11 #ifdef HAVE_IOSTREAM_H 13 #elif defined(HAVE_IOSTREAM) 58 int n=
tmax (F.level(), G.level());
62 for (
int i = 0;
i <= n;
i++)
63 degsf[
i]= degsg[
i]= 0;
75 for (
int i= 1;
i <= n;
i++)
77 if (degsf[
i] != 0 && degsg[
i] != 0)
82 if (degsf[
i] == 0 && degsg[
i] != 0 &&
i <= G.level())
87 if (degsg[
i] == 0 && degsf[
i] &&
i <= F.level())
94 if (both_non_zero == 0)
104 for (
int i= 1;
i <= n;
i++)
106 if (degsf[
i] != 0 && degsg[
i] == 0 &&
i <= F.level())
108 if (k + both_non_zero !=
i)
115 if (degsf[
i] == 0 && degsg[
i] != 0 &&
i <= G.level())
117 if (l + g_zero + both_non_zero !=
i)
128 int m=
tmax (F.level(), G.level());
135 if (degsf [i] != 0 && degsg [i] != 0)
136 min_max_deg=
tmax (degsf[i], degsg[i]);
139 while (min_max_deg == 0)
142 min_max_deg=
tmax (degsf[i], degsg[i]);
143 if (degsf [i] != 0 && degsg [i] != 0)
144 min_max_deg=
tmax (degsf[i], degsg[i]);
148 for (
int j= i + 1;
j <=
m;
j++)
150 if (
tmax (degsf[
j],degsg[j]) <= min_max_deg && degsf[j] != 0 && degsg [j] != 0)
152 min_max_deg=
tmax (degsf[j], degsg[j]);
195 for (
int i= 1;
i <= n;
i++)
197 if (degsf[
i] == 0 && degsg[
i] == 0)
274 for (
int i= degA -degB;
i >= 0;
i--)
322 result=
reduce (result, M);
330 tryDivrem (P, result, Q, rem, inv, M, fail);
336 result=
reduce (result, M);
362 tryInvert (newtonPoly (alpha, x), M, inv, fail);
366 interPoly= oldInterPoly+
reduce ((u - oldInterPoly (alpha, x))*inv*newtonPoly, M);
394 result=
reduce (result, M);
413 result=
reduce (result, M);
459 zz_pE::init (NTLMipo);
475 tryEuclid(f,g,M,result,fail);
480 result= NN (
reduce (result, M));
500 tryEuclid(cf,cg,M,c,fail);
529 int *L =
new int[mv+1];
530 int *N =
new int[mv+1];
531 for(
int i=2;
i<=mv;
i++)
550 for(
int i=2;
i<=mv;
i++)
554 int *dg_im =
new int[mv+1];
555 for(
int i=2; i<=mv; i++)
566 gamma_image =
reduce(gamma(alpha, x),M);
570 tryBrownGCD(
f(alpha, x),
g(alpha, x), M, g_image, fail,
false );
572 "time for recursive calls in alg gcd mod p: ")
575 g_image =
reduce(g_image, M);
584 for(
int i=2; i<=mv; i++)
586 dg_im =
leadDeg(g_image, dg_im);
594 g_image *= gamma_image;
595 g_image=
reduce (g_image, M);
599 "time for Newton interpolation in alg gcd mod p: ")
606 if((
firstLC(gnew) == gamma) || (gnew == gm))
614 g_image.
tryDiv (cf, M, fail);
627 result = NN(
reduce (c*g_image, M));
629 "time for successful termination test in alg gcd mod p: ")
634 "time for unsuccessful termination test in alg gcd mod p: ")
640 if(
isLess(L, dg_im, 2, mv))
646 for(
int i=2; i<=mv; i++)
670 fmpz_poly_t FLINTf, FLINTc;
673 fmpz_poly_gcd (FLINTc, FLINTc, FLINTf);
679 fmpz_poly_clear (FLINTc);
680 fmpz_poly_clear (FLINTf);
685 NTLc= GCD (NTLc, NTLf);
764 tmp = gcdcfcg*
gcd( f, g );
781 bound =
new int[mv+1];
782 other =
new int[mv+1];
783 for(
int i=1; i<=mv; i++)
784 bound[i] = other[i] = 0;
787 for(
int i=1; i<=mv; i++)
788 if(other[i] < bound[i])
791 cl =
lc(M) *
lc(f) *
lc(g);
826 for(
int i=1; i<=mv; i++)
830 if(
isEqual(bound, other, 1, mv))
844 "time for rational reconstruction in alg gcd: ")
868 "time for successful termination test in alg gcd: ")
882 "time for successful termination test in alg gcd: ")
886 "time for unsuccessful termination test in alg gcd: ")
891 if(
isLess(bound, other, 1, mv) )
896 for(
int i=1; i<=mv; i++)
902 D = gcdcfcg*
gcd( f, g );
928 for(
int i=upper;
i>=lower;
i--)
939 for(
int i=lower;
i<=upper;
i++)
949 while(ret.
level() > 1)
984 P = F; result =
G; s=v=0; t=u=1;
988 P =
G; result = F; s=v=1; t=u=0;
994 tryDivrem (P, result, q, rem, inv, M, fail);
1004 result=
reduce (result, M);
1028 ASSERT( x.
level() > 0,
"cannot calculate content with respect to algebraic variable" );
1040 ASSERT( x.
level() > 0,
"cannot calculate vcontent with respect to algebraic variable" );
1041 if ( f.
mvar() <=
x )
TIMING_END_AND_PRINT(fac_alg_resultant, "time to compute resultant0: ")
static CanonicalForm myicontent(const CanonicalForm &f, const CanonicalForm &c)
const CanonicalForm int s
void convertFacCF2Fmpz_poly_t(fmpz_poly_t result, const CanonicalForm &f)
conversion of a factory univariate polynomial over Z to a fmpz_poly_t
const CanonicalForm int const CFList const Variable & y
Conversion to and from NTL.
void rem(unsigned long *a, unsigned long *q, unsigned long p, int °a, int degq)
static CanonicalForm bound(const CFMatrix &M)
This file defines functions for conversion to FLINT (www.flintlib.org) and back.
some useful template functions.
