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#include "misc/auxiliary.h"
#include "reporter/reporter.h"
#include "coeffs/coeffs.h"
#include "coeffs/numbers.h"
#include "coeffs/longrat.h"
#include "polys/monomials/ring.h"
#include "polys/monomials/p_polys.h"
#include "polys/simpleideals.h"
#include "polys/PolyEnumerator.h"
#include "factory/factory.h"
#include "polys/clapconv.h"
#include "polys/clapsing.h"
#include "polys/prCopy.h"
#include "polys/ext_fields/algext.h"
#include "polys/ext_fields/transext.h"
Go to the source code of this file.
Macros | |
#define | TRANSEXT_PRIVATES 1 |
ABSTRACT: numbers in an algebraic extension field K[a] / < f(a) > Assuming that we have a coeffs object cf, then these numbers are polynomials in the polynomial ring K[a] represented by cf->extRing. More... | |
#define | naTest(a) naDBTest(a,__FILE__,__LINE__,cf) |
#define | naRing cf->extRing |
#define | naCoeffs cf->extRing->cf |
#define | naMinpoly naRing->qideal->m[0] |
#define | n2pTest(a) n2pDBTest(a,__FILE__,__LINE__,cf) |
ABSTRACT: numbers as polys in the ring K[a] Assuming that we have a coeffs object cf, then these numbers are polynomials in the polynomial ring K[a] represented by cf->extRing. More... | |
#define | n2pRing cf->extRing |
#define | n2pCoeffs cf->extRing->cf |
Functions | |
BOOLEAN | naDBTest (number a, const char *f, const int l, const coeffs r) |
BOOLEAN | naGreaterZero (number a, const coeffs cf) |
forward declarations More... | |
BOOLEAN | naGreater (number a, number b, const coeffs cf) |
BOOLEAN | naEqual (number a, number b, const coeffs cf) |
BOOLEAN | naIsOne (number a, const coeffs cf) |
BOOLEAN | naIsMOne (number a, const coeffs cf) |
number | naInit (long i, const coeffs cf) |
number | naNeg (number a, const coeffs cf) |
this is in-place, modifies a More... | |
number | naInvers (number a, const coeffs cf) |
number | naAdd (number a, number b, const coeffs cf) |
number | naSub (number a, number b, const coeffs cf) |
number | naMult (number a, number b, const coeffs cf) |
number | naDiv (number a, number b, const coeffs cf) |
void | naPower (number a, int exp, number *b, const coeffs cf) |
number | naCopy (number a, const coeffs cf) |
void | naWriteLong (number a, const coeffs cf) |
void | naWriteShort (number a, const coeffs cf) |
number | naGetDenom (number &a, const coeffs cf) |
number | naGetNumerator (number &a, const coeffs cf) |
number | naGcd (number a, number b, const coeffs cf) |
void | naDelete (number *a, const coeffs cf) |
void | naCoeffWrite (const coeffs cf, BOOLEAN details) |
const char * | naRead (const char *s, number *a, const coeffs cf) |
static BOOLEAN | naCoeffIsEqual (const coeffs cf, n_coeffType n, void *param) |
static void | p_Monic (poly p, const ring r) |
returns NULL if p == NULL, otherwise makes p monic by dividing by its leading coefficient (only done if this is not already 1); this assumes that we are over a ground field so that division is well-defined; modifies p More... | |
static poly | p_GcdHelper (poly &p, poly &q, const ring r) |
see p_Gcd; additional assumption: deg(p) >= deg(q); must destroy p and q (unless one of them is returned) More... | |
static poly | p_Gcd (const poly p, const poly q, const ring r) |
static poly | p_ExtGcdHelper (poly &p, poly &pFactor, poly &q, poly &qFactor, ring r) |
poly | p_ExtGcd (poly p, poly &pFactor, poly q, poly &qFactor, ring r) |
