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Data Structures | Enumerations | Functions
nforder.h File Reference

Go to the source code of this file.

Data Structures

class  nforder
 

Enumerations

enum  order_flags_log { one_is_one , is_maximal_known , is_maximal }
 

Functions

void basis_elt (bigintmat *m, int i)
 
nforderonestep (nforder *o, number p, coeffs c)
 
nforderpmaximal (nforder *o, number p)
 
nforderround2 (nforder *o)
 
bigintmatradicalmodpbase (nforder *o, number p, coeffs c)
 
number multring (bigintmat *nbase, nforder *o, number p)
 
void nforder_delete (nforder *o)
 

Enumeration Type Documentation

◆ order_flags_log

Enumerator
one_is_one 
is_maximal_known 
is_maximal 

Definition at line 17 of file nforder.h.

17 {
18 one_is_one, //if 1 is the first basis element
21};
@ is_maximal
Definition: nforder.h:20
@ one_is_one
Definition: nforder.h:18
@ is_maximal_known
Definition: nforder.h:19

Function Documentation

◆ basis_elt()

void basis_elt ( bigintmat m,
int  i 
)

Definition at line 422 of file nforder.cpp.

422 {
423 if (((m->rows() == 1) && (i <= m->cols())) || ((m->cols() == 1) && (i <= m->rows()))) {
424 // Falls m Zeilen- oder Spaltenvektor ist, setze alle Einträge auf 0 und Eintrag i auf 1 (Koeff-Vektor des i-ten Basiselements)
425 number t1 = n_Init(0,m->basecoeffs());
426 for (int j=0; ((j<m->rows()) || (j<m->cols())); j++) {
427 m->set(j, t1);
428
429 }
430 n_Delete(&t1,m->basecoeffs());
431 number t2 = n_Init(1,m->basecoeffs());
432 m->set(i-1, t2);
433 n_Delete(&t2,m->basecoeffs());
434 }
435 else
436 Werror("Error in basis_elt. Not a vector.");
437}
int m
Definition: cfEzgcd.cc:128
int i
Definition: cfEzgcd.cc:132
static FORCE_INLINE void n_Delete(number *p, const coeffs r)
delete 'p'
Definition: coeffs.h:452
static FORCE_INLINE number n_Init(long i, const coeffs r)
a number representing i in the given coeff field/ring r
Definition: coeffs.h:535
int j
Definition: facHensel.cc:110
void Werror(const char *fmt,...)
Definition: reporter.cc:189

◆ multring()

number multring ( bigintmat nbase,
nforder o,
number  p 
)

Definition at line 553 of file nforder.cpp.

553 {
554 coeffs R = o->basecoeffs();
555 number divi;
556 int n = o->getDim();
557
558 bigintmat *inv = new bigintmat(n, n, R);
559 divi = nbase->pseudoinv(inv);
560
561 // Zusammenbau der "langen" Matrix
562 bigintmat *lon = new bigintmat(n, 0, R);
563 bigintmat *oldlon;
564 bigintmat *mm = new bigintmat(n, n, R);
565 bigintmat *temp = new bigintmat(n, 1, R);
566 bigintmat *nochnetemp = new bigintmat(n, n, R);
567
568 for (int i=1; i<=n; i++) {
569 nbase->getcol(i, temp);
570 o->multmap(temp, mm);
571 bimMult(inv, mm, nochnetemp);
572 mm->copy(nochnetemp);
573 mm->inpTranspose();
574 oldlon = lon;
575 lon = new bigintmat(n, (i)*n, o->basecoeffs());
576 lon->concatcol(oldlon, mm);
577 delete oldlon;
578 }
579
580 lon->skaldiv(divi);
581
582 bigintmat * red;
583 if (1) {
584 bigintmat * cmp = lon->modhnf(p, o->basecoeffs());
585 red = cmp;
586 } else {
587 lon->hnf();
588 red = new bigintmat(n, n, o->basecoeffs());
589 lon->getColRange((n-1)*n+1, n, red);
590 }
591 delete lon;
592 red->inpTranspose();
593
594 number divisor = red->pseudoinv(nbase);
595 nbase->hnf();
596
597 delete inv;
598 delete mm;
599 delete temp;
600 delete red;
601 delete nochnetemp;
602 n_Delete(&divi, o->basecoeffs());
603 return divisor;
604}
bigintmat * bimMult(bigintmat *a, bigintmat *b)
Definition: bigintmat.cc:255
int p
Definition: cfModGcd.cc:4078
Matrices of numbers.
Definition: bigintmat.h:51
void hnf()
transforms INPLACE to HNF
Definition: bigintmat.cc:1660
bigintmat * modhnf(number p, coeffs c)
computes HNF(this | p*I)
Definition: bigintmat.cc:1832
void skaldiv(number b)
Macht Ganzzahldivision aller Matrixeinträge mit b.
Definition: bigintmat.cc:1861
bool copy(bigintmat *b)
Kopiert Einträge von b auf Bigintmat.
Definition: bigintmat.cc:1259
void getcol(int j, bigintmat *a)
copies the j-th column into the matrix a - which needs to be pre-allocated with the correct size.
Definition: bigintmat.cc:747
number pseudoinv(bigintmat *a)
Speichert in Matrix a die Pseudoinverse, liefert den Nenner zurück.
Definition: bigintmat.cc:1415
void getColRange(int j, int no, bigintmat *a)
copies the no-columns staring by j (so j...j+no-1) into the pre-allocated a
Definition: bigintmat.cc:778
void concatcol(bigintmat *a, bigintmat *b)
Definition: bigintmat.cc:1098
void inpTranspose()
transpose in place
Definition: bigintmat.cc:50
void multmap(bigintmat *a, bigintmat *m)
Definition: nforder.cpp:404
coeffs basecoeffs() const
Definition: nforder.h:76
int getDim()
Definition: nforder.cpp:235
The main handler for Singular numbers which are suitable for Singular polynomials.
#define R
Definition: sirandom.c:27

