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CanonicalForm | QGCD (const CanonicalForm &, const CanonicalForm &) |
| gcd over Q(a) More...
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void | tryInvert (const CanonicalForm &, const CanonicalForm &, CanonicalForm &, bool &) |
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void | tryBrownGCD (const CanonicalForm &F, const CanonicalForm &G, const CanonicalForm &M, CanonicalForm &result, bool &fail, bool topLevel=true) |
| modular gcd over F_p[x]/(M) for not necessarily irreducible M. If a zero divisor is encountered fail is set to true. More...
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int * | leadDeg (const CanonicalForm &f, int *degs) |
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bool | isLess (int *a, int *b, int lower, int upper) |
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bool | isEqual (int *a, int *b, int lower, int upper) |
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CanonicalForm | firstLC (const CanonicalForm &f) |
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GCD over Q(a)
ABSTRACT: Implementation of Encarnacion's GCD algorithm over number fields, see M.J. Encarnacion "Computing GCDs of polynomials over number fields", extended to the multivariate case.
- See also
- cfNTLzzpEXGCD.h
Definition in file cfGcdAlgExt.h.
◆ firstLC()
◆ isEqual()
bool isEqual |
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a, |
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int * |
b, |
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lower, |
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upper |
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◆ isLess()
bool isLess |
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int * |
a, |
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int * |
b, |
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lower, |
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◆ leadDeg()
◆ QGCD()
gcd over Q(a)
Definition at line 715 of file cfGcdAlgExt.cc.
728 if(F.inCoeffDomain())
779 int mv =
f.level();
i =
g.level();
783 bound =
new int[mv+1];
784 other =
new int[mv+1];
785 for(
int i=1;
i<=mv;
i++)
789 for(
int i=1;
i<=mv;
i++)
830 for(
int i=1;
i<=mv;
i++)
848 "time for rational reconstruction in alg gcd: ")
858 if (
equal && tmp.isUnivariate() &&
f.isUnivariate() &&
g.isUnivariate()
859 &&
f.level() == tmp.level() && tmp.level() ==
g.level())
872 "time for successful termination test in alg gcd: ")
888 "time for successful termination test in alg gcd: ")
894 "time
for unsuccessful termination
test in alg
gcd: ")
◆ tryBrownGCD()
modular gcd over F_p[x]/(M) for not necessarily irreducible M. If a zero divisor is encountered fail is set to true.
Definition at line 372 of file cfGcdAlgExt.cc.
461 zz_pE::init (NTLMipo);
502 tryEuclid(
cf,
cg,
M,c,fail);
507 f.tryDiv (
cf,
M, fail);
511 g.tryDiv (
cg,
M, fail);
515 if(
f.inCoeffDomain())
523 if(
g.inCoeffDomain())
531 int *L =
new int[mv+1];
532 int *
N =
new int[mv+1];
533 for(
int i=2;
i<=mv;
i++)
556 int *dg_im = new
int[mv+1];
574 "time for recursive calls in alg gcd mod p: ")
578 if(g_image.inCoeffDomain())
586 for(
int i=2;
i<=mv;
i++)
588 dg_im =
leadDeg(g_image, dg_im);
596 g_image *= gamma_image;
601 "time for Newton interpolation in alg gcd mod p: ")
608 if((
firstLC(gnew) == gamma) || (gnew == gm))
631 "time for successful termination test in alg gcd mod p: ")
◆ tryInvert()
static CanonicalForm tryvcontent(const CanonicalForm &f, const Variable &x, const CanonicalForm &M, bool &fail)
static const int SW_RATIONAL
set to 1 for computations over Q
const CanonicalForm CFMap CFMap & N
zz_pX convertFacCF2NTLzzpX(const CanonicalForm &f)
bool isZero(const CFArray &A)
checks if entries of A are zero
CanonicalForm firstLC(const CanonicalForm &f)
bool isEqual(int *a, int *b, int lower, int upper)
bool tryFdivides(const CanonicalForm &f, const CanonicalForm &g, const CanonicalForm &M, bool &fail)
same as fdivides but handles zero divisors in Z_p[t]/(f)[x1,...,xn] for reducible f
static CanonicalForm tryNewtonInterp(const CanonicalForm &alpha, const CanonicalForm &u, const CanonicalForm &newtonPoly, const CanonicalForm &oldInterPoly, const Variable &x, const CanonicalForm &M, bool &fail)
int cf_getBigPrime(int i)
CanonicalForm extgcd(const CanonicalForm &f, const CanonicalForm &g, CanonicalForm &a, CanonicalForm &b)
CanonicalForm extgcd ( const CanonicalForm & f, const CanonicalForm & g, CanonicalForm & a,...
int * leadDeg(const CanonicalForm &f, int *degs)
CanonicalForm getMipo(const Variable &alpha, const Variable &x)
zz_pEX convertFacCF2NTLzz_pEX(const CanonicalForm &f, const zz_pX &mipo)
TIMING_START(fac_alg_resultant)
generate all elements in F_p starting from 0
for(int i=0;i<=n;i++) degsf[i]
CanonicalForm convertNTLzz_pEX2CF(const zz_pEX &f, const Variable &x, const Variable &alpha)
void chineseRemainder(const CanonicalForm &x1, const CanonicalForm &q1, const CanonicalForm &x2, const CanonicalForm &q2, CanonicalForm &xnew, CanonicalForm &qnew)
void chineseRemainder ( const CanonicalForm & x1, const CanonicalForm & q1, const CanonicalForm & x2,...
static CanonicalForm myicontent(const CanonicalForm &f, const CanonicalForm &c)
bool fdivides(const CanonicalForm &f, const CanonicalForm &g)
bool fdivides ( const CanonicalForm & f, const CanonicalForm & g )
void newtonDivrem(const CanonicalForm &F, const CanonicalForm &G, CanonicalForm &Q, CanonicalForm &R)
division with remainder of univariate polynomials over Q and Q(a) using Newton inversion,...
CanonicalForm bCommonDen(const CanonicalForm &f)
CanonicalForm bCommonDen ( const CanonicalForm & f )
void setReduce(const Variable &alpha, bool reduce)
TIMING_END_AND_PRINT(fac_alg_resultant, "time to compute resultant0: ")
factory's class for variables
static CanonicalForm bound(const CFMatrix &M)
const CanonicalForm CFMap CFMap bool topLevel
const CanonicalForm CFMap & M
const Variable & v
< [in] a sqrfree bivariate poly
void tryInvert(const CanonicalForm &F, const CanonicalForm &M, CanonicalForm &inv, bool &fail)
static number Farey(number p, number n, const coeffs)
static const int SW_USE_QGCD
set to 1 to use Encarnacion GCD over Q(a)
void tryNTLGCD(zz_pEX &x, const zz_pEX &a, const zz_pEX &b, bool &fail)
compute the GCD x of a and b, fail is set to true if a zero divisor is encountered
int myCompress(const CanonicalForm &F, const CanonicalForm &G, CFMap &M, CFMap &N, bool topLevel)
compressing two polynomials F and G, M is used for compressing, N to reverse the compression
CanonicalForm alg_content(const CanonicalForm &f, const CFList &as)
bool isLess(int *a, int *b, int lower, int upper)