61 if (i.
exp() > exp_f[e]) exp_f[e]=i.
exp();
73 int *exp_f=
new int[mv+1];
75 for(i=mv;i>0;i--) exp_f[i]=0;
79 if ((exp_f[i]>0) && (exp_f[i]<exp_f[mv]))
93 if (f.
isZero()) printf(
"+0");
101 if (
i.coeff().isOne())
104 if (e==0) printf(
"1");
108 if (e!=1) printf(
"^%d",e);
117 if (e!=1) printf(
"^%d",e);
142 printf(
"+%ld",f.
intval());
151 char * str =
new char[mpz_sizeinbase( m, 10 ) + 2];
152 str = mpz_get_str( str, 10, m );
161 char * str =
new char[mpz_sizeinbase( m, 10 ) + 2];
162 str = mpz_get_str( str, 10, m );
167 str =
new char[mpz_sizeinbase( m, 10 ) + 2];
168 str = mpz_get_str( str, 10, m );
192 for ( ; J.
hasItem(); J++, j++ )
195 printf(
"%d\n", J.
getItem().exp());
204 if (!(L.
getFirst().factor().inCoeffDomain()))
205 printf(
"first entry is not const\n");
206 for ( ; J.
hasItem(); J++, j++ )
210 printf(
"other entry is const\n");
212 while(j>0) { t*=tt; j--; }
214 if (!(f-t).
isZero()) { printf(
"problem:\n");
out_cf(
"factor:",f,
" has problems\n");}
222 if (f.
level()<0)
return false;
231 if (f.
level()<=0)
return false;
234 if (!(
i.coeff().inBaseDomain()))
return false;
249 for (
int i=1;
i<=n;
i++ )
284 for ( j=dummy; j.
hasItem(); j++ )
310 result += elem *
power(x,maxdeg-deg);
321 for (i=Termlist; i.
hasItem(); i++)
330 for (i=Newlist; i.
hasItem(); i++)
350 result += elem *
power(x,maxdeg-deg);
361 for (i=Termlist; i.
hasItem(); i++)
370 for (i=Newlist; i.
hasItem(); i++)
381 if (f.
exp() > g.
exp())
return 1;
382 if (f.
exp() < g.
exp())
return 0;
397 ( const CanonicalForm & f, const Variable & alpha ) instead");
412 for ( j=Intermediatelist; j.
hasItem(); j++ )
419 for ( j=Homoglist; j.
hasItem(); j++ )
442 nmod_poly_factor_t
result;
443 nmod_poly_factor_init (result);
444 mp_limb_t leadingCoeff= nmod_poly_factor (result, f1);
446 nmod_poly_factor_clear (result);
463 zz_p leadcoeff = LeadCoeff(f1);
466 f1=f1 / LeadCoeff(f1);
468 vec_pair_zz_pX_long factors;
486 vec_pair_GF2X_long factors;
495 factoryError (
"univariate factorization depends on NTL(missing)");
523 factoryError (
"multivariate factorization depends on NTL(missing)");
542 vec_pair_ZZX_long factors;
550 if ( F.
getFirst().factor().inCoeffDomain() )
561 if ( !F.
getFirst().factor().inCoeffDomain() )
568 factoryError (
"univariate factorization over Z depends on NTL(missing)");
587 factoryError (
"multivariate factorization depends on NTL(missing)");
596 if ( F.
