[35aab3] | 1 | /**************************************** |
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| 2 | * Computer Algebra System SINGULAR * |
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| 3 | ****************************************/ |
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| 4 | /*************************************************************** |
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| 5 | * File: gring.cc |
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| 6 | * Purpose: noncommutative kernel procedures |
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| 7 | * Author: levandov (Viktor Levandovsky) |
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| 8 | * Created: 8/00 - 11/00 |
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[3c8a31] | 9 | * Version: $Id: gring.cc,v 1.17 2004-10-29 18:48:41 levandov Exp $ |
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[35aab3] | 10 | *******************************************************************/ |
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| 11 | #include "mod2.h" |
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| 12 | #ifdef HAVE_PLURAL |
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| 13 | #include "gring.h" |
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| 14 | #include "febase.h" |
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| 15 | #include "ring.h" |
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| 16 | #include "polys.h" |
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| 17 | #include "numbers.h" |
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| 18 | #include "ideals.h" |
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| 19 | #include "matpol.h" |
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| 20 | #include "kbuckets.h" |
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| 21 | #include "kstd1.h" |
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| 22 | #include "sbuckets.h" |
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| 23 | #include "prCopy.h" |
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| 24 | #include "p_Mult_q.h" |
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| 25 | |
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| 26 | /* global nc_macros : */ |
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| 27 | #define freeT(A,v) omFreeSize((ADDRESS)A,(v+1)*sizeof(int)) |
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| 28 | #define freeN(A,k) omFreeSize((ADDRESS)A,k*sizeof(number)) |
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| 29 | |
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| 30 | /* poly functions defined in p_Procs : */ |
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| 31 | poly nc_pp_Mult_mm(poly p, poly m, const ring r, poly &last) |
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| 32 | { |
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| 33 | return( nc_p_Mult_mm_Common(p_Copy(p,r), m, 1, r) ); |
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| 34 | } |
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| 35 | |
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| 36 | poly nc_p_Mult_mm(poly p, const poly m, const ring r) |
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| 37 | { |
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| 38 | return( nc_p_Mult_mm_Common(p, m, 1, r) ); |
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| 39 | } |
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| 40 | |
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| 41 | poly nc_mm_Mult_p(const poly m, poly p, const ring r) |
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| 42 | { |
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| 43 | return( nc_p_Mult_mm_Common(p, m, 0, r) ); |
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| 44 | } |
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| 45 | |
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| 46 | /* poly nc_p_Mult_mm(poly p, poly m, const ring r); defined below */ |
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| 47 | poly nc_p_Minus_mm_Mult_qq(poly p, const poly m, poly q, const ring r) |
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| 48 | { |
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| 49 | poly mc=p_Neg(p_Copy(m,r),r); |
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| 50 | poly mmc=nc_mm_Mult_p(mc,p_Copy(q,r),r); |
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| 51 | p_Delete(&mc,r); |
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| 52 | p=p_Add_q(p,mmc,r); |
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| 53 | return(p); |
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| 54 | } |
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| 55 | |
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| 56 | //----------- auxiliary routines-------------------------- |
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| 57 | poly _nc_p_Mult_q(poly p, poly q, const int copy, const ring r) |
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| 58 | /* destroy p,q unless copy=1 */ |
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| 59 | { |
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| 60 | poly res=NULL; |
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| 61 | poly ghost=NULL; |
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| 62 | poly qq,pp; |
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| 63 | if (copy) |
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| 64 | { |
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| 65 | qq=p_Copy(q,r); |
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| 66 | pp=p_Copy(p,r); |
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| 67 | } |
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| 68 | else |
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| 69 | { |
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| 70 | qq=q; |
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| 71 | pp=p; |
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| 72 | } |
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| 73 | while (qq!=NULL) |
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| 74 | { |
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| 75 | res=p_Add_q(res, nc_pp_Mult_mm(pp, p_Head(qq,r), r, ghost), r); |
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| 76 | qq=p_LmDeleteAndNext(qq,r); |
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| 77 | } |
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| 78 | p_Delete(&pp,r); |
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| 79 | return(res); |
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| 80 | } |
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| 81 | |
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| 82 | poly nc_p_Mult_mm_Common(poly p, const poly m, int side, const ring r) |
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| 83 | /* p is poly, m is mono with coeff, destroys p */ |
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| 84 | /* if side==1, computes p_Mult_mm; otherwise, mm_Mult_p */ |
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| 85 | { |
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| 86 | if ((p==NULL) || (m==NULL)) return NULL; |
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| 87 | /* if (pNext(p)==NULL) return(nc_mm_Mult_nn(p,pCopy(m),r)); */ |
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| 88 | /* excluded - the cycle will do it anyway - OK. */ |
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| 89 | if (p_IsConstant(m,r)) return(p_Mult_nn(p,p_GetCoeff(m,r),r)); |
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| 90 | |
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| 91 | #ifdef PDEBUG |
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| 92 | p_Test(p,r); |
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| 93 | p_Test(m,r); |
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| 94 | #endif |
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| 95 | poly v=NULL; |
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| 96 | int rN=r->N; |
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| 97 | int *P=(int *)omAlloc0((rN+1)*sizeof(int)); |
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| 98 | int *M=(int *)omAlloc0((rN+1)*sizeof(int)); |
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| 99 | /* coefficients: */ |
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| 100 | number cP,cM,cOut; |
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| 101 | p_GetExpV(m, M, r); |
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| 102 | cM=p_GetCoeff(m,r); |
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| 103 | /* components:*/ |
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| 104 | const int expM=p_GetComp(m,r); |
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| 105 | int expP=0; |
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| 106 | int expOut=0; |
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| 107 | /* bucket constraints: */ |
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| 108 | int UseBuckets=1; |
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| 109 | if (pLength(p)< MIN_LENGTH_BUCKET || TEST_OPT_NOT_BUCKETS) UseBuckets=0; |
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| 110 | sBucket_pt bu_out; |
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| 111 | poly out=NULL; |
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| 112 | if (UseBuckets) bu_out=sBucketCreate(r); |
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| 113 | |
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| 114 | while (p!=NULL) |
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| 115 | { |
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| 116 | #ifdef PDEBUG |
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| 117 | p_Test(p,r); |
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| 118 | #endif |
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| 119 | expP=p_GetComp(p,r); |
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| 120 | if (expP==0) |
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| 121 | { |
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| 122 | expOut=expM; |
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| 123 | } |
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| 124 | else |
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| 125 | { |
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| 126 | if (expM==0) |
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| 127 | { |
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| 128 | expOut=expP; |
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| 129 | #ifdef PDEBUG |
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| 130 | if (side) |
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| 131 | { |
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| 132 | Print("Multiplication in the left module from the right"); |
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| 133 | } |
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| 134 | #endif |
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| 135 | } |
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| 136 | else |
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| 137 | { |
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| 138 | /* REPORT_ERROR */ |
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| 139 | const char* s; |
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| 140 | if (side==1) s="nc_p_Mult_mm"; |
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| 141 | else s="nc_mm_Mult_p"; |
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| 142 | Print("%s: exponent mismatch %d and %d\n",s,expP,expM); |
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| 143 | expOut=0; |
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| 144 | } |
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| 145 | } |
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| 146 | p_GetExpV(p,P,r); |
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| 147 | cP=p_GetCoeff(p,r); |
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| 148 | cOut=n_Mult(cP,cM,r); |
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| 149 | if (side==1) |
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| 150 | { |
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| 151 | v = nc_mm_Mult_nn(P, M, r); |
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| 152 | } |
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| 153 | else |
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| 154 | { |
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| 155 | v = nc_mm_Mult_nn(M, P, r); |
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| 156 | } |
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| 157 | v = p_Mult_nn(v,cOut,r); |
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| 158 | p_SetCompP(v,expOut,r); |
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| 159 | if (UseBuckets) sBucket_Add_p(bu_out,v,pLength(v)); |
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| 160 | else out = p_Add_q(out,v,r); |
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| 161 | p_DeleteLm(&p,r); |