◆ nforder_delete()

void nforder_delete ( nforder o)

Definition at line 132 of file nforder.cpp.

132 {
133 if (o->ref_count_decref()>0) {
134 return;
135 }
136 delete o;
137}
int ref_count_decref()
Definition: nforder.h:51

◆ onestep()

nforder * onestep ( nforder o,
number  p,
coeffs  c 
)

Definition at line 608 of file nforder.cpp.

608 {
609 // Berechne F_p-Basis von I_p/pI_p
610 bigintmat *basis;
611 basis = radicalmodpbase(o, p, c);
612
613
614 // Bestimme Basis vom Ring der Multiplikatoren (speicher diese in basis), und Nenner davon (in divisor)
615 number divisor = multring(basis, o, p);
616 // Erzeuge neue Ordnung, der o zu Grunde liegt, mit Basis basis und Nenner divisor
617 if (basis->isOne() && n_IsOne(divisor, c)) {
618 delete basis;
619 n_Delete(&divisor, c);
620 return o;
621 }
622
623 nforder *no = new nforder(o, basis, divisor, c);
624
625 delete basis;
626 n_Delete(&divisor, c);
627 return no;
628}
int isOne()
is matrix is identity
Definition: bigintmat.cc:1300
static FORCE_INLINE BOOLEAN n_IsOne(number n, const coeffs r)
TRUE iff 'n' represents the one element.
Definition: coeffs.h:465
bigintmat * radicalmodpbase(nforder *o, number p, coeffs c)
Definition: nforder.cpp:446
number multring(bigintmat *nbase, nforder *o, number p)
Definition: nforder.cpp:553

◆ pmaximal()

nforder * pmaximal ( nforder o,
number  p 
)

Definition at line 632 of file nforder.cpp.

632 {
633 coeffs c = o->basecoeffs();
634 nforder *no = o;
635 nforder *otemp;
636 // TODO: check if p^2 still divides disc (maybe in onestep)
637 // simplify the tower
638 do {
639 otemp = no;
640 no = onestep(otemp, p, c);
641 if (no==otemp)
642 break;
643 nforder_delete (otemp);
644 otemp = no->simplify();
645 nforder_delete (no);
646 no = otemp;
647 } while (1);
648 return no;
649}
nforder * simplify()
Definition: nforder.cpp:275
void nforder_delete(nforder *o)
Definition: nforder.cpp:132
nforder * onestep(nforder *o, number p, coeffs c)
Definition: nforder.cpp:608

◆ radicalmodpbase()

bigintmat * radicalmodpbase ( nforder o,
number  p,
coeffs  c 
)

Definition at line 446 of file nforder.cpp.

