[35aab3] | 1 | /**************************************** |
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| 2 | * Computer Algebra System SINGULAR * |
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| 3 | ****************************************/ |
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[5d68a6] | 4 | /* $Id: ffields.cc,v 1.10 2008-12-17 15:07:46 Singular Exp $ */ |
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[35aab3] | 5 | /* |
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| 6 | * ABSTRACT: finite fields with a none-prime number of elements (via tables) |
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| 7 | */ |
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| 8 | |
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| 9 | #include <string.h> |
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| 10 | #include "mod2.h" |
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| 11 | #include <mylimits.h> |
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| 12 | #include "febase.h" |
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| 13 | #include "omalloc.h" |
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| 14 | #include "numbers.h" |
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| 15 | #include "ring.h" |
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| 16 | #include "ffields.h" |
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| 17 | |
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| 18 | int nfCharQ=0; /* the number of elemts: q*/ |
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| 19 | int nfM1; /*representation of -1*/ |
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[5d68a6] | 20 | int nfCharP=0; /* the characteristic: p*/ |
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[35aab3] | 21 | static int nfCharQ1=0; /* q-1 */ |
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| 22 | CARDINAL *nfPlus1Table=NULL; /* the table i=log(z^i) -> log(z^i+1) */ |
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| 23 | char * nfParameter; /* the name of the primitive element */ |
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| 24 | /* the q's from the table 'fftable' */ |
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[6f8225] | 25 | unsigned short fftable[]={ |
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| 26 | 4, 8, 16, 32, 64, 128, 256, 512,1024,2048,4096,8192,16384, 32768, |
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| 27 | /*2^2 2^3 2^4 2^5 2^6 2^7 2^8 2^9 2^10 2^11 2^12 2^13 2^14 2^15*/ |
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| 28 | 9, 27, 81,243,729,2187, 6561,19683,59049, |
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| 29 | /*3^2 3^3 3^4 3^5 3^6 3^7 3^8 3^9 3^10*/ |
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[35aab3] | 30 | 25,125,625,3125,15625, |
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| 31 | /*5^2 5^3 5^4 5^5 5^6*/ |
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| 32 | 49,343,2401,16807, |
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| 33 | /*7^2 7^3 7^4 7^5*/ |
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| 34 | 121,1331, 14641, |
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| 35 | /*11^2 11^3 11^4*/ |
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| 36 | 169, 2197, 28561, |
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| 37 | /*13^2 13^3 13^4*/ |
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| 38 | 289, 4913, |
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| 39 | /*17^2 17^3*/ |
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| 40 | 361, 6859, |
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| 41 | /*19^2 19^3*/ |
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| 42 | 529, 12167, |
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| 43 | /*23^2 23^3*/ |
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| 44 | 841, 24389, |
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| 45 | /*29^2 29^3*/ |
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| 46 | 961, 29791, |
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| 47 | /*31^2 31^3*/ |
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[6f8225] | 48 | 1369, 50653, |
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| 49 | /*37^2 37^3*/ |
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| 50 | 1681, /*41^2*/ |
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| 51 | 1849, /*43^2*/ |
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| 52 | 2209, /*47^2*/ |
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| 53 | 2809, /*53^2*/ |
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| 54 | 3481, /*59^2*/ |
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| 55 | 3721, /*61^2*/ |
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| 56 | 4489, /*67^2*/ |
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| 57 | 5041, /*71^2*/ |
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| 58 | 5329, /*73^2*/ |
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| 59 | 6241, /*79^2*/ |
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| 60 | 6889, /*83^2*/ |
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| 61 | 7921, /*89^2*/ |
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| 62 | 9409, /*97^2*/ |
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| 63 | 10201, /*101^2*/ |
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| 64 | 10609, /*103^2*/ |
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| 65 | 11449, /*107^2*/ |
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| 66 | 11881, /*109^2*/ |
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| 67 | 12769, /*113^2*/ |
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| 68 | 16129, /*127^2*/ |
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| 69 | 17161, /*131^2*/ |
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| 70 | 18769, /*137^2*/ |
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| 71 | 19321, /*139^2*/ |
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| 72 | 22201, /*149^2*/ |
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| 73 | 22801, /*151^2*/ |
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| 74 | 24649, /*157^2*/ |
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| 75 | 26569, /*163^2*/ |
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| 76 | 27889, /*167^2*/ |
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| 77 | 29929, /*173^2*/ |
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| 78 | 32041, /*179^2*/ |
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| 79 | 32761, /*181^2*/ |
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| 80 | 36481, /*191^2*/ |
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| 81 | 37249, /*193^2*/ |
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| 82 | 38809, /*197^2*/ |
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| 83 | 39601, /*199^2*/ |