CanonicalForm extgcd(const CanonicalForm &f, const CanonicalForm &g, CanonicalForm &a, CanonicalForm &b)
CanonicalForm extgcd ( const CanonicalForm & f, const CanonicalForm & g, CanonicalForm & a...
template CanonicalForm tmax(const CanonicalForm &, const CanonicalForm &)
TIMING_START(fac_alg_resultant)
factory's class for variables
CF_NO_INLINE CanonicalForm coeff() const
get the current coefficient
const CanonicalForm CFMap & M
generate all elements in F_p starting from 0
static CanonicalForm trycf_content(const CanonicalForm &f, const CanonicalForm &g, const CanonicalForm &M, bool &fail)
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 ...
const CanonicalForm CFMap CFMap bool topLevel
ZZX convertFacCF2NTLZZX(const CanonicalForm &f)
void tryInvert(const CanonicalForm &F, const CanonicalForm &M, CanonicalForm &inv, bool &fail)
CanonicalForm getMipo(const Variable &alpha, const Variable &x)
Rational abs(const Rational &a)
CanonicalForm item() const
TIMING_DEFINE_PRINT(alg_content_p) TIMING_DEFINE_PRINT(alg_content) TIMING_DEFINE_PRINT(alg_compress) TIMING_DEFINE_PRINT(alg_termination) TIMING_DEFINE_PRINT(alg_termination_p) TIMING_DEFINE_PRINT(alg_reconstruction) TIMING_DEFINE_PRINT(alg_newton_p) TIMING_DEFINE_PRINT(alg_recursion_p) TIMING_DEFINE_PRINT(alg_gcd_p) TIMING_DEFINE_PRINT(alg_euclid_p) static int myCompress(const CanonicalForm &F
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)
univariate Gcd over finite fields and Z, extended GCD over finite fields and Q
generate integers, elements of finite fields
This file defines functions for fast multiplication and division with remainder.
const CanonicalForm CFMap CFMap & N
zz_pEX convertFacCF2NTLzz_pEX(const CanonicalForm &f, const zz_pX &mipo)
void setReduce(const Variable &alpha, bool reduce)
CanonicalForm firstLC(const CanonicalForm &f)
bool getReduce(const Variable &alpha)
static const int SW_RATIONAL
set to 1 for computations over Q
Iterators for CanonicalForm's.
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, satisfying F=G*Q+R, deg(R) < deg(G)
static CanonicalForm tryvcontent(const CanonicalForm &f, const Variable &x, const CanonicalForm &M, bool &fail)
declarations of higher level algorithms.
This file defines functions for univariate GCD and extended GCD over Z/p[t]/(f)[x] for reducible f...
CanonicalForm bCommonDen(const CanonicalForm &f)
CanonicalForm bCommonDen ( const CanonicalForm & f )
CanonicalForm convertNTLzz_pEX2CF(const zz_pEX &f, const Variable &x, const Variable &alpha)
bool isEqual(int *a, int *b, int lower, int upper)
class to iterate through CanonicalForm's
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...
bool fdivides(const CanonicalForm &f, const CanonicalForm &g)
bool fdivides ( const CanonicalForm & f, const CanonicalForm & g )
const Variable & v
< [in] a sqrfree bivariate poly
CanonicalForm convertFmpz_poly_t2FacCF(const fmpz_poly_t poly, const Variable &x)
conversion of a FLINT poly over Z to CanonicalForm
static CanonicalForm trycontent(const CanonicalForm &f, const Variable &x, const CanonicalForm &M, bool &fail)
static CanonicalForm tryNewtonInterp(const CanonicalForm &alpha, const CanonicalForm &u, const CanonicalForm &newtonPoly, const CanonicalForm &oldInterPoly, const Variable &x, const CanonicalForm &M, bool &fail)
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 ...
zz_pX convertFacCF2NTLzzpX(const CanonicalForm &f)
CF_NO_INLINE int hasTerms() const
check if iterator has reached the end of CanonicalForm
CanonicalForm QGCD(const CanonicalForm &F, const CanonicalForm &G)
gcd over Q(a)
static const int SW_USE_QGCD
set to 1 to use Encarnacion GCD over Q(a)
int cf_getBigPrime(int i)
static number Farey(number p, number n, const coeffs)
bool isZero(const CFArray &A)
checks if entries of A are zero
void tryBrownGCD(const CanonicalForm &F, const CanonicalForm &G, const CanonicalForm &M, CanonicalForm &result, bool &fail, bool topLevel)
modular gcd over F_p[x]/(M) for not necessarily irreducible M. If a zero divisor is encountered fail ...
#define ASSERT(expression, message)
int * leadDeg(const CanonicalForm &f, int *degs)
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 ...
CanonicalForm convertNTLZZX2CF(const ZZX &polynom, const Variable &x)