[6438a12] | 1 | </**************************************** |
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[a6904c] | 2 | * Computer Algebra System SINGULAR * |
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| 3 | ****************************************/ |
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| 4 | /* $Id$ */ |
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| 5 | |
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| 6 | /* |
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| 7 | * ABSTRACT - all basic methods to manipulate polynomials: |
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| 8 | * independent of representation |
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| 9 | */ |
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| 10 | |
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| 11 | /* includes */ |
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| 12 | #include <string.h> |
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[20b794] | 13 | #include "polys/config.h" |
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| 14 | // #include <polys/options.h> |
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| 15 | #include <coeffs/numbers.h> |
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| 16 | #include <coeffs/ffields.h> |
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[b1dfaf] | 17 | #include <omalloc/omalloc.h> |
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[20b794] | 18 | // #include <???/febase.h> |
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[6bec87] | 19 | // #include <???/weight.h> |
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| 20 | // #include <???/intvec.h> |
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[20b794] | 21 | #include <polys/ext_fields/longalg.h> |
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| 22 | #include <polys/monomials/ring.h> |
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[6bec87] | 23 | // #include <???/ideals.h> |
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[78eba1] | 24 | // #include <polys/polys.h> |
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[6bec87] | 25 | // #include "ipid.h" |
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[a6904c] | 26 | #ifdef HAVE_FACTORY |
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[6bec87] | 27 | // #include <???/clapsing.h> |
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[a6904c] | 28 | #endif |
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| 29 | |
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| 30 | #ifdef HAVE_RATGRING |
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[20b794] | 31 | // #include <polys/ratgring.h> |
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[a6904c] | 32 | #endif |
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| 33 | |
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| 34 | |
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| 35 | poly pSeries(int n,poly p,poly u, intvec *w) |
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| 36 | { |
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| 37 | short *ww=iv2array(w); |
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| 38 | if(p!=NULL) |
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| 39 | { |
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| 40 | if(u==NULL) |
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| 41 | p=pJetW(p,n,ww); |
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| 42 | else |
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| 43 | p=pJetW(pMult(p,pInvers(n-pMinDeg(p,w),u,w)),n,ww); |
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| 44 | } |
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| 45 | omFreeSize((ADDRESS)ww,(pVariables+1)*sizeof(short)); |
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| 46 | return p; |
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| 47 | } |
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| 48 | |
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| 49 | poly pInvers(int n,poly u,intvec *w) |
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| 50 | { |
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| 51 | short *ww=iv2array(w); |
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| 52 | if(n<0) |
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| 53 | return NULL; |
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| 54 | number u0=nInvers(pGetCoeff(u)); |
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| 55 | poly v=pNSet(u0); |
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| 56 | if(n==0) |
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| 57 | return v; |
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| 58 | poly u1=pJetW(pSub(pOne(),pMult_nn(u,u0)),n,ww); |
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| 59 | if(u1==NULL) |
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| 60 | return v; |
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| 61 | poly v1=pMult_nn(pCopy(u1),u0); |
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| 62 | v=pAdd(v,pCopy(v1)); |
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| 63 | for(int i=n/pMinDeg(u1,w);i>1;i--) |
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| 64 | { |
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| 65 | v1=pJetW(pMult(v1,pCopy(u1)),n,ww); |
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| 66 | v=pAdd(v,pCopy(v1)); |
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| 67 | } |
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| 68 | pDelete(&u1); |
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| 69 | pDelete(&v1); |
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| 70 | omFreeSize((ADDRESS)ww,(pVariables+1)*sizeof(short)); |
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| 71 | return v; |
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| 72 | } |
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| 73 | |
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| 74 | /*-----------type conversions ----------------------------*/ |
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[815d74] | 75 | #if 0 |
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[a6904c] | 76 | /*2 |
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| 77 | * convert a vector to a set of polys, |
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| 78 | * allocates the polyset, (entries 0..(*len)-1) |
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| 79 | * the vector will not be changed |
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| 80 | */ |
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| 81 | void pVec2Polys(poly v, polyset *p, int *len) |
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| 82 | { |
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| 83 | poly h; |
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| 84 | int k; |
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| 85 | |
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| 86 | *len=pMaxComp(v); |
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| 87 | if (*len==0) *len=1; |
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| 88 | *p=(polyset)omAlloc0((*len)*sizeof(poly)); |
