[6ccdd3a] | 1 | /**************************************** |
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| 2 | * Computer Algebra System SINGULAR * |
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| 3 | ****************************************/ |
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| 4 | /* |
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[2c7f28] | 5 | * ABSTRACT: numbers in a rational function field K(t_1, .., t_s) with |
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| 6 | * transcendental variables t_1, ..., t_s, where s >= 1. |
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| 7 | * Denoting the implemented coeffs object by cf, then these numbers |
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[06df101] | 8 | * are represented as quotients of polynomials living in the |
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| 9 | * polynomial ring K[t_1, .., t_s] represented by cf->extring. |
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| 10 | * |
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| 11 | * An element of K(t_1, .., t_s) may have numerous representations, |
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| 12 | * due to the possibility of common polynomial factors in the |
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| 13 | * numerator and denominator. This problem is handled by a |
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| 14 | * cancellation heuristic: Each number "knows" its complexity |
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| 15 | * which is 0 if and only if common factors have definitely been |
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| 16 | * cancelled, and some positive integer otherwise. |
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| 17 | * Each arithmetic operation of two numbers with complexities c1 |
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| 18 | * and c2 will result in a number of complexity c1 + c2 + some |
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| 19 | * penalty (specific for each arithmetic operation; see constants |
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| 20 | * in the *.h file). Whenever the resulting complexity exceeds a |
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| 21 | * certain threshold (see constant in the *.h file), then the |
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| 22 | * cancellation heuristic will call 'factory' to compute the gcd |
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| 23 | * and cancel it out in the given number. (This definite cancel- |
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| 24 | * lation will also be performed at the beginning of ntWrite, |
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| 25 | * ensuring that any output is free of common factors. |
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| 26 | * For the special case of K = Q (i.e., when computing over the |
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| 27 | * rationals), this definite cancellation procedure will also take |
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| 28 | * care of nested fractions: If there are fractional coefficients |
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| 29 | * in the numerator or denominator of a number, then this number |
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| 30 | * is being replaced by a quotient of two polynomials over Z, or |
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| 31 | * - if the denominator is a constant - by a polynomial over Q. |
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[dc79bd] | 32 | * |
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| 33 | * TODO: the description above needs a major update!!! |
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[6ccdd3a] | 34 | */ |
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[1f414c8] | 35 | #define TRANSEXT_PRIVATES |
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[6ccdd3a] | 36 | |
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| 37 | #include "config.h" |
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| 38 | #include <misc/auxiliary.h> |
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| 39 | |
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| 40 | #include <omalloc/omalloc.h> |
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| 41 | |
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| 42 | #include <reporter/reporter.h> |
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| 43 | |
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| 44 | #include <coeffs/coeffs.h> |
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| 45 | #include <coeffs/numbers.h> |
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| 46 | #include <coeffs/longrat.h> |
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| 47 | |
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| 48 | #include <polys/monomials/ring.h> |
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| 49 | #include <polys/monomials/p_polys.h> |
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| 50 | #include <polys/simpleideals.h> |
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| 51 | |
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[e5d267] | 52 | #ifdef HAVE_FACTORY |
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| 53 | #include <polys/clapsing.h> |
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[fc4977] | 54 | #include <polys/clapconv.h> |
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| 55 | #include <factory/factory.h> |
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[e5d267] | 56 | #endif |
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| 57 | |
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[dc79bd] | 58 | #include <polys/ext_fields/transext.h> |
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| 59 | #include <polys/prCopy.h> |
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| 60 | |
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| 61 | #include <polys/PolyEnumerator.h> |
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| 62 | |
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[1f414c8] | 63 | |
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| 64 | /* constants for controlling the complexity of numbers */ |
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| 65 | #define ADD_COMPLEXITY 1 /**< complexity increase due to + and - */ |
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| 66 | #define MULT_COMPLEXITY 2 /**< complexity increase due to * and / */ |
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| 67 | #define BOUND_COMPLEXITY 10 /**< maximum complexity of a number */ |
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| 68 | |
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[dc79bd] | 69 | /// TRUE iff num. represents 1 |
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| 70 | #define NUMIS1(f) (p_IsOne(NUM(f), cf->extRing)) |
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| 71 | |
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[1f414c8] | 72 | #define COM(f) f->complexity |
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| 73 | |
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| 74 | |
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| 75 | #ifdef LDEBUG |
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[dc79bd] | 76 | #define ntTest(a) assume(ntDBTest(a,__FILE__,__LINE__,cf)) |
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[1f414c8] | 77 | BOOLEAN ntDBTest(number a, const char *f, const int l, const coeffs r); |
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| 78 | #else |
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[d101b1] | 79 | #define ntTest(a) do {} while (0) |
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[1f414c8] | 80 | #endif |
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| 81 | |
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| 82 | /// Our own type! |
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| 83 | static const n_coeffType ID = n_transExt; |
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| 84 | |
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| 85 | /* polynomial ring in which the numerators and denominators of our |
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| 86 | numbers live */ |
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| 87 | #define ntRing cf->extRing |
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| 88 | |
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| 89 | /* coeffs object in which the coefficients of our numbers live; |
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| 90 | * methods attached to ntCoeffs may be used to compute with the |
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| 91 | * coefficients of our numbers, e.g., use ntCoeffs->nAdd to add |
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| 92 | * coefficients of our numbers */ |
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| 93 | #define ntCoeffs cf->extRing->cf |
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| 94 | |
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[6ccdd3a] | 95 | |
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[fc4977] | 96 | omBin fractionObjectBin = omGetSpecBin(sizeof(fractionObject)); |
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[de90c01] | 97 | |
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[6ccdd3a] | 98 | /// forward declarations |
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[c14846c] | 99 | BOOLEAN ntGreaterZero(number a, const coeffs cf); |
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[6ccdd3a] | 100 | BOOLEAN ntGreater(number a, number b, const coeffs cf); |
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| 101 | BOOLEAN ntEqual(number a, number b, const coeffs cf); |
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| 102 | BOOLEAN ntIsOne(number a, const coeffs cf); |
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| 103 | BOOLEAN ntIsMOne(number a, const coeffs cf); |
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| 104 | BOOLEAN ntIsZero(number a, const coeffs cf); |
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[2f3764] | 105 | number ntInit(long i, const coeffs cf); |
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[6ccdd3a] | 106 | int ntInt(number &a, const coeffs cf); |
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| 107 | number ntNeg(number a, const coeffs cf); |
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| 108 | number ntInvers(number a, const coeffs cf); |
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| 109 | number ntAdd(number a, number b, const coeffs cf); |
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| 110 | number ntSub(number a, number b, const coeffs cf); |
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| 111 | number ntMult(number a, number b, const coeffs cf); |
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| 112 | number ntDiv(number a, number b, const coeffs cf); |
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| 113 | void ntPower(number a, int exp, number *b, const coeffs cf); |
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| 114 | number ntCopy(number a, const coeffs cf); |
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[ce1f78] | 115 | void ntWriteLong(number &a, const coeffs cf); |
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| 116 | void ntWriteShort(number &a, const coeffs cf); |
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[6ccdd3a] | 117 | number ntRePart(number a, const coeffs cf); |
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| 118 | number ntImPart(number a, const coeffs cf); |
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| 119 | number ntGetDenom(number &a, const coeffs cf); |
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| 120 | number ntGetNumerator(number &a, const coeffs cf); |
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| 121 | number ntGcd(number a, number b, const coeffs cf); |
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| 122 | number ntLcm(number a, number b, const coeffs cf); |
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[2c7f28] | 123 | int ntSize(number a, const coeffs cf); |
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[6ccdd3a] | 124 | void ntDelete(number * a, const coeffs cf); |
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[03f7b5] | 125 | void ntCoeffWrite(const coeffs cf, BOOLEAN details); |
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[6ccdd3a] | 126 | number ntIntDiv(number a, number b, const coeffs cf); |
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| 127 | const char * ntRead(const char *s, number *a, const coeffs cf); |
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| 128 | static BOOLEAN ntCoeffIsEqual(const coeffs cf, n_coeffType n, void * param); |
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| 129 | |
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[2c7f28] | 130 | void heuristicGcdCancellation(number a, const coeffs cf); |
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[010f3b] | 131 | void definiteGcdCancellation(number a, const coeffs cf, |
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[06df101] | 132 | BOOLEAN simpleTestsHaveAlreadyBeenPerformed); |
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| 133 | void handleNestedFractionsOverQ(fraction f, const coeffs cf); |
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[2c7f28] | 134 | |
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[6ccdd3a] | 135 | #ifdef LDEBUG |
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| 136 | BOOLEAN ntDBTest(number a, const char *f, const int l, const coeffs cf) |
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| 137 | { |