getFirst().factor().inCoeffDomain() )
629 ASSERT (beta == alpha,
"f has an algebraic variable that \ 630 does not coincide with alpha");
639 #if (HAVE_FLINT && __FLINT_RELEASE >= 20400) 640 nmod_poly_t FLINTmipo, leadingCoeff;
648 fq_nmod_poly_t FLINTF;
650 fq_nmod_poly_factor_t
res;
651 fq_nmod_poly_factor_init (res, fq_con);
652 fq_nmod_poly_factor (res, leadingCoeff, FLINTF, fq_con);
656 fq_nmod_poly_factor_clear (res, fq_con);
676 zz_pE leadcoeff= LeadCoeff(f1);
682 vec_pair_zz_pEX_long factors;
710 GF2E f1_coef=LeadCoeff(f1);
714 vec_pair_GF2EX_long factors;
721 factoryError (
"univariate factorization depends on NTL(missing)");
731 factoryError (
"multivariate factorization depends on NTL(missing)");
746 factoryError (
"multivariate factorization depends on NTL(missing)");
768 result =
FqSqrf( f, alpha );
GF2EX convertFacCF2NTLGF2EX(const CanonicalForm &f, const GF2X &mipo)
CanonicalForm in Z_2(a)[X] to NTL GF2EX.
nmod_poly_init(FLINTmipo, getCharacteristic())
bool isPurePoly_m(const CanonicalForm &f)
CFFList convertNTLvec_pair_GF2EX_long2FacCFFList(const vec_pair_GF2EX_long &e, const GF2E &multi, const Variable &x, const Variable &alpha)
NAME: convertNTLvec_pair_GF2EX_long2FacCFFList.
Conversion to and from NTL.
CFFList convertNTLvec_pair_GF2X_long2FacCFFList(const vec_pair_GF2X_long &e, GF2, const Variable &x)
NAME: convertNTLvec_pair_GF2X_long2FacCFFList.
CFFList ratFactorize(const CanonicalForm &G, const Variable &v=Variable(1), bool substCheck=true)
factorize a multivariate polynomial over
This file defines functions for conversion to FLINT (www.flintlib.org) and back.
int find_mvar(const CanonicalForm &f)
CFFList FpSqrf(const CanonicalForm &F, bool sort=true)
squarefree factorization over . If input is not monic, the leading coefficient is dropped ...
CanonicalForm cd(bCommonDen(FF))
int cmpCF(const CFFactor &f, const CFFactor &g)
Univariate factorization over algebraic extension of Q using Trager's algorithm.
CFFList sqrFreeZ(const CanonicalForm &a)
factory's class for variables
CF_NO_INLINE CanonicalForm coeff() const
get the current coefficient
GF2X convertFacCF2NTLGF2X(const CanonicalForm &f)
NAME: convertFacCF2NTLGF2X.
void convertFacCF2Fq_nmod_poly_t(fq_nmod_poly_t result, const CanonicalForm &f, const fq_nmod_ctx_t ctx)
conversion of a factory univariate poly over F_q to a FLINT fq_nmod_poly_t
CFFList convertNTLvec_pair_zzpX_long2FacCFFList(const vec_pair_zz_pX_long &e, const zz_p multi, const Variable &x)
CFFList convertFLINTFq_nmod_poly_factor2FacCFFList(const fq_nmod_poly_factor_t fac, const Variable &x, const Variable &alpha, const fq_nmod_ctx_t fq_con)
conversion of a FLINT factorization over Fq (for word size p) to a CFFList
static const int SW_USE_NTL_SORT
set to 1 to sort factors in a factorization
nmod_poly_clear(FLINTmipo)
CFFList FqSqrf(const CanonicalForm &F, const Variable &alpha, bool sort=true)
squarefree factorization over . If input is not monic, the leading coefficient is dropped ...
CFList ratSqrfFactorize(const CanonicalForm &G, const Variable &v=Variable(1))
factorize a squarefree multivariate polynomial over
ZZX convertFacCF2NTLZZX(const CanonicalForm &f)
CFList FpSqrfFactorize(const CanonicalForm &F)
factorize a squarefree multivariate polynomial over
This file provides functions for factorizing a multivariate polynomial over , or GF...