assumes that p and q are univariate polynomials in r, mentioning the same variable; assumes a global monomial ordering in r; assumes that not both p and q are NULL; returns the gcd of p and q; moreover, afterwards pFactor and qFactor contain appropriate factors such that gcd(p, q) = p * pFactor + q * qFactor; leaves p and q unmodified More... | |
void | heuristicReduce (poly &p, poly reducer, const coeffs cf) |
void | definiteReduce (poly &p, poly reducer, const coeffs cf) |
static coeffs | nCoeff_bottom (const coeffs r, int &height) |
BOOLEAN | naIsZero (number a, const coeffs cf) |
long | naInt (number &a, const coeffs cf) |
number | napNormalizeHelper (number b, const coeffs cf) |
number | naLcmContent (number a, number b, const coeffs cf) |
int | naSize (number a, const coeffs cf) |
void | naNormalize (number &a, const coeffs cf) |
number | naConvFactoryNSingN (const CanonicalForm n, const coeffs cf) |
CanonicalForm | naConvSingNFactoryN (number n, BOOLEAN, const coeffs cf) |
number | naMap00 (number a, const coeffs src, const coeffs dst) |
number | naMapZ0 (number a, const coeffs src, const coeffs dst) |
number | naMapP0 (number a, const coeffs src, const coeffs dst) |
number | naCopyTrans2AlgExt (number a, const coeffs src, const coeffs dst) |
number | naMap0P (number a, const coeffs src, const coeffs dst) |
number | naMapPP (number a, const coeffs src, const coeffs dst) |
number | naMapUP (number a, const coeffs src, const coeffs dst) |
number | naGenMap (number a, const coeffs cf, const coeffs dst) |
number | naGenTrans2AlgExt (number a, const coeffs cf, const coeffs dst) |
nMapFunc | naSetMap (const coeffs src, const coeffs dst) |
Get a mapping function from src into the domain of this type (n_algExt) More... | |
int | naParDeg (number a, const coeffs cf) |
number | naParameter (const int iParameter, const coeffs cf) |
return the specified parameter as a number in the given alg. field More... | |
int | naIsParam (number m, const coeffs cf) |
if m == var(i)/1 => return i, More... | |
static void | naClearContent (ICoeffsEnumerator &numberCollectionEnumerator, number &c, const coeffs cf) |
void | naClearDenominators (ICoeffsEnumerator &numberCollectionEnumerator, number &c, const coeffs cf) |
void | naKillChar (coeffs cf) |
char * | naCoeffName (const coeffs r) |
number | naChineseRemainder (number *x, number *q, int rl, BOOLEAN, CFArray &inv_cache, const coeffs cf) |
number | naFarey (number p, number n, const coeffs cf) |
BOOLEAN | naInitChar (coeffs cf, void *infoStruct) |
Initialize the coeffs object. More... | |
BOOLEAN | n2pDBTest (number a, const char *f, const int l, const coeffs r) |
void | n2pNormalize (number &a, const coeffs cf) |
number | n2pMult (number a, number b, const coeffs cf) |
number | n2pDiv (number a, number b, const coeffs cf) |
void | n2pPower (number a, int exp, number *b, const coeffs cf) |
const char * | n2pRead (const char *s, number *a, const coeffs cf) |
static BOOLEAN | n2pCoeffIsEqual (const coeffs cf, n_coeffType n, void *param) |
char * | n2pCoeffName (const coeffs cf) |
void | n2pCoeffWrite (const coeffs cf, BOOLEAN details) |
number | n2pInvers (number a, const coeffs cf) |
BOOLEAN | n2pInitChar (coeffs cf, void *infoStruct) |
ABSTRACT: numbers as polys in the ring K[a] Assuming that we have a coeffs object cf, then these numbers are polynomials in the polynomial ring K[a] represented by cf->extRing.
IMPORTANT ASSUMPTIONS: 1.) So far we assume that cf->extRing is a valid polynomial ring
#define TRANSEXT_PRIVATES 1 |
ABSTRACT: numbers in an algebraic extension field K[a] / < f(a) > Assuming that we have a coeffs object cf, then these numbers are polynomials in the polynomial ring K[a] represented by cf->extRing.