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[1f414c8] | 138 | assume(getCoeffType(cf) == ID); |
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[dc79bd] | 139 | |
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| 140 | if (IS0(a)) return TRUE; |
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| 141 | |
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| 142 | const fraction t = (fraction)a; |
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| 143 | |
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| 144 | const poly num = NUM(t); |
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| 145 | assume(num != NULL); /**< t != 0 ==> numerator(t) != 0 */ |
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[f7286a] | 146 | assume( _p_Test(num, ntRing,1) ); |
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[dc79bd] | 147 | |
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| 148 | const poly den = DEN(t); |
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[a355723] | 149 | |
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[dc79bd] | 150 | if (den != NULL) // !DENIS1(f) |
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[1374bc] | 151 | { |
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[f7286a] | 152 | assume( _p_Test(den, ntRing,1) ); |
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[a355723] | 153 | |
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[e5c9e5] | 154 | if(p_IsConstant(den, ntRing) && (n_IsOne(pGetCoeff(den), ntCoeffs))) |
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[1374bc] | 155 | { |
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| 156 | Print("?/1 in %s:%d\n",f,l); |
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[dc79bd] | 157 | return FALSE; |
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| 158 | } |
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[a355723] | 159 | |
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[e5c9e5] | 160 | if( !n_GreaterZero(pGetCoeff(den), ntCoeffs) ) |
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[dc79bd] | 161 | { |
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| 162 | Print("negative sign of DEN. of a fraction in %s:%d\n",f,l); |
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| 163 | return FALSE; |
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[1374bc] | 164 | } |
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[a355723] | 165 | |
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[dc79bd] | 166 | // test that den is over integers!? |
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[a355723] | 167 | |
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[dc79bd] | 168 | } else |
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| 169 | { // num != NULL // den == NULL |
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[a355723] | 170 | |
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[dc79bd] | 171 | // if( COM(t) != 0 ) |
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| 172 | // { |
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[a355723] | 173 | // Print("?//NULL with non-zero complexity: %d in %s:%d\n", COM(t), f, l); |
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[dc79bd] | 174 | // return FALSE; |
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| 175 | // } |
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| 176 | // test that nume is over integers!? |
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[1374bc] | 177 | } |
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[6ccdd3a] | 178 | return TRUE; |
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| 179 | } |
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| 180 | #endif |
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| 181 | |
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| 182 | /* returns the bottom field in this field extension tower; if the tower |
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| 183 | is flat, i.e., if there is no extension, then r itself is returned; |
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| 184 | as a side-effect, the counter 'height' is filled with the height of |
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| 185 | the extension tower (in case the tower is flat, 'height' is zero) */ |
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| 186 | static coeffs nCoeff_bottom(const coeffs r, int &height) |
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| 187 | { |
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| 188 | assume(r != NULL); |
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| 189 | coeffs cf = r; |
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| 190 | height = 0; |
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| 191 | while (nCoeff_is_Extension(cf)) |
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| 192 | { |
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| 193 | assume(cf->extRing != NULL); assume(cf->extRing->cf != NULL); |
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| 194 | cf = cf->extRing->cf; |
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| 195 | height++; |
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| 196 | } |
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| 197 | return cf; |
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| 198 | } |
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| 199 | |
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[2c7f28] | 200 | BOOLEAN ntIsZero(number a, const coeffs cf) |
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[6ccdd3a] | 201 | { |
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[dc79bd] | 202 | ntTest(a); // !!! |
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[e5d267] | 203 | return (IS0(a)); |
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[6ccdd3a] | 204 | } |
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| 205 | |
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[2c7f28] | 206 | void ntDelete(number * a, const coeffs cf) |
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[6ccdd3a] | 207 | { |
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[dc79bd] | 208 | ntTest(*a); // !!! |
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[2c7f28] | 209 | fraction f = (fraction)(*a); |
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[e5d267] | 210 | if (IS0(f)) return; |
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| 211 | p_Delete(&NUM(f), ntRing); |
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| 212 | if (!DENIS1(f)) p_Delete(&DEN(f), ntRing); |
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[2c7f28] | 213 | omFreeBin((ADDRESS)f, fractionObjectBin); |
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[6ccdd3a] | 214 | *a = NULL; |
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| 215 | } |
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| 216 | |
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[2c7f28] | 217 | BOOLEAN ntEqual(number a, number b, const coeffs cf) |
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[6ccdd3a] | 218 | { |
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[dc79bd] | 219 | ntTest(a); |
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| 220 | ntTest(b); |
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[c14846c] | 221 | |
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[6ccdd3a] | 222 | /// simple tests |
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| 223 | if (a == b) return TRUE; |
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[e5d267] | 224 | if ((IS0(a)) && (!IS0(b))) return FALSE; |
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| 225 | if ((IS0(b)) && (!IS0(a))) return FALSE; |
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[c14846c] | 226 | |
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| 227 | /// cheap test if gcd's have been cancelled in both numbers |
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[2c7f28] | 228 | fraction fa = (fraction)a; |
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| 229 | fraction fb = (fraction)b; |
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[e5d267] | 230 | if ((COM(fa) == 1) && (COM(fb) == 1)) |
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[2c7f28] | 231 | { |
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[e5d267] | 232 | poly f = p_Add_q(p_Copy(NUM(fa), ntRing), |
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| 233 | p_Neg(p_Copy(NUM(fb), ntRing), ntRing), |
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[2c7f28] | 234 | ntRing); |
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| 235 | if (f != NULL) { p_Delete(&f, ntRing); return FALSE; } |
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[e5d267] | 236 | if (DENIS1(fa) && DENIS1(fb)) return TRUE; |
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| 237 | if (DENIS1(fa) && !DENIS1(fb)) return FALSE; |
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| 238 | if (!DENIS1(fa) && DENIS1(fb)) return FALSE; |
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| 239 | f = p_Add_q(p_Copy(DEN(fa), ntRing), |
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| 240 | p_Neg(p_Copy(DEN(fb), ntRing), ntRing), |
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[2c7f28] | 241 | ntRing); |
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| 242 | if (f != NULL) { p_Delete(&f, ntRing); return FALSE; } |
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| 243 | return TRUE; |
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| 244 | } |
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[c14846c] | 245 | |
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[2c7f28] | 246 | /* default: the more expensive multiplication test |
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| 247 | a/b = c/d <==> a*d = b*c */ |
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[e5d267] | 248 | poly f = p_Copy(NUM(fa), ntRing); |
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| 249 | if (!DENIS1(fb)) f = p_Mult_q(f, p_Copy(DEN(fb), ntRing), ntRing); |
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| 250 | poly g = p_Copy(NUM(fb), ntRing); |
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| 251 | if (!DENIS1(fa)) g = p_Mult_q(g, p_Copy(DEN(fa), ntRing), ntRing); |
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[2c7f28] | 252 | poly h = p_Add_q(f, p_Neg(g, ntRing), ntRing); |
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| 253 | if (h == NULL) return TRUE; |
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| 254 | else |
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| 255 | { |
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| 256 | p_Delete(&h, ntRing); |
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| 257 | return FALSE; |
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| 258 | } |
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[6ccdd3a] | 259 | } |
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| 260 | |
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[2c7f28] | 261 | number ntCopy(number a, const coeffs cf) |
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[6ccdd3a] | 262 | { |
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[dc79bd] | 263 | ntTest(a); // !!! |
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[e5d267] | 264 | if (IS0(a)) return NULL; |
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[2c7f28] | 265 | fraction f = (fraction)a; |
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[e5d267] | 266 | poly g = p_Copy(NUM(f), ntRing); |
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| 267 | poly h = NULL; if (!DENIS1(f)) h = p_Copy(DEN(f), ntRing); |
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[2c7f28] | 268 | fraction result = (fraction)omAlloc0Bin(fractionObjectBin); |
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[e5d267] | 269 | NUM(result) = g; |
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| 270 | DEN(result) = h; |
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| 271 | COM(result) = COM(f); |
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[dc79bd] | 272 | ntTest((number)result); |
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[2c7f28] | 273 | return (number)result; |
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[6ccdd3a] | 274 | } |
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| 275 | |
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[dc79bd] | 276 | /// TODO: normalization of a!? |
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[2c7f28] | 277 | number ntGetNumerator(number &a, const coeffs cf) |
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[6ccdd3a] | 278 | { |
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[2c7f28] | 279 | ntTest(a); |
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[e5d267] | 280 | if (IS0(a)) return NULL; |
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[dc79bd] | 281 | |
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[9d68fd] | 282 | definiteGcdCancellation(a, cf, FALSE); |
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| 283 | |
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[2c7f28] | 284 | fraction f = (fraction)a; |
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| 285 | fraction result = (fraction)omAlloc0Bin(fractionObjectBin); |
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[dc79bd] | 286 | |
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| 287 | const BOOLEAN denis1= DENIS1 (f); |
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| 288 | |
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[28216f] | 289 | if (getCoeffType (ntCoeffs) == n_Q && !denis1) |
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| 290 | handleNestedFractionsOverQ (f, cf); |
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[dc79bd] | 291 | |