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| 84 | 49729, /*223^2*/ |
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| 85 | 44521, /*211^2*/ |
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| 86 | 51529, /*227^2*/ |
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| 87 | 52441, /*229^2*/ |
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| 88 | 54289, /*233^2*/ |
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| 89 | 57121, /*239^2*/ |
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| 90 | 58081, /*241^2*/ |
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[85e68dd] | 91 | 63001, /*251^2*/ |
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[35aab3] | 92 | 0 }; |
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| 93 | |
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| 94 | /*1 |
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| 95 | * numbers in GF(p^n): |
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| 96 | * let nfCharQ=q=nfCharP^n=p^n |
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| 97 | * GF(q)\{0} will be generated by powers of an element Z |
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| 98 | * Z^i will be represented by the int i, 1 by the int 0, 0 by the int q=nfChar |
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| 99 | */ |
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| 100 | |
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| 101 | #ifdef LDEBUG |
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| 102 | /*2 |
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| 103 | * debugging: is a a valid representation of a number ? |
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| 104 | */ |
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[85e68dd] | 105 | BOOLEAN nfDBTest (number a, const char *f, const int l) |
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[35aab3] | 106 | { |
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[7447d8] | 107 | if (((long)a<0L) || ((long)a>(long)nfCharQ)) |
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[35aab3] | 108 | { |
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[7447d8] | 109 | Print("wrong %d in %s:%d\n",(int)((long)a),f,l); |
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[35aab3] | 110 | return FALSE; |
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| 111 | } |
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| 112 | int i=0; |
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| 113 | do |
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| 114 | { |
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| 115 | if (nfPlus1Table[i]>nfCharQ) |
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| 116 | { |
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| 117 | Print("wrong table %d=%d in %s:%d\n",i,nfPlus1Table[i],f,l); |
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| 118 | return FALSE; |
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| 119 | } |
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| 120 | i++; |
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| 121 | } while (i<nfCharQ); |
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| 122 | return TRUE; |
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| 123 | } |
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| 124 | #define nfTest(N) nfDBTest(N,__FILE__,__LINE__) |
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| 125 | #endif |
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| 126 | |
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| 127 | /*2 |
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| 128 | * k >= 0 ? |
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| 129 | */ |
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| 130 | BOOLEAN nfGreaterZero (number k) |
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| 131 | { |
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| 132 | #ifdef LDEBUG |
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| 133 | nfTest(k); |
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| 134 | #endif |
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| 135 | return !nfIsZero(k) && !nfIsMOne(k); |
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| 136 | } |
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| 137 | |
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| 138 | /*2 |
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| 139 | * a*b |
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| 140 | */ |
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| 141 | number nfMult (number a,number b) |
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| 142 | { |
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| 143 | #ifdef LDEBUG |
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| 144 | nfTest(a); |
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| 145 | nfTest(b); |
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| 146 | #endif |
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[7447d8] | 147 | if (((long)a == (long)nfCharQ) || ((long)b == (long)nfCharQ)) |
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[1c7953] | 148 | return (number)(long)nfCharQ; |
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[35aab3] | 149 | /*else*/ |
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[7447d8] | 150 | int i=(int)((long)a+(long)b); |
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[35aab3] | 151 | if (i>=nfCharQ1) i-=nfCharQ1; |
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| 152 | #ifdef LDEBUG |
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[1c7953] | 153 | nfTest((number)(long)i); |
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[35aab3] | 154 | #endif |
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[1c7953] | 155 | return (number)(long)i; |
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[35aab3] | 156 | } |
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| 157 | |
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| 158 | /*2 |
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| 159 | * int -> number |
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| 160 | */ |
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| 161 | number nfInit (int i) |
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| 162 | { |
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| 163 | // Hmm .. this is just to prevent initialization |
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| 164 | // from nfInitChar to go into an infinite loop |
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[1c7953] | 165 | if (i==0) return (number)(long)nfCharQ; |
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[35aab3] | 166 | while (i < 0) i += nfCharP; |
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| 167 | while (i >= nfCharP) i -= nfCharP; |
