14#include "factory/factory.h"
28#define TRANSEXT_PRIVATES
61 #if __FLINT_RELEASE >= 20503
65 if (!convSingRFlintR(ctx,r))
75 if (!convSingRFlintR(ctx,r))
87 if (!convSingRFlintR(ctx,r))
109 else if ( r->cf->extRing!=
NULL )
113 if (r->cf->extRing->qideal!=
NULL)
225 else if ( r->cf->extRing )
229 if (r->cf->extRing->qideal!=
NULL)
328 WerrorS(
"3rd argument must be a ring variable");
329 goto resultant_returns_res;
332 goto resultant_returns_res;
343 goto resultant_returns_res;
346 else if (r->cf->extRing!=
NULL)
351 if (r->cf->extRing->qideal!=
NULL)
396 goto resultant_returns_res;
400resultant_returns_res:
494 else if ( r->cf->extRing!=
NULL )
499 if (r->cf->extRing->qideal!=
NULL)
566 else if (r->cf->extRing!=
NULL)
570 if (r->cf->extRing->qideal!=
NULL)
592 res = convFactoryGFSingGF( F *
G );
606 #if __FLINT_RELEASE >= 20503
613 nmod_mpoly_ctx_t ctx;
614 if (!convSingRFlintR(ctx,r))
616 res = Flint_Divide_MP(
f,0,
g,0,ctx,r);
624 fmpq_mpoly_ctx_t ctx;
625 if (!convSingRFlintR(ctx,r))
627 res = Flint_Divide_MP(
f,0,
g,0,ctx,r);
644 else if (r->cf->extRing!=
NULL)
648 if (r->cf->extRing->qideal!=
NULL)
670 res = convFactoryGFSingGF( F /
G );
694 else if (r->cf->extRing!=
NULL)
698 if (r->cf->extRing->qideal!=
NULL)
726 res = convFactoryGFSingGF( F /
G );
737void singclap_divide_content ( poly
f,
const ring r )
766 int sz1=
n_Size(g1, r->cf);
767 int sz2=
n_Size(g2, r->cf);
800 while ( (
p !=
NULL) && (
g != 1) && (
g != 0))
809 if ((
g == 1 ) || (
g == 0))
842#ifdef FACTORIZE2_DEBUG
855 else if (r->cf->extRing!=
NULL)
857 if (r->cf->extRing->qideal!=
NULL)
889 else if (r->cf->extRing!=
NULL)
891 if (r->cf->extRing->qideal!=
NULL)
907 if (r->cf->extRing!=
NULL)
908 if (r->cf->extRing->qideal!=
NULL)
929#ifdef FACTORIZE2_DEBUG
957 if (with_exps==0) n++;
990 if (with_exps!=1) (**v)[n]=e;
1057 else if (r->cf->extRing!=
NULL)
1062 if (r->cf->extRing->qideal!=
NULL)
1093 if ( ! L.
getFirst().factor().inCoeffDomain() )
1102 if ((with_exps==2)&&(n>1))
1112 if (with_exps!=1) (**v)[
j] = J.
getItem().exp();
1121 res->m[
j] = convFactoryGFSingGF( J.
getItem().factor() );
1123 else if (r->cf->extRing!=
NULL)
1129 if (r->cf->extRing->qideal==
NULL)
1157 if (r->cf->extRing!=
NULL)
1158 if (r->cf->extRing->qideal!=
NULL)
1167#ifdef FACTORIZE2_DEBUG
1168 printf(
"factorize_retry\n");
1174 int l=(*v)->length();
1176 for(jj=0;jj<ww->
length();jj++)
1177 (**
v)[jj+
l]=(*ww)[jj];
1182 hh->m[jj]=
res->m[jj];
1198 WarnS(
"problem with factorize");
1262 (**v)[
j]=(*w)[
i];
j++;
1278 if (with_exps!=0) stop=0;
1284 else n_Delete(&old_lead_coeff,r->cf);
1294 if ((
v!=
NULL) && ((*
v)!=
NULL) &&(with_exps==2))
1318#ifdef FACTORIZE2_DEBUG
1332 if (with_exps!=1 && with_exps!=3)
1346 if (with_exps==0 || with_exps==3) n++;
1371 if (with_exps!=1) (**v)[n]=e;
1391 number n0=
n_Copy(old_lead_coeff,r->cf);
1392 if (with_exps==0 || with_exps==3)
1399 if (with_exps==0 || with_exps==3)
1410 number n0=
n_Copy(old_lead_coeff,r->cf);
1411 if (with_exps==0 || with_exps==3)
1417 if (with_exps==0 || with_exps==3)
1431 else if (r->cf->extRing!=
NULL)
1435 if (r->cf->extRing->qideal!=
NULL)
1477 if ((with_exps==2)&&(n>1))
1484 else if (L.