IMPORTANT ASSUMPTIONS: 1.) So far we assume that cf->extRing is a valid polynomial ring in exactly one variable, i.e., K[a], where K is allowed to be any field (representable in SINGULAR and which may itself be some extension field, thus allowing for extension towers). 2.) Moreover, this implementation assumes that cf->extRing->qideal is not NULL but an ideal with at least one non-zero generator which may be accessed by cf->extRing->qideal->m[0] and which represents the minimal polynomial f(a) of the extension variable 'a' in K[a]. 3.) As soon as an std method for polynomial rings becomes availabe, all reduction steps modulo f(a) should be replaced by a call to std. Moreover, in this situation one can finally move from K[a] / < f(a) > to K[a_1, ..., a_s] / I, with I some zero-dimensional ideal in K[a_1, ..., a_s] given by a lex Gröbner basis. The code in algext.h and algext.cc is then capable of computing in K[a_1, ..., a_s] / I.
Definition at line 730 of file algext.cc.
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static |
Definition at line 1552 of file algext.cc.
Definition at line 1572 of file algext.cc.
Definition at line 1527 of file algext.cc.
first check whether cf->extRing != NULL and delete old ring???
Definition at line 1627 of file algext.cc.
Definition at line 1611 of file algext.cc.
number naChineseRemainder | ( | number * | x, |
number * | q, | ||
int | rl, | ||
BOOLEAN | , | ||
CFArray & | inv_cache, | ||
const coeffs | cf | ||
) |
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static |
Definition at line 1102 of file algext.cc.
void naClearDenominators | ( | ICoeffsEnumerator & | numberCollectionEnumerator, |
number & | c, | ||
const coeffs | cf | ||
) |
Definition at line 1307 of file algext.cc.
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static |
Definition at line 1330 of file algext.cc.
Definition at line 387 of file algext.cc.
number naConvFactoryNSingN | ( | const CanonicalForm | n, |
const coeffs | cf | ||
) |
Definition at line 750 of file algext.cc.
CanonicalForm naConvSingNFactoryN | ( | number | n, |
BOOLEAN | , | ||
const coeffs | cf | ||
) |
Definition at line 890 of file algext.cc.
Definition at line 770 of file algext.cc.
Definition at line 358 of file algext.cc.
Initialize the coeffs object.
first check whether cf->extRing != NULL and delete old ring???
Definition at line 1373 of file algext.cc.
Definition at line 345 of file algext.cc.
Definition at line 818 of file algext.cc.
Definition at line 323 of file algext.cc.
Definition at line 643 of file algext.cc.
Definition at line 848 of file algext.cc.
return the specified parameter as a number in the given alg. field
Definition at line 1076 of file algext.cc.
Definition at line 629 of file algext.cc.
Definition at line 493 of file algext.cc.
Get a mapping function from src into the domain of this type (n_algExt)
Q or Z --> Q(a)
Z --> Q(a)
Z/p --> Q(a)
Q --> Z/p(a)
Z --> Z/p(a)
Z/p --> Z/p(a)
Z/u --> Z/p(a)
default
Definition at line 1017 of file algext.cc.
Definition at line 570 of file algext.cc.
Definition at line 588 of file algext.cc.
Definition at line 258 of file algext.cc.
poly p_ExtGcd | ( | poly | p, |
poly & | pFactor, | ||
poly | q, | ||
poly & | qFactor, | ||
ring | r | ||
) |
assumes that p and q are univariate polynomials in r, mentioning the same variable; assumes a global monomial ordering in r; assumes that not both p and q are NULL; returns the gcd of p and q; moreover, afterwards pFactor and qFactor contain appropriate factors such that gcd(p, q) = p * pFactor + q * qFactor; leaves p and q unmodified
Definition at line 216 of file algext.cc.
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inlinestatic |
Definition at line 183 of file algext.cc.
Definition at line 165 of file algext.cc.
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inlinestatic |
see p_Gcd; additional assumption: deg(p) >= deg(q); must destroy p and q (unless one of them is returned)
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inlinestatic |
returns NULL if p == NULL, otherwise makes p monic by dividing by its leading coefficient (only done if this is not already 1); this assumes that we are over a ground field so that division is well-defined; modifies p
assumes that p and q are univariate polynomials in r, mentioning the same variable; assumes a global monomial ordering in r; assumes that not both p and q are NULL; returns the gcd of p and q; leaves p and q unmodified
Definition at line 120 of file algext.cc.