446 {
447
448 number dimen = n_Init(o->getDim(), o->basecoeffs());
449 int n = o->getDim();
450
451 bigintmat *m, *bas;
452 // Berechnet F_p-Basis von I_p/pI_p (Radical mod p)
453 // Dazu:
454 if (n_Greater(p, dimen, c)) {
455 // Falls Primzahl größer gleich Dimension der Ordnung, so berechne Kern der Spurmatrix modulo p.
456 // also works it p is no prime.
457 m = o->traceMatrix();
458 bas = new bigintmat(n, 1, o->basecoeffs());
459 } else {
460 // Sonst: Berechne Kern der Abbildung x -> x^(p^j) mod p, wobei j>0 mit p^j >= dimension
461 int j = 1;
462 // ex als number, oder reicht long long int?
463 // Finde j von oben und berechne p^j
464 number ex = n_Init(1, o->basecoeffs());
465 number temp;
466 while (n_Greater(dimen, ex, o->basecoeffs())) {
467 temp = n_Mult(ex, p, o->basecoeffs());
468 n_Delete(&ex, o->basecoeffs());
469 ex = temp;
470 j++;
471 }
472
473 // Berechne Abbildungsmatrix der oben genannten Abbildung und speichere diese in m (genauere Erklärung dazu: Siehe multmap())
474 m = new bigintmat(n, n, o->basecoeffs());
475 bas = new bigintmat(n, 1, o->basecoeffs());
476 bigintmat *prod = new bigintmat(n, 1, o->basecoeffs());
477
478 number klauf;
479 number eins = n_Init(1, o->basecoeffs());
480
481 for (int i=1; i<=n; i++) {
482 basis_elt(bas, i);
483 prod->copy(bas);
484 klauf = n_Init(1, o->basecoeffs());
485 for (; n_Greater(ex, klauf, o->basecoeffs());) {
486 o->elMult(prod, bas);
487 prod->mod(p);
488 temp = n_Add(klauf, eins, o->basecoeffs());
489 n_Delete(&klauf, o->basecoeffs());
490 klauf = temp;
491 }
492 n_Delete(&klauf, o->basecoeffs());
493 m->setcol(i, prod);
494 }
495
496 delete prod;
497 n_Delete(&ex, o->basecoeffs());
498 n_Delete(&eins, o->basecoeffs());
499
500 }
501
502 bigintmat *kbase = new bigintmat(n, n, o->basecoeffs());
503
504 // Speichere Basiselemente von Kern der Matrix m (Spurmatrix oder Abbildungsmatrix, je nach if-else-Fall) (von Z/pZ -> Z/pZ) in kbase (ersten kdim Spalten bilden Basis)
505 int kdim = kernbase(m, kbase, p, c);
506 // Schreibe für jedes i=1,, .., dimension p*(i-tes Basiselement) als Spalten in Matrix gen, dahinter die oben errechnete Basis vom Kern
507 // Wir erhalten (als Spalten) ein Erzeugendensystem vom Kern von Z->Z/pZ: x->x^(p^j)
508 bigintmat *gen = new bigintmat(n, n+kdim, o->basecoeffs());
509
510 for (int i=1; i<=n; i++) {
511 basis_elt(bas, i);
512 bas->skalmult(p, c);
513 gen->setcol(i, bas);
514 }
515 for (int i=1; i<=kdim; i++) {
516 kbase->getcol(i, bas);
517 gen->setcol(i+n, bas);
518 }
519
520 // HNF auf EZS anwenden liefert (als letzten dimension Spalten) eine Basis des Kerns
521 gen->hnf();
522 bigintmat *tmp = new bigintmat(n, 1, o->basecoeffs());
523 bigintmat *nbase = new bigintmat(n, n, o->basecoeffs());
524 // Schreibe diese als Spalten in nbase und gib nbase zurück
525 for (int i=1; i<=n; i++) {
526 gen->getcol(gen->cols()-n+i, tmp);
527 nbase->setcol(i, tmp);
528 }
529
530 n_Delete(&dimen, o->basecoeffs());
531 delete m;
532 delete bas;
533 delete kbase;
534 delete gen;
535 delete tmp;
536 return nbase;
537
538}
int kernbase(bigintmat *a, bigintmat *c, number p, coeffs q)
a basis for the nullspace of a mod p: only used internally in Round2. Don't use it.
Definition: bigintmat.cc:2600
int cols() const
Definition: bigintmat.h:144
void setcol(int j, bigintmat *m)
Setzt j-te Spalte gleich übergebenem Vektor (Matrix) m.
Definition: bigintmat.cc:826
bool skalmult(number b, coeffs c)
Multipliziert zur Matrix den Skalar b hinzu.
Definition: bigintmat.cc:938
void elMult(bigintmat *a, bigintmat *b)
Definition: nforder.cpp:321
bigintmat * traceMatrix()
Definition: nforder.cpp:196
static FORCE_INLINE number n_Mult(number a, number b, const coeffs r)
return the product of 'a' and 'b', i.e., a*b
Definition: coeffs.h:633
static FORCE_INLINE number n_Add(number a, number b, const coeffs r)
return the sum of 'a' and 'b', i.e., a+b
Definition: coeffs.h:647
static FORCE_INLINE BOOLEAN n_Greater(number a, number b, const coeffs r)
ordered fields: TRUE iff 'a' is larger than 'b'; in Z/pZ: TRUE iff la > lb, where la and lb are the l...
Definition: coeffs.h:508
fq_nmod_poly_t prod
Definition: facHensel.cc:100
void basis_elt(bigintmat *m, int i)
Definition: nforder.cpp:422

◆ round2()

nforder * round2 ( nforder o)