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