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41 int M = 0,
i,
k =
f.level();
63 if (!
f.inBaseDomain() )
100 int M = 0,
i,
k =
f.level();
102 for (
i = 1;
i <=
k;
i++ )
130 result.append (
i.getItem().factor());
192 bool extension= (
v.
level() != 1);
203 if (
A.isUnivariate())
211 if (
result.getFirst().inCoeffDomain())
226 A=
A/(contentAx*contentAy);
227 CFFList contentAxFactors, contentAyFactors;
234 if (contentAxFactors.
getFirst().factor().inCoeffDomain())
240 if (contentAyFactors.
getFirst().factor().inCoeffDomain())
248 contentAxFactors=
factorize (contentAx,
true);
249 if (contentAxFactors.
getFirst().factor().inCoeffDomain())
254 contentAyFactors=
factorize (contentAy,
true);
255 if (contentAyFactors.
getFirst().factor().inCoeffDomain())
268 conv (contentAyFactors),
false,
false,
N);
276 if (
A.inCoeffDomain())
283 else if (
A.isUnivariate())
301 conv (contentAyFactors),
false,
false,
N);
314 CFList uniFactors, list, bufUniFactors;
319 CFList bufUniFactors2, list2, uniFactors2;
331 int evaluation, evaluation2, bufEvaluation= 0, bufEvaluation2= 0;
332 for (
int i= 0;
i < factorNums;
i++)
343 "time for eval point over Q in y: ");
352 "time for univariate factorization over Q: ");
353 DEBOUTLN (cerr,
"prod (bufUniFactors)== bufAeval " <<
354 (
prod (bufUniFactors) == bufAeval));
359 if (bufUniFactors.
length() == 1)
364 conv (contentAyFactors),
swap, swap2,
N);
377 "time for univariate factorization in y over Q: ");
378 DEBOUTLN (cerr,
"prod (bufuniFactors2)== bufAeval2 " <<
379 (
prod (bufUniFactors2) == bufAeval2));
383 if (bufUniFactors2.
length() == 1)
388 conv (contentAyFactors),
swap, swap2,
N);
401 if (subCheck > 1 && (subCheck1%subCheck == 0))
404 subst (bufA, bufA, subCheck,
x);
408 conv (contentAyFactors),
swap, swap2,
N);
419 if (subCheck > 1 && (subCheck2%subCheck == 0))
422 subst (bufA, bufA, subCheck,
y);
426 conv (contentAyFactors),
swap, swap2,
N);
442 uniFactors= bufUniFactors;
445 evaluation2= bufEvaluation2;
446 uniFactors2= bufUniFactors2;
455 uniFactors2= bufUniFactors2;
457 evaluation2= bufEvaluation2;
461 uniFactors= bufUniFactors;
466 if (bufEvaluation > 0)
469 bufEvaluation= -bufEvaluation + 1;
470 if (bufEvaluation > 0)
473 bufEvaluation2= -bufEvaluation2 + 1;
481 uniFactors= uniFactors2;
492 conv (contentAyFactors),
swap, swap2,
N);
504 bool mipoHasDen=
false;
514 printf (
"out of primes\n");
519 if (bb.
getk() >
b.getk() )
b=bb;
521 if (bb.
getk() >
b.getk() )
b=bb;
531 ZZ NTLD= discriminant (NTLmipo);
554 if (bb.
getk() >
b.getk() )
b=bb;
556 if (bb.
getk() >
b.getk() )
b=bb;
562 bool earlySuccess=
false;
566 (
A, earlySuccess, earlyFactors, degs, liftBound,
569 "time for bivariate hensel lifting over Q: ");
570 DEBOUTLN (cerr,
"lifted factors= " << uniFactors);
593 "time for bivariate factor recombination over Q: ");
598 factors=
Union (earlyFactors, factors);
599 else if (!earlySuccess && degs.
getLength() == 1)
600 factors= earlyFactors;
603 conv (contentAyFactors),
swap, swap2,
N);
TIMING_DEFINE_PRINT(fac_uni_factorizer) TIMING_DEFINE_PRINT(fac_bi_hensel_lift) TIMING_DEFINE_PRINT(fac_bi_factor_recombination) TIMING_DEFINE_PRINT(fac_bi_evaluation) TIMING_DEFINE_PRINT(fac_bi_shift_to_zero) modpk coeffBound(const CanonicalForm &f
CanonicalForm convertZZ2CF(const ZZ &a)
NAME: convertZZ2CF.