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| 162 | } |
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| 163 | freeT(P,rN); |
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| 164 | freeT(M,rN); |
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| 165 | if (UseBuckets) |
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| 166 | { |
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| 167 | out = NULL; |
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| 168 | int len = pLength(out); |
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| 169 | sBucketDestroyAdd(bu_out, &out, &len); |
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| 170 | } |
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| 171 | #ifdef PDEBUG |
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| 172 | p_Test(out,r); |
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| 173 | #endif |
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| 174 | return(out); |
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| 175 | } |
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| 176 | |
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| 177 | poly nc_mm_Mult_nn(int *F0, int *G0, const ring r) |
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| 178 | /* destroys nothing, no coeffs and exps */ |
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| 179 | { |
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| 180 | poly out=NULL; |
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| 181 | int i,j; |
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| 182 | int iF,jG,iG; |
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| 183 | int rN=r->N; |
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| 184 | int ExpSize=(((rN+1)*sizeof(int)+sizeof(long)-1)/sizeof(long))*sizeof(long); |
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| 185 | |
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| 186 | int *F=(int *)omAlloc0((rN+1)*sizeof(int)); |
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| 187 | int *G=(int *)omAlloc0((rN+1)*sizeof(int)); |
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| 188 | |
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| 189 | memcpy(F, F0,(rN+1)*sizeof(int)); |
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| 190 | // pExpVectorCopy(F,F0); |
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| 191 | memcpy(G, G0,(rN+1)*sizeof(int)); |
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| 192 | // pExpVectorCopy(G,G0); |
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| 193 | F[0]=0; /* important for p_MemAdd */ |
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| 194 | G[0]=0; |
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| 195 | |
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| 196 | iF=rN; |
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| 197 | while ((F[iF]==0)&&(iF>=1)) iF--; /* last exp_num of F */ |
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| 198 | if (iF==0) /* F0 is zero vector */ |
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| 199 | { |
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| 200 | out=pOne(); |
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| 201 | p_SetExpV(out,G0,r); |
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| 202 | p_Setm(out,r); |
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| 203 | freeT(F,rN); |
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| 204 | freeT(G,rN); |
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| 205 | return(out); |
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| 206 | } |
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| 207 | jG=1; |
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| 208 | while ((G[jG]==0)&&(jG<rN)) jG++; /* first exp_num of G */ |
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| 209 | iG=rN; |
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| 210 | while ((G[iG]==0)&&(iG>1)) iG--; /* last exp_num of G */ |
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| 211 | |
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| 212 | out=pOne(); |
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| 213 | |
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| 214 | if (iF<=jG) |
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| 215 | /* i.e. no mixed exp_num , MERGE case */ |
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| 216 | { |
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| 217 | p_MemAdd_LengthGeneral(F, G, ExpSize/sizeof(long)); |
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| 218 | p_SetExpV(out,F,r); |
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| 219 | p_Setm(out,r); |
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| 220 | // omFreeSize((ADDRESS)F,ExpSize); |
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| 221 | freeT(F,rN); |
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| 222 | freeT(G,rN); |
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| 223 | return(out); |
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| 224 | } |
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| 225 | |
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| 226 | number cff=n_Init(1,r); |
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| 227 | number tmp_num=NULL; |
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| 228 | int cpower=0; |
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| 229 | |
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| 230 | if (r->nc->type==nc_skew) |
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| 231 | { |
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| 232 | if (r->nc->IsSkewConstant==1) |
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| 233 | { |
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| 234 | int tpower=0; |
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| 235 | for(j=jG; j<=iG; j++) |
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| 236 | { |
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| 237 | if (G[j]!=0) |
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| 238 | { |
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| 239 | cpower = 0; |
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| 240 | for(i=j+1; i<=iF; i++) |
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| 241 | { |
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| 242 | cpower = cpower + F[i]; |
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| 243 | } |
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| 244 | cpower = cpower*G[j]; |
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| 245 | tpower = tpower + cpower; |
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| 246 | } |
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| 247 | } |
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| 248 | cff = n_Copy(p_GetCoeff(MATELEM(r->nc->COM,1,2),r),r); |
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| 249 | nPower(cff,tpower,&tmp_num); |
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| 250 | n_Delete(&cff,r); |
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| 251 | cff = tmp_num; |
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| 252 | } |
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| 253 | else /* skew commutative with nonequal coeffs */ |
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| 254 | { |
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| 255 | number totcff=n_Init(1,r); |
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| 256 | for(j=jG; j<=iG; j++) |
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| 257 | { |
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| 258 | if (G[j]!=0) |
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| 259 | { |
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| 260 | cpower = 0; |
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| 261 | for(i=j+1; i<=iF; i++) |
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| 262 | { |
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| 263 | if (F[i]!=0) |
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| 264 | { |
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| 265 | cpower = F[i]*G[j]; |
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| 266 | cff = n_Copy(p_GetCoeff(MATELEM(r->nc->COM,j,i),r),r); |
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| 267 | nPower(cff,cpower,&tmp_num); |
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| 268 | cff = nMult(totcff,tmp_num); |
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| 269 | nDelete(&totcff); |
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| 270 | nDelete(&tmp_num); |
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| 271 | totcff = n_Copy(cff,r); |
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| 272 | n_Delete(&cff,r); |
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| 273 | } |
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| 274 | } /* end 2nd for */ |
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| 275 | } |
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| 276 | } |
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| 277 | cff=totcff; |
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| 278 | } |
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| 279 | p_MemAdd_LengthGeneral(F, G, ExpSize/sizeof(long)); |
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| 280 | p_SetExpV(out,F,r); |
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| 281 | p_Setm(out,r); |
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| 282 | p_SetCoeff(out,cff,r); |
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| 283 | // p_MemAdd_NegWeightAdjust(p, r); ??? do we need this? |
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| 284 | freeT(F,rN); |
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| 285 | freeT(G,rN); |
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| 286 | return(out); |
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| 287 | } /* end nc_skew */ |
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| 288 | |
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| 289 | /* now we have to destroy out! */ |
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| 290 | p_Delete(&out,r); |
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| 291 | out = NULL; |
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| 292 | |
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| 293 | if (iG==jG) |
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| 294 | /* g is univariate monomial */ |
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| 295 | { |
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| 296 | /* if (ri->nc->type==nc_skew) -- postpone to TU */ |
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| 297 | out = nc_mm_Mult_uu(F,jG,G[jG],r); |
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| 298 | freeT(F,rN); |
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| 299 | freeT(G,rN); |
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| 300 | return(out); |
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| 301 | } |
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| 302 | |
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| 303 | number n1=n_Init(1,r); |
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| 304 | int *Prv=(int *)omAlloc0((rN+1)*sizeof(int)); |
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| 305 | int *Nxt=(int *)omAlloc0((rN+1)*sizeof(int)); |
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| 306 | |
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| 307 | int *log=(int *)omAlloc0((rN+1)*sizeof(int)); |
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| 308 | int cnt=0; int cnf=0; |
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| 309 | |
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| 310 | /* splitting F wrt jG */ |
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| 311 | for (i=1;i<=jG;i++) |
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| 312 | { |
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| 313 | Prv[i]=F[i]; Nxt[i]=0; /* mult at the very end */ |
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| 314 | if (F[i]!=0) cnf++; |
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| 315 | } |
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| 316 | |
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| 317 | if (cnf==0) freeT(Prv,rN); |
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| 318 | |
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| 319 | for (i=jG+1;i<=rN;i++) |
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| 320 | { |
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| 321 | Nxt[i]=F[i]; |
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| 322 | /* if (cnf!=0) Prv[i]=0; */ |
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| 323 | if (F[i]!=0) |
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| 324 | { |
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| 325 | cnt++; |
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| 326 | } /* effective part for F */ |
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| 327 | } |
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| 328 | freeT(F,rN); |
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| 329 | cnt=0; |
