algext.h
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1 #ifndef ALGEXT_H
2 #define ALGEXT_H
3 /****************************************
4 * Computer Algebra System SINGULAR *
5 ****************************************/
6 /*
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.
11 * IMPORTANT ASSUMPTIONS:
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->qideal is not NULL but an ideal with at
19 * least one non-zero generator which may be accessed by
20 * cf->extRing->qideal->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 algext.cc is then capable of
30 * computing in K[a_1, ..., a_s] / I.
31 */
32 
33 #include "coeffs/coeffs.h"
34 #include "polys/monomials/ring.h"
35 
36 /// struct for passing initialization parameters to naInitChar
37 typedef struct { ring r; /*ideal i;*/ } AlgExtInfo; // `r.qideal` is supposed to be `i`
38 
39 /// Get a mapping function from src into the domain of this type (n_algExt)
40 nMapFunc naSetMap(const coeffs src, const coeffs dst);
41 
42 /// Initialize the coeffs object
43 BOOLEAN naInitChar(coeffs cf, void* infoStruct);
44 BOOLEAN n2pInitChar(coeffs cf, void * infoStruct);
45 
46 /// if m == var(i)/1 => return i,
47 int naIsParam(number, const coeffs);
48 
49 /// assumes that p and q are univariate polynomials in r,
50 /// mentioning the same variable;
51 /// assumes a global monomial ordering in r;
52 /// assumes that not both p and q are NULL;
53 /// returns the gcd of p and q;
54 /// moreover, afterwards pFactor and qFactor contain appropriate
55 /// factors such that gcd(p, q) = p * pFactor + q * qFactor;
56 /// leaves p and q unmodified
57 poly p_ExtGcd(poly p, poly &pFactor, poly q, poly &qFactor, ring r);
58 
59 char* naCoeffString(const coeffs r); // will be reused in tranext.cc...
60 char* naCoeffName(const coeffs r);
61 #endif
62 /* ALGEXT_H */
ring r
Definition: algext.h:37
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:1019
Coefficient rings, fields and other domains suitable for Singular polynomials.
char * naCoeffString(const coeffs r)
Definition: algext.cc:1329
The main handler for Singular numbers which are suitable for Singular polynomials.
number(* nMapFunc)(number a, const coeffs src, const coeffs dst)
maps "a", which lives in src, into dst
Definition: coeffs.h:74
int naIsParam(number, const coeffs)
if m == var(i)/1 => return i,
Definition: algext.cc:1095
CanonicalForm cf
Definition: cfModGcd.cc:4024
struct for passing initialization parameters to naInitChar
Definition: algext.h:37
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:218
BOOLEAN n2pInitChar(coeffs cf, void *infoStruct)
Definition: algext.cc:1679
int p
Definition: cfModGcd.cc:4019
char * naCoeffName(const coeffs r)
Definition: algext.cc:1352
int BOOLEAN
Definition: auxiliary.h:85
BOOLEAN naInitChar(coeffs cf, void *infoStruct)
Initialize the coeffs object.
Definition: algext.cc:1395