source: git/libpolys/polys/ext_fields/algext.h @ 69672d

Last change on this file since 69672d was 69672d, checked in by Hans Schoenemann <hannes@…>, 12 years ago
fix: pardeg
  • Property mode set to 100644
File size: 3.8 KB
1#ifndef ALGEXT_H
2#define ALGEXT_H
4*  Computer Algebra System SINGULAR     *
7* ABSTRACT: numbers in an algebraic extension field K[a] / < f(a) >
8*           Assuming that we have a coeffs object cf, then these numbers
9*           are polynomials in the polynomial ring K[a] represented by
10*           cf->extRing.
12*           1.) So far we assume that cf->extRing is a valid polynomial
13*               ring in exactly one variable, i.e., K[a], where K is allowed
14*               to be any field (representable in SINGULAR and which may
15*               itself be some extension field, thus allowing for extension
16*               towers).
17*           2.) Moreover, this implementation assumes that
18*               cf->extRing->minideal is not NULL but an ideal with at
19*               least one non-zero generator which may be accessed by
20*               cf->extRing->minideal->m[0] and which represents the minimal
21*               polynomial f(a) of the extension variable 'a' in K[a].
22*           3.) As soon as an std method for polynomial rings becomes
23*               availabe, all reduction steps modulo f(a) should be replaced
24*               by a call to std. Moreover, in this situation one can finally
25*               move from K[a] / < f(a) > to
26*                  K[a_1, ..., a_s] / I, with I some zero-dimensional ideal
27*                                        in K[a_1, ..., a_s] given by a lex
28*                                        Gröbner basis.
29*               The code in algext.h and is then capable of
30*               computing in K[a_1, ..., a_s] / I.
33#include <coeffs/coeffs.h>
35// Forward declarations
36struct ip_sring; typedef struct ip_sring * ring;
37struct sip_sideal; typedef struct sip_sideal * ideal;
39/// struct for passing initialization parameters to naInitChar
40typedef struct { ring r; ideal i; } AlgExtInfo;
42/// Get a mapping function from src into the domain of this type (n_algExt)
43nMapFunc naSetMap(const coeffs src, const coeffs dst);
45/// Initialize the coeffs object
46BOOLEAN  naInitChar(coeffs cf, void* infoStruct);
48/* Private hidden interface
49BOOLEAN  naGreaterZero(number a, const coeffs cf);
50BOOLEAN  naGreater(number a, number b, const coeffs cf);
51BOOLEAN  naEqual(number a, number b, const coeffs cf);
52BOOLEAN  naIsOne(number a, const coeffs cf);
53BOOLEAN  naIsMOne(number a, const coeffs cf);
54BOOLEAN  naIsZero(number a, const coeffs cf);
55number   naInit(int i, const coeffs cf);
56int      naInt(number &a, const coeffs cf);
57number   naNeg(number a, const coeffs cf);
58number   naInvers(number a, const coeffs cf);
59number   naAdd(number a, number b, const coeffs cf);
60number   naSub(number a, number b, const coeffs cf);
61number   naMult(number a, number b, const coeffs cf);
62number   naDiv(number a, number b, const coeffs cf);
63void     naPower(number a, int exp, number *b, const coeffs cf);
64number   naCopy(number a, const coeffs cf);
65void     naWrite(number &a, const coeffs cf);
66number   naRePart(number a, const coeffs cf);
67number   naImPart(number a, const coeffs cf);
68number   naGetDenom(number &a, const coeffs cf);
69number   naGetNumerator(number &a, const coeffs cf);
70number   naGcd(number a, number b, const coeffs cf);
71number   naLcm(number a, number b, const coeffs cf);
72number   naSize(number a, const coeffs cf);
73void     naDelete(number * a, const coeffs cf);
74void     naCoeffWrite(const coeffs cf);
75number   naIntDiv(number a, number b, const coeffs cf);
76const char * naRead(const char *s, number *a, const coeffs cf);
77static BOOLEAN naCoeffIsEqual(const coeffs cf, n_coeffType n, void * param);
80/// return the specified parameter as a number in the given alg. field
81number naParam(short iParameter, const coeffs cf);
84/// if m == var(i)/1 => return i,
85int naIsParam(number, const coeffs);
88/* ALGEXT_H */
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