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| 330 | |
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| 331 | for (i=1;i<=rN;i++) |
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| 332 | { |
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| 333 | if (G[i]!=0) |
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| 334 | { |
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| 335 | cnt++; |
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| 336 | log[cnt]=i; |
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| 337 | } /* lG for G */ |
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| 338 | } |
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| 339 | |
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| 340 | /* ---------------------- A C T I O N ------------------------ */ |
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| 341 | poly D=NULL; |
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| 342 | poly Rout=NULL; |
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| 343 | number *c=(number *)omAlloc0((rN+1)*sizeof(number)); |
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| 344 | c[0]=n_Init(1,r); |
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| 345 | |
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| 346 | int *Op=Nxt; |
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| 347 | int *On=G; |
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| 348 | int *U=(int *)omAlloc0((rN+1)*sizeof(int)); |
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| 349 | |
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| 350 | for (i=jG;i<=rN;i++) U[i]=Nxt[i]+G[i]; /* make leadterm */ |
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| 351 | Nxt=NULL; |
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| 352 | G=NULL; |
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| 353 | cnt=1; |
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| 354 | int t=0; |
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| 355 | poly w=NULL; |
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| 356 | poly Pn=pOne(); |
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| 357 | p_SetExpV(Pn,On,r); |
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| 358 | p_Setm(Pn,r); |
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| 359 | |
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| 360 | while (On[iG]!=0) |
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| 361 | { |
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| 362 | t=log[cnt]; |
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| 363 | |
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| 364 | w=nc_mm_Mult_uu(Op,t,On[t],r); |
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| 365 | c[cnt]=n_Mult(c[cnt-1],p_GetCoeff(w,r),r); |
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| 366 | D = pNext(w); /* getting coef and rest D */ |
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| 367 | p_DeleteLm(&w,r); |
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| 368 | w=NULL; |
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| 369 | |
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| 370 | Op[t] += On[t]; /* update exp_vectors */ |
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| 371 | On[t] = 0; |
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| 372 | |
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| 373 | if (t!=iG) /* not the last step */ |
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| 374 | { |
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| 375 | p_SetExpV(Pn,On,r); |
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| 376 | p_Setm(Pn,r); |
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| 377 | #ifdef PDEBUG |
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| 378 | p_Test(Pn,r); |
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| 379 | #endif |
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| 380 | |
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| 381 | // if (pNext(D)==0) |
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| 382 | // is D a monomial? could be postponed higher |
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| 383 | // { |
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| 384 | // Rout=nc_mm_Mult_nn(D,Pn,r); |
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| 385 | // } |
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| 386 | // else |
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| 387 | // { |
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| 388 | Rout=nc_p_Mult_mm(D,Pn,r); |
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| 389 | // } |
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| 390 | } |
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| 391 | else |
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| 392 | { |
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| 393 | Rout=D; |
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| 394 | D=NULL; |
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| 395 | } |
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| 396 | |
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| 397 | if (Rout!=NULL) |
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| 398 | { |
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| 399 | Rout=p_Mult_nn(Rout,c[cnt-1],r); /* Rest is ready */ |
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| 400 | out=p_Add_q(out,Rout,r); |
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| 401 | Rout=NULL; |
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| 402 | } |
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| 403 | cnt++; |
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| 404 | } |
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| 405 | freeT(On,rN); |
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| 406 | freeT(Op,rN); |
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| 407 | p_Delete(&Pn,r); |
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| 408 | omFreeSize((ADDRESS)log,(rN+1)*sizeof(int)); |
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| 409 | |
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| 410 | /* leadterm and Prv-part */ |
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| 411 | |
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| 412 | Rout=pOne(); |
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| 413 | /* U is lead.monomial */ |
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| 414 | U[0]=0; |
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| 415 | p_SetExpV(Rout,U,r); |
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| 416 | p_Setm(Rout,r); /* use again this name Rout */ |
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| 417 | #ifdef PDEBUG |
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| 418 | p_Test(Rout,r); |
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| 419 | #endif |
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| 420 | p_SetCoeff(Rout,c[cnt-1],r); |
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| 421 | out=p_Add_q(out,Rout,r); |
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| 422 | freeT(U,rN); |
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| 423 | freeN(c,rN+1); |
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| 424 | if (cnf!=0) /* Prv is non-zero vector */ |
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| 425 | { |
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| 426 | Rout=pOne(); |
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| 427 | Prv[0]=0; |
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| 428 | p_SetExpV(Rout,Prv,r); |
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| 429 | p_Setm(Rout,r); |
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| 430 | #ifdef PDEBUG |
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| 431 | p_Test(Rout,r); |
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| 432 | #endif |
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| 433 | out=nc_mm_Mult_p(Rout,out,r); /* getting the final result */ |
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| 434 | freeT(Prv,rN); |
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| 435 | p_Delete(&Rout,r); |
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| 436 | } |
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| 437 | return (out); |
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| 438 | } |
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| 439 | |
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| 440 | |
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| 441 | poly nc_mm_Mult_uu(int *F,int jG,int bG, const ring r) |
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| 442 | /* f=mono(F),g=(x_iG)^bG */ |
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| 443 | { |
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| 444 | poly out=NULL; |
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| 445 | int i; |
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| 446 | number num=NULL; |
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| 447 | |
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| 448 | int rN=r->N; |
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| 449 | int iF=r->N; |
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| 450 | while ((F[iF]==0)&&(iF>0)) iF-- ; /* last exponent_num of F */ |
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| 451 | |
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| 452 | if (iF==0) /* F==zero vector in other words */ |
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| 453 | { |
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| 454 | out=pOne(); |
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| 455 | p_SetExp(out,jG,bG,r); |
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| 456 | p_Setm(out,r); |
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| 457 | return(out); |
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| 458 | } |
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| 459 | |
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| 460 | int jF=1; |
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| 461 | while ((F[jF]==0)&&(jF<=rN)) jF++; /* first exp of F */ |
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| 462 | |
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| 463 | if (iF<=jG) /* i.e. no mixed exp_num */ |
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| 464 | { |
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| 465 | out=pOne(); |
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| 466 | F[jG]=F[jG]+bG; |
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| 467 | p_SetExpV(out,F,r); |
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| 468 | p_Setm(out,r); |
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| 469 | return(out); |
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| 470 | } |
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| 471 | |
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| 472 | if (iF==jF) /* uni times uni */ |
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| 473 | { |
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| 474 | out=nc_uu_Mult_ww(iF,F[iF],jG,bG,r); |
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| 475 | return(out); |
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| 476 | } |
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| 477 | |
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| 478 | /* Now: F is mono with >=2 exponents, jG<iF */ |
---|
| 479 | /* check the quasi-commutative case */ |
---|
| 480 | // matrix LCOM=r->nc->COM; |
---|
| 481 | // number rescoef=n_Init(1,r); |
---|
| 482 | // number tmpcoef=n_Init(1,r); |
---|
| 483 | // int tmpint; |
---|
| 484 | // i=iF; |
---|
| 485 | // while (i>=jG+1) |
---|
| 486 | // /* all the non-zero exponents */ |
---|
| 487 | // { |
---|
| 488 | // if (MATELEM(LCOM,jG,i)!=NULL) |
---|
| 489 | // { |
---|
| 490 | // tmpcoef=pGetCoeff(MATELEM(LCOM,jG,i)); |
---|
| 491 | // tmpint=(int)F[i]; |
---|
| 492 | // nPower(tmpcoef,F[i],&tmpcoef); |
---|
| 493 | // rescoef=nMult(rescoef,tmpcoef); |
---|
| 494 | // i--; |
---|
| 495 | // } |
---|
| 496 | // else |
---|
| 497 | // { |
---|
| 498 | // if (F[i]!=0) break; |
---|
| 499 | // } |
---|
| 500 | // } |
---|
| 501 | // if (iF==i) |
---|
| 502 | // /* no action took place*/ |
---|
| 503 | // { |
---|
| 504 | |
---|
| 505 | // } |
---|
| 506 | // else /* power the result up to bG */ |
---|
| 507 | // { |
---|
| 508 | // nPower(rescoef,bG,&rescoef); |
---|
| 509 | // /* + cleanup, post-processing */ |
---|
| 510 | // } |
---|
| 511 | |
---|
| 512 | int *Prv=(int*)omAlloc0((rN+1)*sizeof(int)); |
---|
| 513 | int *Nxt=(int*)omAlloc0((rN+1)*sizeof(int)); |
---|
| 514 | int *lF=(int *)omAlloc0((rN+1)*sizeof(int)); |
---|
| 515 | int cnt=0; int cnf=0; |
---|
| 516 | /* splitting F wrt jG */ |
---|
| 517 | for (i=1;i<=jG;i++) /* mult at the very end */ |
---|
| 518 | { |
---|
| 519 | Prv[i]=F[i]; Nxt[i]=0; |
---|
| 520 | if (F[i]!=0) cnf++; |
---|
| 521 | } |
---|
| 522 | if (cnf==0) freeT(Prv,rN); |
---|
| 523 | for (i=jG+1;i<=rN;i++) |
---|
| 524 | { |
---|
| 525 | Nxt[i]=F[i]; |
---|
| 526 | if (cnf!=0) { Prv[i]=0;} |
---|
| 527 | if (F[i]!=0) |
---|
| 528 | { |
---|
