| 1 | #ifndef ALGEXT_H |
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| 2 | #define ALGEXT_H |
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| 3 | /**************************************** |
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| 4 | * Computer Algebra System SINGULAR * |
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| 5 | ****************************************/ |
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| 6 | /* $Id$ */ |
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| 7 | /* |
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| 8 | * ABSTRACT: numbers in an algebraic extension field K[a] / < f(a) > |
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| 9 | * Assuming that we have a coeffs object cf, then these numbers |
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| 10 | * are polynomials in the polynomial ring K[a] represented by |
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| 11 | * cf->extRing. |
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| 12 | * IMPORTANT ASSUMPTIONS: |
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| 13 | * 1.) So far we assume that cf->extRing is a valid polynomial |
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| 14 | * ring in exactly one variable, i.e., K[a], where K is allowed |
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| 15 | * to be any field (representable in SINGULAR and which may |
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| 16 | * itself be some extension field, thus allowing for extension |
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| 17 | * towers). |
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| 18 | * 2.) Moreover, this implementation assumes that |
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| 19 | * cf->extRing->minideal is not NULL but an ideal with at |
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| 20 | * least one non-zero generator which may be accessed by |
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| 21 | * cf->extRing->minideal->m[0] and which represents the minimal |
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| 22 | * polynomial f(a) of the extension variable 'a' in K[a]. |
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| 23 | * 3.) As soon as an std method for polynomial rings becomes |
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| 24 | * availabe, all reduction steps modulo f(a) should be replaced |
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| 25 | * by a call to std. Moreover, in this situation one can finally |
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| 26 | * move from K[a] / < f(a) > to |
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| 27 | * K[a_1, ..., a_s] / I, with I some zero-dimensional ideal |
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| 28 | * in K[a_1, ..., a_s] given by a lex |
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| 29 | * Gröbner basis. |
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| 30 | * The code in algext.h and algext.cc is then capable of |
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| 31 | * computing in K[a_1, ..., a_s] / I. |
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| 32 | */ |
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| 33 | |
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| 34 | #include <coeffs/coeffs.h> |
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| 35 | |
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| 36 | struct ip_sring; |
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| 37 | typedef struct ip_sring * ring; |
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| 38 | |
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| 39 | struct sip_sideal; |
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| 40 | typedef struct sip_sideal * ideal; |
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| 41 | |
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| 42 | /// struct for passing initialization parameters to naInitChar |
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| 43 | typedef struct { ring r; ideal i; } AlgExtInfo; |
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| 44 | |
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| 45 | /// Get a mapping function from src into the domain of this type (n_algExt) |
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| 46 | nMapFunc naSetMap(const coeffs src, const coeffs dst); |
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| 47 | |
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| 48 | /// Initialize the coeffs object |
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| 49 | BOOLEAN naInitChar(coeffs cf, void* infoStruct); |
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| 50 | |
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| 51 | /* Private hidden interface |
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| 52 | BOOLEAN naGreaterZero(number a, const coeffs cf); |
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| 53 | BOOLEAN naGreater(number a, number b, const coeffs cf); |
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| 54 | BOOLEAN naEqual(number a, number b, const coeffs cf); |
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| 55 | BOOLEAN naIsOne(number a, const coeffs cf); |
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| 56 | BOOLEAN naIsMOne(number a, const coeffs cf); |
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| 57 | BOOLEAN naIsZero(number a, const coeffs cf); |
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| 58 | number naInit(int i, const coeffs cf); |
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| 59 | int naInt(number &a, const coeffs cf); |
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| 60 | number naNeg(number a, const coeffs cf); |
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| 61 | number naInvers(number a, const coeffs cf); |
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| 62 | number naPar(int i, const coeffs cf); |
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| 63 | number naAdd(number a, number b, const coeffs cf); |
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| 64 | number naSub(number a, number b, const coeffs cf); |
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| 65 | number naMult(number a, number b, const coeffs cf); |
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| 66 | number naDiv(number a, number b, const coeffs cf); |
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| 67 | void naPower(number a, int exp, number *b, const coeffs cf); |
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| 68 | number naCopy(number a, const coeffs cf); |
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| 69 | void naWrite(number &a, const coeffs cf); |
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| 70 | number naRePart(number a, const coeffs cf); |
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| 71 | number naImPart(number a, const coeffs cf); |
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| 72 | number naGetDenom(number &a, const coeffs cf); |
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| 73 | number naGetNumerator(number &a, const coeffs cf); |
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| 74 | number naGcd(number a, number b, const coeffs cf); |
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| 75 | number naLcm(number a, number b, const coeffs cf); |
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| 76 | number naSize(number a, const coeffs cf); |
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| 77 | void naDelete(number * a, const coeffs cf); |
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| 78 | void naCoeffWrite(const coeffs cf); |
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| 79 | number naIntDiv(number a, number b, const coeffs cf); |
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| 80 | const char * naRead(const char *s, number *a, const coeffs cf); |
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| 81 | static BOOLEAN naCoeffIsEqual(const coeffs cf, n_coeffType n, void * param); |
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| 82 | */ |
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| 83 | |
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| 84 | #ifdef LDEBUG |
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| 85 | #define naTest(a) naDBTest(a,__FILE__,__LINE__,cf) |
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| 86 | BOOLEAN naDBTest(number a, const char *f, const int l, const coeffs r); |
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| 87 | #else |
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| 88 | #define naTest(a) |
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| 89 | #endif |
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| 90 | |
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| 91 | /* our own type */ |
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| 92 | #define naID n_algExt |
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| 93 | |
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| 94 | /* polynomial ring in which our numbers live */ |
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| 95 | #define naRing cf->extRing |
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| 96 | |
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| 97 | /* coeffs object in which the coefficients of our numbers live; |
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| 98 | * methods attached to naCoeffs may be used to compute with the |
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| 99 | * coefficients of our numbers, e.g., use naCoeffs->nAdd to add |
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| 100 | * coefficients of our numbers */ |
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| 101 | #define naCoeffs cf->extRing->cf |
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| 102 | |
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| 103 | /* minimal polynomial */ |
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| 104 | #define naMinpoly naRing->minideal->m[0] |
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| 105 | |
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| 106 | #endif |
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| 107 | /* ALGEXT_H */ |
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