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| 89 | while (v!=NULL) |
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| 90 | { |
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| 91 | h=pHead(v); |
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| 92 | k=pGetComp(h); |
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| 93 | pSetComp(h,0); |
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| 94 | (*p)[k-1]=pAdd((*p)[k-1],h); |
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| 95 | pIter(v); |
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| 96 | } |
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| 97 | } |
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| 98 | |
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| 99 | int p_Var(poly m,const ring r) |
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| 100 | { |
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| 101 | if (m==NULL) return 0; |
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| 102 | if (pNext(m)!=NULL) return 0; |
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| 103 | int i,e=0; |
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| 104 | for (i=r->N; i>0; i--) |
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| 105 | { |
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| 106 | int exp=p_GetExp(m,i,r); |
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| 107 | if (exp==1) |
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| 108 | { |
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| 109 | if (e==0) e=i; |
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| 110 | else return 0; |
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| 111 | } |
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| 112 | else if (exp!=0) |
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| 113 | { |
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| 114 | return 0; |
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| 115 | } |
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| 116 | } |
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| 117 | return e; |
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| 118 | } |
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| 119 | |
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| 120 | /*2 |
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| 121 | * returns TRUE if p1 = p2 |
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| 122 | */ |
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| 123 | BOOLEAN p_EqualPolys(poly p1,poly p2, const ring r) |
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| 124 | { |
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| 125 | while ((p1 != NULL) && (p2 != NULL)) |
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| 126 | { |
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| 127 | if (! p_LmEqual(p1, p2,r)) |
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| 128 | return FALSE; |
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| 129 | if (! n_Equal(p_GetCoeff(p1,r), p_GetCoeff(p2,r),r )) |
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| 130 | return FALSE; |
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| 131 | pIter(p1); |
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| 132 | pIter(p2); |
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| 133 | } |
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| 134 | return (p1==p2); |
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| 135 | } |
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| 136 | |
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| 137 | /*2 |
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| 138 | *returns TRUE if p1 is a skalar multiple of p2 |
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| 139 | *assume p1 != NULL and p2 != NULL |
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| 140 | */ |
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| 141 | BOOLEAN pComparePolys(poly p1,poly p2) |
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| 142 | { |
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| 143 | number n,nn; |
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| 144 | pAssume(p1 != NULL && p2 != NULL); |
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| 145 | |
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| 146 | if (!pLmEqual(p1,p2)) //compare leading mons |
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| 147 | return FALSE; |
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| 148 | if ((pNext(p1)==NULL) && (pNext(p2)!=NULL)) |
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| 149 | return FALSE; |
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| 150 | if ((pNext(p2)==NULL) && (pNext(p1)!=NULL)) |
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| 151 | return FALSE; |
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| 152 | if (pLength(p1) != pLength(p2)) |
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| 153 | return FALSE; |
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[dd5534] | 154 | #ifdef HAVE_RINGS |
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| 155 | if (rField_is_Ring(currRing)) |
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| 156 | { |
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[a8b44d] | 157 | if (!nDivBy(pGetCoeff(p1), pGetCoeff(p2))) return FALSE; |
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[dd5534] | 158 | } |
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| 159 | #endif |
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[a6904c] | 160 | n=nDiv(pGetCoeff(p1),pGetCoeff(p2)); |
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| 161 | while ((p1 != NULL) /*&& (p2 != NULL)*/) |
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| 162 | { |
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| 163 | if ( ! pLmEqual(p1, p2)) |
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| 164 | { |
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| 165 | nDelete(&n); |
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| 166 | return FALSE; |
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| 167 | } |
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| 168 | if (!nEqual(pGetCoeff(p1),nn=nMult(pGetCoeff(p2),n))) |
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| 169 | { |
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| 170 | nDelete(&n); |
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| 171 | nDelete(&nn); |
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| 172 | return FALSE; |
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| 173 | } |
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| 174 | nDelete(&nn); |
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| 175 | pIter(p1); |
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| 176 | pIter(p2); |
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| 177 | } |
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| 178 | nDelete(&n); |
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| 179 | return TRUE; |
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| 180 | } |
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