| 529 | cnt++; |
---|
| 530 | lF[cnt]=i; |
---|
| 531 | } /* eff_part,lF_for_F */ |
---|
| 532 | } |
---|
| 533 | |
---|
| 534 | if (cnt==1) /* Nxt consists of 1 nonzero el-t only */ |
---|
| 535 | { |
---|
| 536 | int q=lF[1]; |
---|
| 537 | poly Rout=pOne(); |
---|
| 538 | out=nc_uu_Mult_ww(q,Nxt[q],jG,bG,r); |
---|
| 539 | freeT(Nxt,rN); |
---|
| 540 | |
---|
| 541 | if (cnf!=0) |
---|
| 542 | { |
---|
| 543 | Prv[0]=0; |
---|
| 544 | p_SetExpV(Rout,Prv,r); |
---|
| 545 | p_Setm(Rout,r); |
---|
| 546 | #ifdef PDEBUG |
---|
| 547 | p_Test(Rout,r); |
---|
| 548 | #endif |
---|
| 549 | freeT(Prv,rN); |
---|
| 550 | out=nc_mm_Mult_p(Rout,out,r); /* getting the final result */ |
---|
| 551 | } |
---|
| 552 | |
---|
| 553 | omFreeSize((ADDRESS)lF,(rN+1)*sizeof(int)); |
---|
| 554 | p_Delete(&Rout,r); |
---|
| 555 | return (out); |
---|
| 556 | } |
---|
| 557 | /* -------------------- MAIN ACTION --------------------- */ |
---|
| 558 | |
---|
| 559 | poly D=NULL; |
---|
| 560 | poly Rout=NULL; |
---|
| 561 | number *c=(number *)omAlloc0((cnt+2)*sizeof(number)); |
---|
| 562 | c[cnt+1]=n_Init(1,r); |
---|
| 563 | i=cnt+2; /* later in freeN */ |
---|
| 564 | int *Op=Nxt; |
---|
| 565 | int *On=(int *)omAlloc0((rN+1)*sizeof(int)); |
---|
| 566 | int *U=(int *)omAlloc0((rN+1)*sizeof(int)); |
---|
| 567 | |
---|
| 568 | |
---|
| 569 | // pExpVectorCopy(U,Nxt); |
---|
| 570 | memcpy(U, Nxt,(rN+1)*sizeof(int)); |
---|
| 571 | U[jG] = U[jG] + bG; |
---|
| 572 | |
---|
| 573 | /* Op=Nxt and initial On=(0); */ |
---|
| 574 | Nxt=NULL; |
---|
| 575 | |
---|
| 576 | poly Pp; |
---|
| 577 | poly Pn; |
---|
| 578 | int t=0; |
---|
| 579 | int first=lF[1]; |
---|
| 580 | int nlast=lF[cnt]; |
---|
| 581 | int kk=0; |
---|
| 582 | /* cnt--; */ |
---|
| 583 | /* now lF[cnt] should be <=iF-1 */ |
---|
| 584 | |
---|
| 585 | while (Op[first]!=0) |
---|
| 586 | { |
---|
| 587 | t=lF[cnt]; /* cnt as it was computed */ |
---|
| 588 | |
---|
| 589 | poly w=nc_uu_Mult_ww(t,Op[t],jG,bG,r); |
---|
| 590 | c[cnt]=n_Copy(p_GetCoeff(w,r),r); |
---|
| 591 | D = pNext(w); /* getting coef and rest D */ |
---|
| 592 | p_DeleteLm(&w,r); |
---|
| 593 | w=NULL; |
---|
| 594 | |
---|
| 595 | Op[t]= 0; |
---|
| 596 | Pp=pOne(); |
---|
| 597 | p_SetExpV(Pp,Op,r); |
---|
| 598 | p_Setm(Pp,r); |
---|
| 599 | |
---|
| 600 | if (t<nlast) |
---|
| 601 | { |
---|
| 602 | kk=lF[cnt+1]; |
---|
| 603 | On[kk]=F[kk]; |
---|
| 604 | |
---|
| 605 | Pn=pOne(); |
---|
| 606 | p_SetExpV(Pn,On,r); |
---|
| 607 | p_Setm(Pn,r); |
---|
| 608 | |
---|
| 609 | if (t!=first) /* typical expr */ |
---|
| 610 | { |
---|
| 611 | w=nc_p_Mult_mm(D,Pn,r); |
---|
| 612 | Rout=nc_mm_Mult_p(Pp,w,r); |
---|
| 613 | w=NULL; |
---|
| 614 | } |
---|
| 615 | else /* last step */ |
---|
| 616 | { |
---|
| 617 | On[t]=0; |
---|
| 618 | p_SetExpV(Pn,On,r); |
---|
| 619 | p_Setm(Pn,r); |
---|
| 620 | Rout=nc_p_Mult_mm(D,Pn,r); |
---|
| 621 | } |
---|
| 622 | #ifdef PDEBUG |
---|
| 623 | p_Test(Pp,r); |
---|
| 624 | #endif |
---|
| 625 | p_Delete(&Pn,r); |
---|
| 626 | } |
---|
| 627 | else /* first step */ |
---|
| 628 | { |
---|
| 629 | Rout=nc_mm_Mult_p(Pp,D,r); |
---|
| 630 | } |
---|
| 631 | #ifdef PDEBUG |
---|
| 632 | p_Test(Pp,r); |
---|
| 633 | #endif |
---|
| 634 | p_Delete(&Pp,r); |
---|
| 635 | num=n_Mult(c[cnt+1],c[cnt],r); |
---|
| 636 | n_Delete(&c[cnt],r); |
---|
| 637 | c[cnt]=num; |
---|
| 638 | Rout=p_Mult_nn(Rout,c[cnt+1],r); /* Rest is ready */ |
---|
| 639 | out=p_Add_q(out,Rout,r); |
---|
| 640 | Pp=NULL; |
---|
| 641 | cnt--; |
---|
| 642 | } |
---|
| 643 | /* only to feel safe:*/ |
---|
| 644 | Pn=Pp=NULL; |
---|
| 645 | freeT(On,rN); |
---|
| 646 | freeT(Op,rN); |
---|
| 647 | |
---|
| 648 | /* leadterm and Prv-part with coef 1 */ |
---|
| 649 | /* U[0]=exp; */ |
---|
| 650 | /* U[jG]=U[jG]+bG; */ |
---|
| 651 | /* make leadterm */ |
---|
| 652 | /* ??????????? we have done it already :-0 */ |
---|
| 653 | Rout=pOne(); |
---|
| 654 | p_SetExpV(Rout,U,r); |
---|
| 655 | p_Setm(Rout,r); /* use again this name */ |
---|
| 656 | p_SetCoeff(Rout,c[cnt+1],r); /* last computed coef */ |
---|
| 657 | out=p_Add_q(out,Rout,r); |
---|
| 658 | Rout=NULL; |
---|
| 659 | freeT(U,rN); |
---|
| 660 | freeN(c,i); |
---|
| 661 | omFreeSize((ADDRESS)lF,(rN+1)*sizeof(int)); |
---|
| 662 | |
---|
| 663 | if (cnf!=0) |
---|
| 664 | { |
---|
| 665 | Rout=pOne(); |
---|
| 666 | p_SetExpV(Rout,Prv,r); |
---|
| 667 | p_Setm(Rout,r); |
---|
| 668 | freeT(Prv,rN); |
---|
| 669 | out=nc_mm_Mult_p(Rout,out,r); /* getting the final result */ |
---|
| 670 | p_Delete(&Rout,r); |
---|
| 671 | } |
---|
| 672 | return (out); |
---|
| 673 | } |
---|
| 674 | |
---|
| 675 | poly nc_uu_Mult_ww_vert (int i, int a, int j, int b, const ring r) |
---|
| 676 | { |
---|
| 677 | int k,m; |
---|
| 678 | int rN=r->N; |
---|
| 679 | matrix cMT=r->nc->MT[UPMATELEM(j,i,rN)]; /* cMT=current MT */ |
---|
| 680 | |
---|
| 681 | poly x=pOne();p_SetExp(x,j,1,r);p_Setm(x,r); |
---|
| 682 | /* var(j); */ |
---|
| 683 | poly y=pOne();p_SetExp(y,i,1,r);p_Setm(y,r); |
---|
| 684 | /*var(i); for convenience */ |
---|
| 685 | #ifdef PDEBUG |
---|
| 686 | p_Test(x,r); |
---|
| 687 | p_Test(y,r); |
---|
| 688 | #endif |
---|
| 689 | poly t=NULL; |
---|
| 690 | /* ------------ Main Cycles ----------------------------*/ |
---|
| 691 | |
---|
| 692 | for (k=2;k<=a;k++) |
---|
| 693 | { |
---|
| 694 | t = nc_p_CopyGet(MATELEM(cMT,k,1),r); |
---|
| 695 | |
---|
| 696 | if (t==NULL) /* not computed yet */ |
---|
| 697 | { |
---|
| 698 | t = nc_p_CopyGet(MATELEM(cMT,k-1,1),r); |
---|
| 699 | // t=p_Copy(MATELEM(cMT,k-1,1),r); |
---|
| 700 | t = nc_mm_Mult_p(y,t,r); |
---|
| 701 | MATELEM(cMT,k,1) = nc_p_CopyPut(t,r); |
---|
| 702 | // omCheckAddr(cMT->m); |
---|
| 703 | p_Delete(&t,r); |
---|
| 704 | } |
---|
| 705 | t=NULL; |
---|
| 706 | } |
---|
| 707 | |
---|
| 708 | for (m=2;m<=b;m++) |
---|
| 709 | { |
---|
| 710 | t = nc_p_CopyGet(MATELEM(cMT,a,m),r); |
---|
| 711 | // t=MATELEM(cMT,a,m); |
---|
| 712 | if (t==NULL) //not computed yet |
---|
| 713 | { |
---|
| 714 | t = nc_p_CopyGet(MATELEM(cMT,a,m-1),r); |
---|
| 715 | // t=p_Copy(MATELEM(cMT,a,m-1),r); |
---|
| 716 | t = nc_p_Mult_mm(t,x,r); |
---|
| 717 | MATELEM(cMT,a,m) = nc_p_CopyPut(t,r); |
---|
| 718 | // MATELEM(cMT,a,m) = t; |
---|
| 719 | // omCheckAddr(cMT->m); |
---|
| 720 | p_Delete(&t,r); |
---|
| 721 | } |
---|
| 722 | t=NULL; |
---|
| 723 | } |
---|
| 724 | p_Delete(&x,r); |
---|
| 725 | p_Delete(&y,r); |
---|
| 726 | // t=MATELEM(cMT,a,b); |
---|
| 727 | t= nc_p_CopyGet(MATELEM(cMT,a,b),r); |
---|
| 728 | // return(p_Copy(t,r)); |
---|
| 729 | /* since the last computed element was cMT[a,b] */ |
---|
| 730 | return(t); |
---|
| 731 | } |
---|
| 732 | |
---|
| 733 | poly nc_uu_Mult_ww (int i, int a, int j, int b, const ring r) |
---|
| 734 | /* (x_i)^a times (x_j)^b */ |
---|
| 735 | /* x_i = y, x_j = x ! */ |
---|
| 736 | { |
---|
| 737 | /* Check zero exceptions, (q-)commutativity and is there something to do? */ |
---|
| 738 | assume(a!=0); |
---|
| 739 | assume(b!=0); |
---|
| 740 | poly out=pOne(); |
---|
| 741 | if (i<=j) |
---|
| 742 | { |
---|
| 743 | p_SetExp(out,i,a,r); |
---|
| 744 | p_AddExp(out,j,b,r); |
---|
| 745 | p_Setm(out,r); |
---|
| 746 | return(out); |
---|
| 747 | }/* zero exeptions and usual case */ |
---|
| 748 | /* if ((a==0)||(b==0)||(i<=j)) return(out); */ |
---|
| 749 | |
---|
| 750 | if (MATELEM(r->nc->COM,j,i)!=NULL) |
---|
| 751 | /* commutative or quasicommutative case */ |
---|
| 752 | { |
---|
| 753 | p_SetExp(out,i,a,r); |
---|
| 754 | p_AddExp(out,j,b,r); |
---|
| 755 | p_Setm(out,r); |
---|
| 756 | if (r->cf->nIsOne(p_GetCoeff(MATELEM(r->nc->COM,j,i),r))) /* commutative case */ |
---|
| 757 | { |
---|
| 758 | return(out); |
---|
| 759 | } |
---|
| 760 | else |
---|
| 761 | { |
---|
| 762 | number tmp_number=p_GetCoeff(MATELEM(r->nc->COM,j,i),r); /* quasicommutative case */ |
---|
| 763 | nPower(tmp_number,a*b,&tmp_number); |
---|
| 764 | p_SetCoeff(out,tmp_number,r); |
---|
| 765 | return(out); |
---|
| 766 | } |
---|
| 767 | }/* end_of commutative or quasicommutative case */ |
---|
| 768 | p_Delete(&out,r); |
---|
| 769 | |
---|
| 770 | /* we are here if i>j and variables do not commute or quasicommute */ |
---|
| 771 | /* in fact, now a>=1 and b>=1; and j<i */ |
---|
| 772 | /* now check whether the polynomial is already computed */ |
---|
| 773 | int rN=r->N; |
---|
| 774 | int vik = UPMATELEM(j,i,rN); |
---|
| 775 | int cMTsize=r->nc->MTsize[vik]; |
---|
| 776 | int newcMTsize=0; |
---|
[4bbe3b] | 777 | newcMTsize=si_max(a,b); |
---|
[35aab3] | 778 | |
---|
| 779 | if (newcMTsize<=cMTsize) |
---|
| 780 | { |
---|
| 781 | out = nc_p_CopyGet(MATELEM(r->nc->MT[vik],a,b),r); |
---|
| 782 | if (out !=NULL) return (out); |
---|
| 783 | } |
---|
| 784 | int k,m; |
---|
| 785 | if (newcMTsize > cMTsize) |
---|
| 786 | { |
---|
| 787 | int inM=(((newcMTsize+6)/7)*7); |
---|
| 788 | assume (inM>=newcMTsize); |
---|
| 789 | newcMTsize = inM; |
---|
| 790 | // matrix tmp = (matrix)omAlloc0(inM*inM*sizeof(poly)); |
---|
| 791 | matrix tmp = mpNew(newcMTsize,newcMTsize); |
---|
| 792 | |
---|
| 793 | for (k=1;k<=cMTsize;k++) |
---|
| 794 | { |
---|
| 795 | for (m=1;m<=cMTsize;m++) |
---|
| 796 | { |
---|
| 797 | out = MATELEM(r->nc->MT[UPMATELEM(j,i,rN)],k,m); |
---|
| 798 | if ( out != NULL ) |
---|
| 799 | { |
---|
| 800 | MATELEM(tmp,k,m) = out;/*MATELEM(r->nc->MT[UPMATELEM(j,i,rN)],k,m)*/ |
---|
| 801 | // omCheckAddr(tmp->m); |
---|
| 802 | MATELEM(r->nc->MT[UPMATELEM(j,i,rN)],k,m)=NULL; |
---|
| 803 | // omCheckAddr(r->nc->MT[UPMATELEM(j,i,rN)]->m); |
---|
| 804 | } |
---|
| 805 | } |
---|
| 806 | } |
---|
| 807 | id_Delete((ideal *)&(r->nc->MT[UPMATELEM(j,i,rN)]),r); |
---|
| 808 | r->nc->MT[UPMATELEM(j,i,rN)] = tmp; |
---|
| 809 | tmp=NULL; |
---|
| 810 | r->nc->MTsize[UPMATELEM(j,i,rN)] = newcMTsize; |
---|
| 811 | } |
---|
| 812 | /* The update of multiplication matrix is finished */ |
---|
| 813 | pDelete(&out); |
---|
| 814 | out = nc_uu_Mult_ww_vert(i, a, j, b, r); |
---|
| 815 | // out = nc_uu_Mult_ww_horvert(i, a, j, b, r); |
---|
| 816 | return(out); |
---|
| 817 | } |
---|
| 818 | |
---|
| 819 | poly nc_uu_Mult_ww_horvert (int i, int a, int j, int b, const ring r) |
---|
| 820 | |
---|
| 821 | { |
---|
| 822 | int k,m; |
---|
| 823 | int rN=r->N; |
---|
| 824 | matrix cMT=r->nc->MT[UPMATELEM(j,i,rN)]; /* cMT=current MT */ |
---|
| 825 | |
---|
| 826 | poly x=pOne();p_SetExp(x,j,1,r);p_Setm(x,r);/* var(j); */ |
---|
| 827 | poly y=pOne();p_SetExp(y,i,1,r);p_Setm(y,r); /*var(i); for convenience */ |
---|
| 828 | #ifdef PDEBUG |
---|
| 829 | p_Test(x,r); |
---|
| 830 | p_Test(y,r); |
---|
| 831 | #endif |
---|
| 832 | |
---|
| 833 | poly t=NULL; |
---|
| 834 | |
---|
| 835 | int toXY; |
---|
| 836 | int toYX; |
---|
| 837 | |
---|
| 838 | if (a==1) /* y*x^b, b>=2 */ |
---|
| 839 | { |
---|
| 840 | toXY=b-1; |
---|
| 841 | while ( (MATELEM(cMT,1,toXY)==NULL) && (toXY>=2)) toXY--; |
---|
| 842 | for (m=toXY+1;m<=b;m++) |
---|
| 843 | { |
---|
| 844 | t=MATELEM(cMT,1,m); |
---|
| 845 | if (t==NULL) /* remove after debug */ |
---|
| 846 | { |
---|
| 847 | t = p_Copy(MATELEM(cMT,1,m-1),r); |
---|
| 848 | t = nc_p_Mult_mm(t,x,r); |
---|
| 849 | MATELEM(cMT,1,m) = t; |
---|
| 850 | /* omCheckAddr(cMT->m); */ |
---|
| 851 | } |
---|
| 852 | else |
---|
| 853 | { |
---|
| 854 | /* Error, should never get there */ |
---|
| 855 | WarnS("Error: a=1; MATELEM!=0"); |
---|
| 856 | } |
---|
| 857 | t=NULL; |
---|
| 858 | } |
---|
| 859 | return(p_Copy(MATELEM(cMT,1,b),r)); |
---|
| 860 | } |
---|
| 861 | |
---|
| 862 | if (b==1) /* y^a*x, a>=2 */ |
---|
| 863 | { |
---|
| 864 | toYX=a-1; |
---|
| 865 | while ( (MATELEM(cMT,toYX,1)==NULL) && (toYX>=2)) toYX--; |
---|
| 866 | for (m=toYX+1;m<=a;m++) |
---|
| 867 | { |
---|
| 868 | t=MATELEM(cMT,m,1); |
---|
| 869 | if (t==NULL) /* remove after debug */ |
---|
| 870 | { |
---|
| 871 | t = p_Copy(MATELEM(cMT,m-1,1),r); |
---|
| 872 | t = nc_mm_Mult_p(y,t,r); |
---|
| 873 | MATELEM(cMT,m,1) = t; |
---|
| 874 | /* omCheckAddr(cMT->m); */ |
---|
| 875 | } |
---|
| 876 | else |
---|
| 877 | { |
---|
| 878 | /* Error, should never get there */ |
---|
| 879 | WarnS("Error: b=1, MATELEM!=0"); |
---|
| 880 | } |
---|
| 881 | t=NULL; |
---|
| 882 | } |
---|
| 883 | return(p_Copy(MATELEM(cMT,a,1),r)); |
---|
| 884 | } |
---|
| 885 | |
---|
| 886 | /* ------------ Main Cycles ----------------------------*/ |
---|
| 887 | /* a>1, b>1 */ |
---|
| 888 | |
---|
| 889 | int dXY=0; int dYX=0; |
---|
| 890 | /* dXY = distance for computing x-mult, then y-mult */ |
---|
| 891 | /* dYX = distance for computing y-mult, then x-mult */ |
---|
| 892 | int toX=a-1; int toY=b-1; /* toX = to axe X, toY = to axe Y */ |
---|
| 893 | toXY=b-1; toYX=a-1; |
---|
| 894 | /* if toX==0, toXY = dist. to computed y * x^toXY */ |
---|
| 895 | /* if toY==0, toYX = dist. to computed y^toYX * x */ |
---|
| 896 | while ( (MATELEM(cMT,toX,b)==NULL) && (toX>=1)) toX--; |
---|
| 897 | if (toX==0) /* the whole column is not computed yet */ |
---|
| 898 | { |
---|
| 899 | while ( (MATELEM(cMT,1,toXY)==NULL) && (toXY>=1)) toXY--; |
---|
| 900 | /* toXY >=1 */ |
---|
| 901 | dXY=b-1-toXY; |
---|
| 902 | } |
---|
| 903 | dXY=dXY+a-toX; /* the distance to nearest computed y^toX x^b */ |
---|
| 904 | |
---|
| 905 | while ( (MATELEM(cMT,a,toY)==NULL) && (toY>=1)) toY--; |
---|
| 906 | if (toY==0) /* the whole row is not computed yet */ |
---|
| 907 | { |
---|