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[28216f] | 292 | if (getCoeffType (ntCoeffs) == n_Q && denis1) |
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| 293 | { |
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[dc79bd] | 294 | assume( DEN (f) == NULL ); |
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[a355723] | 295 | |
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[dc79bd] | 296 | number g; |
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| 297 | // TODO/NOTE: the following should not be necessary (due to |
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[a355723] | 298 | // Hannes!) as NUM (f) should be over Z!!! |
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[dc79bd] | 299 | CPolyCoeffsEnumerator itr(NUM(f)); |
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| 300 | |
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| 301 | |
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[e5c9e5] | 302 | n_ClearDenominators(itr, g, ntCoeffs); |
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[dc79bd] | 303 | |
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[e5c9e5] | 304 | if( !n_GreaterZero(g, ntCoeffs) ) |
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[28216f] | 305 | { |
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[dc79bd] | 306 | NUM (f) = p_Neg(NUM (f), ntRing); // Ugly :((( |
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[e5c9e5] | 307 | g = n_Neg(g, ntCoeffs); |
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[28216f] | 308 | } |
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[dc79bd] | 309 | |
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| 310 | // g should be a positive integer now! |
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[e5c9e5] | 311 | assume( n_GreaterZero(g, ntCoeffs) ); |
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[a355723] | 312 | |
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[e5c9e5] | 313 | if( !n_IsOne(g, ntCoeffs) ) |
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[dc79bd] | 314 | { |
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| 315 | DEN (f) = p_NSet(g, ntRing); // update COM(f)??? |
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| 316 | COM (f) ++; |
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[a355723] | 317 | assume( DEN (f) != NULL ); |
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[dc79bd] | 318 | } |
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| 319 | else |
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[e5c9e5] | 320 | n_Delete(&g, ntCoeffs); |
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[dc79bd] | 321 | |
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| 322 | ntTest(a); |
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[28216f] | 323 | } |
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[dc79bd] | 324 | |
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| 325 | // Call ntNormalize instead of above?!? |
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[a355723] | 326 | |
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[dc79bd] | 327 | NUM (result) = p_Copy (NUM (f), ntRing); // ??? |
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| 328 | DEN (result) = NULL; |
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| 329 | COM (result) = 0; |
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[a355723] | 330 | |
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[dc79bd] | 331 | ntTest((number)result); |
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[2c7f28] | 332 | return (number)result; |
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[6ccdd3a] | 333 | } |
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| 334 | |
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[dc79bd] | 335 | /// TODO: normalization of a!? |
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[2c7f28] | 336 | number ntGetDenom(number &a, const coeffs cf) |
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[6ccdd3a] | 337 | { |
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[2c7f28] | 338 | ntTest(a); |
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[010f3b] | 339 | definiteGcdCancellation(a, cf, FALSE); |
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[2c7f28] | 340 | fraction f = (fraction)a; |
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[dc79bd] | 341 | |
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[2c7f28] | 342 | fraction result = (fraction)omAlloc0Bin(fractionObjectBin); |
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[dc79bd] | 343 | DEN (result)= NULL; |
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| 344 | COM (result)= 0; |
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| 345 | |
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| 346 | |
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| 347 | const BOOLEAN denis1 = DENIS1 (f); |
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[a355723] | 348 | |
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[dc79bd] | 349 | if( IS0(f) || (denis1 && getCoeffType (ntCoeffs) != n_Q) ) // */1 or 0 |
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[28216f] | 350 | { |
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| 351 | NUM (result)= p_One(ntRing); |
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[dc79bd] | 352 | ntTest((number)result); |
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| 353 | return (number)result; |
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[28216f] | 354 | } |
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[dc79bd] | 355 | |
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| 356 | if (!denis1) // */* / Q |
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[28216f] | 357 | { |
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[dc79bd] | 358 | assume( DEN (f) != NULL ); |
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| 359 | |
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[28216f] | 360 | if (getCoeffType (ntCoeffs) == n_Q) |
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| 361 | handleNestedFractionsOverQ (f, cf); |
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[dc79bd] | 362 | |
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| 363 | ntTest(a); |
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| 364 | |
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| 365 | if( DEN (f) != NULL ) // is it ?? // 1 now??? |
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| 366 | { |
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| 367 | assume( !p_IsOne(DEN (f), ntRing) ); |
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| 368 | |
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| 369 | NUM (result) = p_Copy (DEN (f), ntRing); |
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| 370 | ntTest((number)result); |
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| 371 | return (number)result; |
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| 372 | } |
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| 373 | // NUM (result) = p_One(ntRing); // NOTE: just in order to be sure... |
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| 374 | } |
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[a355723] | 375 | |
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[dc79bd] | 376 | // */1 / Q |
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| 377 | assume( getCoeffType (ntCoeffs) == n_Q ); |
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[a355723] | 378 | assume( DEN (f) == NULL ); |
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| 379 | |
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| 380 | number g; |
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[dc79bd] | 381 | // poly num= p_Copy (NUM (f), ntRing); // ??? |
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| 382 | |
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| 383 | |
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| 384 | // TODO/NOTE: the following should not be necessary (due to |
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| 385 | // Hannes!) as NUM (f) should be over Z!!! |
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| 386 | CPolyCoeffsEnumerator itr(NUM(f)); |
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[a355723] | 387 | |
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[e5c9e5] | 388 | n_ClearDenominators(itr, g, ntCoeffs); // may return -1 :((( |
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[a355723] | 389 | |
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[e5c9e5] | 390 | if( !n_GreaterZero(g, ntCoeffs) ) |
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[dc79bd] | 391 | { |
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| 392 | // NUM (f) = p_Neg(NUM (f), ntRing); // Ugly :((( |
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[e5c9e5] | 393 | // g = n_Neg(g, ntCoeffs); |
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[dc79bd] | 394 | NUM (f) = p_Neg(NUM (f), ntRing); // Ugly :((( |
---|
[e5c9e5] | 395 | g = n_Neg(g, ntCoeffs); |
---|
[dc79bd] | 396 | } |
---|
| 397 | |
---|
| 398 | // g should be a positive integer now! |
---|
[e5c9e5] | 399 | assume( n_GreaterZero(g, ntCoeffs) ); |
---|
[dc79bd] | 400 | |
---|
[e5c9e5] | 401 | if( !n_IsOne(g, ntCoeffs) ) |
---|
[dc79bd] | 402 | { |
---|
[e5c9e5] | 403 | assume( n_GreaterZero(g, ntCoeffs) ); |
---|
| 404 | assume( !n_IsOne(g, ntCoeffs) ); |
---|
[a355723] | 405 | |
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[dc79bd] | 406 | DEN (f) = p_NSet(g, ntRing); // update COM(f)??? |
---|
| 407 | assume( DEN (f) != NULL ); |
---|
| 408 | COM (f) ++; |
---|
[a355723] | 409 | |
---|
[28216f] | 410 | NUM (result)= p_Copy (DEN (f), ntRing); |
---|
| 411 | } |
---|
[dc79bd] | 412 | else |
---|
| 413 | { // common denom == 1? |
---|
| 414 | NUM (result)= p_NSet(g, ntRing); // p_Copy (DEN (f), ntRing); |
---|
[e5c9e5] | 415 | // n_Delete(&g, ntCoeffs); |
---|
[a355723] | 416 | } |
---|
| 417 | |
---|
[dc79bd] | 418 | // if (!p_IsConstant (num, ntRing) && pNext(num) != NULL) |
---|
| 419 | // else |
---|
| 420 | // g= p_GetAllDenom (num, ntRing); |
---|
[e5c9e5] | 421 | // result= (fraction) ntSetMap (ntCoeffs, cf) (g, ntCoeffs, cf); |
---|
[dc79bd] | 422 | |
---|
| 423 | ntTest((number)result); |
---|
[2c7f28] | 424 | return (number)result; |
---|
[6ccdd3a] | 425 | } |
---|
| 426 | |
---|
[2c7f28] | 427 | BOOLEAN ntIsOne(number a, const coeffs cf) |
---|
[6ccdd3a] | 428 | { |
---|
[a355723] | 429 | ntTest(a); // !!! |
---|
[010f3b] | 430 | definiteGcdCancellation(a, cf, FALSE); |
---|
[2c7f28] | 431 | fraction f = (fraction)a; |
---|
[31c731] | 432 | return (f!=NULL) && DENIS1(f) && NUMIS1(f); |
---|
[6ccdd3a] | 433 | } |
---|
| 434 | |
---|
[2c7f28] | 435 | BOOLEAN ntIsMOne(number a, const coeffs cf) |
---|
[6ccdd3a] | 436 | { |
---|
[2c7f28] | 437 | ntTest(a); |
---|
[010f3b] | 438 | definiteGcdCancellation(a, cf, FALSE); |
---|
[2c7f28] | 439 | fraction f = (fraction)a; |
---|
[31c731] | 440 | if ((f==NULL) || (!DENIS1(f))) return FALSE; |
---|
[e5d267] | 441 | poly g = NUM(f); |
---|
[2c7f28] | 442 | if (!p_IsConstant(g, ntRing)) return FALSE; |
---|
| 443 | return n_IsMOne(p_GetCoeff(g, ntRing), ntCoeffs); |
---|
[6ccdd3a] | 444 | } |
---|
| 445 | |
---|
| 446 | /// this is in-place, modifies a |
---|
[2c7f28] | 447 | number ntNeg(number a, const coeffs cf) |
---|
[6ccdd3a] | 448 | { |
---|
[2c7f28] | 449 | ntTest(a); |
---|
[e5d267] | 450 | if (!IS0(a)) |
---|
[2c7f28] | 451 | { |
---|
| 452 | fraction f = (fraction)a; |
---|
[e5d267] | 453 | NUM(f) = p_Neg(NUM(f), ntRing); |
---|
[2c7f28] | 454 | } |
---|
[dc79bd] | 455 | ntTest(a); |
---|
[6ccdd3a] | 456 | return a; |
---|
| 457 | } |
---|
| 458 | |
---|
[2c7f28] | 459 | number ntImPart(number a, const coeffs cf) |
---|
[6ccdd3a] | 460 | { |
---|
[2c7f28] | 461 | ntTest(a); |
---|
[6ccdd3a] | 462 | return NULL; |
---|
| 463 | } |
---|
| 464 | |
---|
[61b2e16] | 465 | number ntInit_bigint(number longratBigIntNumber, const coeffs src, const coeffs cf) |
---|
| 466 | { |
---|
| 467 | assume( cf != NULL ); |
---|
| 468 | |
---|
| 469 | const ring A = cf->extRing; |
---|
| 470 | |
---|
| 471 | assume( A != NULL ); |
---|
| 472 | |
---|
| 473 | const coeffs C = A->cf; |
---|
| 474 | |
---|
| 475 | assume( C != NULL ); |
---|
| 476 | |
---|
| 477 | number n = n_Init_bigint(longratBigIntNumber, src, C); |
---|
| 478 | |
---|
| 479 | if ( n_IsZero(n, C) ) |
---|
| 480 | { |
---|
| 481 | n_Delete(&n, C); |
---|
| 482 | return NULL; |
---|
[a355723] | 483 | } |
---|
[61b2e16] | 484 | |
---|
| 485 | fraction result = (fraction)omAlloc0Bin(fractionObjectBin); |
---|
[a355723] | 486 | |
---|
[dc79bd] | 487 | number den = n_GetDenom(n, C); |
---|
[a355723] | 488 | |
---|
[dc79bd] | 489 | assume( n_GreaterZero(den, C) ); |
---|
[a355723] | 490 | |
---|
[dc79bd] | 491 | if( n_IsOne(den, C) ) |
---|
| 492 | { |
---|
| 493 | NUM(result) = p_NSet(n, A); |
---|
[a355723] | 494 | DEN(result) = NULL; |
---|
| 495 | n_Delete(&den, C); |
---|
[dc79bd] | 496 | } else |
---|
| 497 | { |
---|
[a355723] | 498 | DEN(result) = p_NSet(den, A); |
---|
| 499 | NUM(result) = p_NSet(n_GetNumerator(n, C), A); |
---|
| 500 | n_Delete(&n, C); |
---|
[dc79bd] | 501 | } |
---|
[61b2e16] | 502 | |
---|
| 503 | COM(result) = 0; |
---|
[dc79bd] | 504 | |
---|
| 505 | ntTest((number)result); |
---|
| 506 | |
---|
[61b2e16] | 507 | return (number)result; |
---|
| 508 | } |
---|
| 509 | |
---|
[a355723] | 510 | |
---|
[2f3764] | 511 | number ntInit(long i, const coeffs cf) |
---|
[6ccdd3a] | 512 | { |
---|
[6ac003] | 513 | if (i != 0) |
---|
[2c7f28] | 514 | { |
---|
[6ac003] | 515 | poly p=p_ISet(i, ntRing); |
---|
| 516 | if (p!=NULL) |
---|
| 517 | { |
---|
| 518 | fraction result = (fraction)omAlloc0Bin(fractionObjectBin); |
---|
| 519 | NUM(result) = p; |
---|