getFirst().factor().inCoeffDomain() && with_exps!=3)
1492 if (with_exps!=1 && with_exps!=3) (**v)[
j] = J.
getItem().exp();
1496 else if (r->cf->extRing!=
NULL)
1498 if (r->cf->extRing->qideal==
NULL)
1515 if (r->cf->extRing!=
NULL)
1516 if (r->cf->extRing->qideal!=
NULL)
1522 if (with_exps!=0 || with_exps==3) stop=0;
1527 if (with_exps==0 || with_exps==3)
p_SetCoeff(
res->m[0],old_lead_coeff,r);
1528 else n_Delete(&old_lead_coeff,r->cf);
1608 for ( LLi = LL; LLi.
hasItem(); LLi++ )
1612 if ((
m!=0) && (n!=0))
break;
1614 if (tries>=5)
break;
1616 if ((
m==0) || (n==0))
1618 Warn(
"char_series returns %d x %d matrix from %d input polys (%d)",
1626 for (
m=1, LLi = LL; LLi.
hasItem(); LLi++,
m++ )
1689 int cnt=
rVar(r)+offs;
1730 if (
s[strlen(
s)-1]==
',')
s[strlen(
s)-1]=
'\0';
1739 Werror(
"det of %d x %d matrix",r,
m->cols());
1764 for(
i=
m->rows();
i>0;
i--)
1766 for(
j=
m->cols();
j>0;
j--)
1781 for(
i=
m->rows();
i>0;
i--)
1783 for(
j=
m->cols();
j>0;
j--)
1793#if defined(HAVE_NTL) || defined(AHVE_FLINT)
1799 Werror(
"HNF of %d x %d matrix",r,
m->cols());
1835 Werror(
"HNF of %d x %d matrix",r,
m->cols());
1866 Werror(
"HNF of %d x %d matrix",r,
b->cols());
1973#if defined(HAVE_NTL) || defined(HAVE_FLINT)
1999 int n= absFactors.
length();
2039 numFactors +=
count;
2053 WerrorS(
"NTL/FLINT missing: absFactorize");
static int si_max(const int a, const int b)
static int si_min(const int a, const int b)
bigintmat * bimCopy(const bigintmat *b)
same as copy constructor - apart from it being able to accept NULL as input
#define BIMATELEM(M, I, J)
ListCFList irrCharSeries(const CFList &PS)
irreducible characteristic series
IntList neworderint(const CFList &PolyList)
const CanonicalForm CFMap CFMap & N
CanonicalForm extgcd(const CanonicalForm &f, const CanonicalForm &g, CanonicalForm &a, CanonicalForm &b)
CanonicalForm extgcd ( const CanonicalForm & f, const CanonicalForm & g, CanonicalForm & a,...
CanonicalForm bCommonDen(const CanonicalForm &f)
CanonicalForm bCommonDen ( const CanonicalForm & f )
CanonicalForm FACTORY_PUBLIC determinant(const CFMatrix &M, int n)
CFFList FACTORY_PUBLIC sqrFree(const CanonicalForm &f, bool sort=false)
squarefree factorization
CFFList FACTORY_PUBLIC factorize(const CanonicalForm &f, bool issqrfree=false)
factorization over or
CanonicalForm FACTORY_PUBLIC resultant(const CanonicalForm &f, const CanonicalForm &g, const Variable &x)
CanonicalForm resultant ( const CanonicalForm & f, const CanonicalForm & g, const Variable & x )
static const int SW_USE_QGCD
set to 1 to use Encarnacion GCD over Q(a)
static const int SW_USE_EZGCD_P
set to 1 to use EZGCD over F_q
static const int SW_RATIONAL
set to 1 for computations over Q
static const int SW_SYMMETRIC_FF
set to 1 for symmetric representation over F_q
CFMatrix * cf_LLL(CFMatrix &A)
performs LLL reduction.