| 908 | while ( (MATELEM(cMT,toYX,1)==NULL) && (toYX>=1)) toYX--; |
---|
| 909 | /* toYX >=1 */ |
---|
| 910 | dYX=a-1-toYX; |
---|
| 911 | } |
---|
| 912 | dYX=dYX+b-toY; /* the distance to nearest computed y^a x^toY */ |
---|
| 913 | |
---|
| 914 | if (dYX>=dXY) |
---|
| 915 | { |
---|
| 916 | /* first x, then y */ |
---|
| 917 | if (toX==0) /* start with the row*/ |
---|
| 918 | { |
---|
| 919 | for (m=toXY+1;m<=b;m++) |
---|
| 920 | { |
---|
| 921 | t=MATELEM(cMT,1,m); |
---|
| 922 | if (t==NULL) /* remove after debug */ |
---|
| 923 | { |
---|
| 924 | t = p_Copy(MATELEM(cMT,1,m-1),r); |
---|
| 925 | t = nc_p_Mult_mm(t,x,r); |
---|
| 926 | MATELEM(cMT,1,m) = t; |
---|
| 927 | /* omCheckAddr(cMT->m); */ |
---|
| 928 | } |
---|
| 929 | else |
---|
| 930 | { |
---|
| 931 | /* Error, should never get there */ |
---|
| 932 | WarnS("dYX>=dXY,toXY; MATELEM==0"); |
---|
| 933 | } |
---|
| 934 | t=NULL; |
---|
| 935 | } |
---|
| 936 | toX=1; /* y*x^b is computed */ |
---|
| 937 | } |
---|
| 938 | /* Now toX>=1 */ |
---|
| 939 | for (k=toX+1;k<=a;k++) |
---|
| 940 | { |
---|
| 941 | t=MATELEM(cMT,k,b); |
---|
| 942 | if (t==NULL) /* remove after debug */ |
---|
| 943 | { |
---|
| 944 | t = p_Copy(MATELEM(cMT,k-1,b),r); |
---|
| 945 | t = nc_mm_Mult_p(y,t,r); |
---|
| 946 | MATELEM(cMT,k,b) = t; |
---|
| 947 | /* omCheckAddr(cMT->m); */ |
---|
| 948 | } |
---|
| 949 | else |
---|
| 950 | { |
---|
| 951 | /* Error, should never get there */ |
---|
| 952 | WarnS("dYX>=dXY,toX; MATELEM==0"); |
---|
| 953 | } |
---|
| 954 | t=NULL; |
---|
| 955 | } |
---|
| 956 | } /* endif (dYX>=dXY) */ |
---|
| 957 | |
---|
| 958 | |
---|
| 959 | if (dYX<dXY) |
---|
| 960 | { |
---|
| 961 | /* first y, then x */ |
---|
| 962 | if (toY==0) /* start with the column*/ |
---|
| 963 | { |
---|
| 964 | for (m=toYX+1;m<=a;m++) |
---|
| 965 | { |
---|
| 966 | t=MATELEM(cMT,m,1); |
---|
| 967 | if (t==NULL) /* remove after debug */ |
---|
| 968 | { |
---|
| 969 | t = p_Copy(MATELEM(cMT,m-1,1),r); |
---|
| 970 | t = nc_mm_Mult_p(y,t,r); |
---|
| 971 | MATELEM(cMT,m,1) = t; |
---|
| 972 | /* omCheckAddr(cMT->m); */ |
---|
| 973 | } |
---|
| 974 | else |
---|
| 975 | { |
---|
| 976 | /* Error, should never get there */ |
---|
| 977 | WarnS("dYX<dXY,toYX; MATELEM==0"); |
---|
| 978 | } |
---|
| 979 | t=NULL; |
---|
| 980 | } |
---|
| 981 | toY=1; /* y^a*x is computed */ |
---|
| 982 | } |
---|
| 983 | /* Now toY>=1 */ |
---|
| 984 | for (k=toY+1;k<=b;k++) |
---|
| 985 | { |
---|
| 986 | t=MATELEM(cMT,a,k); |
---|
| 987 | if (t==NULL) /* remove after debug */ |
---|
| 988 | { |
---|
| 989 | t = p_Copy(MATELEM(cMT,a,k-1),r); |
---|
| 990 | t = nc_p_Mult_mm(t,x,r); |
---|
| 991 | MATELEM(cMT,a,k) = t; |
---|
| 992 | /* omCheckAddr(cMT->m); */ |
---|
| 993 | } |
---|
| 994 | else |
---|
| 995 | { |
---|
| 996 | /* Error, should never get there */ |
---|
| 997 | WarnS("dYX<dXY,toY; MATELEM==0"); |
---|
| 998 | } |
---|
| 999 | t=NULL; |
---|
| 1000 | } |
---|
| 1001 | } /* endif (dYX<dXY) */ |
---|
| 1002 | |
---|
| 1003 | p_Delete(&x,r); |
---|
| 1004 | p_Delete(&y,r); |
---|
| 1005 | t=p_Copy(MATELEM(cMT,a,b),r); |
---|
| 1006 | return(t); /* since the last computed element was cMT[a,b] */ |
---|
| 1007 | } |
---|
| 1008 | |
---|
| 1009 | |
---|
| 1010 | /* ----------------------------- Syzygies ---------------------- */ |
---|
| 1011 | |
---|
| 1012 | /*2 |
---|
| 1013 | * reduction of p2 with p1 |
---|
| 1014 | * do not destroy p1, but p2 |
---|
| 1015 | * p1 divides p2 -> for use in NF algorithm |
---|
| 1016 | */ |
---|
| 1017 | |
---|
[4bbe3b] | 1018 | poly nc_ReduceSpoly(poly p1, poly p2,poly spNoether, const ring r) |
---|
[35aab3] | 1019 | { |
---|
| 1020 | if (p_GetComp(p1,r)!=p_GetComp(p2,r) |
---|
| 1021 | && (p_GetComp(p1,r)!=0) |
---|
| 1022 | && (p_GetComp(p2,r)!=0)) |
---|
| 1023 | { |
---|
| 1024 | #ifdef PDEBUG |
---|
[4bbe3b] | 1025 | Print("nc_ReduceSpoly: different components"); |
---|
[35aab3] | 1026 | #endif |
---|
| 1027 | return(NULL); |
---|
| 1028 | } |
---|
[6b5dd2] | 1029 | poly m = pOne(); |
---|
[35aab3] | 1030 | p_ExpVectorDiff(m,p2,p1,r); |
---|
[ec547b3] | 1031 | //p_Setm(m,r); |
---|
[35aab3] | 1032 | #ifdef PDEBUG |
---|
| 1033 | p_Test(m,r); |
---|
| 1034 | #endif |
---|
| 1035 | /* pSetComp(m,r)=0? */ |
---|
[6b5dd2] | 1036 | poly N = nc_mm_Mult_p(m, p_Head(p1,r), r); |
---|
| 1037 | number C = n_Copy( p_GetCoeff(N, r), r); |
---|
| 1038 | number cF = n_Copy( p_GetCoeff(p2, r),r); |
---|
[4bbe3b] | 1039 | /* GCD stuff */ |
---|
[6b5dd2] | 1040 | number cG = nGcd(C, cF, r); |
---|
| 1041 | if ( !nEqual(cG, n_Init(1,r) ) ) |
---|
[4bbe3b] | 1042 | { |
---|
[6b5dd2] | 1043 | cF = nDiv(cF, cG); |
---|
| 1044 | C = nDiv(C, cG); |
---|
[4bbe3b] | 1045 | } |
---|
[6b5dd2] | 1046 | p2 = p_Mult_nn(p2, C, r); |
---|
[35aab3] | 1047 | poly out = nc_mm_Mult_p(m, p_Copy(pNext(p1),r), r); |
---|
[6b5dd2] | 1048 | N = p_Add_q(N, out, r); |
---|
| 1049 | p_Test(p2,r); |
---|
| 1050 | p_Test(N,r); |
---|
| 1051 | number MinusOne = n_Init(-1,r); |
---|
[35aab3] | 1052 | if (!n_Equal(cF,MinusOne,r)) |
---|
| 1053 | { |
---|
[6b5dd2] | 1054 | cF = n_Neg(cF,r); |
---|
| 1055 | N = p_Mult_nn(N, cF, r); |
---|
| 1056 | p_Test(N,r); |
---|
[35aab3] | 1057 | } |
---|
[6b5dd2] | 1058 | out = p_Add_q(p2,N,r); |
---|
| 1059 | p_Test(out,r); |
---|
| 1060 | if ( out!=NULL ) pContent(out); |
---|
[35aab3] | 1061 | p_Delete(&m,r); |
---|
| 1062 | n_Delete(&cF,r); |
---|
| 1063 | n_Delete(&C,r); |
---|
| 1064 | n_Delete(&MinusOne,r); |
---|
| 1065 | return(out); |
---|
| 1066 | } |
---|
| 1067 | |
---|
| 1068 | |
---|
| 1069 | /*3 |
---|
| 1070 | * reduction of p2 with p1 |
---|
| 1071 | * do not destroy p1 and p2 |
---|
| 1072 | * p1 divides p2 -> for use in NF algorithm |
---|
| 1073 | */ |
---|
[4bbe3b] | 1074 | poly nc_ReduceSpolyNew(poly p1, poly p2,poly spNoether, const ring r) |
---|
[35aab3] | 1075 | { |
---|
[4bbe3b] | 1076 | return(nc_ReduceSpoly(p1,p_Copy(p2,r),spNoether,r)); |
---|
[35aab3] | 1077 | } |
---|
| 1078 | |
---|
| 1079 | /*4 |
---|
| 1080 | * creates the S-polynomial of p1 and p2 |
---|
| 1081 | * do not destroy p1 and p2 |
---|
| 1082 | */ |
---|
[4bbe3b] | 1083 | poly nc_CreateSpoly(poly p1, poly p2,poly spNoether, const ring r) |
---|
[35aab3] | 1084 | { |
---|
| 1085 | if ((p_GetComp(p1,r)!=p_GetComp(p2,r)) |
---|
| 1086 | && (p_GetComp(p1,r)!=0) |
---|
| 1087 | && (p_GetComp(p2,r)!=0)) |
---|
| 1088 | { |
---|
| 1089 | #ifdef PDEBUG |
---|
[4bbe3b] | 1090 | Print("nc_CreateSpoly : different components!"); |
---|
[35aab3] | 1091 | #endif |
---|
| 1092 | return(NULL); |
---|
| 1093 | } |
---|
| 1094 | if ((r->nc->type==nc_lie) && pHasNotCF(p1,p2)) /* prod crit */ |
---|
| 1095 | { |
---|
| 1096 | return(nc_p_Bracket_qq(pCopy(p2),p1)); |
---|
| 1097 | } |
---|
| 1098 | poly pL=pOne(); |
---|
| 1099 | poly m1=pOne(); |
---|
| 1100 | poly m2=pOne(); |
---|
| 1101 | pLcm(p1,p2,pL); |
---|
| 1102 | p_Setm(pL,r); |
---|
| 1103 | #ifdef PDEBUG |
---|
| 1104 | p_Test(pL,r); |
---|
| 1105 | #endif |
---|
| 1106 | p_ExpVectorDiff(m1,pL,p1,r); |
---|
| 1107 | //p_SetComp(m1,0,r); |
---|
[ec547b3] | 1108 | //p_Setm(m1,r); |
---|
[35aab3] | 1109 | #ifdef PDEBUG |
---|
| 1110 | p_Test(m1,r); |
---|
| 1111 | #endif |
---|
| 1112 | p_ExpVectorDiff(m2,pL,p2,r); |
---|
| 1113 | //p_SetComp(m2,0,r); |
---|
[ec547b3] | 1114 | //p_Setm(m2,r); |
---|
[35aab3] | 1115 | #ifdef PDEBUG |
---|
| 1116 | p_Test(m2,r); |
---|
| 1117 | #endif |
---|
| 1118 | p_Delete(&pL,r); |
---|
| 1119 | /* zero exponents ! */ |
---|
[4bbe3b] | 1120 | poly M1 = nc_mm_Mult_p(m1,p_Head(p1,r),r); |
---|
| 1121 | number C1 = n_Copy(p_GetCoeff(M1,r),r); |
---|
| 1122 | poly M2 = nc_mm_Mult_p(m2,p_Head(p2,r),r); |
---|
| 1123 | number C2 = n_Copy(p_GetCoeff(M2,r),r); |
---|
| 1124 | /* GCD stuff */ |
---|
| 1125 | number C = nGcd(C1,C2,r); |
---|
| 1126 | if (!nEqual(C,n_Init(1,r))) |
---|
| 1127 | { |
---|
| 1128 | C1=nDiv(C1,C); |
---|
| 1129 | C2=nDiv(C2,C); |
---|
| 1130 | } |
---|
[35aab3] | 1131 | M1=p_Mult_nn(M1,C2,r); |
---|
| 1132 | p_SetCoeff(m1,C2,r); |
---|
| 1133 | number MinusOne=n_Init(-1,r); |
---|
| 1134 | if (n_Equal(C1,MinusOne,r)) |
---|
| 1135 | { |
---|
| 1136 | M2=p_Add_q(M1,M2,r); |
---|
| 1137 | } |
---|
| 1138 | else |
---|
| 1139 | { |
---|
| 1140 | C1=n_Neg(C1,r); |
---|
| 1141 | M2=p_Mult_nn(M2,C1,r); |
---|
| 1142 | M2=p_Add_q(M1,M2,r); |
---|
| 1143 | p_SetCoeff(m2,C1,r); |
---|
| 1144 | } |
---|
| 1145 | /* M1 is killed, M2=res = C2 M1 - C1 M2 */ |
---|
| 1146 | poly tmp=p_Copy(p1,r); |
---|
| 1147 | tmp=p_LmDeleteAndNext(tmp,r); |
---|
| 1148 | M1=nc_mm_Mult_p(m1,tmp,r); |
---|
| 1149 | tmp=p_Copy(p2,r); |
---|
| 1150 | tmp=p_LmDeleteAndNext(tmp,r); |
---|
| 1151 | M2=p_Add_q(M2,M1,r); |
---|
| 1152 | M1=nc_mm_Mult_p(m2,tmp,r); |
---|
| 1153 | M2=p_Add_q(M2,M1,r); |
---|
| 1154 | p_Delete(&m1,r); |
---|
| 1155 | p_Delete(&m2,r); |
---|
| 1156 | // n_Delete(&C1,r); |
---|
| 1157 | // n_Delete(&C2,r); |
---|
| 1158 | n_Delete(&MinusOne,r); |
---|
| 1159 | #ifdef PDEBUG |
---|
| 1160 | p_Test(M2,r); |
---|
| 1161 | #endif |
---|
[4bbe3b] | 1162 | if (M2!=NULL) pContent(M2); |
---|
[35aab3] | 1163 | return(M2); |
---|
| 1164 | } |
---|
| 1165 | |
---|
| 1166 | /*5 |
---|
| 1167 | * reduction of tail(q) with p1 |
---|
| 1168 | * lead(p1) divides lead(pNext(q2)) and pNext(q2) is reduced |
---|
| 1169 | * do not destroy p1, but tail(q) |
---|
| 1170 | */ |
---|
[4bbe3b] | 1171 | void nc_ReduceSpolyTail(poly p1, poly q, poly q2, poly spNoether, const ring r) |
---|
[35aab3] | 1172 | { |
---|
| 1173 | poly a1=p_Head(p1,r); |
---|
| 1174 | poly Q=pNext(q2); |
---|
| 1175 | number cQ=p_GetCoeff(Q,r); |
---|
| 1176 | poly m=pOne(); |
---|
| 1177 | p_ExpVectorDiff(m,Q,p1,r); |
---|
| 1178 | // p_SetComp(m,0,r); |
---|
[ec547b3] | 1179 | //p_Setm(m,r); |
---|
[35aab3] | 1180 | #ifdef PDEBUG |
---|
| 1181 | p_Test(m,r); |
---|
| 1182 | #endif |
---|
| 1183 | /* pSetComp(m,r)=0? */ |
---|
| 1184 | poly M=nc_mm_Mult_p(m,p_Copy(p1,r),r); |
---|
| 1185 | number C=p_GetCoeff(M,r); |
---|
| 1186 | M=p_Add_q(M,nc_mm_Mult_p(m,p_LmDeleteAndNext(p_Copy(p1,r),r),r),r); |
---|
| 1187 | q=p_Mult_nn(q,C,r); |
---|
| 1188 | number MinusOne=n_Init(-1,r); |
---|
| 1189 | if (!n_Equal(cQ,MinusOne,r)) |
---|
| 1190 | { |
---|
| 1191 | cQ=nNeg(cQ); |
---|
| 1192 | M=p_Mult_nn(M,cQ,r); |
---|
| 1193 | } |
---|
| 1194 | Q=p_Add_q(Q,M,r); |
---|
| 1195 | pNext(q2)=Q; |
---|
| 1196 | |
---|
| 1197 | p_Delete(&m,r); |
---|
| 1198 | n_Delete(&C,r); |
---|
| 1199 | n_Delete(&cQ,r); |
---|
| 1200 | n_Delete(&MinusOne,r); |
---|
| 1201 | /* return(q); */ |
---|
| 1202 | } |
---|
| 1203 | |
---|
| 1204 | /*6 |
---|
| 1205 | * creates the commutative lcm(lm(p1),lm(p2)) |
---|
| 1206 | * do not destroy p1 and p2 |
---|
| 1207 | */ |
---|
[4bbe3b] | 1208 | poly nc_CreateShortSpoly(poly p1, poly p2, const ring r) |
---|
[35aab3] | 1209 | { |
---|
| 1210 | if (p_GetComp(p1,r)!=p_GetComp(p2,r)) |
---|
| 1211 | { |
---|
| 1212 | Print("spShort:exponent mismatch!"); |
---|
| 1213 | return(NULL); |
---|
| 1214 | } |
---|
| 1215 | poly m=pOne(); |
---|
| 1216 | pLcm(p1,p2,m); |
---|
| 1217 | p_Setm(m,r); |
---|
| 1218 | #ifdef PDEBUG |
---|
| 1219 | p_Test(m,r); |
---|
| 1220 | #endif |
---|
| 1221 | return(m); |
---|
| 1222 | } |
---|
| 1223 | |
---|
| 1224 | void nc_kBucketPolyRed(kBucket_pt b, poly p, number *c) |
---|
| 1225 | { |
---|
| 1226 | // b will not by multiplied by any constant in this impl. |
---|
| 1227 | // ==> *c=1 |
---|
| 1228 | *c=nInit(1); |
---|
| 1229 | poly m=pOne(); |
---|
| 1230 | pExpVectorDiff(m,kBucketGetLm(b),p); |
---|
[ec547b3] | 1231 | //pSetm(m); |
---|
[35aab3] | 1232 | #ifdef PDEBUG |
---|
| 1233 | pTest(m); |
---|
| 1234 | #endif |
---|
| 1235 | poly pp=nc_mm_Mult_p(m,pCopy(p),currRing); |
---|
| 1236 | pDelete(&m); |
---|
| 1237 | number n=nCopy(pGetCoeff(pp)); |
---|
| 1238 | number MinusOne=nInit(-1); |
---|
| 1239 | number nn; |
---|
| 1240 | if (!nEqual(n,MinusOne)) |
---|
| 1241 | { |
---|
| 1242 | nn=nNeg(nInvers(n)); |
---|
| 1243 | } |
---|
| 1244 | else nn=nInit(1); |
---|
| 1245 | nDelete(&n); |
---|
| 1246 | n=nMult(nn,pGetCoeff(kBucketGetLm(b))); |
---|
| 1247 | nDelete(&nn); |
---|
| 1248 | pp=p_Mult_nn(pp,n,currRing); |
---|
| 1249 | nDelete(&n); |
---|
| 1250 | nDelete(&MinusOne); |
---|
| 1251 | int l=pLength(pp); |
---|
| 1252 | kBucket_Add_q(b,pp,&l); |
---|
| 1253 | } |
---|
| 1254 | |
---|
| 1255 | void nc_PolyPolyRed(poly &b, poly p, number *c) |
---|
| 1256 | // reduces b with p, do not delete both |
---|
| 1257 | { |
---|
| 1258 | // b will not by multiplied by any constant in this impl. |
---|
| 1259 | // ==> *c=1 |
---|
| 1260 | *c=nInit(1); |
---|
| 1261 | poly m=pOne(); |
---|
| 1262 | pExpVectorDiff(m,pHead(b),p); |
---|
[ec547b3] | 1263 | //pSetm(m); |
---|
[35aab3] | 1264 | #ifdef PDEBUG |
---|
| 1265 | pTest(m); |
---|
| 1266 | #endif |
---|
| 1267 | poly pp=nc_mm_Mult_p(m,pCopy(p),currRing); |
---|
| 1268 | pDelete(&m); |
---|
| 1269 | number n=nCopy(pGetCoeff(pp)); |
---|
| 1270 | number MinusOne=nInit(-1); |
---|
| 1271 | number nn; |
---|
| 1272 | if (!nEqual(n,MinusOne)) |
---|
| 1273 | { |
---|
| 1274 | nn=nNeg(nInvers(n)); |
---|
| 1275 | } |
---|
| 1276 | else nn=nInit(1); |
---|
| 1277 | nDelete(&n); |
---|
| 1278 | n=nMult(nn,pGetCoeff(b)); |
---|
| 1279 | nDelete(&nn); |
---|
| 1280 | pp=p_Mult_nn(pp,n,currRing); |
---|
| 1281 | nDelete(&n); |
---|
| 1282 | nDelete(&MinusOne); |
---|
| 1283 | b=p_Add_q(b,pp,currRing); |
---|
| 1284 | } |
---|
| 1285 | |
---|