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[1c7953] | 168 | if (i==0) return (number)(long)nfCharQ; |
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[54cc79] | 169 | CARDINAL c=0; |
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[35aab3] | 170 | while (i>1) |
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| 171 | { |
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| 172 | c=nfPlus1Table[c]; |
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| 173 | i--; |
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| 174 | } |
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| 175 | #ifdef LDEBUG |
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[1c7953] | 176 | nfTest((number)(long)c); |
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[35aab3] | 177 | #endif |
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[1c7953] | 178 | return (number)(long)c; |
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[35aab3] | 179 | } |
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| 180 | |
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| 181 | /* |
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| 182 | * the generating element `z` |
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| 183 | */ |
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| 184 | number nfPar (int i) |
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| 185 | { |
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| 186 | return (number)1; |
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| 187 | } |
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| 188 | |
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| 189 | /*2 |
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| 190 | * the degree of the "alg. number" |
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| 191 | */ |
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| 192 | int nfParDeg(number n) |
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| 193 | { |
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| 194 | #ifdef LDEBUG |
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| 195 | nfTest(n); |
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| 196 | #endif |
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[7447d8] | 197 | if((long)nfCharQ == (long)n) return -1; |
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| 198 | return (int)((long)n); |
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[35aab3] | 199 | } |
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| 200 | |
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| 201 | /*2 |
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| 202 | * number -> int |
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| 203 | */ |
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| 204 | int nfInt (number &n) |
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| 205 | { |
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| 206 | return 0; |
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| 207 | } |
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| 208 | |
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| 209 | /*2 |
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| 210 | * a + b |
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| 211 | */ |
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| 212 | number nfAdd (number a, number b) |
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| 213 | { |
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| 214 | /*4 z^a+z^b=z^b*(z^(a-b)+1), if a>=b; * |
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| 215 | * =z^a*(z^(b-a)+1) if a<b */ |
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| 216 | #ifdef LDEBUG |
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| 217 | nfTest(a); |
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| 218 | nfTest(b); |
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| 219 | #endif |
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[7447d8] | 220 | if ((long)nfCharQ == (long)a) return b; |
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| 221 | if ((long)nfCharQ == (long)b) return a; |
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| 222 | long zb,zab,r; |
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| 223 | if ((long)a >= (long)b) |
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[35aab3] | 224 | { |
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[7447d8] | 225 | zb = (long)b; |
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| 226 | zab = (long)a-(long)b; |
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[35aab3] | 227 | } |
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| 228 | else |
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| 229 | { |
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[7447d8] | 230 | zb = (long)a; |
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| 231 | zab = (long)b-(long)a; |
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[35aab3] | 232 | } |
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| 233 | #ifdef LDEBUG |
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| 234 | nfTest((number)zab); |
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| 235 | #endif |
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[7447d8] | 236 | if (nfPlus1Table[zab]==nfCharQ) r=(long)nfCharQ; /*if z^(a-b)+1 =0*/ |
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[35aab3] | 237 | else |
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| 238 | { |
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[7447d8] | 239 | r= zb+(long)nfPlus1Table[zab]; |
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| 240 | if(r>=(long)nfCharQ1) r-=(long)nfCharQ1; |
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[35aab3] | 241 | } |
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| 242 | #ifdef LDEBUG |
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| 243 | nfTest((number)r); |
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| 244 | #endif |
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| 245 | return (number)r; |
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| 246 | } |
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| 247 | |
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| 248 | /*2 |
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| 249 | * a - b |
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| 250 | */ |
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| 251 | number nfSub (number a, number b) |
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| 252 | { |
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| 253 | number mb = nfNeg(b); |
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| 254 | return nfAdd(a,mb); |
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| 255 | } |
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| 256 | |