CFMatrix * cf_HNF(CFMatrix &A)
The input matrix A is an n x m matrix of rank m (so n >= m), and D is a multiple of the determinant o...
CanonicalForm convSingPFactoryP(poly p, const ring r)
BOOLEAN convSingTrP(poly p, const ring r)
poly convFactoryPSingTrP(const CanonicalForm &f, const ring r)
poly convFactoryAPSingAP(const CanonicalForm &f, const ring r)
CanonicalForm convSingAPFactoryAP(poly p, const Variable &a, const ring r)
poly convFactoryPSingP(const CanonicalForm &f, const ring r)
int convFactoryISingI(const CanonicalForm &f)
CanonicalForm convSingTrPFactoryP(poly p, const ring r)
poly singclap_resultant(poly f, poly g, poly x, const ring r)
BOOLEAN count_Factors(ideal I, intvec *v, int j, poly &f, poly fac, const ring r)
matrix singntl_HNF(matrix m, const ring s)
poly singclap_pmod(poly f, poly g, const ring r)
ideal singclap_factorize(poly f, intvec **v, int with_exps, const ring r)
matrix singclap_irrCharSeries(ideal I, const ring r)
int pGetExp_Var(poly p, int i, const ring r)
VAR int singclap_factorize_retry
poly singclap_pdivide(poly f, poly g, const ring r)
int * Zp_roots(poly p, const ring r)
void out_cf(const char *s1, const CanonicalForm &f, const char *s2)
BOOLEAN singclap_extgcd(poly f, poly g, poly &res, poly &pa, poly &pb, const ring r)
poly singclap_det(const matrix m, const ring s)
poly singclap_gcd_and_divide(poly &f, poly &g, const ring r)
clears denominators of f and g, divides by gcd(f,g)
matrix singntl_LLL(matrix m, const ring s)
number singclap_det_bi(bigintmat *m, const coeffs cf)
poly singclap_pmult(poly f, poly g, const ring r)
poly singclap_gcd_r(poly f, poly g, const ring r)
int singclap_det_i(intvec *m, const ring)
ideal singclap_absFactorize(poly f, ideal &mipos, intvec **exps, int &numFactors, const ring r)
ideal singclap_sqrfree(poly f, intvec **v, int with_exps, const ring r)
char * singclap_neworder(ideal I, const ring r)
factory's class for variables
Coefficient rings, fields and other domains suitable for Singular polynomials.
static FORCE_INLINE number n_Copy(number n, const coeffs r)
return a copy of 'n'
static FORCE_INLINE number n_convFactoryNSingN(const CanonicalForm n, const coeffs r)
static FORCE_INLINE number n_Invers(number a, const coeffs r)
return the multiplicative inverse of 'a'; raise an error if 'a' is not invertible
static FORCE_INLINE BOOLEAN n_GreaterZero(number n, const coeffs r)
ordered fields: TRUE iff 'n' is positive; in Z/pZ: TRUE iff 0 < m <= roundedBelow(p/2),...
static FORCE_INLINE number n_Div(number a, number b, const coeffs r)
return the quotient of 'a' and 'b', i.e., a/b; raises an error if 'b' is not invertible in r exceptio...
static FORCE_INLINE CanonicalForm n_convSingNFactoryN(number n, BOOLEAN setChar, const coeffs r)
static FORCE_INLINE int n_Size(number n, const coeffs r)
return a non-negative measure for the complexity of n; return 0 only when n represents zero; (used fo...
static FORCE_INLINE void n_Delete(number *p, const coeffs r)
delete 'p'
static FORCE_INLINE number n_Init(long i, const coeffs r)
a number representing i in the given coeff field/ring r
static FORCE_INLINE BOOLEAN n_IsOne(number n, const coeffs r)
TRUE iff 'n' represents the one element.
static FORCE_INLINE BOOLEAN nCoeff_is_transExt(const coeffs r)
TRUE iff r represents a transcendental extension field.