| 520 | //DEN(result) = NULL; // done by omAlloc0Bin |
---|
| 521 | //COM(result) = 0; // done by omAlloc0Bin |
---|
| 522 | ntTest((number)result); |
---|
| 523 | return (number)result; |
---|
| 524 | } |
---|
[2c7f28] | 525 | } |
---|
[6ac003] | 526 | return NULL; |
---|
[6ccdd3a] | 527 | } |
---|
| 528 | |
---|
[dc79bd] | 529 | |
---|
| 530 | /// takes over p! |
---|
[b38d70] | 531 | number ntInit(poly p, const coeffs cf) |
---|
| 532 | { |
---|
[6ac003] | 533 | if (p == NULL) return NULL; |
---|
[a355723] | 534 | |
---|
[e5c9e5] | 535 | fraction f = (fraction)omAlloc0Bin(fractionObjectBin); |
---|
| 536 | |
---|
| 537 | if (nCoeff_is_Q(ntCoeffs)) |
---|
| 538 | { |
---|
[dc79bd] | 539 | number g; |
---|
| 540 | // TODO/NOTE: the following should not be necessary (due to |
---|
[a355723] | 541 | // Hannes!) as NUM (f) should be over Z!!! |
---|
[e5c9e5] | 542 | // but it is not: normalize it |
---|
[dc79bd] | 543 | CPolyCoeffsEnumerator itr(p); |
---|
| 544 | |
---|
[e5c9e5] | 545 | n_ClearDenominators(itr, g, ntCoeffs); |
---|
[dc79bd] | 546 | |
---|
[e5c9e5] | 547 | if( !n_GreaterZero(g, ntCoeffs) ) |
---|
[dc79bd] | 548 | { |
---|
[e5c9e5] | 549 | p = p_Neg(p, ntRing); |
---|
| 550 | g = n_Neg(g, ntCoeffs); |
---|
[dc79bd] | 551 | } |
---|
| 552 | |
---|
| 553 | // g should be a positive integer now! |
---|
[e5c9e5] | 554 | assume( n_GreaterZero(g, ntCoeffs) ); |
---|
[a355723] | 555 | |
---|
[e5c9e5] | 556 | if( !n_IsOne(g, ntCoeffs) ) |
---|
[dc79bd] | 557 | { |
---|
[a355723] | 558 | DEN (f) = p_NSet(g, ntRing); |
---|
| 559 | assume( DEN (f) != NULL ); |
---|
[dc79bd] | 560 | } |
---|
| 561 | else |
---|
| 562 | { |
---|
[e5c9e5] | 563 | //DEN(f) = NULL; // done by omAlloc0 |
---|
| 564 | n_Delete(&g, ntCoeffs); |
---|
[a355723] | 565 | } |
---|
[e5c9e5] | 566 | } |
---|
[a355723] | 567 | |
---|
[e5c9e5] | 568 | NUM(f) = p; |
---|
| 569 | COM(f) = 0; |
---|
[dc79bd] | 570 | |
---|
[e5c9e5] | 571 | ntTest((number)f); |
---|
| 572 | return (number)f; |
---|
[b38d70] | 573 | } |
---|
| 574 | |
---|
[2c7f28] | 575 | int ntInt(number &a, const coeffs cf) |
---|
[6ccdd3a] | 576 | { |
---|
[2c7f28] | 577 | ntTest(a); |
---|
[e5d267] | 578 | if (IS0(a)) return 0; |
---|
[010f3b] | 579 | definiteGcdCancellation(a, cf, FALSE); |
---|
[2c7f28] | 580 | fraction f = (fraction)a; |
---|
[e5d267] | 581 | if (!DENIS1(f)) return 0; |
---|
[a355723] | 582 | |
---|
[1090a98] | 583 | const poly aAsPoly = NUM(f); |
---|
| 584 | |
---|
| 585 | if(aAsPoly == NULL) |
---|
| 586 | return 0; |
---|
[a355723] | 587 | |
---|
[1090a98] | 588 | if (!p_IsConstant(aAsPoly, ntRing)) |
---|
| 589 | return 0; |
---|
| 590 | |
---|
| 591 | assume( aAsPoly != NULL ); |
---|
[a355723] | 592 | |
---|
[1090a98] | 593 | return n_Int(p_GetCoeff(aAsPoly, ntRing), ntCoeffs); |
---|
[2c7f28] | 594 | } |
---|
| 595 | |
---|
| 596 | /* This method will only consider the numerators of a and b, without |
---|
| 597 | cancelling gcd's before. |
---|
| 598 | Moreover it may return TRUE only if one or both numerators |
---|
| 599 | are zero or if their degrees are equal. Then TRUE is returned iff |
---|
| 600 | coeff(numerator(a)) > coeff(numerator(b)); |
---|
| 601 | In all other cases, FALSE will be returned. */ |
---|
| 602 | BOOLEAN ntGreater(number a, number b, const coeffs cf) |
---|
| 603 | { |
---|
[dc79bd] | 604 | ntTest(a); |
---|
| 605 | ntTest(b); |
---|
[95c826] | 606 | number aNumCoeff = NULL; int aNumDeg = -1; |
---|
[fd60be] | 607 | number aDenCoeff = NULL; int aDenDeg = -1; |
---|
[95c826] | 608 | number bNumCoeff = NULL; int bNumDeg = -1; |
---|
[fd60be] | 609 | number bDenCoeff = NULL; int bDenDeg = -1; |
---|
[e5d267] | 610 | if (!IS0(a)) |
---|
[2c7f28] | 611 | { |
---|
| 612 | fraction fa = (fraction)a; |
---|
[e5d267] | 613 | aNumDeg = p_Totaldegree(NUM(fa), ntRing); |
---|
| 614 | aNumCoeff = p_GetCoeff(NUM(fa), ntRing); |
---|
[fd60be] | 615 | if (DEN(fa)!=NULL) |
---|
| 616 | { |
---|
| 617 | aDenDeg = p_Totaldegree(DEN(fa), ntRing); |
---|
| 618 | aDenCoeff=p_GetCoeff(DEN(fa),ntRing); |
---|
| 619 | } |
---|
[2c7f28] | 620 | } |
---|
[95c826] | 621 | else return !(ntGreaterZero (b,cf)); |
---|
[e5d267] | 622 | if (!IS0(b)) |
---|
[2c7f28] | 623 | { |
---|
| 624 | fraction fb = (fraction)b; |
---|
[e5d267] | 625 | bNumDeg = p_Totaldegree(NUM(fb), ntRing); |
---|
| 626 | bNumCoeff = p_GetCoeff(NUM(fb), ntRing); |
---|
[fd60be] | 627 | if (DEN(fb)!=NULL) |
---|
| 628 | { |
---|
| 629 | bDenDeg = p_Totaldegree(DEN(fb), ntRing); |
---|
| 630 | bDenCoeff=p_GetCoeff(DEN(fb),ntRing); |
---|
| 631 | } |
---|
[2c7f28] | 632 | } |
---|
[95c826] | 633 | else return ntGreaterZero(a,cf); |
---|
[fd60be] | 634 | if (aNumDeg-aDenDeg > bNumDeg-bDenDeg) return TRUE; |
---|
| 635 | if (aNumDeg-aDenDeg < bNumDeg-bDenDeg) return FALSE; |
---|
| 636 | number aa; |
---|
| 637 | number bb; |
---|
[e5c9e5] | 638 | if (bDenCoeff==NULL) aa=n_Copy(aNumCoeff,ntCoeffs); |
---|
| 639 | else aa=n_Mult(aNumCoeff,bDenCoeff,ntCoeffs); |
---|
| 640 | if (aDenCoeff==NULL) bb=n_Copy(bNumCoeff,ntCoeffs); |
---|
| 641 | else bb=n_Mult(bNumCoeff,aDenCoeff,ntCoeffs); |
---|
[fd60be] | 642 | BOOLEAN rr= n_Greater(aa, bb, ntCoeffs); |
---|
[e5c9e5] | 643 | n_Delete(&aa,ntCoeffs); |
---|
| 644 | n_Delete(&bb,ntCoeffs); |
---|
[fd60be] | 645 | return rr; |
---|
[6ccdd3a] | 646 | } |
---|
| 647 | |
---|
[2c7f28] | 648 | /* this method will only consider the numerator of a, without cancelling |
---|
| 649 | the gcd before; |
---|
| 650 | returns TRUE iff the leading coefficient of the numerator of a is > 0 |
---|
| 651 | or the leading term of the numerator of a is not a |
---|
| 652 | constant */ |
---|
| 653 | BOOLEAN ntGreaterZero(number a, const coeffs cf) |
---|
[6ccdd3a] | 654 | { |
---|
[2c7f28] | 655 | ntTest(a); |
---|
[e5d267] | 656 | if (IS0(a)) return FALSE; |
---|
[2c7f28] | 657 | fraction f = (fraction)a; |
---|
[e5d267] | 658 | poly g = NUM(f); |
---|
[7964f9c] | 659 | return (!p_LmIsConstant(g,ntRing)|| n_GreaterZero(pGetCoeff(g), ntCoeffs)); |
---|
[6ccdd3a] | 660 | } |
---|
| 661 | |
---|
[03f7b5] | 662 | void ntCoeffWrite(const coeffs cf, BOOLEAN details) |
---|
[6ccdd3a] | 663 | { |
---|
[a55ef0] | 664 | assume( cf != NULL ); |
---|
| 665 | |
---|
| 666 | const ring A = cf->extRing; |
---|
| 667 | |
---|
| 668 | assume( A != NULL ); |
---|
| 669 | assume( A->cf != NULL ); |
---|
| 670 | |
---|
[03f7b5] | 671 | n_CoeffWrite(A->cf, details); |
---|
[a55ef0] | 672 | |
---|
| 673 | // rWrite(A); |
---|
| 674 | |
---|
| 675 | const int P = rVar(A); |
---|
| 676 | assume( P > 0 ); |
---|
[c14846c] | 677 | |
---|
[a55ef0] | 678 | Print("// %d parameter : ", P); |
---|
[c14846c] | 679 | |
---|
[a55ef0] | 680 | for (int nop=0; nop < P; nop ++) |
---|
| 681 | Print("%s ", rRingVar(nop, A)); |
---|
| 682 | |
---|
[dd668f] | 683 | assume( A->qideal == NULL ); |
---|
[c14846c] | 684 | |
---|
[a55ef0] | 685 | PrintS("\n// minpoly : 0\n"); |
---|
| 686 | |
---|
| 687 | /* |
---|
[2c7f28] | 688 | PrintS("// Coefficients live in the rational function field\n"); |
---|
| 689 | Print("// K("); |
---|
| 690 | for (int i = 0; i < rVar(ntRing); i++) |
---|
| 691 | { |
---|
[a55ef0] | 692 | if (i > 0) PrintS(" "); |
---|
[2c7f28] | 693 | Print("%s", rRingVar(i, ntRing)); |
---|
| 694 | } |
---|
| 695 | PrintS(") with\n"); |
---|
| 696 | PrintS("// K: "); n_CoeffWrite(cf->extRing->cf); |
---|
[a55ef0] | 697 | */ |
---|
[6ccdd3a] | 698 | } |
---|
| 699 | |
---|
[2c7f28] | 700 | number ntAdd(number a, number b, const coeffs cf) |
---|
[6ccdd3a] | 701 | { |
---|
[dc79bd] | 702 | ntTest(a); |
---|
| 703 | ntTest(b); |
---|
[e5d267] | 704 | if (IS0(a)) return ntCopy(b, cf); |
---|
| 705 | if (IS0(b)) return ntCopy(a, cf); |
---|
[c14846c] | 706 | |
---|
[2c7f28] | 707 | fraction fa = (fraction)a; |
---|
| 708 | fraction fb = (fraction)b; |
---|
[c14846c] | 709 | |
---|
[e5d267] | 710 | poly g = p_Copy(NUM(fa), ntRing); |
---|
| 711 | if (!DENIS1(fb)) g = p_Mult_q(g, p_Copy(DEN(fb), ntRing), ntRing); |
---|
| 712 | poly h = p_Copy(NUM(fb), ntRing); |
---|
| 713 | if (!DENIS1(fa)) h = p_Mult_q(h, p_Copy(DEN(fa), ntRing), ntRing); |
---|
[de90c01] | 714 | g = p_Add_q(g, h, ntRing); |
---|
[c14846c] | 715 | |
---|
[de90c01] | 716 | if (g == NULL) return NULL; |
---|
[c14846c] | 717 | |
---|
[2c7f28] | 718 | poly f; |
---|
[e5d267] | 719 | if (DENIS1(fa) && DENIS1(fb)) f = NULL; |
---|
| 720 | else if (!DENIS1(fa) && DENIS1(fb)) f = p_Copy(DEN(fa), ntRing); |
---|
| 721 | else if (DENIS1(fa) && !DENIS1(fb)) f = p_Copy(DEN(fb), ntRing); |
---|
| 722 | else /* both denom's are != 1 */ f = p_Mult_q(p_Copy(DEN(fa), ntRing), |
---|
| 723 | p_Copy(DEN(fb), ntRing), |
---|
[2c7f28] | 724 | ntRing); |
---|
[c14846c] | 725 | |
---|
[2c7f28] | 726 | fraction result = (fraction)omAlloc0Bin(fractionObjectBin); |
---|
[e5d267] | 727 | NUM(result) = g; |
---|
| 728 | DEN(result) = f; |
---|
| 729 | COM(result) = COM(fa) + COM(fb) + ADD_COMPLEXITY; |
---|
[2c7f28] | 730 | heuristicGcdCancellation((number)result, cf); |
---|
[dc79bd] | 731 | |
---|
| 732 | // ntTest((number)result); |
---|
[a355723] | 733 | |
---|
[2c7f28] | 734 | return (number)result; |
---|
[6ccdd3a] | 735 | } |
---|
| 736 | |
---|
[2c7f28] | 737 | number ntSub(number a, number b, const coeffs cf) |
---|
[6ccdd3a] | 738 | { |
---|
[dc79bd] | 739 | ntTest(a); |
---|
| 740 | ntTest(b); |
---|
[e5d267] | 741 | if (IS0(a)) return ntNeg(ntCopy(b, cf), cf); |
---|
| 742 | if (IS0(b)) return ntCopy(a, cf); |
---|
[c14846c] | 743 | |
---|
[2c7f28] | 744 | fraction fa = (fraction)a; |
---|
| 745 | fraction fb = (fraction)b; |
---|
[c14846c] | 746 | |
---|
[e5d267] | 747 | poly g = p_Copy(NUM(fa), ntRing); |
---|
| 748 | if (!DENIS1(fb)) g = p_Mult_q(g, p_Copy(DEN(fb), ntRing), ntRing); |
---|
| 749 | poly h = p_Copy(NUM(fb), ntRing); |
---|
| 750 | if (!DENIS1(fa)) h = p_Mult_q(h, p_Copy(DEN(fa), ntRing), ntRing); |
---|
[de90c01] | 751 | g = p_Add_q(g, p_Neg(h, ntRing), ntRing); |
---|
[c14846c] | 752 | |
---|
[de90c01] | 753 | if (g == NULL) return NULL; |
---|
[c14846c] | 754 | |
---|
[2c7f28] | 755 | poly f; |
---|
[e5d267] | 756 | if (DENIS1(fa) && DENIS1(fb)) f = NULL; |
---|
| 757 | else if (!DENIS1(fa) && DENIS1(fb)) f = p_Copy(DEN(fa), ntRing); |
---|
| 758 | else if (DENIS1(fa) && !DENIS1(fb)) f = p_Copy(DEN(fb), ntRing); |
---|
| 759 | else /* both den's are != 1 */ f = p_Mult_q(p_Copy(DEN(fa), ntRing), |
---|
| 760 | p_Copy(DEN(fb), ntRing), |
---|
[2c7f28] | 761 | ntRing); |
---|
[c14846c] | 762 | |
---|
[2c7f28] | 763 | fraction result = (fraction)omAlloc0Bin(fractionObjectBin); |
---|
[e5d267] | 764 | NUM(result) = g; |
---|
| 765 | DEN(result) = f; |
---|
| 766 | COM(result) = COM(fa) + COM(fb) + ADD_COMPLEXITY; |
---|
[2c7f28] | 767 | heuristicGcdCancellation((number)result, cf); |
---|
[dc79bd] | 768 | // ntTest((number)result); |
---|
[2c7f28] | 769 | return (number)result; |
---|
[6ccdd3a] | 770 | } |
---|
| 771 | |
---|
[2c7f28] | 772 | number ntMult(number a, number b, const coeffs cf) |
---|
[6ccdd3a] | 773 | { |
---|
[dc79bd] | 774 | ntTest(a); // !!!? |
---|
| 775 | ntTest(b); // !!!? |
---|
[a355723] | 776 | |
---|
[e5d267] | 777 | if (IS0(a) || IS0(b)) return NULL; |
---|
[c14846c] | 778 | |
---|
[2c7f28] | 779 | fraction fa = (fraction)a; |
---|
| 780 | fraction fb = (fraction)b; |
---|
[c14846c] | 781 | |
---|
[dc79bd] | 782 | const poly g = pp_Mult_qq(NUM(fa), NUM(fb), ntRing); |
---|
[c14846c] | 783 | |
---|
[dc79bd] | 784 | if (g == NULL) return NULL; // may happen due to zero divisors??? |
---|
[c14846c] | 785 | |
---|
[2c7f28] | 786 | fraction result = (fraction)omAlloc0Bin(fractionObjectBin); |
---|
[dc79bd] | 787 | |
---|
[e5d267] | 788 | NUM(result) = g; |
---|
[dc79bd] | 789 | |
---|
| 790 | const poly da = DEN(fa); |
---|
| 791 | const poly db = DEN(fb); |
---|
| 792 | |
---|
[a355723] | 793 | |
---|
[dc79bd] | 794 | if (db == NULL) |
---|
| 795 | { |
---|
| 796 | // b = ? // NULL |
---|
[a355723] | 797 | |
---|
[dc79bd] | 798 | if(da == NULL) |
---|
| 799 | { // both fa && fb are ?? // NULL! |
---|
| 800 | assume (da == NULL && db == NULL); |
---|
| 801 | DEN(result) = NULL; |
---|
| 802 | COM(result) = 0; |
---|
| 803 | } |
---|
[a355723] | 804 | else |
---|
[dc79bd] | 805 | { |
---|
| 806 | assume (da != NULL && db == NULL); |
---|
| 807 | DEN(result) = p_Copy(da, ntRing); |
---|
| 808 | COM(result) = COM(fa) + MULT_COMPLEXITY; |
---|
| 809 | heuristicGcdCancellation((number)result, cf); |
---|
| 810 | } |
---|
| 811 | } else |
---|
| 812 | { // b = ?? / ?? |
---|
| 813 | if (da == NULL) |
---|
| 814 | { // a == ? // NULL |
---|
| 815 | assume( db != NULL && da == NULL); |
---|
| 816 | DEN(result) = p_Copy(db, ntRing); |
---|
| 817 | COM(result) = COM(fb) + MULT_COMPLEXITY; |
---|
| 818 | heuristicGcdCancellation((number)result, cf); |
---|
| 819 | } |
---|
| 820 | else /* both den's are != 1 */ |
---|
| 821 | { |
---|
| 822 | assume (da != NULL && db != NULL); |
---|
| 823 | DEN(result) = pp_Mult_qq(da, db, ntRing); |
---|
| 824 | COM(result) = COM(fa) + COM(fb) + MULT_COMPLEXITY; |
---|
| 825 | heuristicGcdCancellation((number)result, cf); |
---|
| 826 | } |
---|
| 827 | } |
---|
| 828 | |
---|
| 829 | // ntTest((number)result); |
---|
[a355723] | 830 | |
---|
[2c7f28] | 831 | return (number)result; |
---|
[6ccdd3a] | 832 | } |
---|
| 833 | |
---|
[2c7f28] | 834 | number ntDiv(number a, number b, const coeffs cf) |
---|
[6ccdd3a] | 835 | { |
---|
[dc79bd] | 836 | ntTest(a); |
---|
| 837 | ntTest(b); |
---|
[e5d267] | 838 | if (IS0(a)) return NULL; |
---|
| 839 | if (IS0(b)) WerrorS(nDivBy0); |
---|
[c14846c] | 840 | |
---|
[2c7f28] | 841 | fraction fa = (fraction)a; |
---|
| 842 | fraction fb = (fraction)b; |
---|
[c14846c] | 843 | |
---|
[e5d267] | 844 | poly g = p_Copy(NUM(fa), ntRing); |
---|
| 845 | if (!DENIS1(fb)) g = p_Mult_q(g, p_Copy(DEN(fb), ntRing), ntRing); |
---|
[c14846c] | 846 | |
---|
[de90c01] | 847 | if (g == NULL) return NULL; /* may happen due to zero divisors */ |
---|
[c14846c] | 848 | |
---|