| 1286 | poly nc_p_Bracket_qq(poly p, poly q) |
---|
| 1287 | /* returns [p,q], destroys p */ |
---|
| 1288 | { |
---|
| 1289 | if (!rIsPluralRing(currRing)) return(NULL); |
---|
| 1290 | if (pComparePolys(p,q)) return(NULL); |
---|
| 1291 | /* Components !? */ |
---|
| 1292 | poly Q=NULL; |
---|
| 1293 | number coef=NULL; |
---|
| 1294 | poly res=NULL; |
---|
| 1295 | poly pres=NULL; |
---|
| 1296 | int UseBuckets=1; |
---|
| 1297 | if ((pLength(p)< MIN_LENGTH_BUCKET/2) && (pLength(q)< MIN_LENGTH_BUCKET/2) || TEST_OPT_NOT_BUCKETS) UseBuckets=0; |
---|
| 1298 | sBucket_pt bu_out; |
---|
| 1299 | if (UseBuckets) bu_out=sBucketCreate(currRing); |
---|
| 1300 | while (p!=NULL) |
---|
| 1301 | { |
---|
| 1302 | Q=q; |
---|
| 1303 | while(Q!=NULL) |
---|
| 1304 | { |
---|
| 1305 | pres=nc_mm_Bracket_nn(p,Q); /* since no coeffs are taken into account there */ |
---|
| 1306 | if (pres!=NULL) |
---|
| 1307 | { |
---|
[f56364] | 1308 | coef = nMult(pGetCoeff(p),pGetCoeff(Q)); |
---|
| 1309 | pres = p_Mult_nn(pres,coef,currRing); |
---|
[35aab3] | 1310 | if (UseBuckets) sBucket_Add_p(bu_out,pres,pLength(pres)); |
---|
| 1311 | else res=p_Add_q(res,pres,currRing); |
---|
| 1312 | nDelete(&coef); |
---|
| 1313 | } |
---|
| 1314 | pIter(Q); |
---|
| 1315 | } |
---|
| 1316 | p=pLmDeleteAndNext(p); |
---|
| 1317 | } |
---|
| 1318 | if (UseBuckets) |
---|
| 1319 | { |
---|
| 1320 | res = NULL; |
---|
| 1321 | int len = pLength(res); |
---|
| 1322 | sBucketDestroyAdd(bu_out, &res, &len); |
---|
| 1323 | } |
---|
| 1324 | return(res); |
---|
| 1325 | } |
---|
| 1326 | |
---|
| 1327 | poly nc_mm_Bracket_nn(poly m1, poly m2) |
---|
| 1328 | /*returns [m1,m2] for two monoms, destroys nothing */ |
---|
| 1329 | /* without coeffs */ |
---|
| 1330 | { |
---|
| 1331 | if (pLmIsConstant(m1) || pLmIsConstant(m1)) return(NULL); |
---|
| 1332 | if (pLmCmp(m1,m2)==0) return(NULL); |
---|
| 1333 | int rN=currRing->N; |
---|
| 1334 | int *M1=(int *)omAlloc0((rN+1)*sizeof(int)); |
---|
| 1335 | int *M2=(int *)omAlloc0((rN+1)*sizeof(int)); |
---|
| 1336 | int *PREFIX=(int *)omAlloc0((rN+1)*sizeof(int)); |
---|
| 1337 | int *SUFFIX=(int *)omAlloc0((rN+1)*sizeof(int)); |
---|
| 1338 | pGetExpV(m1,M1); |
---|
| 1339 | pGetExpV(m2,M2); |
---|
| 1340 | poly res=NULL; |
---|
| 1341 | poly ares=NULL; |
---|
| 1342 | poly bres=NULL; |
---|
| 1343 | poly prefix=NULL; |
---|
| 1344 | poly suffix=NULL; |
---|
| 1345 | int nMin,nMax; |
---|
| 1346 | number nTmp=NULL; |
---|
| 1347 | int i,j,k; |
---|
| 1348 | for (i=1;i<=rN;i++) |
---|
| 1349 | { |
---|
| 1350 | if (M2[i]!=0) |
---|
| 1351 | { |
---|
| 1352 | ares=NULL; |
---|
| 1353 | for (j=1;j<=rN;j++) |
---|
| 1354 | { |
---|
| 1355 | if (M1[j]!=0) |
---|
| 1356 | { |
---|
| 1357 | bres=NULL; |
---|
| 1358 | /* compute [ x_j^M1[j],x_i^M2[i] ] */ |
---|
| 1359 | if (i<j) {nMax=j; nMin=i;} else {nMax=i; nMin=j;} |
---|
| 1360 | if ( (i==j) || ((MATELEM(currRing->nc->COM,nMin,nMax)!=NULL) && nIsOne(pGetCoeff(MATELEM(currRing->nc->C,nMin,nMax))) )) /* not (the same exp. or commuting exps)*/ |
---|
| 1361 | { bres=NULL; } |
---|
| 1362 | else |
---|
| 1363 | { |
---|
| 1364 | if (i<j) { bres=nc_uu_Mult_ww(j,M1[j],i,M2[i],currRing); } |
---|
| 1365 | else bres=nc_uu_Mult_ww(i,M2[i],j,M1[j],currRing); |
---|
| 1366 | if (nIsOne(pGetCoeff(bres))) |
---|
| 1367 | { |
---|
| 1368 | bres=pLmDeleteAndNext(bres); |
---|
| 1369 | } |
---|
| 1370 | else |
---|
| 1371 | { |
---|
| 1372 | nTmp=nSub(pGetCoeff(bres),nInit(1)); |
---|
| 1373 | pSetCoeff(bres,nTmp); /* only lc ! */ |
---|
| 1374 | } |
---|
| 1375 | #ifdef PDEBUG |
---|
| 1376 | pTest(bres); |
---|
| 1377 | #endif |
---|
| 1378 | if (i>j) bres=p_Neg(bres, currRing); |
---|
| 1379 | } |
---|
| 1380 | if (bres!=NULL) |
---|
| 1381 | { |
---|
| 1382 | /* now mult (prefix, bres, suffix) */ |
---|
| 1383 | memcpy(SUFFIX, M1,(rN+1)*sizeof(int)); |
---|
| 1384 | memcpy(PREFIX, M1,(rN+1)*sizeof(int)); |
---|
| 1385 | for (k=1;k<=j;k++) SUFFIX[k]=0; |
---|
| 1386 | for (k=j;k<=rN;k++) PREFIX[k]=0; |
---|
| 1387 | SUFFIX[0]=0; |
---|
| 1388 | PREFIX[0]=0; |
---|
| 1389 | prefix=pOne(); |
---|
| 1390 | suffix=pOne(); |
---|
| 1391 | pSetExpV(prefix,PREFIX); |
---|
| 1392 | pSetm(prefix); |
---|
| 1393 | pSetExpV(suffix,SUFFIX); |
---|
| 1394 | pSetm(suffix); |
---|
| 1395 | if (!pLmIsConstant(prefix)) bres = nc_mm_Mult_p(prefix, bres,currRing); |
---|
| 1396 | if (!pLmIsConstant(suffix)) bres = nc_p_Mult_mm(bres, suffix,currRing); |
---|
| 1397 | ares=p_Add_q(ares, bres,currRing); |
---|
| 1398 | /* What to give free? */ |
---|
[68349d] | 1399 | /* Do we have to free PREFIX/SUFFIX? it seems so */ |
---|
[35aab3] | 1400 | pDelete(&prefix); |
---|
| 1401 | pDelete(&suffix); |
---|
| 1402 | } |
---|
| 1403 | } |
---|
| 1404 | } |
---|
| 1405 | if (ares!=NULL) |
---|
| 1406 | { |
---|
| 1407 | /* now mult (prefix, bres, suffix) */ |
---|
| 1408 | memcpy(SUFFIX, M2,(rN+1)*sizeof(int)); |
---|
| 1409 | memcpy(PREFIX, M2,(rN+1)*sizeof(int)); |
---|
| 1410 | for (k=1;k<=i;k++) SUFFIX[k]=0; |
---|
| 1411 | for (k=i;k<=rN;k++) PREFIX[k]=0; |
---|
| 1412 | SUFFIX[0]=0; |
---|
| 1413 | PREFIX[0]=0; |
---|
| 1414 | prefix=pOne(); |
---|
| 1415 | suffix=pOne(); |
---|
| 1416 | pSetExpV(prefix,PREFIX); |
---|
| 1417 | pSetm(prefix); |
---|
| 1418 | pSetExpV(suffix,SUFFIX); |
---|
| 1419 | pSetm(suffix); |
---|
| 1420 | bres=ares; |
---|
| 1421 | if (!pLmIsConstant(prefix)) bres = nc_mm_Mult_p(prefix, bres,currRing); |
---|
| 1422 | if (!pLmIsConstant(suffix)) bres = nc_p_Mult_mm(bres, suffix,currRing); |
---|
| 1423 | res=p_Add_q(res, bres,currRing); |
---|
| 1424 | pDelete(&prefix); |
---|
| 1425 | pDelete(&suffix); |
---|
| 1426 | } |
---|
| 1427 | } |
---|
| 1428 | } |
---|
| 1429 | freeT(M1, rN); |
---|
| 1430 | freeT(M2, rN); |
---|
| 1431 | freeT(PREFIX, rN); |
---|
| 1432 | freeT(SUFFIX, rN); |
---|
[f56364] | 1433 | pTest(res); |
---|
[35aab3] | 1434 | return(res); |
---|
| 1435 | } |
---|
| 1436 | |
---|
| 1437 | ideal twostd(ideal I) |
---|
| 1438 | { |
---|
| 1439 | int i; |
---|
| 1440 | int j; |
---|
| 1441 | int s; |
---|
| 1442 | int flag; |
---|
| 1443 | poly p=NULL; |
---|
| 1444 | poly q=NULL; |
---|
| 1445 | ideal J=kStd(I, currQuotient,testHomog,NULL,NULL,0,0,NULL); |
---|
| 1446 | idSkipZeroes(J); |
---|
| 1447 | ideal K=NULL; |
---|
| 1448 | poly varj=NULL; |
---|
| 1449 | ideal Q=NULL; |
---|
| 1450 | ideal id_tmp=NULL; |
---|
| 1451 | int rN=currRing->N; |
---|
| 1452 | int iSize=0; |
---|
| 1453 | loop |
---|
| 1454 | { |
---|
| 1455 | flag=0; |
---|
| 1456 | K=NULL; |
---|
| 1457 | s=idElem(J); |
---|
| 1458 | for (i=0;i<=s-1;i++) |
---|
| 1459 | { |
---|
| 1460 | p=J->m[i]; |
---|
| 1461 | for (j=1;j<=rN;j++) |
---|
| 1462 | { |
---|
| 1463 | varj = pOne(); |
---|
| 1464 | pSetExp(varj,j,1); |
---|
| 1465 | pSetm(varj); |
---|
| 1466 | q = nc_p_Mult_mm(pCopy(p),varj,currRing); |
---|
| 1467 | pDelete(&varj); |
---|
[4bbe3b] | 1468 | q = nc_ReduceSpoly(p,q,NULL,currRing); |
---|
[35aab3] | 1469 | q = kNF(J,currQuotient,q,0,0); |
---|
| 1470 | if (q!=NULL) |
---|
| 1471 | { |
---|
| 1472 | if (pIsConstant(q)) |
---|
| 1473 | { |
---|
| 1474 | Q=idInit(1,1); |
---|
| 1475 | Q->m[0]=pOne(); |
---|
| 1476 | idDelete(&J); |
---|
| 1477 | pDelete(&q); |
---|
| 1478 | if (K!=NULL) idDelete(&K); |
---|
| 1479 | return(Q); |
---|
| 1480 | } |
---|
| 1481 | flag=1; |
---|
| 1482 | Q=idInit(1,1); |
---|
| 1483 | Q->m[0]=q; |
---|
| 1484 | id_tmp=idSimpleAdd(K,Q); |
---|
| 1485 | idDelete(&K); |
---|
| 1486 | K=id_tmp; |
---|
| 1487 | idDelete(&Q); |
---|
| 1488 | } |
---|
| 1489 | } |
---|
| 1490 | } |
---|
| 1491 | if (flag==0) |
---|
| 1492 | /* i.e. all elements are two-sided */ |
---|
| 1493 | { |
---|
| 1494 | idDelete(&K); |
---|
| 1495 | return(J); |
---|
| 1496 | } |
---|
| 1497 | /* now we update GrBasis J with K */ |
---|
[8e165ec] | 1498 | // iSize=IDELEMS(J); |
---|
| 1499 | iSize=idElem(J); |
---|
[35aab3] | 1500 | id_tmp=idSimpleAdd(J,K); |
---|
| 1501 | idDelete(&K); |
---|
| 1502 | idDelete(&J); |
---|
| 1503 | BITSET save_test=test; |
---|
| 1504 | test|=Sy_bit(OPT_SB_1); |
---|
| 1505 | J=kStd(id_tmp, currQuotient, testHomog,NULL,NULL,0,iSize); |
---|
| 1506 | test=save_test; |
---|
| 1507 | idSkipZeroes(J); |
---|
| 1508 | } |
---|
| 1509 | } |
---|
| 1510 | |
---|
| 1511 | matrix nc_PrintMat(int a, int b, ring r, int metric) |
---|
| 1512 | /* returns matrix with the info on noncomm multiplication */ |
---|
| 1513 | { |
---|
| 1514 | |
---|
| 1515 | if ( (a==b) || !rIsPluralRing(r) ) return(NULL); |
---|
| 1516 | int i; |
---|
| 1517 | int j; |
---|
| 1518 | if (a>b) {j=b; i=a;} |
---|
| 1519 | else {j=a; i=b;} |
---|
| 1520 | /* i<j */ |
---|
| 1521 | int rN=r->N; |
---|
| 1522 | int size=r->nc->MTsize[UPMATELEM(i,j,rN)]; |
---|
| 1523 | matrix M = r->nc->MT[UPMATELEM(i,j,rN)]; |
---|
| 1524 | /* return(M); */ |
---|
| 1525 | int sizeofres; |
---|
| 1526 | if (metric==0) |
---|
| 1527 | { |
---|
| 1528 | sizeofres=sizeof(int); |
---|
| 1529 | } |
---|
| 1530 | if (metric==1) |
---|
| 1531 | { |
---|
| 1532 | sizeofres=sizeof(number); |
---|
| 1533 | } |
---|
| 1534 | matrix res=mpNew(size,size); |
---|
| 1535 | int s; |
---|
| 1536 | int t; |
---|
| 1537 | int length; |
---|
| 1538 | long totdeg; |
---|
| 1539 | poly p; |
---|
| 1540 | for(s=1;s<=size;s++) |
---|
| 1541 | { |
---|
| 1542 | for(t=1;t<=size;t++) |
---|
| 1543 | { |
---|
| 1544 | p=MATELEM(M,s,t); |
---|
| 1545 | if (p==NULL) |
---|
| 1546 | { |
---|
| 1547 | MATELEM(res,s,t)=0; |
---|
| 1548 | } |
---|
| 1549 | else |
---|
| 1550 | { |
---|
| 1551 | length = pLength(p); |
---|
| 1552 | if (metric==0) /* length */ |
---|
| 1553 | { |
---|
| 1554 | MATELEM(res,s,t)= p_ISet(length,r); |
---|
| 1555 | } |
---|
| 1556 | else if (metric==1) /* sum of deg divided by the length */ |
---|
| 1557 | { |
---|
| 1558 | totdeg=0; |
---|
| 1559 | while (p!=NULL) |
---|
| 1560 | { |
---|
| 1561 | totdeg=totdeg+pDeg(p,r); |
---|
| 1562 | pIter(p); |
---|
| 1563 | } |
---|
| 1564 | number ntd = nInit(totdeg); |
---|
| 1565 | number nln = nInit(length); |
---|
| 1566 | number nres=nDiv(ntd,nln); |
---|
| 1567 | nDelete(&ntd); |
---|
| 1568 | nDelete(&nln); |
---|
| 1569 | MATELEM(res,s,t)=p_NSet(nres,r); |
---|
| 1570 | } |
---|
| 1571 | } |
---|
| 1572 | } |
---|
| 1573 | } |
---|
| 1574 | return(res); |
---|
| 1575 | } |
---|
| 1576 | |
---|
| 1577 | void ncKill(ring r) |
---|
| 1578 | /* kills the nc extension of ring r */ |
---|
| 1579 | { |
---|
| 1580 | int i,j; |
---|
| 1581 | int rN=r->N; |
---|
[e90187] | 1582 | if ( rN > 1 ) |
---|
[35aab3] | 1583 | { |
---|
[e90187] | 1584 | for(i=1;i<rN;i++) |
---|
[35aab3] | 1585 | { |
---|
[e90187] | 1586 | for(j=i+1;j<=rN;j++) |
---|
| 1587 | { |
---|
| 1588 | id_Delete((ideal *)&(r->nc->MT[UPMATELEM(i,j,rN)]),r->nc->basering); |
---|
| 1589 | } |
---|
[35aab3] | 1590 | } |
---|
[e90187] | 1591 | omFreeSize((ADDRESS)r->nc->MT,rN*(rN-1)/2*sizeof(matrix)); |
---|
| 1592 | omFreeSize((ADDRESS)r->nc->MTsize,rN*(rN-1)/2*sizeof(int)); |
---|
| 1593 | id_Delete((ideal *)&(r->nc->COM),r->nc->basering); |
---|
[35aab3] | 1594 | } |
---|
| 1595 | id_Delete((ideal *)&(r->nc->C),r->nc->basering); |
---|
| 1596 | id_Delete((ideal *)&(r->nc->D),r->nc->basering); |
---|
| 1597 | omFreeSize((ADDRESS)r->nc,sizeof(nc_struct)); |
---|
| 1598 | r->nc=NULL; |
---|
| 1599 | } |
---|
| 1600 | |
---|
[6c0f53] | 1601 | void ncCleanUp(ring r) |
---|
| 1602 | { |
---|
| 1603 | /* small CleanUp of r->nc */ |
---|
| 1604 | omFreeSize((ADDRESS)r->nc,sizeof(nc_struct)); |
---|
| 1605 | r->nc = NULL; |
---|
| 1606 | } |
---|
| 1607 | |
---|
[262fc3] | 1608 | poly nc_p_CopyGet(poly a, const ring r) |
---|
| 1609 | /* for use in getting the mult. matrix elements*/ |
---|
[35aab3] | 1610 | { |
---|
| 1611 | if (!rIsPluralRing(r)) return(p_Copy(a,r)); |
---|
| 1612 | if (r==r->nc->basering) return(p_Copy(a,r)); |
---|
| 1613 | else |
---|
| 1614 | { |
---|
[3c8a31] | 1615 | // nFunc nMap = nSetMap(); |
---|
[35aab3] | 1616 | return(prCopyR_NoSort(a,r->nc->basering,r)); |
---|
| 1617 | } |
---|
| 1618 | } |
---|
| 1619 | |
---|
[262fc3] | 1620 | poly nc_p_CopyPut(poly a, const ring r) |
---|
| 1621 | /* for use in defining the mult. matrix elements*/ |
---|
[35aab3] | 1622 | { |
---|
| 1623 | if (!rIsPluralRing(r)) return(p_Copy(a,r)); |
---|
| 1624 | if (r==r->nc->basering) return(p_Copy(a,r)); |
---|
| 1625 | else |
---|
| 1626 | { |
---|
| 1627 | return(prCopyR_NoSort(a,r,r->nc->basering)); |
---|
| 1628 | } |
---|
| 1629 | } |
---|
| 1630 | |
---|
| 1631 | int nc_CheckSubalgebra(poly PolyVar, ring r) |
---|
| 1632 | /* returns TRUE if product of vars from PolyVar defines */ |
---|
| 1633 | /* an admissible subalgebra of r */ |
---|
| 1634 | { |
---|
| 1635 | int rN=r->N; |
---|
| 1636 | int *ExpVar=(int*)omAlloc0((rN+1)*sizeof(int)); |
---|
| 1637 | int *ExpTmp=(int*)omAlloc0((rN+1)*sizeof(int)); |
---|
| 1638 | p_GetExpV(PolyVar, ExpVar, r); |
---|
| 1639 | int i; int j; int k; |
---|
| 1640 | poly test=NULL; |
---|
| 1641 | int OK=1; |
---|
| 1642 | for (i=1;i<rN;i++) |
---|
| 1643 | { |
---|
| 1644 | if (ExpVar[i]==0) /* i.e. not in PolyVar */ |
---|
| 1645 | { |
---|
| 1646 | for (j=i+1;j<=rN;j++) |
---|
| 1647 | { |
---|
| 1648 | if (ExpVar[j]==0) |
---|
| 1649 | { |
---|
| 1650 | test=nc_p_CopyGet(MATELEM(r->nc->D,i,j),r); |
---|
| 1651 | while (test!=NULL) |
---|
| 1652 | { |
---|
| 1653 | p_GetExpV(test, ExpTmp, r); |
---|
| 1654 | OK=1; |
---|
| 1655 | for (k=1;k<=rN;k++) |
---|
| 1656 | { |
---|
| 1657 | if (ExpTmp[k]!=0) |
---|
| 1658 | { |
