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#include <misc/auxiliary.h>
#include <omalloc/omalloc.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... | |
void | naClearContent (ICoeffsEnumerator &numberCollectionEnumerator, number &c, const coeffs cf) |
void | naClearDenominators (ICoeffsEnumerator &numberCollectionEnumerator, number &c, const coeffs cf) |
void | naKillChar (coeffs cf) |
char * | naCoeffString (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 * | n2pCoeffString (const coeffs r) |
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 743 of file algext.cc.
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static |
Definition at line 1568 of file algext.cc.
Definition at line 1588 of file algext.cc.
Definition at line 1543 of file algext.cc.
first check whether cf->extRing != NULL and delete old ring???
Definition at line 1639 of file algext.cc.
Definition at line 1623 of file algext.cc.
Definition at line 1534 of file algext.cc.
Definition at line 1552 of file algext.cc.
number naChineseRemainder | ( | number * | x, |
number * | q, | ||
int | rl, | ||
BOOLEAN | , | ||
CFArray & | inv_cache, | ||
const coeffs | cf | ||
) |
Definition at line 1363 of file algext.cc.
void naClearContent | ( | ICoeffsEnumerator & | numberCollectionEnumerator, |
number & | c, | ||
const coeffs | cf | ||
) |
Definition at line 1117 of file algext.cc.
void naClearDenominators | ( | ICoeffsEnumerator & | numberCollectionEnumerator, |
number & | c, | ||
const coeffs | cf | ||
) |
Definition at line 1318 of file algext.cc.
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static |
Definition at line 687 of file algext.cc.
Definition at line 1340 of file algext.cc.
Definition at line 394 of file algext.cc.
number naConvFactoryNSingN | ( | const CanonicalForm | n, |
const coeffs | cf | ||
) |
Definition at line 763 of file algext.cc.
CanonicalForm naConvSingNFactoryN | ( | number | n, |
BOOLEAN | , | ||
const coeffs | cf | ||
) |
Definition at line 903 of file algext.cc.
Definition at line 240 of file algext.cc.
Definition at line 783 of file algext.cc.
Definition at line 985 of file algext.cc.
Definition at line 1000 of file algext.cc.
Definition at line 365 of file algext.cc.
forward declarations
Definition at line 385 of file algext.cc.
Definition at line 346 of file algext.cc.
Initialize the coeffs object.
first check whether cf->extRing != NULL and delete old ring???
Definition at line 1383 of file algext.cc.
Definition at line 352 of file algext.cc.
Definition at line 831 of file algext.cc.
Definition at line 330 of file algext.cc.
Definition at line 322 of file algext.cc.
if m == var(i)/1 => return i,
Definition at line 1106 of file algext.cc.
Definition at line 652 of file algext.cc.
Definition at line 861 of file algext.cc.
Definition at line 951 of file algext.cc.
Definition at line 883 of file algext.cc.
Definition at line 964 of file algext.cc.
Definition at line 974 of file algext.cc.
Definition at line 871 of file algext.cc.
return the specified parameter as a number in the given alg. field
Definition at line 1091 of file algext.cc.
Definition at line 638 of file algext.cc.
Definition at line 501 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 1030 of file algext.cc.
Definition at line 721 of file algext.cc.
Definition at line 578 of file algext.cc.
Definition at line 596 of file algext.cc.
Definition at line 265 of file algext.cc.
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 223 of file algext.cc.
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inlinestatic |
Definition at line 190 of file algext.cc.
Definition at line 172 of file algext.cc.
see p_Gcd; additional assumption: deg(p) >= deg(q); must destroy p and q (unless one of them is returned)
Definition at line 152 of file algext.cc.
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 127 of file algext.cc.