[e5d267] | 849 | poly f = p_Copy(NUM(fb), ntRing); |
---|
| 850 | if (!DENIS1(fa)) f = p_Mult_q(f, p_Copy(DEN(fa), ntRing), ntRing); |
---|
[c14846c] | 851 | |
---|
[2c7f28] | 852 | fraction result = (fraction)omAlloc0Bin(fractionObjectBin); |
---|
[e5d267] | 853 | NUM(result) = g; |
---|
[e5c9e5] | 854 | if (!n_GreaterZero(pGetCoeff(f),ntCoeffs)) |
---|
[644b31] | 855 | { |
---|
| 856 | g=p_Neg(g,ntRing); |
---|
| 857 | f=p_Neg(f,ntRing); |
---|
| 858 | NUM(result) = g; |
---|
| 859 | } |
---|
[e5c9e5] | 860 | if (!p_IsConstant(f,ntRing) || !n_IsOne(pGetCoeff(f),ntCoeffs)) |
---|
[644b31] | 861 | { |
---|
[1374bc] | 862 | DEN(result) = f; |
---|
[644b31] | 863 | } |
---|
[e5d267] | 864 | COM(result) = COM(fa) + COM(fb) + MULT_COMPLEXITY; |
---|
[2c7f28] | 865 | heuristicGcdCancellation((number)result, cf); |
---|
[dc79bd] | 866 | // ntTest((number)result); |
---|
[2c7f28] | 867 | return (number)result; |
---|
[6ccdd3a] | 868 | } |
---|
| 869 | |
---|
| 870 | /* 0^0 = 0; |
---|
| 871 | for |exp| <= 7 compute power by a simple multiplication loop; |
---|
| 872 | for |exp| >= 8 compute power along binary presentation of |exp|, e.g. |
---|
| 873 | p^13 = p^1 * p^4 * p^8, where we utilise that |
---|
[2c7f28] | 874 | p^(2^(k+1)) = p^(2^k) * p^(2^k); |
---|
| 875 | intermediate cancellation is controlled by the in-place method |
---|
| 876 | heuristicGcdCancellation; see there. |
---|
[6ccdd3a] | 877 | */ |
---|
[2c7f28] | 878 | void ntPower(number a, int exp, number *b, const coeffs cf) |
---|
[6ccdd3a] | 879 | { |
---|
[2c7f28] | 880 | ntTest(a); |
---|
[c14846c] | 881 | |
---|
[6ccdd3a] | 882 | /* special cases first */ |
---|
[e5d267] | 883 | if (IS0(a)) |
---|
[6ccdd3a] | 884 | { |
---|
| 885 | if (exp >= 0) *b = NULL; |
---|
| 886 | else WerrorS(nDivBy0); |
---|
| 887 | } |
---|
[35e86e] | 888 | else if (exp == 0) { *b = ntInit(1, cf); return;} |
---|
| 889 | else if (exp == 1) { *b = ntCopy(a, cf); return;} |
---|
| 890 | else if (exp == -1) { *b = ntInvers(a, cf); return;} |
---|
[c14846c] | 891 | |
---|
[6ccdd3a] | 892 | int expAbs = exp; if (expAbs < 0) expAbs = -expAbs; |
---|
[c14846c] | 893 | |
---|
[2c7f28] | 894 | /* now compute a^expAbs */ |
---|
| 895 | number pow; number t; |
---|
[6ccdd3a] | 896 | if (expAbs <= 7) |
---|
| 897 | { |
---|
[2c7f28] | 898 | pow = ntCopy(a, cf); |
---|
[6ccdd3a] | 899 | for (int i = 2; i <= expAbs; i++) |
---|
| 900 | { |
---|
[2c7f28] | 901 | t = ntMult(pow, a, cf); |
---|
| 902 | ntDelete(&pow, cf); |
---|
| 903 | pow = t; |
---|
| 904 | heuristicGcdCancellation(pow, cf); |
---|
[6ccdd3a] | 905 | } |
---|
| 906 | } |
---|
| 907 | else |
---|
| 908 | { |
---|
[2c7f28] | 909 | pow = ntInit(1, cf); |
---|
| 910 | number factor = ntCopy(a, cf); |
---|
[6ccdd3a] | 911 | while (expAbs != 0) |
---|
| 912 | { |
---|
| 913 | if (expAbs & 1) |
---|
| 914 | { |
---|
[2c7f28] | 915 | t = ntMult(pow, factor, cf); |
---|
| 916 | ntDelete(&pow, cf); |
---|
| 917 | pow = t; |
---|
| 918 | heuristicGcdCancellation(pow, cf); |
---|
[6ccdd3a] | 919 | } |
---|
| 920 | expAbs = expAbs / 2; |
---|
| 921 | if (expAbs != 0) |
---|
| 922 | { |
---|
[2c7f28] | 923 | t = ntMult(factor, factor, cf); |
---|
| 924 | ntDelete(&factor, cf); |
---|
| 925 | factor = t; |
---|
| 926 | heuristicGcdCancellation(factor, cf); |
---|
[6ccdd3a] | 927 | } |
---|
| 928 | } |
---|
[2c7f28] | 929 | ntDelete(&factor, cf); |
---|
[6ccdd3a] | 930 | } |
---|
[c14846c] | 931 | |
---|
[6ccdd3a] | 932 | /* invert if original exponent was negative */ |
---|
| 933 | if (exp < 0) |
---|
| 934 | { |
---|
[2c7f28] | 935 | t = ntInvers(pow, cf); |
---|
| 936 | ntDelete(&pow, cf); |
---|
| 937 | pow = t; |
---|
[6ccdd3a] | 938 | } |
---|
[2c7f28] | 939 | *b = pow; |
---|
[dc79bd] | 940 | ntTest(*b); |
---|
[6ccdd3a] | 941 | } |
---|
| 942 | |
---|
[06df101] | 943 | /* assumes that cf represents the rationals, i.e. Q, and will only |
---|
| 944 | be called in that case; |
---|
| 945 | assumes furthermore that f != NULL and that the denominator of f != 1; |
---|
| 946 | generally speaking, this method removes denominators in the rational |
---|
| 947 | coefficients of the numerator and denominator of 'a'; |
---|
| 948 | more concretely, the following normalizations will be performed, |
---|
| 949 | where t^alpha denotes a monomial in the transcendental variables t_k |
---|
| 950 | (1) if 'a' is of the form |
---|
| 951 | (sum_alpha a_alpha/b_alpha * t^alpha) |
---|
| 952 | ------------------------------------- |
---|
| 953 | (sum_beta c_beta/d_beta * t^beta) |
---|
| 954 | with integers a_alpha, b_alpha, c_beta, d_beta, then both the |
---|
| 955 | numerator and the denominator will be multiplied by the LCM of |
---|
| 956 | the b_alpha's and the d_beta's (if this LCM is != 1), |
---|
| 957 | (2) if 'a' is - e.g. after having performed step (1) - of the form |
---|
| 958 | (sum_alpha a_alpha * t^alpha) |
---|
| 959 | ----------------------------- |
---|
| 960 | (sum_beta c_beta * t^beta) |
---|
| 961 | with integers a_alpha, c_beta, and with a non-constant denominator, |
---|
| 962 | then both the numerator and the denominator will be divided by the |
---|
| 963 | GCD of the a_alpha's and the c_beta's (if this GCD is != 1), |
---|
| 964 | (3) if 'a' is - e.g. after having performed steps (1) and (2) - of the |
---|
| 965 | form |
---|
| 966 | (sum_alpha a_alpha * t^alpha) |
---|
| 967 | ----------------------------- |
---|
| 968 | c |
---|
| 969 | with integers a_alpha, and c != 1, then 'a' will be replaced by |
---|
| 970 | (sum_alpha a_alpha/c * t^alpha); |
---|
| 971 | this procedure does not alter COM(f) (this has to be done by the |
---|
| 972 | calling procedure); |
---|
| 973 | modifies f */ |
---|
| 974 | void handleNestedFractionsOverQ(fraction f, const coeffs cf) |
---|
| 975 | { |
---|
| 976 | assume(nCoeff_is_Q(ntCoeffs)); |
---|
| 977 | assume(!IS0(f)); |
---|
| 978 | assume(!DENIS1(f)); |
---|
[c14846c] | 979 | |
---|
[06df101] | 980 | if (!p_IsConstant(DEN(f), ntRing)) |
---|
| 981 | { /* step (1); see documentation of this procedure above */ |
---|
[d12f186] | 982 | p_Normalize(NUM(f), ntRing); |
---|
| 983 | p_Normalize(DEN(f), ntRing); |
---|
[06df101] | 984 | number lcmOfDenominators = n_Init(1, ntCoeffs); |
---|
| 985 | number c; number tmp; |
---|
| 986 | poly p = NUM(f); |
---|
| 987 | /* careful when using n_Lcm!!! It computes the lcm of the numerator |
---|
| 988 | of the 1st argument and the denominator of the 2nd!!! */ |
---|
| 989 | while (p != NULL) |
---|
| 990 | { |
---|
| 991 | c = p_GetCoeff(p, ntRing); |
---|
| 992 | tmp = n_Lcm(lcmOfDenominators, c, ntCoeffs); |
---|
| 993 | n_Delete(&lcmOfDenominators, ntCoeffs); |
---|
| 994 | lcmOfDenominators = tmp; |
---|
| 995 | pIter(p); |
---|
| 996 | } |
---|
| 997 | p = DEN(f); |
---|
| 998 | while (p != NULL) |
---|
| 999 | { |
---|
| 1000 | c = p_GetCoeff(p, ntRing); |
---|
| 1001 | tmp = n_Lcm(lcmOfDenominators, c, ntCoeffs); |
---|
| 1002 | n_Delete(&lcmOfDenominators, ntCoeffs); |
---|
| 1003 | lcmOfDenominators = tmp; |
---|
| 1004 | pIter(p); |
---|
| 1005 | } |
---|
| 1006 | if (!n_IsOne(lcmOfDenominators, ntCoeffs)) |
---|
| 1007 | { /* multiply NUM(f) and DEN(f) with lcmOfDenominators */ |
---|
| 1008 | NUM(f) = p_Mult_nn(NUM(f), lcmOfDenominators, ntRing); |
---|
[d12f186] | 1009 | p_Normalize(NUM(f), ntRing); |
---|
[06df101] | 1010 | DEN(f) = p_Mult_nn(DEN(f), lcmOfDenominators, ntRing); |
---|
[d12f186] | 1011 | p_Normalize(DEN(f), ntRing); |
---|
[06df101] | 1012 | } |
---|
| 1013 | n_Delete(&lcmOfDenominators, ntCoeffs); |
---|
| 1014 | if (!p_IsConstant(DEN(f), ntRing)) |
---|
| 1015 | { /* step (2); see documentation of this procedure above */ |
---|
| 1016 | p = NUM(f); |
---|
| 1017 | number gcdOfCoefficients = n_Copy(p_GetCoeff(p, ntRing), ntCoeffs); |
---|
| 1018 | pIter(p); |
---|
| 1019 | while ((p != NULL) && (!n_IsOne(gcdOfCoefficients, ntCoeffs))) |
---|
| 1020 | { |
---|
| 1021 | c = p_GetCoeff(p, ntRing); |
---|
| 1022 | tmp = n_Gcd(c, gcdOfCoefficients, ntCoeffs); |
---|
| 1023 | n_Delete(&gcdOfCoefficients, ntCoeffs); |
---|
| 1024 | gcdOfCoefficients = tmp; |
---|
| 1025 | pIter(p); |
---|
| 1026 | } |
---|
| 1027 | p = DEN(f); |
---|
| 1028 | while ((p != NULL) && (!n_IsOne(gcdOfCoefficients, ntCoeffs))) |
---|
| 1029 | { |
---|
| 1030 | c = p_GetCoeff(p, ntRing); |
---|
| 1031 | tmp = n_Gcd(c, gcdOfCoefficients, ntCoeffs); |
---|
| 1032 | n_Delete(&gcdOfCoefficients, ntCoeffs); |
---|
| 1033 | gcdOfCoefficients = tmp; |
---|
| 1034 | pIter(p); |
---|
| 1035 | } |
---|
| 1036 | if (!n_IsOne(gcdOfCoefficients, ntCoeffs)) |
---|
| 1037 | { /* divide NUM(f) and DEN(f) by gcdOfCoefficients */ |
---|
| 1038 | number inverseOfGcdOfCoefficients = n_Invers(gcdOfCoefficients, |
---|
| 1039 | ntCoeffs); |
---|
| 1040 | NUM(f) = p_Mult_nn(NUM(f), inverseOfGcdOfCoefficients, ntRing); |
---|
[d12f186] | 1041 | p_Normalize(NUM(f), ntRing); |
---|
[06df101] | 1042 | DEN(f) = p_Mult_nn(DEN(f), inverseOfGcdOfCoefficients, ntRing); |
---|
[d12f186] | 1043 | p_Normalize(DEN(f), ntRing); |
---|
[06df101] | 1044 | n_Delete(&inverseOfGcdOfCoefficients, ntCoeffs); |
---|
| 1045 | } |
---|
| 1046 | n_Delete(&gcdOfCoefficients, ntCoeffs); |
---|
| 1047 | } |
---|
| 1048 | } |
---|
| 1049 | if (p_IsConstant(DEN(f), ntRing) && |
---|
| 1050 | (!n_IsOne(p_GetCoeff(DEN(f), ntRing), ntCoeffs))) |
---|
| 1051 | { /* step (3); see documentation of this procedure above */ |
---|
| 1052 | number inverseOfDen = n_Invers(p_GetCoeff(DEN(f), ntRing), ntCoeffs); |
---|
| 1053 | NUM(f) = p_Mult_nn(NUM(f), inverseOfDen, ntRing); |
---|
| 1054 | n_Delete(&inverseOfDen, ntCoeffs); |
---|
| 1055 | p_Delete(&DEN(f), ntRing); |
---|
| 1056 | DEN(f) = NULL; |
---|
| 1057 | } |
---|
[c14846c] | 1058 | |
---|
[06df101] | 1059 | /* Now, due to the above computations, DEN(f) may have become the |
---|
| 1060 | 1-polynomial which needs to be represented by NULL: */ |
---|
| 1061 | if ((DEN(f) != NULL) && |
---|
| 1062 | p_IsConstant(DEN(f), ntRing) && |
---|
| 1063 | n_IsOne(p_GetCoeff(DEN(f), ntRing), ntCoeffs)) |
---|
| 1064 | { |
---|
| 1065 | p_Delete(&DEN(f), ntRing); DEN(f) = NULL; |
---|
| 1066 | } |
---|
[a355723] | 1067 | |
---|
[dc79bd] | 1068 | if( DEN(f) != NULL ) |
---|
| 1069 | if( !n_GreaterZero(pGetCoeff(DEN(f)), ntCoeffs) ) |
---|
| 1070 | { |
---|
| 1071 | NUM(f) = p_Neg(NUM(f), ntRing); |
---|
| 1072 | DEN(f) = p_Neg(DEN(f), ntRing); |
---|
[a355723] | 1073 | } |
---|
| 1074 | |
---|
[dc79bd] | 1075 | ntTest((number)f); // TODO! |
---|
[06df101] | 1076 | } |
---|
| 1077 | |
---|
[2c7f28] | 1078 | /* modifies a */ |
---|
| 1079 | void heuristicGcdCancellation(number a, const coeffs cf) |
---|
[6ccdd3a] | 1080 | { |
---|
[dc79bd] | 1081 | // ntTest(a); // !!!!???? |
---|
[e5d267] | 1082 | if (IS0(a)) return; |
---|
[c14846c] | 1083 | |
---|
[2c7f28] | 1084 | fraction f = (fraction)a; |
---|
[dc79bd] | 1085 | if (DENIS1(f) || NUMIS1(f)) { COM(f) = 0; ntTest(a); return; } |
---|
| 1086 | |
---|
| 1087 | assume( DEN(f) != NULL ); |
---|
[c14846c] | 1088 | |
---|
[e5d267] | 1089 | /* check whether NUM(f) = DEN(f), and - if so - replace 'a' by 1 */ |
---|
| 1090 | if (p_EqualPolys(NUM(f), DEN(f), ntRing)) |
---|
| 1091 | { /* numerator and denominator are both != 1 */ |
---|
| 1092 | p_Delete(&NUM(f), ntRing); NUM(f) = p_ISet(1, ntRing); |
---|
| 1093 | p_Delete(&DEN(f), ntRing); DEN(f) = NULL; |
---|
| 1094 | COM(f) = 0; |
---|
[603ac7a] | 1095 | } |
---|
| 1096 | else |
---|
[dc79bd] | 1097 | { |
---|
[a355723] | 1098 | if (COM(f) > BOUND_COMPLEXITY) |
---|
[dc79bd] | 1099 | definiteGcdCancellation(a, cf, TRUE); |
---|
[c14846c] | 1100 | |
---|
[7964f9c] | 1101 | // TODO: check if it is enough to put the following into definiteGcdCancellation?! |
---|
| 1102 | if( DEN(f) != NULL ) |
---|
[dc79bd] | 1103 | { |
---|
[7964f9c] | 1104 | if( !n_GreaterZero(pGetCoeff(DEN(f)), ntCoeffs) ) |
---|
| 1105 | { |
---|
| 1106 | NUM(f) = p_Neg(NUM(f), ntRing); |
---|
| 1107 | DEN(f) = p_Neg(DEN(f), ntRing); |
---|
| 1108 | } |
---|
| 1109 | if (ntCoeffs->has_simple_Inverse) |
---|
| 1110 | { |
---|
| 1111 | if (!n_IsOne(pGetCoeff(DEN(f)),ntCoeffs)) |
---|
| 1112 | { |
---|
| 1113 | number inv=n_Invers(pGetCoeff(DEN(f)),ntCoeffs); |
---|
| 1114 | DEN(f)=p_Mult_nn(DEN(f),inv,ntRing); |
---|
| 1115 | NUM(f)=p_Mult_nn(NUM(f),inv,ntRing); |
---|
| 1116 | } |
---|
| 1117 | if(p_LmIsConstant(DEN(f),ntRing)) |
---|
| 1118 | { |
---|
| 1119 | p_Delete(&DEN(f),ntRing); |
---|
| 1120 | COM(f)=0; |
---|
| 1121 | } |
---|
| 1122 | } |
---|
[a355723] | 1123 | } |
---|
[dc79bd] | 1124 | } |
---|
[a355723] | 1125 | |
---|
[603ac7a] | 1126 | ntTest(a); |
---|
[6ccdd3a] | 1127 | } |
---|
| 1128 | |
---|
[dc79bd] | 1129 | /// modifies a |
---|
[010f3b] | 1130 | void definiteGcdCancellation(number a, const coeffs cf, |
---|
[06df101] | 1131 | BOOLEAN simpleTestsHaveAlreadyBeenPerformed) |
---|
[6ccdd3a] | 1132 | { |
---|
[dc79bd] | 1133 | ntTest(a); // !!!! |
---|
[c14846c] | 1134 | |
---|
[2c7f28] | 1135 | fraction f = (fraction)a; |
---|
[c14846c] | 1136 | |
---|
[603ac7a] | 1137 | if (IS0(a)) return; |
---|
| 1138 | if (NUM(f)!=NULL) p_Normalize(NUM(f), ntRing); |
---|
| 1139 | if (DEN(f)!=NULL) p_Normalize(DEN(f), ntRing); |
---|
[06df101] | 1140 | if (!simpleTestsHaveAlreadyBeenPerformed) |
---|
[2c7f28] | 1141 | { |
---|
[e5d267] | 1142 | if (DENIS1(f) || NUMIS1(f)) { COM(f) = 0; return; } |
---|
[c14846c] | 1143 | |
---|
[e5d267] | 1144 | /* check whether NUM(f) = DEN(f), and - if so - replace 'a' by 1 */ |
---|
| 1145 | if (p_EqualPolys(NUM(f), DEN(f), ntRing)) |
---|
| 1146 | { /* numerator and denominator are both != 1 */ |
---|
| 1147 | p_Delete(&NUM(f), ntRing); NUM(f) = p_ISet(1, ntRing); |
---|
| 1148 | p_Delete(&DEN(f), ntRing); DEN(f) = NULL; |
---|
| 1149 | COM(f) = 0; |
---|
[dc79bd] | 1150 | ntTest(a); // !!!! |
---|
[010f3b] | 1151 | return; |
---|
| 1152 | } |
---|
[2c7f28] | 1153 | } |
---|
[c14846c] | 1154 | |
---|
| 1155 | #ifdef HAVE_FACTORY |
---|
