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algext.h
Go to the documentation of this file.
#ifndef ALGEXT_H
#define ALGEXT_H
/****************************************
* Computer Algebra System SINGULAR *
****************************************/
/*
* 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
* available, 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.
*/
#include "coeffs/coeffs.h"
#include "polys/monomials/ring.h"
/// struct for passing initialization parameters to naInitChar
typedef struct { ring r; /*ideal i;*/ } AlgExtInfo; // `r.qideal` is supposed to be `i`
/// Get a mapping function from src into the domain of this type (n_algExt)
nMapFunc naSetMap(const coeffs src, const coeffs dst);
/// Initialize the coeffs object
BOOLEAN naInitChar(coeffs cf, void* infoStruct);
BOOLEAN n2pInitChar(coeffs cf, void * infoStruct);
/// if m == var(i)/1 => return i,
int naIsParam(number, const coeffs);
/// 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
poly p_ExtGcd(poly p, poly &pFactor, poly q, poly &qFactor, ring r);
char* naCoeffName(const coeffs r);
#endif
/* ALGEXT_H */
p_ExtGcd
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 ...
Definition algext.cc:214
AlgExtInfo::r
ring r
Definition algext.h:37
naIsParam
int naIsParam(number, const coeffs)
if m == var(i)/1 => return i,
Definition algext.cc:1151
naCoeffName
char * naCoeffName(const coeffs r)
Definition algext.cc:1390
naSetMap
nMapFunc naSetMap(const coeffs src, const coeffs dst)
Get a mapping function from src into the domain of this type (n_algExt).
Definition algext.cc:1077
naInitChar
BOOLEAN naInitChar(coeffs cf, void *infoStruct)
Initialize the coeffs object.
Definition algext.cc:1433
n2pInitChar
BOOLEAN n2pInitChar(coeffs cf, void *infoStruct)
Definition algext.cc:1687
AlgExtInfo
struct for passing initialization parameters to naInitChar
Definition algext.h:37
BOOLEAN
int BOOLEAN
Definition auxiliary.h:88
p
int p
Definition cfModGcd.cc:4086
cf
CanonicalForm cf
Definition cfModGcd.cc:4091
coeffs.h
Coefficient rings, fields and other domains suitable for Singular polynomials.
nMapFunc
number(* nMapFunc)(number a, const coeffs src, const coeffs dst)
maps "a", which lives in src, into dst
Definition coeffs.h:80
coeffs
The main handler for Singular numbers which are suitable for Singular polynomials.
ring.h