static const int SW_RATIONAL
set to 1 for computations over Q
class to iterate through CanonicalForm's
#define DEBOUTLN(stream, objects)
const CanonicalForm int const CFList const Variable & y
const CanonicalForm CFMap CFMap & N
bool testPoint(const CanonicalForm &F, CanonicalForm &G, int i)
int cf_getBigPrime(int i)
CanonicalForm reverseSubst(const CanonicalForm &F, const int d, const Variable &x)
reverse a substitution x^d->x
CanonicalForm maxNorm(const CanonicalForm &f)
CanonicalForm maxNorm ( const CanonicalForm & f )
const CanonicalForm int const CFList & evaluation
CanonicalForm getMipo(const Variable &alpha, const Variable &x)
Rational abs(const Rational &a)
int status int void * buf
void appendSwapDecompress(CFList &factors1, const CFList &factors2, const CFList &factors3, const bool swap1, const bool swap2, const CFMap &N)
first swap Variables in factors1 if necessary, then append factors2 and factors3 on factors1 and fina...
TIMING_START(fac_alg_resultant)
CFList *& Aeval
<[in] poly
CFList conv(const CFFList &L)
convert a CFFList to a CFList by dropping the multiplicity
CFList factorRecombination(CFList &factors, CanonicalForm &F, const CanonicalForm &N, DegreePattern °s, const CanonicalForm &eval, int s, int thres, const modpk &b, const CanonicalForm &den)
naive factor recombination as decribed in "Factoring multivariate polynomials over a finite field" by...
void intersect(const DegreePattern °Pat)
intersect two degree patterns
CanonicalForm compress(const CanonicalForm &f, CFMap &m)
CanonicalForm compress ( const CanonicalForm & f, CFMap & m )
void prune(Variable &alpha)
CFFList append(const CFFList &Inputlist, const CFFactor &TheFactor)
CFFList factorize(const CanonicalForm &f, bool issqrfree=false)
factorization over or
ZZX convertFacCF2NTLZZX(const CanonicalForm &f)
CanonicalForm decompress(const CanonicalForm &F, const mpz_t *inverseM, const mpz_t *A)
decompress a bivariate poly
int substituteCheck(const CanonicalForm &F, const Variable &x)
check if a substitution x^n->x is possible
class to do operations mod p^k for int's p and k
int getLength() const
getter
CanonicalForm bCommonDen(const CanonicalForm &f)
CanonicalForm bCommonDen ( const CanonicalForm & f )
TIMING_END_AND_PRINT(fac_alg_resultant, "time to compute resultant0: ")
static poly normalize(poly next_p, ideal add_generators, syStrategy syzstr, int *g_l, int *p_l, int crit_comp)
factory's class for variables
modpk coeffBound(const CanonicalForm &f, int p, const CanonicalForm &mipo)
compute p^k larger than the bound on the coefficients of a factor of f over Q (mipo)
CanonicalForm resultant(const CanonicalForm &f, const CanonicalForm &g, const Variable &x)
CanonicalForm resultant ( const CanonicalForm & f, const CanonicalForm & g, const Variable & x )
template List< Variable > Union(const List< Variable > &, const List< Variable > &)
const Variable & v
< [in] a sqrfree bivariate poly
void findGoodPrime(const CanonicalForm &f, int &start)
find a big prime p from our tables such that no term of f vanishes mod p
CFList henselLiftAndEarly(CanonicalForm &A, bool &earlySuccess, CFList &earlyFactors, DegreePattern °s, int &liftBound, const CFList &uniFactors, const ExtensionInfo &info, const CanonicalForm &eval, modpk &b, CanonicalForm &den)
hensel Lifting and early factor detection
CFList biFactorize(const CanonicalForm &F, const Variable &v)
CanonicalForm subst(const CanonicalForm &f, const CFList &a, const CFList &b, const CanonicalForm &Rstar, bool isFunctionField)
CanonicalForm evalPoint(const CanonicalForm &F, int &i)
bool irreducibilityTest(const CanonicalForm &F)
computes the Newton polygon of F and checks if it satisfies the irreducibility criterion from S....