BOOLEAN pa(leftv res, leftv args)
BOOLEAN pb(leftv res, leftv args)
CFAFList absFactorize(const CanonicalForm &G)
absolute factorization of a multivariate poly over Q
const CanonicalForm int s
const Variable & v
< [in] a sqrfree bivariate poly
Variable FACTORY_PUBLIC rootOf(const CanonicalForm &, char name='@')
returns a symbolic root of polynomial with name name Use it to define algebraic variables
void FACTORY_PUBLIC prune(Variable &alpha)
void WerrorS(const char *s)
STATIC_VAR int nfMinPoly[16]
This file is work in progress and currently not part of the official Singular.
BOOLEAN idIs0(ideal h)
returns true if h is the zero ideal
intvec * ivCopy(const intvec *o)
#define IMATELEM(M, I, J)
matrix mpNew(int r, int c)
create a r x c zero-matrix
void iiWriteMatrix(matrix im, const char *n, int dim, const ring r, int spaces)
set spaces to zero by default
#define MATELEM(mat, i, j)
1-based access to matrix
static number & pGetCoeff(poly p)
return an alias to the leading coefficient of p assumes that p != NULL NOTE: not copy
The main handler for Singular numbers which are suitable for Singular polynomials.
CanonicalForm ndConvSingNFactoryN(number, BOOLEAN, const coeffs)
int p_IsPurePower(const poly p, const ring r)
return i, if head depends only on var(i)
void p_Cleardenom_n(poly ph, const ring r, number &c)
poly p_GcdMon(poly f, poly g, const ring r)
polynomial gcd for f=mon
void p_Content(poly ph, const ring r)
void p_Norm(poly p1, const ring r)
poly p_Div_mm(poly p, const poly m, const ring r)
divide polynomial by monomial
poly p_Cleardenom(poly p, const ring r)
poly p_Sub(poly p1, poly p2, const ring r)
poly p_NSet(number n, const ring r)
returns the poly representing the number n, destroys n
static poly p_Neg(poly p, const ring r)
static poly p_Add_q(poly p, poly q, const ring r)
static poly p_Mult_q(poly p, poly q, const ring r)
void p_Write(poly p, ring lmRing, ring tailRing)
static unsigned long p_SetExp(poly p, const unsigned long e, const unsigned long iBitmask, const int VarOffset)
set a single variable exponent @Note: VarOffset encodes the position in p->exp
static void p_Setm(poly p, const ring r)
static number p_SetCoeff(poly p, number n, ring r)
static long p_GetExp(const poly p, const unsigned long iBitmask, const int VarOffset)
get a single variable exponent @Note: the integer VarOffset encodes:
static BOOLEAN p_IsConstant(const poly p, const ring r)
static void p_Delete(poly *p, const ring r)
static unsigned pLength(poly a)
void p_Write0(poly p, ring lmRing, ring tailRing)
static poly pp_Mult_qq(poly p, poly q, const ring r)
static poly p_Copy(poly p, const ring r)
returns a copy of p
static long p_Totaldegree(poly p, const ring r)
#define __p_Mult_nn(p, n, r)
void p_wrp(poly p, ring lmRing, ring tailRing)
VAR ring currRing
Widely used global variable which specifies the current polynomial ring for Singular interpreter and ...
static long pTotaldegree(poly p)
std::pair< int, int > mark
void StringSetS(const char *st)
void StringAppendS(const char *st)
const char feNotImplemented[]
void PrintS(const char *s)
void Werror(const char *fmt,...)
static BOOLEAN rField_is_Zp_a(const ring r)
static BOOLEAN rField_is_Z(const ring r)
static BOOLEAN rField_is_Zp(const ring r)
static BOOLEAN rField_is_Zn(const ring r)
static int rPar(const ring r)
(r->cf->P)
static int rInternalChar(const ring r)
static BOOLEAN rField_is_Q_a(const ring r)
static BOOLEAN rField_is_Q(const ring r)
static BOOLEAN rField_is_GF(const ring r)
static short rVar(const ring r)
#define rVar(r) (r->N)
int status int void size_t count
ideal idInit(int idsize, int rank)
initialise an ideal / module
void id_Delete(ideal *h, ring r)
deletes an ideal/module/matrix
void idShow(const ideal id, const ring lmRing, const ring tailRing, const int debugPrint)
void idSkipZeroes(ideal ide)
gives an ideal/module the minimal possible size