[06df101] | 1156 | /* Note that, over Q, singclap_gcd will remove the denominators in all |
---|
| 1157 | rational coefficients of pNum and pDen, before starting to compute |
---|
| 1158 | the gcd. Thus, we do not need to ensure that the coefficients of |
---|
| 1159 | pNum and pDen live in Z; they may well be elements of Q\Z. */ |
---|
[dc79bd] | 1160 | /* singclap_gcd destroys its arguments; we hence need copies: */ |
---|
| 1161 | poly pGcd = singclap_gcd(p_Copy(NUM(f), ntRing), p_Copy(DEN(f), ntRing), cf->extRing); |
---|
[e5d267] | 1162 | if (p_IsConstant(pGcd, ntRing) && |
---|
| 1163 | n_IsOne(p_GetCoeff(pGcd, ntRing), ntCoeffs)) |
---|
[06df101] | 1164 | { /* gcd = 1; nothing to cancel; |
---|
| 1165 | Suppose the given rational function field is over Q. Although the |
---|
| 1166 | gcd is 1, we may have produced fractional coefficients in NUM(f), |
---|
| 1167 | DEN(f), or both, due to previous arithmetics. The next call will |
---|
| 1168 | remove those nested fractions, in case there are any. */ |
---|
[9053f02] | 1169 | if (nCoeff_is_Zp(ntCoeffs) && p_IsConstant (DEN (f), ntRing)) |
---|
| 1170 | { |
---|
| 1171 | NUM (f) = p_Div_nn (NUM (f), p_GetCoeff (DEN(f),ntRing), ntRing); |
---|
| 1172 | //poly newNum= singclap_pdivide (NUM(f), DEN (f), ntRing); |
---|
| 1173 | //p_Delete(&NUM (f), ntRing); |
---|
| 1174 | //NUM (f)= newNum; |
---|
| 1175 | p_Delete(&DEN (f), ntRing); |
---|
| 1176 | DEN (f) = NULL; |
---|
| 1177 | COM (f) = 0; |
---|
| 1178 | } else if (nCoeff_is_Q(ntCoeffs)) handleNestedFractionsOverQ(f, cf); |
---|
[e5d267] | 1179 | } |
---|
| 1180 | else |
---|
[06df101] | 1181 | { /* We divide both NUM(f) and DEN(f) by the gcd which is known |
---|
| 1182 | to be != 1. */ |
---|
| 1183 | poly newNum = singclap_pdivide(NUM(f), pGcd, ntRing); |
---|
| 1184 | p_Delete(&NUM(f), ntRing); |
---|
| 1185 | NUM(f) = newNum; |
---|
| 1186 | poly newDen = singclap_pdivide(DEN(f), pGcd, ntRing); |
---|
| 1187 | p_Delete(&DEN(f), ntRing); |
---|
| 1188 | DEN(f) = newDen; |
---|
| 1189 | if (p_IsConstant(DEN(f), ntRing) && |
---|
| 1190 | n_IsOne(p_GetCoeff(DEN(f), ntRing), ntCoeffs)) |
---|
| 1191 | { |
---|
| 1192 | /* DEN(f) = 1 needs to be represented by NULL! */ |
---|
[e5d267] | 1193 | p_Delete(&DEN(f), ntRing); |
---|
[06df101] | 1194 | newDen = NULL; |
---|
| 1195 | } |
---|
| 1196 | else |
---|
| 1197 | { /* Note that over Q, by cancelling the gcd, we may have produced |
---|
| 1198 | fractional coefficients in NUM(f), DEN(f), or both. The next |
---|
| 1199 | call will remove those nested fractions, in case there are |
---|
| 1200 | any. */ |
---|
| 1201 | if (nCoeff_is_Q(ntCoeffs)) handleNestedFractionsOverQ(f, cf); |
---|
| 1202 | } |
---|
[e5d267] | 1203 | } |
---|
| 1204 | COM(f) = 0; |
---|
| 1205 | p_Delete(&pGcd, ntRing); |
---|
[dc79bd] | 1206 | |
---|
| 1207 | if( DEN(f) != NULL ) |
---|
| 1208 | if( !n_GreaterZero(pGetCoeff(DEN(f)), ntCoeffs) ) |
---|
| 1209 | { |
---|
| 1210 | NUM(f) = p_Neg(NUM(f), ntRing); |
---|
| 1211 | DEN(f) = p_Neg(DEN(f), ntRing); |
---|
[a355723] | 1212 | } |
---|
[e5d267] | 1213 | #endif /* HAVE_FACTORY */ |
---|
[a355723] | 1214 | |
---|
[dc79bd] | 1215 | ntTest(a); // !!!! |
---|
[2c7f28] | 1216 | } |
---|
| 1217 | |
---|
[ce1f78] | 1218 | // NOTE: modifies a |
---|
| 1219 | void ntWriteLong(number &a, const coeffs cf) |
---|
| 1220 | { |
---|
| 1221 | ntTest(a); |
---|
| 1222 | definiteGcdCancellation(a, cf, FALSE); |
---|
| 1223 | if (IS0(a)) |
---|
| 1224 | StringAppendS("0"); |
---|
| 1225 | else |
---|
| 1226 | { |
---|
| 1227 | fraction f = (fraction)a; |
---|
| 1228 | // stole logic from napWrite from kernel/longtrans.cc of legacy singular |
---|
| 1229 | BOOLEAN omitBrackets = p_IsConstant(NUM(f), ntRing); |
---|
| 1230 | if (!omitBrackets) StringAppendS("("); |
---|
| 1231 | p_String0Long(NUM(f), ntRing, ntRing); |
---|
| 1232 | if (!omitBrackets) StringAppendS(")"); |
---|
| 1233 | if (!DENIS1(f)) |
---|
| 1234 | { |
---|
| 1235 | StringAppendS("/"); |
---|
| 1236 | omitBrackets = p_IsConstant(DEN(f), ntRing); |
---|
| 1237 | if (!omitBrackets) StringAppendS("("); |
---|
| 1238 | p_String0Long(DEN(f), ntRing, ntRing); |
---|
| 1239 | if (!omitBrackets) StringAppendS(")"); |
---|
[a355723] | 1240 | } |
---|
[ce1f78] | 1241 | } |
---|
[dc79bd] | 1242 | ntTest(a); // !!!! |
---|
[ce1f78] | 1243 | } |
---|
| 1244 | |
---|
| 1245 | // NOTE: modifies a |
---|
| 1246 | void ntWriteShort(number &a, const coeffs cf) |
---|
[2c7f28] | 1247 | { |
---|
| 1248 | ntTest(a); |
---|
[010f3b] | 1249 | definiteGcdCancellation(a, cf, FALSE); |
---|
[e5d267] | 1250 | if (IS0(a)) |
---|
[6ccdd3a] | 1251 | StringAppendS("0"); |
---|
| 1252 | else |
---|
| 1253 | { |
---|
[2c7f28] | 1254 | fraction f = (fraction)a; |
---|
[a5071b9] | 1255 | // stole logic from napWrite from kernel/longtrans.cc of legacy singular |
---|
[a0a9f0] | 1256 | BOOLEAN omitBrackets = p_IsConstant(NUM(f), ntRing); |
---|
[a5071b9] | 1257 | if (!omitBrackets) StringAppendS("("); |
---|
[ce1f78] | 1258 | p_String0Short(NUM(f), ntRing, ntRing); |
---|
[a5071b9] | 1259 | if (!omitBrackets) StringAppendS(")"); |
---|
[e5d267] | 1260 | if (!DENIS1(f)) |
---|
[2c7f28] | 1261 | { |
---|
| 1262 | StringAppendS("/"); |
---|
[a0a9f0] | 1263 | omitBrackets = p_IsConstant(DEN(f), ntRing); |
---|
| 1264 | if (!omitBrackets) StringAppendS("("); |
---|
[ce1f78] | 1265 | p_String0Short(DEN(f), ntRing, ntRing); |
---|
[a0a9f0] | 1266 | if (!omitBrackets) StringAppendS(")"); |
---|
[2c7f28] | 1267 | } |
---|
[6ccdd3a] | 1268 | } |
---|
[dc79bd] | 1269 | ntTest(a); |
---|
[6ccdd3a] | 1270 | } |
---|
| 1271 | |
---|
[2c7f28] | 1272 | const char * ntRead(const char *s, number *a, const coeffs cf) |
---|
[6ccdd3a] | 1273 | { |
---|
[2c7f28] | 1274 | poly p; |
---|
| 1275 | const char * result = p_Read(s, p, ntRing); |
---|
[dc79bd] | 1276 | if (p == NULL) *a = NULL; |
---|
| 1277 | else *a = ntInit(p, cf); |
---|
| 1278 | return result; |
---|
[6ccdd3a] | 1279 | } |
---|
| 1280 | |
---|
[237b4dd] | 1281 | void ntNormalize (number &a, const coeffs cf) |
---|
| 1282 | { |
---|
[e56eb1a] | 1283 | if ((a!=NULL)) |
---|
[6ad7e6] | 1284 | { |
---|
| 1285 | definiteGcdCancellation(a, cf, FALSE); |
---|
| 1286 | if ((DEN(a)!=NULL) |
---|
[e5c9e5] | 1287 | &&(!n_GreaterZero(pGetCoeff(DEN(a)),ntCoeffs))) |
---|
[6ad7e6] | 1288 | { |
---|
| 1289 | NUM(a)=p_Neg(NUM(a),ntRing); |
---|
| 1290 | DEN(a)=p_Neg(DEN(a),ntRing); |
---|
| 1291 | } |
---|
| 1292 | } |
---|
[dc79bd] | 1293 | ntTest(a); // !!!! |
---|
[237b4dd] | 1294 | } |
---|
| 1295 | |
---|
[2c7f28] | 1296 | /* expects *param to be castable to TransExtInfo */ |
---|
| 1297 | static BOOLEAN ntCoeffIsEqual(const coeffs cf, n_coeffType n, void * param) |
---|
[6ccdd3a] | 1298 | { |
---|
[1f414c8] | 1299 | if (ID != n) return FALSE; |
---|
[2c7f28] | 1300 | TransExtInfo *e = (TransExtInfo *)param; |
---|
| 1301 | /* for rational function fields we expect the underlying |
---|
| 1302 | polynomial rings to be IDENTICAL, i.e. the SAME OBJECT; |
---|
[6ccdd3a] | 1303 | this expectation is based on the assumption that we have properly |
---|
| 1304 | registered cf and perform reference counting rather than creating |
---|
| 1305 | multiple copies of the same coefficient field/domain/ring */ |
---|
[4d94c97] | 1306 | if (ntRing == e->r) |
---|
| 1307 | return TRUE; |
---|
| 1308 | |
---|
| 1309 | // NOTE: Q(a)[x] && Q(a)[y] should better share the _same_ Q(a)... |
---|
| 1310 | if( rEqual(ntRing, e->r, TRUE) ) |
---|
| 1311 | { |
---|
| 1312 | rDelete(e->r); |
---|
| 1313 | return TRUE; |
---|
| 1314 | } |
---|
| 1315 | |
---|
[a355723] | 1316 | return FALSE; |
---|
[6ccdd3a] | 1317 | } |
---|
| 1318 | |
---|
[2c7f28] | 1319 | number ntLcm(number a, number b, const coeffs cf) |
---|
[6ccdd3a] | 1320 | { |
---|
[dc79bd] | 1321 | ntTest(a); |
---|
| 1322 | ntTest(b); |
---|
[1577ebd] | 1323 | fraction fb = (fraction)b; |
---|
| 1324 | if ((b==NULL)||(DEN(fb)==NULL)) return ntCopy(a,cf); |
---|
[c14846c] | 1325 | #ifdef HAVE_FACTORY |
---|
[1577ebd] | 1326 | fraction fa = (fraction)a; |
---|
| 1327 | /* singclap_gcd destroys its arguments; we hence need copies: */ |
---|
| 1328 | poly pa = p_Copy(NUM(fa), ntRing); |
---|
| 1329 | poly pb = p_Copy(DEN(fb), ntRing); |
---|
[c14846c] | 1330 | |
---|
[1577ebd] | 1331 | /* Note that, over Q, singclap_gcd will remove the denominators in all |
---|
| 1332 | rational coefficients of pa and pb, before starting to compute |
---|
| 1333 | the gcd. Thus, we do not need to ensure that the coefficients of |
---|
| 1334 | pa and pb live in Z; they may well be elements of Q\Z. */ |
---|
| 1335 | poly pGcd = singclap_gcd(pa, pb, cf->extRing); |
---|
| 1336 | if (p_IsConstant(pGcd, ntRing) && |
---|
| 1337 | n_IsOne(p_GetCoeff(pGcd, ntRing), ntCoeffs)) |
---|
| 1338 | { /* gcd = 1; return pa*pb*/ |
---|
| 1339 | p_Delete(&pGcd,ntRing); |
---|
| 1340 | fraction result = (fraction)omAlloc0Bin(fractionObjectBin); |
---|
| 1341 | NUM(result) = pp_Mult_qq(NUM(fa),DEN(fb),ntRing); |
---|
[dc79bd] | 1342 | |
---|
| 1343 | ntTest((number)result); // !!!! |
---|
[a355723] | 1344 | |
---|
[1577ebd] | 1345 | return (number)result; |
---|
| 1346 | } |
---|
[a355723] | 1347 | |
---|
[dc79bd] | 1348 | |
---|
| 1349 | /* return pa*pb/gcd */ |
---|
[1577ebd] | 1350 | poly newNum = singclap_pdivide(NUM(fa), pGcd, ntRing); |
---|
[331fd0] | 1351 | p_Delete(&pGcd,ntRing); |
---|
[1577ebd] | 1352 | fraction result = (fraction)omAlloc0Bin(fractionObjectBin); |
---|
| 1353 | NUM(result) = p_Mult_q(p_Copy(DEN(fb),ntRing),newNum,ntRing); |
---|
[dc79bd] | 1354 | ntTest((number)result); // !!!! |
---|
[1577ebd] | 1355 | return (number)result; |
---|
[a355723] | 1356 | |
---|
[1577ebd] | 1357 | #else |
---|
| 1358 | Print("// factory needed: transext.cc:ntLcm\n"); |
---|
| 1359 | return NULL; |
---|
| 1360 | #endif /* HAVE_FACTORY */ |
---|
[2c7f28] | 1361 | return NULL; |
---|
[6ccdd3a] | 1362 | } |
---|
| 1363 | |
---|
[2c7f28] | 1364 | number ntGcd(number a, number b, const coeffs cf) |
---|
[6ccdd3a] | 1365 | { |
---|
[dc79bd] | 1366 | ntTest(a); |
---|
| 1367 | ntTest(b); |
---|
[1577ebd] | 1368 | if (a==NULL) return ntCopy(b,cf); |
---|
| 1369 | if (b==NULL) return ntCopy(a,cf); |
---|
[c14846c] | 1370 | #ifdef HAVE_FACTORY |
---|
[1577ebd] | 1371 | fraction fa = (fraction)a; |
---|
| 1372 | fraction fb = (fraction)b; |
---|
| 1373 | /* singclap_gcd destroys its arguments; we hence need copies: */ |
---|
| 1374 | poly pa = p_Copy(NUM(fa), ntRing); |
---|
| 1375 | poly pb = p_Copy(NUM(fb), ntRing); |
---|
[c14846c] | 1376 | |
---|
[1577ebd] | 1377 | /* Note that, over Q, singclap_gcd will remove the denominators in all |
---|
| 1378 | rational coefficients of pa and pb, before starting to compute |
---|
| 1379 | the gcd. Thus, we do not need to ensure that the coefficients of |
---|
| 1380 | pa and pb live in Z; they may well be elements of Q\Z. */ |
---|
| 1381 | poly pGcd = singclap_gcd(pa, pb, cf->extRing); |
---|
| 1382 | fraction result = (fraction)omAlloc0Bin(fractionObjectBin); |
---|
| 1383 | NUM(result) = pGcd; |
---|
[dc79bd] | 1384 | ntTest((number)result); // !!!! |
---|
[1577ebd] | 1385 | return (number)result; |
---|
| 1386 | #else |
---|
| 1387 | Print("// factory needed: transext.cc:ntGcd\n"); |
---|
[2c7f28] | 1388 | return NULL; |
---|
[1577ebd] | 1389 | #endif /* HAVE_FACTORY */ |
---|
[6ccdd3a] | 1390 | } |
---|
| 1391 | |
---|
[2c7f28] | 1392 | int ntSize(number a, const coeffs cf) |
---|
[6ccdd3a] | 1393 | { |
---|
[2c7f28] | 1394 | ntTest(a); |
---|
[e5d267] | 1395 | if (IS0(a)) return -1; |
---|
[2c7f28] | 1396 | /* this has been taken from the old implementation of field extensions, |
---|
| 1397 | where we computed the sum of the degrees and the numbers of terms in |
---|
| 1398 | the numerator and denominator of a; so we leave it at that, for the |
---|
| 1399 | time being */ |
---|
| 1400 | fraction f = (fraction)a; |
---|
[e5d267] | 1401 | poly p = NUM(f); |
---|
[2c7f28] | 1402 | int noOfTerms = 0; |
---|
| 1403 | int numDegree = 0; |
---|
| 1404 | while (p != NULL) |
---|
| 1405 | { |
---|
| 1406 | noOfTerms++; |
---|
| 1407 | int d = 0; |
---|
| 1408 | for (int i = 1; i <= rVar(ntRing); i++) |
---|
| 1409 | d += p_GetExp(p, i, ntRing); |
---|
| 1410 | if (d > numDegree) numDegree = d; |
---|
| 1411 | pIter(p); |
---|
| 1412 | } |
---|
| 1413 | int denDegree = 0; |
---|
[e5d267] | 1414 | if (!DENIS1(f)) |
---|
[2c7f28] | 1415 | { |
---|
[e5d267] | 1416 | p = DEN(f); |
---|
[2c7f28] | 1417 | while (p != NULL) |
---|
| 1418 | { |
---|
| 1419 | noOfTerms++; |
---|
| 1420 | int d = 0; |
---|
| 1421 | for (int i = 1; i <= rVar(ntRing); i++) |
---|
| 1422 | d += p_GetExp(p, i, ntRing); |
---|
| 1423 | if (d > denDegree) denDegree = d; |
---|
| 1424 | pIter(p); |
---|
| 1425 | } |
---|
| 1426 | } |
---|
[dc79bd] | 1427 | ntTest(a); // !!!! |
---|
[2c7f28] | 1428 | return numDegree + denDegree + noOfTerms; |
---|
[6ccdd3a] | 1429 | } |
---|
| 1430 | |
---|
[2c7f28] | 1431 | number ntInvers(number a, const coeffs cf) |
---|
[6ccdd3a] | 1432 | { |
---|
[2c7f28] | 1433 | ntTest(a); |
---|
[dc79bd] | 1434 | if (IS0(a)) |
---|
[a355723] | 1435 | { |
---|
[dc79bd] | 1436 | WerrorS(nDivBy0); |
---|
| 1437 | return NULL; |
---|
[a355723] | 1438 | } |
---|
[2c7f28] | 1439 | fraction f = (fraction)a; |
---|
[dc79bd] | 1440 | assume( f != NULL ); |
---|
| 1441 | |
---|
[2c7f28] | 1442 | fraction result = (fraction)omAlloc0Bin(fractionObjectBin); |
---|
[dc79bd] | 1443 | |
---|
| 1444 | assume( NUM(f) != NULL ); |
---|
| 1445 | const poly den = DEN(f); |
---|
[a355723] | 1446 | |
---|
[dc79bd] | 1447 | if (den == NULL) |
---|
| 1448 | NUM(result) = p_One(ntRing); |
---|
| 1449 | else |
---|
| 1450 | NUM(result) = p_Copy(den, ntRing); |
---|
| 1451 | |
---|
| 1452 | if( !NUMIS1(f) ) |
---|
| 1453 | { |
---|
[a355723] | 1454 | poly num_f=NUM(f); |
---|
[e5c9e5] | 1455 | BOOLEAN neg= !n_GreaterZero(pGetCoeff(num_f),ntCoeffs); |
---|
[a355723] | 1456 | if (neg) |
---|
| 1457 | { |
---|
| 1458 | num_f=p_Neg(p_Copy(num_f, ntRing), ntRing); |
