]=pNext(m[j-1]); |
---|
| 481 | } |
---|
| 482 | } |
---|
| 483 | r[i-1]++; |
---|
| 484 | m[i-1]=pNext(m[i-1]); |
---|
| 485 | |
---|
[b938f4] | 486 | if( m[s->N-1] == (poly)NULL ) |
---|
[35aab3] | 487 | { |
---|
| 488 | stop = TRUE; |
---|
| 489 | } |
---|
| 490 | } while( stop == FALSE ); |
---|
| 491 | } |
---|
| 492 | |
---|
| 493 | #ifdef NPOLYGON_PRINT |
---|
| 494 | |
---|
| 495 | ostream & operator << ( ostream &s,const newtonPolygon &a ) |
---|
| 496 | { |
---|
| 497 | #ifdef NPOLYGON_IOSTREAM |
---|
| 498 | s << "Newton polygon:" << endl; |
---|
| 499 | #else |
---|
| 500 | fprintf( stdout,"Newton polygon:\n" ); |
---|
| 501 | #endif |
---|
| 502 | |
---|
| 503 | for( int i=0; i<a.N; i++ ) |
---|
| 504 | { |
---|
| 505 | s << a.l[i]; |
---|
| 506 | |
---|
| 507 | #ifdef NPOLYGON_IOSTREAM |
---|
| 508 | s << endl; |
---|
| 509 | #else |
---|
| 510 | fprintf( stdout,"\n" ); |
---|
| 511 | #endif |
---|
| 512 | } |
---|
| 513 | |
---|
| 514 | return s; |
---|
| 515 | } |
---|
| 516 | |
---|
| 517 | #endif |
---|
| 518 | |
---|
| 519 | // ---------------------------------------------------------------------------- |
---|
| 520 | // Add a face to the newton polygon |
---|
| 521 | // ---------------------------------------------------------------------------- |
---|
| 522 | |
---|
| 523 | void newtonPolygon::add_linearForm( const linearForm &l0 ) |
---|
| 524 | { |
---|
| 525 | int i; |
---|
| 526 | newtonPolygon np; |
---|
| 527 | |
---|
| 528 | // ------------------------------------- |
---|
| 529 | // test if linear form is already here |
---|
| 530 | // ------------------------------------- |
---|
| 531 | |
---|
| 532 | for( i=0; i<N; i++ ) |
---|
| 533 | { |
---|
| 534 | if( l0==l[i] ) |
---|
| 535 | { |
---|
| 536 | return; |
---|
| 537 | } |
---|
| 538 | } |
---|
| 539 | |
---|
| 540 | np.copy_new( N+1 ); |
---|
| 541 | np.N = N+1; |
---|
| 542 | |
---|
| 543 | for( i=0; i<N; i++ ) |
---|
| 544 | { |
---|
| 545 | np.l[i].copy_shallow( l[i] ); |
---|
| 546 | l[i].copy_zero( ); |
---|
| 547 | } |
---|
| 548 | |
---|
| 549 | np.l[N] = l0; |
---|
| 550 | |
---|
| 551 | copy_delete( ); |
---|
| 552 | copy_shallow( np ); |
---|
| 553 | np.copy_zero( ); |
---|
| 554 | |
---|
| 555 | return; |
---|
| 556 | } |
---|
| 557 | |
---|
| 558 | // ---------------------------------------------------------------------------- |
---|
| 559 | // Newton weight of a monomial |
---|
| 560 | // ---------------------------------------------------------------------------- |
---|
| 561 | |
---|
[b938f4] | 562 | Rational newtonPolygon::weight( poly m, const ring r ) const |
---|
[35aab3] | 563 | { |
---|
[b938f4] | 564 | Rational ret = l[0].weight( m,r ); |
---|
[35aab3] | 565 | Rational tmp; |
---|
| 566 | |
---|
| 567 | for( int i=1; i<N; i++ ) |
---|
| 568 | { |
---|
[b938f4] | 569 | tmp = l[i].weight( m,r ); |
---|
[35aab3] | 570 | |
---|
| 571 | if( tmp < ret ) |
---|
| 572 | { |
---|
| 573 | ret = tmp; |
---|
| 574 | } |
---|
| 575 | } |
---|
| 576 | return ret; |
---|
| 577 | } |
---|
| 578 | |
---|
| 579 | // ---------------------------------------------------------------------------- |
---|
| 580 | // Newton weight of a monomial shifted by the product of the variables |
---|
| 581 | // ---------------------------------------------------------------------------- |
---|
| 582 | |
---|
[b938f4] | 583 | Rational newtonPolygon::weight_shift( poly m, const ring r ) const |
---|
[35aab3] | 584 | { |
---|
[b938f4] | 585 | Rational ret = l[0].weight_shift( m, r ); |
---|