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| 257 | /*2 |
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| 258 | * a == 0 ? |
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| 259 | */ |
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| 260 | BOOLEAN nfIsZero (number a) |
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| 261 | { |
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| 262 | #ifdef LDEBUG |
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| 263 | nfTest(a); |
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| 264 | #endif |
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[7447d8] | 265 | return (long)nfCharQ == (long)a; |
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[35aab3] | 266 | } |
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| 267 | |
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| 268 | /*2 |
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| 269 | * a == 1 ? |
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| 270 | */ |
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| 271 | BOOLEAN nfIsOne (number a) |
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| 272 | { |
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| 273 | #ifdef LDEBUG |
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| 274 | nfTest(a); |
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| 275 | #endif |
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[7447d8] | 276 | return 0L == (long)a; |
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[35aab3] | 277 | } |
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| 278 | |
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| 279 | /*2 |
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| 280 | * a == -1 ? |
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| 281 | */ |
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| 282 | BOOLEAN nfIsMOne (number a) |
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| 283 | { |
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| 284 | #ifdef LDEBUG |
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| 285 | nfTest(a); |
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| 286 | #endif |
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[7447d8] | 287 | if (0L == (long)a) return FALSE; /* special handling of char 2*/ |
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| 288 | return (long)nfM1 == (long)a; |
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[35aab3] | 289 | } |
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| 290 | |
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| 291 | /*2 |
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| 292 | * a / b |
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| 293 | */ |
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| 294 | number nfDiv (number a,number b) |
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| 295 | { |
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| 296 | #ifdef LDEBUG |
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| 297 | nfTest(b); |
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| 298 | #endif |
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[7447d8] | 299 | if ((long)b==(long)nfCharQ) |
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[35aab3] | 300 | { |
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[b7e838] | 301 | WerrorS(nDivBy0); |
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[7447d8] | 302 | return (number)((long)nfCharQ); |
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[35aab3] | 303 | } |
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| 304 | #ifdef LDEBUG |
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| 305 | nfTest(a); |
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| 306 | #endif |
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[7447d8] | 307 | if ((long)a==(long)nfCharQ) |
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| 308 | return (number)((long)nfCharQ); |
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[35aab3] | 309 | /*else*/ |
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[7447d8] | 310 | long s = (long)a - (long)b; |
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| 311 | if (s < 0L) |
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| 312 | s += (long)nfCharQ1; |
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[35aab3] | 313 | #ifdef LDEBUG |
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| 314 | nfTest((number)s); |
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| 315 | #endif |
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| 316 | return (number)s; |
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| 317 | } |
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| 318 | |
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| 319 | /*2 |
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| 320 | * 1 / c |
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| 321 | */ |
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| 322 | number nfInvers (number c) |
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| 323 | { |
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| 324 | #ifdef LDEBUG |
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| 325 | nfTest(c); |
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| 326 | #endif |
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[7447d8] | 327 | if ((long)c==(long)nfCharQ) |
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[35aab3] | 328 | { |
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[b7e838] | 329 | WerrorS(nDivBy0); |
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[7447d8] | 330 | return (number)((long)nfCharQ); |
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[35aab3] | 331 | } |
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| 332 | #ifdef LDEBUG |
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[7447d8] | 333 | nfTest(((number)((long)nfCharQ1-(long)c))); |
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[35aab3] | 334 | #endif |
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[7447d8] | 335 | return (number)((long)nfCharQ1-(long)c); |
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[35aab3] | 336 | } |
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| 337 | |
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| 338 | /*2 |
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| 339 | * -c |
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| 340 | */ |
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| 341 | number nfNeg (number c) |
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| 342 | { |
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| 343 | /*4 -z^c=z^c*(-1)=z^c*nfM1*/ |
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| 344 | #ifdef LDEBUG |
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| 345 | nfTest(c); |