---|
| 1659 | if (ExpVar[k]!=0) OK=0; |
---|
| 1660 | } |
---|
| 1661 | } |
---|
| 1662 | if (!OK) return(FALSE); |
---|
| 1663 | pIter(test); |
---|
| 1664 | } |
---|
| 1665 | } |
---|
| 1666 | } |
---|
| 1667 | } |
---|
| 1668 | } |
---|
| 1669 | p_Delete(&test,r); |
---|
| 1670 | freeT(ExpVar,rN); |
---|
| 1671 | freeT(ExpTmp,rN); |
---|
| 1672 | return(TRUE); |
---|
| 1673 | } |
---|
| 1674 | |
---|
| 1675 | // int Commutative_Context(ring r, leftv expression) |
---|
| 1676 | // /* returns 1 if expression consists */ |
---|
| 1677 | // /* of commutative elements */ |
---|
| 1678 | // { |
---|
| 1679 | // /* crucial: poly -> ideal, module, matrix */ |
---|
| 1680 | |
---|
| 1681 | // } |
---|
| 1682 | |
---|
| 1683 | // int Comm_Context_Poly(ring r, poly p) |
---|
| 1684 | // { |
---|
| 1685 | // poly COMM=r->nc->COMM; |
---|
| 1686 | // poly pp=pOne(); |
---|
| 1687 | // memset(pp->exp,0,r->ExpL_Size*sizeof(long)); |
---|
| 1688 | // while (p!=NULL) |
---|
| 1689 | // { |
---|
| 1690 | // for (i=0;i<=r->ExpL_Size;i++) |
---|
| 1691 | // { |
---|
| 1692 | // if ((p->exp[i]) && (pp->exp[i])) return(FALSE); |
---|
| 1693 | // /* nonzero exponent of non-comm variable */ |
---|
| 1694 | // } |
---|
| 1695 | // pIter(p); |
---|
| 1696 | // } |
---|
| 1697 | // return(TRUE); |
---|
| 1698 | // } |
---|
| 1699 | |
---|
[f12e32] | 1700 | BOOLEAN nc_CallPlural(matrix CCC, matrix DDD, poly CCN, poly DDN, ring r) |
---|
[6c0f53] | 1701 | /* returns TRUE if there were errors */ |
---|
| 1702 | /* analyze inputs, check them for consistency */ |
---|
| 1703 | /* detect nc_type, DO NOT initialize multiplication */ |
---|
| 1704 | /* check the ordering condition and evtl. NDC */ |
---|
| 1705 | { |
---|
[f12e32] | 1706 | matrix CC = NULL; |
---|
| 1707 | matrix DD = NULL; |
---|
| 1708 | poly CN = NULL; |
---|
| 1709 | poly DN = NULL; |
---|
[6c0f53] | 1710 | matrix C; |
---|
| 1711 | matrix D; |
---|
| 1712 | number nN,pN,qN; |
---|
| 1713 | int tmpIsSkewConstant; |
---|
| 1714 | int i,j; |
---|
| 1715 | if (r->nc != NULL) |
---|
| 1716 | { |
---|
| 1717 | WarnS("redefining algebra structure"); |
---|
| 1718 | if (r->nc->ref>1) /* in use by somebody else */ |
---|
| 1719 | { |
---|
| 1720 | r->nc->ref--; |
---|
| 1721 | } |
---|
| 1722 | else /* kill the previous nc data */ |
---|
| 1723 | { |
---|
| 1724 | ncKill(r); |
---|
| 1725 | } |
---|
| 1726 | } |
---|
| 1727 | r->nc = (nc_struct *)omAlloc0(sizeof(nc_struct)); |
---|
| 1728 | r->nc->ref = 1; |
---|
| 1729 | r->nc->basering = r; |
---|
| 1730 | r->nc->type = nc_undef; |
---|
[f12e32] | 1731 | |
---|
[6c0f53] | 1732 | /* initialition of the matrix C */ |
---|
[f12e32] | 1733 | /* check the correctness of arguments */ |
---|
| 1734 | |
---|
| 1735 | if ((CCC != NULL) && ( (MATCOLS(CCC)==1) || MATROWS(CCC)==1 ) ) |
---|
| 1736 | { |
---|
| 1737 | CN = MATELEM(CCC,1,1); |
---|
| 1738 | } |
---|
| 1739 | else |
---|
| 1740 | { |
---|
| 1741 | if ((CCC != NULL) && ( (MATCOLS(CCC)!=r->N) || (MATROWS(CCC)!=r->N) )) |
---|
| 1742 | { |
---|
| 1743 | Werror("Square %d x %d matrix expected",r->N,r->N); |
---|
| 1744 | ncCleanUp(r); |
---|
| 1745 | return TRUE; |
---|
| 1746 | } |
---|
| 1747 | } |
---|
| 1748 | if (( CCC != NULL) && (CC == NULL)) CC = mpCopy(CCC); |
---|
| 1749 | if (( CCN != NULL) && (CN == NULL)) CN = CCN; |
---|
| 1750 | |
---|
| 1751 | /* initialition of the matrix D */ |
---|
| 1752 | /* check the correctness of arguments */ |
---|
| 1753 | |
---|
| 1754 | if ((DDD != NULL) && ( (MATCOLS(DDD)==1) || MATROWS(DDD)==1 ) ) |
---|
| 1755 | { |
---|
| 1756 | DN = MATELEM(DDD,1,1); |
---|
| 1757 | } |
---|
| 1758 | else |
---|
| 1759 | { |
---|
| 1760 | if ((DDD != NULL) && ( (MATCOLS(DDD)!=r->N) || (MATROWS(DDD)!=r->N) )) |
---|
| 1761 | { |
---|
| 1762 | Werror("Square %d x %d matrix expected",r->N,r->N); |
---|
| 1763 | ncCleanUp(r); |
---|
| 1764 | return TRUE; |
---|
| 1765 | } |
---|
| 1766 | } |
---|
| 1767 | if (( DDD != NULL) && (DD == NULL)) DD = mpCopy(DDD); |
---|
| 1768 | if (( DDN != NULL) && (DN == NULL)) DN = DDN; |
---|
| 1769 | |
---|
| 1770 | /* further checks */ |
---|
| 1771 | |
---|
[6c0f53] | 1772 | if (CN != NULL) /* create matrix C = CN * Id */ |
---|
| 1773 | { |
---|
| 1774 | nN = p_GetCoeff(CN,r); |
---|
| 1775 | if (n_IsZero(nN,r)) |
---|
| 1776 | { |
---|
| 1777 | Werror("Incorrect input : zero coefficients are not allowed"); |
---|
| 1778 | ncCleanUp(r); |
---|
| 1779 | return TRUE; |
---|
| 1780 | } |
---|
| 1781 | if (nIsOne(nN)) |
---|
| 1782 | { |
---|
| 1783 | r->nc->type = nc_lie; |
---|
| 1784 | } |
---|
| 1785 | else |
---|
| 1786 | { |
---|
| 1787 | r->nc->type = nc_general; |
---|
| 1788 | } |
---|
| 1789 | r->nc->IsSkewConstant = 1; |
---|
| 1790 | C = mpNew(r->N,r->N); |
---|
| 1791 | for(i=1; i<r->N; i++) |
---|
| 1792 | { |
---|
| 1793 | for(j=i+1; j<=r->N; j++) |
---|
| 1794 | { |
---|
| 1795 | MATELEM(C,i,j) = nc_p_CopyPut(CN,r); |
---|
| 1796 | } |
---|
| 1797 | } |
---|
| 1798 | } |
---|
[f12e32] | 1799 | if ( (CN == NULL) && (CC != NULL) ) /* copy matrix C */ |
---|
[6c0f53] | 1800 | { |
---|
| 1801 | C = mpCopy(CC); |
---|
| 1802 | /* analyze C */ |
---|
| 1803 | pN = p_GetCoeff(MATELEM(C,1,2),r); |
---|
| 1804 | tmpIsSkewConstant = 1; |
---|
| 1805 | for(i=1; i<r->N; i++) |
---|
| 1806 | { |
---|
| 1807 | for(j=i+1; j<=r->N; j++) |
---|
| 1808 | { |
---|
| 1809 | qN = p_GetCoeff(MATELEM(C,i,j),r); |
---|
| 1810 | if ( qN == NULL ) /* check the consistency: Cij!=0 */ |
---|
| 1811 | { |
---|
| 1812 | Werror("Incorrect input : matrix of coefficients contains zeros in the upper triangle"); |
---|
| 1813 | ncCleanUp(r); |
---|
| 1814 | return TRUE; |
---|
| 1815 | } |
---|
| 1816 | if (!nEqual(pN,qN)) tmpIsSkewConstant = 0; |
---|
| 1817 | } |
---|
| 1818 | } |
---|
| 1819 | r->nc->IsSkewConstant=tmpIsSkewConstant; |
---|
| 1820 | if ( (tmpIsSkewConstant) && (nIsOne(pN)) ) |
---|
| 1821 | { |
---|
| 1822 | r->nc->type = nc_lie; |
---|
| 1823 | } |
---|
| 1824 | else |
---|
| 1825 | { |
---|
| 1826 | r->nc->type = nc_general; |
---|
| 1827 | } |
---|
| 1828 | } |
---|
| 1829 | |
---|
| 1830 | /* initialition of the matrix D */ |
---|
[f12e32] | 1831 | if ( DD == NULL ) |
---|
| 1832 | /* we treat DN only (it could also be NULL) */ |
---|
[6c0f53] | 1833 | { |
---|
| 1834 | D = mpNew(r->N,r->N); |
---|
| 1835 | if (DN == NULL) |
---|
| 1836 | { |
---|
| 1837 | if ( (currRing->nc->type == nc_lie) || (currRing->nc->type == nc_undef) ) |
---|
| 1838 | { |
---|
| 1839 | currRing->nc->type = nc_comm; /* it was nc_skew earlier */ |
---|
| 1840 | } |
---|
| 1841 | else /* nc_general, nc_skew */ |
---|
| 1842 | { |
---|
| 1843 | currRing->nc->type = nc_skew; |
---|
| 1844 | } |
---|
| 1845 | } |
---|
| 1846 | else /* DN != NULL */ |
---|
| 1847 | { |
---|
| 1848 | for(i=1; i<r->N; i++) |
---|
| 1849 | { |
---|
| 1850 | for(j=i+1; j<=r->N; j++) |
---|
| 1851 | { |
---|
| 1852 | MATELEM(D,i,j) = nc_p_CopyPut(DN,r); |
---|
| 1853 | } |
---|
| 1854 | } |
---|
| 1855 | } |
---|
| 1856 | } |
---|
| 1857 | else /* DD != NULL */ |
---|
| 1858 | { |
---|
| 1859 | D = mpCopy(DD); |
---|
| 1860 | } |
---|
| 1861 | /* analyze D */ |
---|
| 1862 | /* check the ordering condition for D (both matrix and poly cases) */ |
---|
| 1863 | poly p,q; |
---|
| 1864 | int report = 1; |
---|
| 1865 | for(i=1; i<r->N; i++) |
---|
| 1866 | { |
---|
| 1867 | for(j=i+1; j<=r->N; j++) |
---|
| 1868 | { |
---|
| 1869 | p = MATELEM(D,i,j); |
---|
| 1870 | if ( p != NULL) |
---|
| 1871 | { |
---|
| 1872 | q = pOne(); |
---|
| 1873 | p_SetExp(q,i,1,r); |
---|
| 1874 | p_SetExp(q,j,1,r); |
---|
| 1875 | p_Setm(q,r); |
---|
| 1876 | if (p_LmCmp(q,p,r) != 1) /* i.e. lm(p)<=lm(q) */ |
---|
| 1877 | { |
---|
| 1878 | Print("Bad ordering at %d,%d",i,j); |
---|
| 1879 | report = 0; |
---|
| 1880 | } |
---|
| 1881 | p_Delete(&q,r); |
---|
| 1882 | p = NULL; |
---|
| 1883 | } |
---|
| 1884 | } |
---|
| 1885 | } |
---|
| 1886 | if (!report) |
---|
| 1887 | { |
---|
| 1888 | Werror("Matrix of polynomials violates the ordering condition"); |
---|
| 1889 | ncCleanUp(r); |
---|
| 1890 | return TRUE; |
---|
| 1891 | } |
---|
| 1892 | r->nc->C = C; |
---|
| 1893 | r->nc->D = D; |
---|
| 1894 | return nc_InitMultiplication(r); |
---|
| 1895 | } |
---|
| 1896 | |
---|
| 1897 | BOOLEAN nc_InitMultiplication(ring r) |
---|
| 1898 | { |
---|
| 1899 | /* returns TRUE if there were errors */ |
---|
[8e165ec] | 1900 | /* initialize the multiplication: */ |
---|
| 1901 | /* r->nc->MTsize, r->nc->MT, r->nc->COM, */ |
---|
| 1902 | /* and r->nc->IsSkewConstant for the skew case */ |
---|
[262fc3] | 1903 | if (rVar(r)==1) |
---|
[e90187] | 1904 | { |
---|
| 1905 | r->nc->type=nc_comm; |
---|
| 1906 | r->nc->IsSkewConstant=1; |
---|
| 1907 | return FALSE; |
---|
| 1908 | } |
---|
[3c8a31] | 1909 | ring save = currRing; |
---|
| 1910 | int WeChangeRing = 0; |
---|
| 1911 | if (currRing!=r) |
---|
| 1912 | { |
---|
| 1913 | rChangeCurrRing(r); |
---|
| 1914 | WeChangeRing = 1; |
---|
| 1915 | } |
---|
[6c0f53] | 1916 | int i,j; |
---|
| 1917 | r->nc->MT = (matrix *)omAlloc0(r->N*(r->N-1)/2*sizeof(matrix)); |
---|
| 1918 | r->nc->MTsize = (int *)omAlloc0(r->N*(r->N-1)/2*sizeof(int)); |
---|
[3c8a31] | 1919 | matrix COM = mpCopy(r->nc->C); |
---|
[b147507] | 1920 | poly p,q; |
---|
[6c0f53] | 1921 | short DefMTsize=7; |
---|
| 1922 | int IsNonComm=0; |
---|
| 1923 | int tmpIsSkewConstant; |
---|
| 1924 | |
---|
| 1925 | for(i=1; i<r->N; i++) |
---|
| 1926 | { |
---|
| 1927 | for(j=i+1; j<=r->N; j++) |
---|
| 1928 | { |
---|
| 1929 | if ( MATELEM(r->nc->D,i,j) == NULL ) /* quasicommutative case */ |
---|
| 1930 | { |
---|
| 1931 | /* 1x1 mult.matrix */ |
---|
| 1932 | r->nc->MTsize[UPMATELEM(i,j,r->N)] = 1; |
---|
| 1933 | r->nc->MT[UPMATELEM(i,j,r->N)] = mpNew(1,1); |
---|
| 1934 | } |
---|
| 1935 | else /* pure noncommutative case */ |
---|
| 1936 | { |
---|
| 1937 | /* TODO check the special multiplication properties */ |
---|
| 1938 | IsNonComm = 1; |
---|
[3c8a31] | 1939 | p_Delete(&(MATELEM(COM,i,j)),r); |
---|
[6c0f53] | 1940 | MATELEM(COM,i,j) = NULL; |
---|
| 1941 | r->nc->MTsize[UPMATELEM(i,j,r->N)] = DefMTsize; /* default sizes */ |
---|
| 1942 | r->nc->MT[UPMATELEM(i,j,r->N)] = mpNew(DefMTsize, DefMTsize); |
---|
| 1943 | } |
---|
| 1944 | /* set MT[i,j,1,1] to c_i_j*x_i*x_j + D_i_j */ |
---|
[3c8a31] | 1945 | p = p_ISet(1,r); /* instead of p = pOne(); */ |
---|
[6c0f53] | 1946 | p_SetCoeff(p,nCopy(pGetCoeff(MATELEM(r->nc->C,i,j))),r); |
---|
| 1947 | p_SetExp(p,i,1,r); |
---|
| 1948 | p_SetExp(p,j,1,r); |
---|
| 1949 | p_Setm(p,r); |
---|
[b147507] | 1950 | q = nc_p_CopyGet(MATELEM(r->nc->D,i,j),r); |
---|
| 1951 | p = p_Add_q(p,q,r); |
---|
[6c0f53] | 1952 | MATELEM(r->nc->MT[UPMATELEM(i,j,r->N)],1,1) = nc_p_CopyPut(p,r); |
---|
[3c8a31] | 1953 | p_Delete(&p,r); |
---|
[6c0f53] | 1954 | p = NULL; |
---|
| 1955 | } |
---|
| 1956 | } |
---|
| 1957 | if (r->nc->type==nc_undef) |
---|
| 1958 | { |
---|
| 1959 | if (IsNonComm==1) |
---|
| 1960 | { |
---|
| 1961 | // assume(pN!=NULL); |
---|
| 1962 | // if ((tmpIsSkewConstant==1) && (nIsOne(pGetCoeff(pN)))) r->nc->type=nc_lie; |
---|
| 1963 | // else r->nc->type=nc_general; |
---|
| 1964 | } |
---|
| 1965 | if (IsNonComm==0) |
---|
| 1966 | { |
---|
| 1967 | r->nc->type=nc_skew; /* TODO: check whether it is commutative */ |
---|
| 1968 | r->nc->IsSkewConstant=tmpIsSkewConstant; |
---|
| 1969 | } |
---|
| 1970 | } |
---|
| 1971 | r->nc->COM=COM; |
---|
[3c8a31] | 1972 | if (WeChangeRing) |
---|
| 1973 | { |
---|
| 1974 | rChangeCurrRing(save); |
---|
| 1975 | } |
---|
[6c0f53] | 1976 | return FALSE; |
---|
| 1977 | } |
---|
| 1978 | |
---|
[68349d] | 1979 | /* substitute the n-th variable by e in p |
---|
| 1980 | * destroy p |
---|
| 1981 | * e is not a constant |
---|
| 1982 | */ |
---|
| 1983 | poly nc_pSubst(poly p, int n, poly e) |
---|
| 1984 | { |
---|
| 1985 | int rN=currRing->N; |
---|
| 1986 | int *PRE = (int *)omAlloc0((rN+1)*sizeof(int)); |
---|
| 1987 | int *SUF = (int *)omAlloc0((rN+1)*sizeof(int)); |
---|
| 1988 | int i,j,pow; |
---|
[6a33fd] | 1989 | number C; |
---|
[68349d] | 1990 | poly suf,pre; |
---|
| 1991 | poly res = NULL; |
---|
| 1992 | poly out = NULL; |
---|
| 1993 | while ( p!= NULL ) |
---|
| 1994 | { |
---|
[6a33fd] | 1995 | C = pGetCoeff(p); |
---|
[68349d] | 1996 | pGetExpV(p, PRE); /* faster splitting? */ |
---|
| 1997 | pow = PRE[n]; PRE[n]=0; |
---|
| 1998 | res = NULL; |
---|
| 1999 | if (pow!=0) |
---|
| 2000 | { |
---|
| 2001 | for (i=n+1; i<=rN; i++) |
---|
| 2002 | { |
---|
| 2003 | SUF[i] = PRE[i]; |
---|
| 2004 | PRE[i] = 0; |
---|
| 2005 | } |
---|
| 2006 | res = pPower(pCopy(e),pow); |
---|
| 2007 | /* multiply with prefix */ |
---|
| 2008 | pre = pOne(); |
---|
| 2009 | pSetExpV(pre,PRE); |
---|
| 2010 | pSetm(pre); |
---|
| 2011 | pSetComp(pre,PRE[0]); |
---|
| 2012 | res = nc_mm_Mult_p(pre,res,currRing); |
---|
| 2013 | /* multiply with suffix */ |
---|
| 2014 | suf = pOne(); |
---|
| 2015 | pSetExpV(suf,SUF); |
---|
| 2016 | pSetm(suf); |
---|
| 2017 | pSetComp(suf,PRE[0]); |
---|
| 2018 | res = nc_p_Mult_mm(res,suf,currRing); |
---|
[6a33fd] | 2019 | res = p_Mult_nn(res,C,currRing); |
---|
[68349d] | 2020 | } |
---|
| 2021 | else /* pow==0 */ |
---|
| 2022 | { |
---|
| 2023 | res = pHead(p); |
---|
| 2024 | } |
---|
| 2025 | p = pLmDeleteAndNext(p); |
---|
| 2026 | out = pAdd(out,res); |
---|
| 2027 | } |
---|
| 2028 | freeT(PRE,rN); |
---|
| 2029 | freeT(SUF,rN); |
---|
| 2030 | return(out); |
---|
| 2031 | } |
---|