CFList GFSqrfFactorize(const CanonicalForm &F)
factorize a squarefree multivariate polynomial over GF
CFList get_Terms(const CanonicalForm &f)
CanonicalForm getMipo(const Variable &alpha, const Variable &x)
CanonicalForm compress(const CanonicalForm &f, CFMap &m)
CanonicalForm compress ( const CanonicalForm & f, CFMap & m )
fq_nmod_ctx_clear(fq_con)
CFFList FpFactorize(const CanonicalForm &G, bool substCheck=true)
factorize a multivariate polynomial over
CFFList convertNTLvec_pair_zzpEX_long2FacCFFList(const vec_pair_zz_pEX_long &e, const zz_pE &multi, const Variable &x, const Variable &alpha)
This file provides functions for squarefrees factorizing over , or GF.
helper functions for conversion to and from Singular
CFFList AlgExtFactorize(const CanonicalForm &F, const Variable &alpha)
factorize a univariate polynomial over algebraic extension of Q
CFFList convertFLINTnmod_poly_factor2FacCFFList(const nmod_poly_factor_t fac, const mp_limb_t leadingCoeff, const Variable &x)
conversion of a FLINT factorization over Z/p (for word size p) to a CFFList
static int max(int a, int b)
Variable get_max_degree_Variable(const CanonicalForm &f)
get_max_degree_Variable returns Variable with highest degree.
convertFacCF2nmod_poly_t(FLINTmipo, M)
int status int void * buf
zz_pEX convertFacCF2NTLzz_pEX(const CanonicalForm &f, const zz_pX &mipo)
CanonicalForm homogenize(const CanonicalForm &f, const Variable &x)
homogenize homogenizes f with Variable x
CFFList FqFactorize(const CanonicalForm &G, const Variable &alpha, bool substCheck=true)
factorize a multivariate polynomial over
bool getReduce(const Variable &alpha)
void getTerms(const CanonicalForm &f, const CanonicalForm &t, CFList &result)
get_Terms: Split the polynomial in the containing terms.
static const int SW_RATIONAL
set to 1 for computations over Q
bool isPurePoly(const CanonicalForm &f)
Iterators for CanonicalForm's.
multivariate factorization over Q(a)
CFFList GFFactorize(const CanonicalForm &G, bool substCheck=true)
factorize a multivariate polynomial over GF
CFFList sqrFree(const CanonicalForm &f, bool sort)
squarefree factorization
declarations of higher level algorithms.
CFFList factorize(const CanonicalForm &f, bool issqrfree)
factorization over or
CanonicalForm bCommonDen(const CanonicalForm &f)
CanonicalForm bCommonDen ( const CanonicalForm & f )
void out_cf(const char *s1, const CanonicalForm &f, const char *s2)
cf_algorithm.cc - simple mathematical algorithms.
fq_nmod_poly_clear(prod, fq_con)
class to iterate through CanonicalForm's
void gmp_numerator(const CanonicalForm &f, mpz_ptr result)
void find_exp(const CanonicalForm &f, int *exp_f)
long imm2int(const InternalCF *const imm)
zz_pX convertFacCF2NTLzzpX(const CanonicalForm &f)
CF_NO_INLINE int hasTerms() const
check if iterator has reached the end of CanonicalForm
CFFList sortCFFList(CFFList &F)
#define GaloisFieldDomain
bool isZero(const CFArray &A)
checks if entries of A are zero
void sort(CFArray &A, int l=0)
quick sort A
#define ASSERT(expression, message)
void test_cff(CFFList &L, const CanonicalForm &f)
CF_NO_INLINE int exp() const
get the current exponent
CFFList convertNTLvec_pair_ZZX_long2FacCFFList(const vec_pair_ZZX_long &e, const ZZ &multi, const Variable &x)
NAME: convertNTLvec_pair_ZZX_long2FacCFFList.
squarefree part and factorization over Q, Q(a)
void(* factoryError)(const char *s)
void gmp_denominator(const CanonicalForm &f, mpz_ptr result)
void sort(int(*)(const T &, const T &))
Factory's internal integers.
fq_nmod_ctx_init_modulus(fq_con, FLINTmipo, "Z")