[35aab3] | 586 | Rational tmp; |
---|
| 587 | |
---|
| 588 | for( int i=1; i<N; i++ ) |
---|
| 589 | { |
---|
[b938f4] | 590 | tmp = l[i].weight_shift( m, r ); |
---|
[35aab3] | 591 | |
---|
| 592 | if( tmp < ret ) |
---|
| 593 | { |
---|
| 594 | ret = tmp; |
---|
| 595 | } |
---|
| 596 | } |
---|
| 597 | return ret; |
---|
| 598 | } |
---|
| 599 | |
---|
| 600 | // ---------------------------------------------------------------------------- |
---|
| 601 | // Newton weight of a monomial (forgetting the first variable) |
---|
| 602 | // ---------------------------------------------------------------------------- |
---|
| 603 | |
---|
[b938f4] | 604 | Rational newtonPolygon::weight1( poly m, const ring r ) const |
---|
[35aab3] | 605 | { |
---|
[b938f4] | 606 | Rational ret = l[0].weight1( m, r ); |
---|
[35aab3] | 607 | Rational tmp; |
---|
| 608 | |
---|
| 609 | for( int i=1; i<N; i++ ) |
---|
| 610 | { |
---|
[b938f4] | 611 | tmp = l[i].weight1( m, r ); |
---|
[35aab3] | 612 | |
---|
| 613 | if( tmp < ret ) |
---|
| 614 | { |
---|
| 615 | ret = tmp; |
---|
| 616 | } |
---|
| 617 | } |
---|
| 618 | return ret; |
---|
| 619 | } |
---|
| 620 | |
---|
| 621 | // ---------------------------------------------------------------------------- |
---|
| 622 | // Newton weight of a monomial shifted by the product of the variables |
---|
| 623 | // (forgetting the first variable) |
---|
| 624 | // ---------------------------------------------------------------------------- |
---|
| 625 | |
---|
[b938f4] | 626 | Rational newtonPolygon::weight_shift1( poly m, const ring r ) const |
---|
[35aab3] | 627 | { |
---|
[b938f4] | 628 | Rational ret = l[0].weight_shift1( m, r ); |
---|
[35aab3] | 629 | Rational tmp; |
---|
| 630 | |
---|
| 631 | for( int i=1; i<N; i++ ) |
---|
| 632 | { |
---|
[b938f4] | 633 | tmp = l[i].weight_shift1( m, r ); |
---|
[35aab3] | 634 | |
---|
| 635 | if( tmp < ret ) |
---|
| 636 | { |
---|
| 637 | ret = tmp; |
---|
| 638 | } |
---|
| 639 | } |
---|
| 640 | return ret; |
---|
| 641 | } |
---|
| 642 | |
---|
| 643 | /* |
---|
| 644 | // ---------------------------------------------------------------------------- |
---|
| 645 | // Chcek if the polynomial belonging to the Newton polygon |
---|
| 646 | // is semiquasihomogeneous (sqh) |
---|
| 647 | // ---------------------------------------------------------------------------- |
---|
| 648 | |
---|
| 649 | int newtonPolygon::is_sqh( void ) const |
---|
| 650 | { |
---|
| 651 | return ( N==1 ? TRUE : FALSE ); |
---|
| 652 | } |
---|
| 653 | |
---|
| 654 | // ---------------------------------------------------------------------------- |
---|
| 655 | // If the polynomial belonging to the Newton polygon is sqh, |
---|
| 656 | // return its weights vector |
---|
| 657 | // ---------------------------------------------------------------------------- |
---|
| 658 | |
---|
| 659 | Rational* newtonPolygon::sqh_weights( void ) const |
---|
| 660 | { |
---|
| 661 | return ( N==1 ? l[0].c : (Rational*)NULL ); |
---|
| 662 | } |
---|
| 663 | |
---|
| 664 | int newtonPolygon::sqh_N( void ) const |
---|
| 665 | { |
---|
| 666 | return ( N==1 ? l[0].N : 0 ); |
---|
| 667 | } |
---|
| 668 | */ |
---|
| 669 | |
---|
| 670 | #endif /* HAVE_SPECTRUM */ |
---|
| 671 | // ---------------------------------------------------------------------------- |
---|
| 672 | // npolygon.cc |
---|
| 673 | // end of file |
---|
| 674 | // ---------------------------------------------------------------------------- |
---|
| 675 | |
---|