---|
| 1459 | NUM(result)=p_Neg(NUM(result), ntRing); |
---|
| 1460 | } |
---|
| 1461 | else |
---|
| 1462 | { |
---|
| 1463 | num_f=p_Copy(num_f, ntRing); |
---|
| 1464 | } |
---|
| 1465 | DEN(result) = num_f; |
---|
[dc79bd] | 1466 | COM(result) = COM(f); |
---|
[a355723] | 1467 | if (neg) |
---|
| 1468 | { |
---|
| 1469 | if (p_IsOne(num_f, ntRing)) |
---|
| 1470 | { |
---|
| 1471 | DEN(result)=NULL; |
---|
| 1472 | COM(result) = 0; |
---|
| 1473 | p_Delete(&num_f,ntRing); |
---|
| 1474 | } |
---|
| 1475 | } |
---|
[dc79bd] | 1476 | } |
---|
| 1477 | else |
---|
| 1478 | { |
---|
| 1479 | DEN(result) = NULL; |
---|
| 1480 | COM(result) = 0; |
---|
| 1481 | } |
---|
| 1482 | ntTest((number)result); // !!!! |
---|
[2c7f28] | 1483 | return (number)result; |
---|
[6ccdd3a] | 1484 | } |
---|
| 1485 | |
---|
[2c7f28] | 1486 | /* assumes that src = Q, dst = Q(t_1, ..., t_s) */ |
---|
| 1487 | number ntMap00(number a, const coeffs src, const coeffs dst) |
---|
[6ccdd3a] | 1488 | { |
---|
[2c7f28] | 1489 | if (n_IsZero(a, src)) return NULL; |
---|
[dc79bd] | 1490 | assume(n_Test(a, src)); |
---|
[6ccdd3a] | 1491 | assume(src == dst->extRing->cf); |
---|
[0c516e] | 1492 | if ((SR_HDL(a) & SR_INT) || (a->s==3)) |
---|
[9d68fd] | 1493 | { |
---|
| 1494 | number res=ntInit(p_NSet(n_Copy(a, src), dst->extRing), dst); |
---|
| 1495 | n_Test(res,dst); |
---|
| 1496 | return res; |
---|
| 1497 | } |
---|
[0c516e] | 1498 | number nn=nlGetDenom(a,src); |
---|
| 1499 | number zz=nlGetNumerator(a,src); |
---|
| 1500 | number res=ntInit(p_NSet(zz,dst->extRing), dst); |
---|
| 1501 | fraction ff=(fraction)res; |
---|
[9d68fd] | 1502 | if (n_IsOne(nn,src)) DEN(ff)=NULL; |
---|
| 1503 | else DEN(ff)=p_NSet(nn,dst->extRing); |
---|
| 1504 | n_Test((number)ff,dst); |
---|
[0c516e] | 1505 | return (number)ff; |
---|
[6ccdd3a] | 1506 | } |
---|
| 1507 | |
---|
[2c7f28] | 1508 | /* assumes that src = Z/p, dst = Q(t_1, ..., t_s) */ |
---|
| 1509 | number ntMapP0(number a, const coeffs src, const coeffs dst) |
---|
[6ccdd3a] | 1510 | { |
---|
[2c7f28] | 1511 | if (n_IsZero(a, src)) return NULL; |
---|
[dc79bd] | 1512 | assume(n_Test(a, src)); |
---|
[6ccdd3a] | 1513 | /* mapping via intermediate int: */ |
---|
| 1514 | int n = n_Int(a, src); |
---|
| 1515 | number q = n_Init(n, dst->extRing->cf); |
---|
[2c7f28] | 1516 | if (n_IsZero(q, dst->extRing->cf)) |
---|
| 1517 | { |
---|
| 1518 | n_Delete(&q, dst->extRing->cf); |
---|
| 1519 | return NULL; |
---|
| 1520 | } |
---|
[dc79bd] | 1521 | return ntInit(p_NSet(q, dst->extRing), dst); |
---|
[6ccdd3a] | 1522 | } |
---|
| 1523 | |
---|
[2c7f28] | 1524 | /* assumes that either src = Q(t_1, ..., t_s), dst = Q(t_1, ..., t_s), or |
---|
| 1525 | src = Z/p(t_1, ..., t_s), dst = Z/p(t_1, ..., t_s) */ |
---|
[b38d70] | 1526 | number ntCopyMap(number a, const coeffs cf, const coeffs dst) |
---|
[6ccdd3a] | 1527 | { |
---|
[b38d70] | 1528 | // if (n_IsZero(a, cf)) return NULL; |
---|
[a355723] | 1529 | |
---|
[b38d70] | 1530 | ntTest(a); |
---|
| 1531 | |
---|
| 1532 | if (IS0(a)) return NULL; |
---|
[a355723] | 1533 | |
---|
[b38d70] | 1534 | const ring rSrc = cf->extRing; |
---|
| 1535 | const ring rDst = dst->extRing; |
---|
[a355723] | 1536 | |
---|
[b38d70] | 1537 | if( rSrc == rDst ) |
---|
| 1538 | return ntCopy(a, dst); // USUALLY WRONG! |
---|
[a355723] | 1539 | |
---|
[b38d70] | 1540 | fraction f = (fraction)a; |
---|
| 1541 | poly g = prCopyR(NUM(f), rSrc, rDst); |
---|
[a355723] | 1542 | |
---|
[b38d70] | 1543 | poly h = NULL; |
---|
[a355723] | 1544 | |
---|
[b38d70] | 1545 | if (!DENIS1(f)) |
---|
| 1546 | h = prCopyR(DEN(f), rSrc, rDst); |
---|
[a355723] | 1547 | |
---|
[b38d70] | 1548 | fraction result = (fraction)omAlloc0Bin(fractionObjectBin); |
---|
[a355723] | 1549 | |
---|
[b38d70] | 1550 | NUM(result) = g; |
---|
| 1551 | DEN(result) = h; |
---|
| 1552 | COM(result) = COM(f); |
---|
[dc79bd] | 1553 | assume(n_Test((number)result, dst)); |
---|
[a355723] | 1554 | return (number)result; |
---|
[6ccdd3a] | 1555 | } |
---|
| 1556 | |
---|
[b38d70] | 1557 | number ntCopyAlg(number a, const coeffs cf, const coeffs dst) |
---|
[31c731] | 1558 | { |
---|
[dc79bd] | 1559 | assume( n_Test(a, cf) ); |
---|
[b38d70] | 1560 | if (n_IsZero(a, cf)) return NULL; |
---|
[a355723] | 1561 | |
---|
| 1562 | fraction f = (fraction)omAlloc0Bin(fractionObjectBin); |
---|
[b38d70] | 1563 | // DEN(f) = NULL; COM(f) = 0; |
---|
| 1564 | NUM(f) = prCopyR((poly)a, cf->extRing, dst->extRing); |
---|
[dc79bd] | 1565 | assume(n_Test((number)f, dst)); |
---|
[31c731] | 1566 | return (number)f; |
---|
| 1567 | } |
---|
| 1568 | |
---|
[2c7f28] | 1569 | /* assumes that src = Q, dst = Z/p(t_1, ..., t_s) */ |
---|
| 1570 | number ntMap0P(number a, const coeffs src, const coeffs dst) |
---|
[6ccdd3a] | 1571 | { |
---|
[dc79bd] | 1572 | assume( n_Test(a, src) ); |
---|
[2c7f28] | 1573 | if (n_IsZero(a, src)) return NULL; |
---|
[6909cfb] | 1574 | // int p = rChar(dst->extRing); |
---|
[79020f] | 1575 | number q = nlModP(a, src, dst->extRing->cf); |
---|
| 1576 | |
---|
[2c7f28] | 1577 | if (n_IsZero(q, dst->extRing->cf)) |
---|
| 1578 | { |
---|
| 1579 | n_Delete(&q, dst->extRing->cf); |
---|
| 1580 | return NULL; |
---|
| 1581 | } |
---|
[a355723] | 1582 | |
---|
[79020f] | 1583 | poly g = p_NSet(q, dst->extRing); |
---|
| 1584 | |
---|
[2c7f28] | 1585 | fraction f = (fraction)omAlloc0Bin(fractionObjectBin); |
---|
[31c731] | 1586 | NUM(f) = g; // DEN(f) = NULL; COM(f) = 0; |
---|
[dc79bd] | 1587 | assume(n_Test((number)f, dst)); |
---|
[2c7f28] | 1588 | return (number)f; |
---|
[6ccdd3a] | 1589 | } |
---|
| 1590 | |
---|
[2c7f28] | 1591 | /* assumes that src = Z/p, dst = Z/p(t_1, ..., t_s) */ |
---|
| 1592 | number ntMapPP(number a, const coeffs src, const coeffs dst) |
---|
[6ccdd3a] | 1593 | { |
---|
[dc79bd] | 1594 | assume( n_Test(a, src) ); |
---|
[2c7f28] | 1595 | if (n_IsZero(a, src)) return NULL; |
---|
[6ccdd3a] | 1596 | assume(src == dst->extRing->cf); |
---|
[2c7f28] | 1597 | poly p = p_One(dst->extRing); |
---|
[a0acbc] | 1598 | p_SetCoeff(p, n_Copy(a, src), dst->extRing); |
---|
[2c7f28] | 1599 | fraction f = (fraction)omAlloc0Bin(fractionObjectBin); |
---|
[e5d267] | 1600 | NUM(f) = p; DEN(f) = NULL; COM(f) = 0; |
---|
[dc79bd] | 1601 | assume(n_Test((number)f, dst)); |
---|
[2c7f28] | 1602 | return (number)f; |
---|
[6ccdd3a] | 1603 | } |
---|
| 1604 | |
---|
[2c7f28] | 1605 | /* assumes that src = Z/u, dst = Z/p(t_1, ..., t_s), where u != p */ |
---|
| 1606 | number ntMapUP(number a, const coeffs src, const coeffs dst) |
---|
[6ccdd3a] | 1607 | { |
---|
[dc79bd] | 1608 | assume( n_Test(a, src) ); |
---|
[2c7f28] | 1609 | if (n_IsZero(a, src)) return NULL; |
---|
[6ccdd3a] | 1610 | /* mapping via intermediate int: */ |
---|
| 1611 | int n = n_Int(a, src); |
---|
| 1612 | number q = n_Init(n, dst->extRing->cf); |
---|
[2c7f28] | 1613 | poly p; |
---|
| 1614 | if (n_IsZero(q, dst->extRing->cf)) |
---|
| 1615 | { |
---|
| 1616 | n_Delete(&q, dst->extRing->cf); |
---|
| 1617 | return NULL; |
---|
| 1618 | } |
---|
| 1619 | p = p_One(dst->extRing); |
---|
| 1620 | p_SetCoeff(p, q, dst->extRing); |
---|
| 1621 | fraction f = (fraction)omAlloc0Bin(fractionObjectBin); |
---|
[e5d267] | 1622 | NUM(f) = p; DEN(f) = NULL; COM(f) = 0; |
---|
[dc79bd] | 1623 | assume(n_Test((number)f, dst)); |
---|
[2c7f28] | 1624 | return (number)f; |
---|
[6ccdd3a] | 1625 | } |
---|
| 1626 | |
---|
[2c7f28] | 1627 | nMapFunc ntSetMap(const coeffs src, const coeffs dst) |
---|
[6ccdd3a] | 1628 | { |
---|
[2c7f28] | 1629 | /* dst is expected to be a rational function field */ |
---|
[1f414c8] | 1630 | assume(getCoeffType(dst) == ID); |
---|
[c14846c] | 1631 | |
---|
[da0565b] | 1632 | if( src == dst ) return ndCopyMap; |
---|
| 1633 | |
---|
[6ccdd3a] | 1634 | int h = 0; /* the height of the extension tower given by dst */ |
---|
| 1635 | coeffs bDst = nCoeff_bottom(dst, h); /* the bottom field in the tower dst */ |
---|
[331fd0] | 1636 | coeffs bSrc = nCoeff_bottom(src, h); /* the bottom field in the tower src */ |
---|
[c14846c] | 1637 | |
---|
[6ccdd3a] | 1638 | /* for the time being, we only provide maps if h = 1 and if b is Q or |
---|
| 1639 | some field Z/pZ: */ |
---|
[31c731] | 1640 | if (h==0) |
---|
| 1641 | { |
---|
| 1642 | if (nCoeff_is_Q(src) && nCoeff_is_Q(bDst)) |
---|
| 1643 | return ntMap00; /// Q --> Q(T) |
---|
| 1644 | if (nCoeff_is_Zp(src) && nCoeff_is_Q(bDst)) |
---|
| 1645 | return ntMapP0; /// Z/p --> Q(T) |
---|
| 1646 | if (nCoeff_is_Q(src) && nCoeff_is_Zp(bDst)) |
---|
| 1647 | return ntMap0P; /// Q --> Z/p(T) |
---|
| 1648 | if (nCoeff_is_Zp(src) && nCoeff_is_Zp(bDst)) |
---|
| 1649 | { |
---|
| 1650 | if (src->ch == dst->ch) return ntMapPP; /// Z/p --> Z/p(T) |
---|
| 1651 | else return ntMapUP; /// Z/u --> Z/p(T) |
---|
| 1652 | } |
---|
| 1653 | } |
---|
[6ccdd3a] | 1654 | if (h != 1) return NULL; |
---|
| 1655 | if ((!nCoeff_is_Zp(bDst)) && (!nCoeff_is_Q(bDst))) return NULL; |
---|
[c14846c] | 1656 | |
---|
[2c7f28] | 1657 | /* Let T denote the sequence of transcendental extension variables, i.e., |
---|
| 1658 | K[t_1, ..., t_s] =: K[T]; |
---|
| 1659 | Let moreover, for any such sequence T, T' denote any subsequence of T |
---|
| 1660 | of the form t_1, ..., t_w with w <= s. */ |
---|
[c14846c] | 1661 | |
---|
[6ccdd3a] | 1662 | if ((!nCoeff_is_Zp(bSrc)) && (!nCoeff_is_Q(bSrc))) return NULL; |
---|
[c14846c] | 1663 | |
---|
[6ccdd3a] | 1664 | if (nCoeff_is_Q(bSrc) && nCoeff_is_Q(bDst)) |
---|
| 1665 | { |
---|
[a355723] | 1666 | if (rVar(src->extRing) > rVar(dst->extRing)) |
---|
[b38d70] | 1667 | return NULL; |
---|
[a355723] | 1668 | |
---|
[2c7f28] | 1669 | for (int i = 0; i < rVar(src->extRing); i++) |
---|
[a355723] | 1670 | if (strcmp(rRingVar(i, src->extRing), rRingVar(i, dst->extRing)) != 0) |
---|
| 1671 | return NULL; |
---|
| 1672 | |
---|
[b38d70] | 1673 | if (src->type==n_transExt) |
---|
| 1674 | return ntCopyMap; /// Q(T') --> Q(T) |
---|
| 1675 | else |
---|
| 1676 | return ntCopyAlg; |
---|
[6ccdd3a] | 1677 | } |
---|
[c14846c] | 1678 | |
---|
[6ccdd3a] | 1679 | if (nCoeff_is_Zp(bSrc) && nCoeff_is_Zp(bDst)) |
---|
| 1680 | { |
---|
[a355723] | 1681 | if (rVar(src->extRing) > rVar(dst->extRing)) |
---|
[b38d70] | 1682 | return NULL; |
---|
[a355723] | 1683 | |
---|
[2c7f28] | 1684 | for (int i = 0; i < rVar(src->extRing); i++) |
---|
[a355723] | 1685 | if (strcmp(rRingVar(i, src->extRing), rRingVar(i, dst->extRing)) != 0) |
---|
| 1686 | return NULL; |
---|
| 1687 | |
---|
[b38d70] | 1688 | if (src->type==n_transExt) |
---|
| 1689 | return ntCopyMap; /// Z/p(T') --> Z/p(T) |
---|
| 1690 | else |
---|
| 1691 | return ntCopyAlg; |
---|
[6ccdd3a] | 1692 | } |
---|
[c14846c] | 1693 | |
---|
| 1694 | return NULL; /// default |
---|
[6ccdd3a] | 1695 | } |
---|
[c8e030] | 1696 | #if 0 |
---|
| 1697 | nMapFunc ntSetMap_T(const coeffs src, const coeffs dst) |
---|
| 1698 | { |
---|
| 1699 | nMapFunc n=ntSetMap(src,dst); |
---|
| 1700 | if (n==ntCopyAlg) printf("n=ntCopyAlg\n"); |
---|
| 1701 | else if (n==ntCopyMap) printf("n=ntCopyMap\n"); |
---|
| 1702 | else if (n==ntMapUP) printf("n=ntMapUP\n"); |
---|
| 1703 | else if (n==ntMap0P) printf("n=ntMap0P\n"); |
---|
| 1704 | else if (n==ntMapP0) printf("n=ntMapP0\n"); |
---|
| 1705 | else if (n==ntMap00) printf("n=ntMap00\n"); |
---|
| 1706 | else if (n==NULL) printf("n=NULL\n"); |
---|
| 1707 | else printf("n=?\n"); |
---|
| 1708 | return n; |
---|
| 1709 | } |
---|
| 1710 | #endif |
---|
[6ccdd3a] | 1711 | |
---|
[31c731] | 1712 | void ntKillChar(coeffs cf) |
---|
| 1713 | { |
---|
[a195ed] | 1714 | if ((--cf->extRing->ref) == 0) |
---|
| 1715 | rDelete(cf->extRing); |
---|
| 1716 | } |
---|
[fc4977] | 1717 | #ifdef HAVE_FACTORY |
---|
| 1718 | number ntConvFactoryNSingN( const CanonicalForm n, const coeffs cf) |
---|
| 1719 | { |
---|
| 1720 | if (n.isZero()) return NULL; |
---|
| 1721 | poly p=convFactoryPSingP(n,ntRing); |
---|
| 1722 | fraction result = (fraction)omAlloc0Bin(fractionObjectBin); |
---|
| 1723 | NUM(result) = p; |
---|
| 1724 | //DEN(result) = NULL; // done by omAlloc0Bin |
---|
| 1725 | //COM(result) = 0; // done by omAlloc0Bin |
---|
[dc79bd] | 1726 | ntTest((number)result); |
---|
[fc4977] | 1727 | return (number)result; |
---|
| 1728 | } |
---|
[2e4ec14] | 1729 | CanonicalForm ntConvSingNFactoryN( number n, BOOLEAN /*setChar*/, const coeffs cf ) |
---|
[fc4977] | 1730 | { |
---|
| 1731 | ntTest(n); |
---|
| 1732 | if (IS0(n)) return CanonicalForm(0); |
---|
| 1733 | |
---|
| 1734 | fraction f = (fraction)n; |
---|
| 1735 | return convSingPFactoryP(NUM(f),ntRing); |
---|
| 1736 | } |
---|
| 1737 | #endif |
---|
[a195ed] | 1738 | |
---|
[da5d77] | 1739 | static int ntParDeg(number a, const coeffs cf) |
---|
[48a41a] | 1740 | { |
---|
[dc79bd] | 1741 | ntTest(a); |
---|
[48a41a] | 1742 | if (IS0(a)) return -1; |
---|
| 1743 | fraction fa = (fraction)a; |
---|
| 1744 | return cf->extRing->pFDeg(NUM(fa),cf->extRing); |
---|
| 1745 | } |
---|
| 1746 | |
---|
[7fee876] | 1747 | /// return the specified parameter as a number in the given trans.ext. |
---|
| 1748 | static number ntParameter(const int iParameter, const coeffs cf) |
---|
| 1749 | { |
---|
| 1750 | assume(getCoeffType(cf) == ID); |
---|
| 1751 | |
---|
| 1752 | const ring R = cf->extRing; |
---|
| 1753 | assume( R != NULL ); |
---|
| 1754 | assume( 0 < iParameter && iParameter <= rVar(R) ); |
---|
| 1755 | |
---|
| 1756 | poly p = p_One(R); p_SetExp(p, iParameter, 1, R); p_Setm(p, R); |
---|
[9d68fd] | 1757 | p_Test(p,R); |
---|
[7fee876] | 1758 | |
---|
| 1759 | fraction f = (fraction)omAlloc0Bin(fractionObjectBin); |
---|
| 1760 | NUM(f) = p; |
---|
| 1761 | DEN(f) = NULL; |
---|
| 1762 | COM(f) = 0; |
---|
| 1763 | |
---|
[dc79bd] | 1764 | ntTest((number)f); |
---|
| 1765 | |
---|
[7fee876] | 1766 | return (number)f; |
---|
| 1767 | } |
---|
| 1768 | |
---|
| 1769 | /// if m == var(i)/1 => return i, |
---|
| 1770 | int ntIsParam(number m, const coeffs cf) |
---|