| 2032 | |
---|
[8e165ec] | 2033 | static ideal idPrepareStd(ideal T, ideal s, int k) |
---|
| 2034 | { |
---|
| 2035 | /* T is a left SB, without zeros, s is a list with zeros */ |
---|
| 2036 | #ifdef PDEBUG |
---|
| 2037 | if (IDELEMS(s)!=IDELEMS(T)) |
---|
| 2038 | { |
---|
| 2039 | Print("ideals of diff. size!!!"); |
---|
| 2040 | } |
---|
| 2041 | #endif |
---|
| 2042 | ideal t = idCopy(T); |
---|
| 2043 | int j,rs=idRankFreeModule(s),rt=idRankFreeModule(t); |
---|
| 2044 | poly p,q; |
---|
| 2045 | |
---|
| 2046 | ideal res = idInit(2*idElem(t),1+idElem(t)); |
---|
| 2047 | if (rs == 0) |
---|
| 2048 | { |
---|
| 2049 | for (j=0; j<IDELEMS(t); j++) |
---|
| 2050 | { |
---|
| 2051 | if (s->m[j]!=NULL) pSetCompP(s->m[j],1); |
---|
| 2052 | if (t->m[j]!=NULL) pSetCompP(t->m[j],1); |
---|
| 2053 | } |
---|
| 2054 | k = si_max(k,1); |
---|
| 2055 | } |
---|
| 2056 | for (j=0; j<IDELEMS(t); j++) |
---|
| 2057 | { |
---|
| 2058 | if (s->m[j]!=NULL) |
---|
| 2059 | { |
---|
| 2060 | p = s->m[j]; |
---|
| 2061 | q = pOne(); |
---|
| 2062 | pSetComp(q,k+1+j); |
---|
| 2063 | pSetmComp(q); |
---|
| 2064 | #if 0 |
---|
| 2065 | while (pNext(p)) pIter(p); |
---|
| 2066 | pNext(p) = q; |
---|
| 2067 | #else |
---|
| 2068 | p = pAdd(p,q); |
---|
| 2069 | s->m[j] = p; |
---|
| 2070 | #ifdef PDEBUG |
---|
| 2071 | pTest(p); |
---|
| 2072 | #endif |
---|
| 2073 | #endif |
---|
| 2074 | } |
---|
| 2075 | } |
---|
| 2076 | res = idSimpleAdd(t,s); |
---|
| 2077 | idDelete(&t); |
---|
| 2078 | res->rank = 1+idElem(T); |
---|
| 2079 | return(res); |
---|
| 2080 | } |
---|
| 2081 | |
---|
| 2082 | ideal Approx_Step(ideal L) |
---|
| 2083 | { |
---|
| 2084 | int N=currRing->N; |
---|
| 2085 | int i,j; // k=syzcomp |
---|
| 2086 | int flag, flagcnt, syzcnt=0; |
---|
| 2087 | int syzcomp = 0; |
---|
| 2088 | int k=1; /* for ideals not modules */ |
---|
| 2089 | ideal I = kStd(L, currQuotient,testHomog,NULL,NULL,0,0,NULL); |
---|
| 2090 | idSkipZeroes(I); |
---|
| 2091 | ideal s_I; |
---|
| 2092 | int idI = idElem(I); |
---|
| 2093 | ideal trickyQuotient,s_trickyQuotient; |
---|
| 2094 | if (currQuotient !=NULL) |
---|
| 2095 | { |
---|
| 2096 | trickyQuotient = idSimpleAdd(currQuotient,I); |
---|
| 2097 | } |
---|
| 2098 | else |
---|
| 2099 | trickyQuotient = I; |
---|
| 2100 | idSkipZeroes(trickyQuotient); |
---|
| 2101 | poly *var = (poly *)omAlloc0((N+1)*sizeof(poly)); |
---|
| 2102 | // poly *W = (poly *)omAlloc0((2*N+1)*sizeof(poly)); |
---|
| 2103 | resolvente S = (resolvente)omAlloc0((N+1)*sizeof(ideal)); |
---|
| 2104 | ideal SI, res; |
---|
| 2105 | matrix MI; |
---|
| 2106 | poly x=pOne(); |
---|
| 2107 | var[0]=x; |
---|
| 2108 | ideal h2, h3, s_h2, s_h3; |
---|
| 2109 | poly p,q,qq; |
---|
| 2110 | /* init vars */ |
---|
| 2111 | for (i=1; i<=N; i++ ) |
---|
| 2112 | { |
---|
| 2113 | x = pOne(); |
---|
| 2114 | pSetExp(x,i,1); |
---|
| 2115 | pSetm(x); |
---|
| 2116 | var[i]=pCopy(x); |
---|
| 2117 | } |
---|
| 2118 | /* init NF's */ |
---|
| 2119 | for (i=1; i<=N; i++ ) |
---|
| 2120 | { |
---|
| 2121 | h2 = idInit(idI,1); |
---|
| 2122 | flag = 0; |
---|
| 2123 | for (j=0; j< idI; j++ ) |
---|
| 2124 | { |
---|
| 2125 | q = nc_p_Mult_mm(pCopy(I->m[j]),var[i],currRing); |
---|
| 2126 | q = kNF(I,currQuotient,q,0,0); |
---|
| 2127 | if (q!=0) |
---|
| 2128 | { |
---|
| 2129 | h2->m[j]=pCopy(q); |
---|
| 2130 | // pShift(&(h2->m[flag]),1); |
---|
| 2131 | flag++; |
---|
| 2132 | pDelete(&q); |
---|
| 2133 | } |
---|
| 2134 | else |
---|
| 2135 | h2->m[j]=0; |
---|
| 2136 | } |
---|
| 2137 | /* W[1..idElems(I)] */ |
---|
| 2138 | if (flag >0) |
---|
| 2139 | { |
---|
| 2140 | /* compute syzygies with values in I*/ |
---|
| 2141 | // idSkipZeroes(h2); |
---|
| 2142 | // h2 = idSimpleAdd(h2,I); |
---|
| 2143 | // h2->rank=flag+idI+1; |
---|
| 2144 | idTest(h2); |
---|
| 2145 | idShow(h2); |
---|
| 2146 | ring orig_ring=currRing; |
---|
| 2147 | ring syz_ring=rCurrRingAssure_SyzComp(); |
---|
| 2148 | syzcomp = 1; |
---|
| 2149 | rSetSyzComp(syzcomp); |
---|
| 2150 | if (orig_ring != syz_ring) |
---|
| 2151 | { |
---|
| 2152 | s_h2=idrCopyR_NoSort(h2,orig_ring); |
---|
| 2153 | // s_trickyQuotient=idrCopyR_NoSort(trickyQuotient,orig_ring); |
---|
| 2154 | // rDebugPrint(syz_ring); |
---|
| 2155 | s_I=idrCopyR_NoSort(I,orig_ring); |
---|
| 2156 | } |
---|
| 2157 | else |
---|
| 2158 | { |
---|
| 2159 | s_h2 = h2; |
---|
| 2160 | s_I = I; |
---|
| 2161 | // s_trickyQuotient=trickyQuotient; |
---|
| 2162 | } |
---|
| 2163 | idTest(s_h2); |
---|
| 2164 | // idTest(s_trickyQuotient); |
---|
| 2165 | Print(".proceeding with the variable %d\n",i); |
---|
| 2166 | s_h3 = idPrepareStd(s_I, s_h2, 1); |
---|
| 2167 | BITSET save_test=test; |
---|
| 2168 | test|=Sy_bit(OPT_SB_1); |
---|
| 2169 | idTest(s_h3); |
---|
| 2170 | idDelete(&s_h2); |
---|
| 2171 | s_h2=idCopy(s_h3); |
---|
| 2172 | idDelete(&s_h3); |
---|
| 2173 | Print("...computing Syz"); |
---|
[c315ad] | 2174 | s_h3 = kStd(s_h2, currQuotient,(tHomog)FALSE,NULL,NULL,syzcomp,idI); |
---|
[8e165ec] | 2175 | test=save_test; |
---|
| 2176 | idShow(s_h3); |
---|
| 2177 | if (orig_ring != syz_ring) |
---|
| 2178 | { |
---|
| 2179 | idDelete(&s_h2); |
---|
| 2180 | for (j=0; j<IDELEMS(s_h3); j++) |
---|
| 2181 | { |
---|
| 2182 | if (s_h3->m[j] != NULL) |
---|
| 2183 | { |
---|
| 2184 | if (p_MinComp(s_h3->m[j],syz_ring) > syzcomp) /* i.e. it is a syzygy */ |
---|
| 2185 | pShift(&s_h3->m[j], -syzcomp); |
---|
| 2186 | else |
---|
| 2187 | pDelete(&s_h3->m[j]); |
---|
| 2188 | } |
---|
| 2189 | } |
---|
| 2190 | idSkipZeroes(s_h3); |
---|
| 2191 | s_h3->rank -= syzcomp; |
---|
| 2192 | rChangeCurrRing(orig_ring); |
---|
| 2193 | // s_h3 = idrMoveR_NoSort(s_h3, syz_ring); |
---|
| 2194 | s_h3 = idrMoveR_NoSort(s_h3, syz_ring); |
---|
| 2195 | rKill(syz_ring); |
---|
| 2196 | } |
---|
| 2197 | idTest(s_h3); |
---|
[c315ad] | 2198 | S[syzcnt]=kStd(s_h3,currQuotient,(tHomog)FALSE,NULL,NULL); |
---|
[8e165ec] | 2199 | syzcnt++; |
---|
| 2200 | idDelete(&s_h3); |
---|
| 2201 | } /* end if flag >0 */ |
---|
| 2202 | else |
---|
| 2203 | { |
---|
| 2204 | flagcnt++; |
---|
| 2205 | } |
---|
| 2206 | } |
---|
| 2207 | if (flagcnt == N) |
---|
| 2208 | { |
---|
| 2209 | Print("the input is a two--sided ideal"); |
---|
| 2210 | return(I); |
---|
| 2211 | } |
---|
| 2212 | if (syzcnt >0) |
---|
| 2213 | { |
---|
| 2214 | Print("..computing Intersect of %d modules\n",syzcnt); |
---|
| 2215 | if (syzcnt == 1) |
---|
| 2216 | SI = S[0]; |
---|
| 2217 | else |
---|
| 2218 | SI = idMultSect(S, syzcnt); |
---|
| 2219 | idShow(SI); |
---|
| 2220 | MI = idModule2Matrix(SI); |
---|
| 2221 | res= idInit(MATCOLS(MI),1); |
---|
| 2222 | for (i=1; i<= MATCOLS(MI); i++) |
---|
| 2223 | { |
---|
| 2224 | p = NULL; |
---|
| 2225 | for (j=0; j< idElem(I); j++) |
---|
| 2226 | { |
---|
| 2227 | q = pCopy(MATELEM(MI,j+1,i)); |
---|
| 2228 | if (q!=NULL) |
---|
| 2229 | { |
---|
| 2230 | q = pMult(q,pCopy(I->m[j])); |
---|
| 2231 | p = pAdd(p,q); |
---|
| 2232 | } |
---|
| 2233 | } |
---|
| 2234 | res->m[i-1]=p; |
---|
| 2235 | } |
---|
| 2236 | Print("final std"); |
---|
| 2237 | res = kStd(res, currQuotient,testHomog,NULL,NULL,0,0,NULL); |
---|
| 2238 | idSkipZeroes(res); |
---|
| 2239 | return(res); |
---|
| 2240 | } |
---|
| 2241 | else |
---|
| 2242 | { |
---|
| 2243 | Print("No syzygies"); |
---|
| 2244 | return(I); |
---|
| 2245 | } |
---|
| 2246 | } |
---|
| 2247 | |
---|
| 2248 | |
---|
| 2249 | ring nc_rCreateNCcomm(ring r) |
---|
| 2250 | /* creates a commutative nc extension; "converts" comm.ring to a Plural ring */ |
---|
| 2251 | { |
---|
| 2252 | if (rIsPluralRing(r)) return r; |
---|
[3c8a31] | 2253 | ring save = currRing; |
---|
| 2254 | int WeChangeRing = 0; |
---|
| 2255 | if (currRing!=r) |
---|
| 2256 | { |
---|
| 2257 | rChangeCurrRing(r); |
---|
| 2258 | WeChangeRing = 1; |
---|
| 2259 | } |
---|
[8e165ec] | 2260 | r->nc = (nc_struct *)omAlloc0(sizeof(nc_struct)); |
---|
| 2261 | r->nc->ref = 1; |
---|
| 2262 | r->nc->basering = r; |
---|
| 2263 | r->nc->type = nc_comm; |
---|
| 2264 | r->nc->IsSkewConstant = 1; |
---|
| 2265 | matrix C = mpNew(r->N,r->N); |
---|
| 2266 | matrix D = mpNew(r->N,r->N); |
---|
| 2267 | int i,j; |
---|
| 2268 | for(i=1; i<r->N; i++) |
---|
| 2269 | { |
---|
| 2270 | for(j=i+1; j<=r->N; j++) |
---|
| 2271 | { |
---|
| 2272 | MATELEM(C,i,j) = pOne(); |
---|
| 2273 | } |
---|
| 2274 | } |
---|
| 2275 | r->nc->C = C; |
---|
| 2276 | r->nc->D = D; |
---|
| 2277 | if (nc_InitMultiplication(r)) |
---|
| 2278 | { |
---|
| 2279 | WarnS("Error initializing multiplication!"); |
---|
| 2280 | } |
---|
[3c8a31] | 2281 | if (WeChangeRing) |
---|
| 2282 | { |
---|
| 2283 | rChangeCurrRing(save); |
---|
| 2284 | } |
---|
[8e165ec] | 2285 | return r; |
---|
| 2286 | } |
---|
| 2287 | |
---|
[6b5dd2] | 2288 | poly p_CopyEmbed(poly p, ring srcRing, int shift, int par_shift) |
---|
| 2289 | /* NOT USED ANYMORE: replaced by maFindPerm in ring.cc */ |
---|
| 2290 | /* for use with embeddings: currRing is a sum of smaller rings */ |
---|
| 2291 | /* and srcRing is one of such smaller rings */ |
---|
[8e165ec] | 2292 | /* shift defines the position of a subring in srcRing */ |
---|
[6b5dd2] | 2293 | /* par_shift defines the position of a subfield in basefield of CurrRing */ |
---|
[8e165ec] | 2294 | { |
---|
| 2295 | if (currRing == srcRing) |
---|
| 2296 | { |
---|
| 2297 | return(p_Copy(p,currRing)); |
---|
| 2298 | } |
---|
| 2299 | nMapFunc nMap=nSetMap(srcRing); |
---|
| 2300 | poly q; |
---|
[6b5dd2] | 2301 | // if ( nMap == nCopy) |
---|
| 2302 | // { |
---|
| 2303 | // q = prCopyR(p,srcRing); |
---|
| 2304 | // } |
---|
| 2305 | // else |
---|
[8e165ec] | 2306 | { |
---|
| 2307 | int *perm = (int *)omAlloc0((srcRing->N+1)*sizeof(int)); |
---|
[6b5dd2] | 2308 | int *par_perm = (int *)omAlloc0((srcRing->P+1)*sizeof(int)); |
---|
[8e165ec] | 2309 | // int *par_perm = (int *)omAlloc0((srcRing->P+1)*sizeof(int)); |
---|
| 2310 | int i; |
---|
| 2311 | // if (srcRing->P > 0) |
---|
| 2312 | // { |
---|
| 2313 | // for (i=0; i<srcRing->P; i++) |
---|
| 2314 | // par_perm[i]=-i; |
---|
| 2315 | // } |
---|
| 2316 | if ((shift<0) || (shift > currRing->N)) |
---|
| 2317 | { |
---|
| 2318 | Werror("bad shifts in p_CopyEmbed"); |
---|
| 2319 | return(0); |
---|
| 2320 | } |
---|
[6b5dd2] | 2321 | for (i=1; i<= srcRing->N; i++) |
---|
| 2322 | { |
---|
| 2323 | perm[i] = shift+i; |
---|
| 2324 | } |
---|
[8e165ec] | 2325 | q = pPermPoly(p,perm,srcRing,nMap,par_perm,srcRing->P); |
---|
| 2326 | } |
---|
| 2327 | return(q); |
---|
| 2328 | } |
---|
| 2329 | |
---|
[b39bc1f] | 2330 | poly pOppose(ring Rop, poly p) |
---|
| 2331 | /* opposes a vector p from Rop to currRing */ |
---|
[71ac89a] | 2332 | { |
---|
| 2333 | /* the simplest case:*/ |
---|
[b39bc1f] | 2334 | if ( Rop == currRing ) return(pCopy(p)); |
---|
| 2335 | /* check Rop == rOpposite(currRing) */ |
---|
| 2336 | if ( !rIsLikeOpposite(currRing, Rop) ) |
---|
| 2337 | { |
---|
| 2338 | WarnS("an opposite ring should be used"); |
---|
| 2339 | return NULL; |
---|
| 2340 | } |
---|
| 2341 | /* nMapFunc nMap = nSetMap(Rop);*/ |
---|
| 2342 | /* since we know that basefields coinside! */ |
---|
[71ac89a] | 2343 | int *perm=(int *)omAlloc0((Rop->N+1)*sizeof(int)); |
---|
[b39bc1f] | 2344 | if (!p_IsConstantPoly(p, Rop)) |
---|
[71ac89a] | 2345 | { |
---|
[b39bc1f] | 2346 | /* we know perm exactly */ |
---|
| 2347 | int i; |
---|
| 2348 | for(i=1; i<=Rop->N; i++) |
---|
| 2349 | { |
---|
| 2350 | perm[i] = Rop->N+1-i; |
---|
| 2351 | } |
---|
[71ac89a] | 2352 | } |
---|
[b39bc1f] | 2353 | poly res = pPermPoly(p, perm, Rop, nCopy); |
---|
[71ac89a] | 2354 | omFreeSize((ADDRESS)perm,(Rop->N+1)*sizeof(int)); |
---|
| 2355 | return res; |
---|
| 2356 | } |
---|
| 2357 | |
---|
[b39bc1f] | 2358 | ideal idOppose(ring Rop, ideal I) |
---|
| 2359 | /* opposes a module I from Rop to currRing */ |
---|
| 2360 | { |
---|
| 2361 | /* the simplest case:*/ |
---|
| 2362 | if ( Rop == currRing ) return idCopy(I); |
---|
| 2363 | /* check Rop == rOpposite(currRing) */ |
---|
| 2364 | if (!rIsLikeOpposite(currRing, Rop)) |
---|
| 2365 | { |
---|
| 2366 | WarnS("an opposite ring should be used"); |
---|
| 2367 | return NULL; |
---|
| 2368 | } |
---|
| 2369 | int i; |
---|
| 2370 | ideal idOp = idInit(I->ncols, I->rank); |
---|
| 2371 | for (i=0; i< (I->ncols)*(I->nrows); i++) |
---|
| 2372 | { |
---|
| 2373 | idOp->m[i] = pOppose(Rop,I->m[i]); |
---|
| 2374 | } |
---|
| 2375 | idTest(idOp); |
---|
| 2376 | return idOp; |
---|
| 2377 | } |
---|
| 2378 | |
---|
| 2379 | BOOLEAN rIsLikeOpposite(ring rBase, ring rCandidate) |
---|
| 2380 | /* checks whether rings rBase and rCandidate */ |
---|
| 2381 | /* could be opposite to each other */ |
---|
| 2382 | /* returns TRUE if it is so */ |
---|
| 2383 | { |
---|
| 2384 | /* the same basefield */ |
---|
| 2385 | int diagnose = TRUE; |
---|
| 2386 | ring save = currRing; |
---|
| 2387 | rChangeCurrRing(rBase); |
---|
| 2388 | nMapFunc nMap = nSetMap(rCandidate); |
---|
| 2389 | if (nMap != nCopy) diagnose = FALSE; |
---|
| 2390 | rChangeCurrRing(save); |
---|
| 2391 | /* same number of variables */ |
---|
| 2392 | if (rBase->N != rCandidate->N) diagnose = FALSE; |
---|
| 2393 | /* nc and comm ring */ |
---|
| 2394 | if ( rIsPluralRing(rBase) != rIsPluralRing(rCandidate) ) diagnose = FALSE; |
---|
| 2395 | /* TODO: varnames are e->E etc */ |
---|
| 2396 | return diagnose; |
---|
| 2397 | } |
---|
[71ac89a] | 2398 | |
---|
[35aab3] | 2399 | #endif |
---|