| 1771 | { |
---|
[dc79bd] | 1772 | ntTest(m); |
---|
[7fee876] | 1773 | assume(getCoeffType(cf) == ID); |
---|
| 1774 | |
---|
| 1775 | const ring R = cf->extRing; |
---|
| 1776 | assume( R != NULL ); |
---|
| 1777 | |
---|
| 1778 | fraction f = (fraction)m; |
---|
| 1779 | |
---|
| 1780 | if( DEN(f) != NULL ) |
---|
| 1781 | return 0; |
---|
| 1782 | |
---|
| 1783 | return p_Var( NUM(f), R ); |
---|
| 1784 | } |
---|
| 1785 | |
---|
[dc79bd] | 1786 | struct NTNumConverter |
---|
| 1787 | { |
---|
| 1788 | static inline poly convert(const number& n) |
---|
| 1789 | { |
---|
| 1790 | // suitable for trans. ext. numbers that are fractions of polys |
---|
| 1791 | return NUM((fraction)n); // return the numerator |
---|
| 1792 | } |
---|
| 1793 | }; |
---|
| 1794 | |
---|
| 1795 | |
---|
| 1796 | static void ntClearContent(ICoeffsEnumerator& numberCollectionEnumerator, number& c, const coeffs cf) |
---|
[de88371] | 1797 | { |
---|
| 1798 | assume(cf != NULL); |
---|
| 1799 | assume(getCoeffType(cf) == ID); |
---|
[dc79bd] | 1800 | // all coeffs are given by fractions of polynomails over integers!!! |
---|
| 1801 | // without denominators!!! |
---|
| 1802 | |
---|
| 1803 | const ring R = cf->extRing; |
---|
| 1804 | assume(R != NULL); |
---|
[a355723] | 1805 | const coeffs Q = R->cf; |
---|
| 1806 | assume(Q != NULL); |
---|
| 1807 | assume(nCoeff_is_Q(Q)); |
---|
| 1808 | |
---|
[dc79bd] | 1809 | |
---|
| 1810 | numberCollectionEnumerator.Reset(); |
---|
| 1811 | |
---|
| 1812 | if( !numberCollectionEnumerator.MoveNext() ) // empty zero polynomial? |
---|
| 1813 | { |
---|
| 1814 | c = ntInit(1, cf); |
---|
| 1815 | return; |
---|
| 1816 | } |
---|
| 1817 | |
---|
| 1818 | // all coeffs are given by integers after returning from this routine |
---|
| 1819 | |
---|
| 1820 | // part 1, collect product of all denominators /gcds |
---|
| 1821 | poly cand = NULL; |
---|
| 1822 | |
---|
| 1823 | do |
---|
| 1824 | { |
---|
| 1825 | number &n = numberCollectionEnumerator.Current(); |
---|
| 1826 | |
---|
| 1827 | ntNormalize(n, cf); |
---|
| 1828 | |
---|
| 1829 | fraction f = (fraction)n; |
---|
| 1830 | |
---|
| 1831 | assume( f != NULL ); |
---|
| 1832 | |
---|
| 1833 | const poly den = DEN(f); |
---|
| 1834 | |
---|
| 1835 | assume( den == NULL ); // ?? / 1 ? |
---|
| 1836 | |
---|
| 1837 | const poly num = NUM(f); |
---|
| 1838 | |
---|
| 1839 | if( cand == NULL ) |
---|
| 1840 | cand = p_Copy(num, R); |
---|
| 1841 | else |
---|
| 1842 | cand = singclap_gcd(cand, p_Copy(num, R), R); // gcd(cand, num) |
---|
| 1843 | |
---|
| 1844 | if( p_IsConstant(cand, R) ) |
---|
| 1845 | break; |
---|
| 1846 | } |
---|
| 1847 | while( numberCollectionEnumerator.MoveNext() ) ; |
---|
| 1848 | |
---|
[a355723] | 1849 | |
---|
[dc79bd] | 1850 | // part2: all coeffs = all coeffs * cand |
---|
| 1851 | if( cand != NULL ) |
---|
| 1852 | { |
---|
| 1853 | if( !p_IsConstant(cand, R) ) |
---|
| 1854 | { |
---|
[a355723] | 1855 | c = ntInit(cand, cf); |
---|
[dc79bd] | 1856 | numberCollectionEnumerator.Reset(); |
---|
| 1857 | while (numberCollectionEnumerator.MoveNext() ) |
---|
| 1858 | { |
---|
| 1859 | number &n = numberCollectionEnumerator.Current(); |
---|
| 1860 | const number t = ntDiv(n, c, cf); // TODO: rewrite!? |
---|
| 1861 | ntDelete(&n, cf); |
---|
| 1862 | n = t; |
---|
| 1863 | } |
---|
| 1864 | } // else NUM (result) = p_One(R); |
---|
| 1865 | else { p_Delete(&cand, R); cand = NULL; } |
---|
| 1866 | } |
---|
[a355723] | 1867 | |
---|
[dc79bd] | 1868 | // Quick and dirty fix for constant content clearing: consider numerators??? |
---|
| 1869 | CRecursivePolyCoeffsEnumerator<NTNumConverter> itr(numberCollectionEnumerator); // recursively treat the NUM(numbers) as polys! |
---|
| 1870 | number cc; |
---|
[a355723] | 1871 | |
---|
[558f3cc] | 1872 | n_ClearContent(itr, cc, Q); |
---|
[dc79bd] | 1873 | number g = ntInit(p_NSet(cc, R), cf); |
---|
[a355723] | 1874 | |
---|
[dc79bd] | 1875 | if( cand != NULL ) |
---|
| 1876 | { |
---|
| 1877 | number gg = ntMult(g, c, cf); |
---|
[a355723] | 1878 | ntDelete(&g, cf); |
---|
[dc79bd] | 1879 | ntDelete(&c, cf); c = gg; |
---|
[a355723] | 1880 | } else |
---|
[dc79bd] | 1881 | c = g; |
---|
| 1882 | ntTest(c); |
---|
[de88371] | 1883 | } |
---|
| 1884 | |
---|
[dc79bd] | 1885 | static void ntClearDenominators(ICoeffsEnumerator& numberCollectionEnumerator, number& c, const coeffs cf) |
---|
[de88371] | 1886 | { |
---|
| 1887 | assume(cf != NULL); |
---|
| 1888 | assume(getCoeffType(cf) == ID); // both over Q(a) and Zp(a)! |
---|
[dc79bd] | 1889 | // all coeffs are given by fractions of polynomails over integers!!! |
---|
| 1890 | |
---|
| 1891 | numberCollectionEnumerator.Reset(); |
---|
| 1892 | |
---|
| 1893 | if( !numberCollectionEnumerator.MoveNext() ) // empty zero polynomial? |
---|
| 1894 | { |
---|
| 1895 | c = ntInit(1, cf); |
---|
| 1896 | return; |
---|
| 1897 | } |
---|
| 1898 | |
---|
| 1899 | // all coeffs are given by integers after returning from this routine |
---|
| 1900 | |
---|
| 1901 | // part 1, collect product of all denominators /gcds |
---|
| 1902 | poly cand = NULL; |
---|
| 1903 | |
---|
| 1904 | const ring R = cf->extRing; |
---|
[a355723] | 1905 | assume(R != NULL); |
---|
[dc79bd] | 1906 | |
---|
[a355723] | 1907 | const coeffs Q = R->cf; |
---|
| 1908 | assume(Q != NULL); |
---|
| 1909 | // assume(nCoeff_is_Q(Q)); |
---|
[dc79bd] | 1910 | |
---|
| 1911 | do |
---|
| 1912 | { |
---|
| 1913 | number &n = numberCollectionEnumerator.Current(); |
---|
[a355723] | 1914 | |
---|
[dc79bd] | 1915 | ntNormalize(n, cf); |
---|
| 1916 | |
---|
[e56eb1a] | 1917 | fraction f = (fraction)ntGetDenom (n, cf); |
---|
[dc79bd] | 1918 | |
---|
| 1919 | assume( f != NULL ); |
---|
| 1920 | |
---|
[e56eb1a] | 1921 | const poly den = NUM(f); |
---|
[dc79bd] | 1922 | |
---|
| 1923 | if( den == NULL ) // ?? / 1 ? |
---|
| 1924 | continue; |
---|
| 1925 | |
---|
| 1926 | if( cand == NULL ) |
---|
| 1927 | cand = p_Copy(den, R); |
---|
| 1928 | else |
---|
| 1929 | { |
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| 1930 | // cand === LCM( cand, den )!!!! |
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| 1931 | // NOTE: maybe it's better to make the product and clearcontent afterwards!? |
---|
| 1932 | // TODO: move the following to factory? |
---|
| 1933 | poly gcd = singclap_gcd(p_Copy(cand, R), p_Copy(den, R), R); // gcd(cand, den) is monic no mater leading coeffs! :(((( |
---|
[e56eb1a] | 1934 | if (nCoeff_is_Q (Q)) |
---|
| 1935 | { |
---|
| 1936 | number LcGcd= n_Gcd (p_GetCoeff (cand, R), p_GetCoeff(den, R), Q); |
---|
| 1937 | gcd = p_Mult_nn(gcd, LcGcd, R); |
---|
[20c99b] | 1938 | n_Delete(&LcGcd,Q); |
---|
[e56eb1a] | 1939 | } |
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[dc79bd] | 1940 | // assume( n_IsOne(pGetCoeff(gcd), Q) ); // TODO: this may be wrong... |
---|
[a355723] | 1941 | cand = p_Mult_q(cand, p_Copy(den, R), R); // cand *= den |
---|
[dc79bd] | 1942 | const poly t = singclap_pdivide( cand, gcd, R ); // cand' * den / gcd(cand', den) |
---|
| 1943 | p_Delete(&cand, R); |
---|
| 1944 | p_Delete(&gcd, R); |
---|
| 1945 | cand = t; |
---|
| 1946 | } |
---|
| 1947 | } |
---|
| 1948 | while( numberCollectionEnumerator.MoveNext() ); |
---|
| 1949 | |
---|
| 1950 | if( cand == NULL ) |
---|
| 1951 | { |
---|
| 1952 | c = ntInit(1, cf); |
---|
| 1953 | return; |
---|
[a355723] | 1954 | } |
---|
[dc79bd] | 1955 | |
---|
[a355723] | 1956 | c = ntInit(cand, cf); |
---|
[dc79bd] | 1957 | |
---|
| 1958 | numberCollectionEnumerator.Reset(); |
---|
[a355723] | 1959 | |
---|
[dc79bd] | 1960 | number d = NULL; |
---|
| 1961 | |
---|
| 1962 | while (numberCollectionEnumerator.MoveNext() ) |
---|
| 1963 | { |
---|
| 1964 | number &n = numberCollectionEnumerator.Current(); |
---|
| 1965 | number t = ntMult(n, c, cf); // TODO: rewrite!? |
---|
| 1966 | ntDelete(&n, cf); |
---|
| 1967 | |
---|
| 1968 | ntNormalize(t, cf); // TODO: needed? |
---|
| 1969 | n = t; |
---|
[a355723] | 1970 | |
---|
[dc79bd] | 1971 | fraction f = (fraction)t; |
---|
| 1972 | assume( f != NULL ); |
---|
[de88371] | 1973 | |
---|
[dc79bd] | 1974 | const poly den = DEN(f); |
---|
| 1975 | |
---|
| 1976 | if( den != NULL ) // ?? / ?? ? |
---|
| 1977 | { |
---|
| 1978 | assume( p_IsConstant(den, R) ); |
---|
| 1979 | assume( pNext(den) == NULL ); |
---|
[a355723] | 1980 | |
---|
[dc79bd] | 1981 | if( d == NULL ) |
---|
[a355723] | 1982 | d = n_Copy(pGetCoeff(den), Q); |
---|
[dc79bd] | 1983 | else |
---|
| 1984 | { |
---|
[a355723] | 1985 | number g = n_Lcm(d, pGetCoeff(den), Q); |
---|
[dc79bd] | 1986 | n_Delete(&d, Q); d = g; |
---|
| 1987 | } |
---|
| 1988 | } |
---|
| 1989 | } |
---|
[a355723] | 1990 | |
---|
[dc79bd] | 1991 | if( d != NULL ) |
---|
| 1992 | { |
---|
| 1993 | numberCollectionEnumerator.Reset(); |
---|
| 1994 | while (numberCollectionEnumerator.MoveNext() ) |
---|
| 1995 | { |
---|
| 1996 | number &n = numberCollectionEnumerator.Current(); |
---|
| 1997 | fraction f = (fraction)n; |
---|
| 1998 | |
---|
| 1999 | assume( f != NULL ); |
---|
| 2000 | |
---|
| 2001 | const poly den = DEN(f); |
---|
| 2002 | |
---|
| 2003 | if( den == NULL ) // ?? / 1 ? |
---|
| 2004 | NUM(f) = p_Mult_nn(NUM(f), d, R); |
---|
| 2005 | else |
---|
| 2006 | { |
---|
| 2007 | assume( p_IsConstant(den, R) ); |
---|
| 2008 | assume( pNext(den) == NULL ); |
---|
[a355723] | 2009 | |
---|
| 2010 | number ddd = n_Div(d, pGetCoeff(den), Q); // but be an integer now!!! |
---|
[dc79bd] | 2011 | NUM(f) = p_Mult_nn(NUM(f), ddd, R); |
---|
[a355723] | 2012 | n_Delete(&ddd, Q); |
---|
| 2013 | |
---|
| 2014 | p_Delete(&DEN(f), R); |
---|
| 2015 | DEN(f) = NULL; // TODO: check if this is needed!? |
---|
| 2016 | } |
---|
| 2017 | |
---|
[dc79bd] | 2018 | assume( DEN(f) == NULL ); |
---|
| 2019 | } |
---|
[a355723] | 2020 | |
---|
[dc79bd] | 2021 | NUM(c) = p_Mult_nn(NUM(c), d, R); |
---|
| 2022 | n_Delete(&d, Q); |
---|
| 2023 | } |
---|
[a355723] | 2024 | |
---|
| 2025 | |
---|
[dc79bd] | 2026 | ntTest(c); |
---|
[de88371] | 2027 | } |
---|
| 2028 | |
---|
[2c7f28] | 2029 | BOOLEAN ntInitChar(coeffs cf, void * infoStruct) |
---|
[a55ef0] | 2030 | { |
---|
| 2031 | |
---|
| 2032 | assume( infoStruct != NULL ); |
---|
[c14846c] | 2033 | |
---|
[2c7f28] | 2034 | TransExtInfo *e = (TransExtInfo *)infoStruct; |
---|
[c14846c] | 2035 | |
---|
[ec5ec8] | 2036 | assume( e->r != NULL); // extRing; |
---|
| 2037 | assume( e->r->cf != NULL); // extRing->cf; |
---|
[dd668f] | 2038 | assume( e->r->qideal == NULL ); |
---|
[2c7f28] | 2039 | |
---|
[ec5ec8] | 2040 | assume( cf != NULL ); |
---|
[1f414c8] | 2041 | assume(getCoeffType(cf) == ID); // coeff type; |
---|
[ec5ec8] | 2042 | |
---|
[7fee876] | 2043 | ring R = e->r; |
---|
| 2044 | assume(R != NULL); |
---|
[a355723] | 2045 | |
---|
[7fee876] | 2046 | R->ref ++; // increase the ref.counter for the ground poly. ring! |
---|
[ec5ec8] | 2047 | |
---|
[7fee876] | 2048 | cf->extRing = R; |
---|
[6ccdd3a] | 2049 | /* propagate characteristic up so that it becomes |
---|
| 2050 | directly accessible in cf: */ |
---|
[7fee876] | 2051 | cf->ch = R->cf->ch; |
---|
| 2052 | cf->factoryVarOffset = R->cf->factoryVarOffset + rVar(R); |
---|
[a355723] | 2053 | |
---|
[2c7f28] | 2054 | cf->cfGreaterZero = ntGreaterZero; |
---|
| 2055 | cf->cfGreater = ntGreater; |
---|
| 2056 | cf->cfEqual = ntEqual; |
---|
| 2057 | cf->cfIsZero = ntIsZero; |
---|
| 2058 | cf->cfIsOne = ntIsOne; |
---|
| 2059 | cf->cfIsMOne = ntIsMOne; |
---|
| 2060 | cf->cfInit = ntInit; |
---|
[61b2e16] | 2061 | cf->cfInit_bigint = ntInit_bigint; |
---|
[2c7f28] | 2062 | cf->cfInt = ntInt; |
---|
| 2063 | cf->cfNeg = ntNeg; |
---|
| 2064 | cf->cfAdd = ntAdd; |
---|
| 2065 | cf->cfSub = ntSub; |
---|
| 2066 | cf->cfMult = ntMult; |
---|
| 2067 | cf->cfDiv = ntDiv; |
---|
| 2068 | cf->cfExactDiv = ntDiv; |
---|
| 2069 | cf->cfPower = ntPower; |
---|
| 2070 | cf->cfCopy = ntCopy; |
---|
[ce1f78] | 2071 | cf->cfWriteLong = ntWriteLong; |
---|
[2c7f28] | 2072 | cf->cfRead = ntRead; |
---|
[237b4dd] | 2073 | cf->cfNormalize = ntNormalize; |
---|
[2c7f28] | 2074 | cf->cfDelete = ntDelete; |
---|
| 2075 | cf->cfSetMap = ntSetMap; |
---|
| 2076 | cf->cfGetDenom = ntGetDenom; |
---|
| 2077 | cf->cfGetNumerator = ntGetNumerator; |
---|
| 2078 | cf->cfRePart = ntCopy; |
---|
| 2079 | cf->cfImPart = ntImPart; |
---|
| 2080 | cf->cfCoeffWrite = ntCoeffWrite; |
---|
[dbcf787] | 2081 | #ifdef LDEBUG |
---|
[2c7f28] | 2082 | cf->cfDBTest = ntDBTest; |
---|
[dbcf787] | 2083 | #endif |
---|
[2c7f28] | 2084 | cf->cfGcd = ntGcd; |
---|
| 2085 | cf->cfLcm = ntLcm; |
---|
| 2086 | cf->cfSize = ntSize; |
---|
| 2087 | cf->nCoeffIsEqual = ntCoeffIsEqual; |
---|
| 2088 | cf->cfInvers = ntInvers; |
---|
| 2089 | cf->cfIntDiv = ntDiv; |
---|
[a195ed] | 2090 | cf->cfKillChar = ntKillChar; |
---|
[c14846c] | 2091 | |
---|
[ce1f78] | 2092 | if( rCanShortOut(ntRing) ) |
---|
| 2093 | cf->cfWriteShort = ntWriteShort; |
---|
| 2094 | else |
---|
| 2095 | cf->cfWriteShort = ntWriteLong; |
---|
| 2096 | |
---|
[e5d267] | 2097 | #ifndef HAVE_FACTORY |
---|
| 2098 | PrintS("// Warning: The 'factory' module is not available.\n"); |
---|
| 2099 | PrintS("// Hence gcd's cannot be cancelled in any\n"); |
---|
| 2100 | PrintS("// computed fraction!\n"); |
---|
[fc4977] | 2101 | #else |
---|
| 2102 | cf->convFactoryNSingN =ntConvFactoryNSingN; |
---|
| 2103 | cf->convSingNFactoryN =ntConvSingNFactoryN; |
---|
[e5d267] | 2104 | #endif |
---|
[48a41a] | 2105 | cf->cfParDeg = ntParDeg; |
---|
[c14846c] | 2106 | |
---|
[7fee876] | 2107 | cf->iNumberOfParameters = rVar(R); |
---|
| 2108 | cf->pParameterNames = R->names; |
---|
| 2109 | cf->cfParameter = ntParameter; |
---|
[6637ee] | 2110 | |
---|
[de88371] | 2111 | if( nCoeff_is_Q(R->cf) ) |
---|
| 2112 | cf->cfClearContent = ntClearContent; |
---|
| 2113 | |
---|
| 2114 | cf->cfClearDenominators = ntClearDenominators; |
---|
[6637ee] | 2115 | |
---|
[7fee876] | 2116 | return FALSE; |
---|
[e82417] | 2117 | } |
---|