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| 346 | #endif |
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[7447d8] | 347 | if ((long)nfCharQ == (long)c) return c; |
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| 348 | long i=(long)c+(long)nfM1; |
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| 349 | if (i>=(long)nfCharQ1) i-=(long)nfCharQ1; |
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[35aab3] | 350 | #ifdef LDEBUG |
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| 351 | nfTest((number)i); |
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| 352 | #endif |
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| 353 | return (number)i; |
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| 354 | } |
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| 355 | |
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| 356 | /*2 |
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| 357 | * a > b ? |
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| 358 | */ |
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| 359 | BOOLEAN nfGreater (number a,number b) |
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| 360 | { |
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| 361 | #ifdef LDEBUG |
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| 362 | nfTest(a); |
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| 363 | nfTest(b); |
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| 364 | #endif |
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[7447d8] | 365 | return (long)a != (long)b; |
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[35aab3] | 366 | } |
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| 367 | |
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| 368 | /*2 |
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| 369 | * a == b ? |
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| 370 | */ |
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| 371 | BOOLEAN nfEqual (number a,number b) |
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| 372 | { |
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| 373 | #ifdef LDEBUG |
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| 374 | nfTest(a); |
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| 375 | nfTest(b); |
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| 376 | #endif |
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[7447d8] | 377 | return (long)a == (long)b; |
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[35aab3] | 378 | } |
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| 379 | |
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| 380 | /*2 |
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| 381 | * write via StringAppend |
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| 382 | */ |
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| 383 | void nfWrite (number &a) |
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| 384 | { |
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| 385 | #ifdef LDEBUG |
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| 386 | nfTest(a); |
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| 387 | #endif |
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[7447d8] | 388 | if ((long)a==(long)nfCharQ) StringAppendS("0"); |
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| 389 | else if ((long)a==0L) StringAppendS("1"); |
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[35aab3] | 390 | else if (nfIsMOne(a)) StringAppendS("-1"); |
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| 391 | else |
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| 392 | { |
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| 393 | StringAppendS(nfParameter); |
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[7447d8] | 394 | if ((long)a!=1L) |
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[35aab3] | 395 | { |
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| 396 | if(currRing->ShortOut==0) StringAppendS("^"); |
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[7447d8] | 397 | StringAppend("%d",(int)((long)a)); |
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[35aab3] | 398 | } |
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| 399 | } |
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| 400 | } |
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| 401 | |
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| 402 | /*2 |
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| 403 | * |
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| 404 | */ |
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| 405 | char * nfName(number a) |
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| 406 | { |
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| 407 | #ifdef LDEBUG |
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| 408 | nfTest(a); |
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| 409 | #endif |
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| 410 | char *s; |
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[7447d8] | 411 | if (((long)a==(long)nfCharQ) || ((long)a==0L)) return NULL; |
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| 412 | else if ((long)a==1L) |
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[35aab3] | 413 | { |
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| 414 | return omStrDup(nfParameter); |
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| 415 | } |
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| 416 | else |
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| 417 | { |
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| 418 | s=(char *)omAlloc(4+strlen(nfParameter)); |
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[7447d8] | 419 | sprintf(s,"%s%d",nfParameter,(int)((long)a)); |
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[35aab3] | 420 | } |
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| 421 | return s; |
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| 422 | } |
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| 423 | /*2 |
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| 424 | * c ^ i with i>=0 |
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| 425 | */ |
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| 426 | void nfPower (number a, int i, number * result) |
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| 427 | { |
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| 428 | #ifdef LDEBUG |
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| 429 | nfTest(a); |
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| 430 | #endif |
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| 431 | if (i==0) |
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| 432 | { |
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| 433 | //*result=nfInit(1); |
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[7447d8] | 434 | *result = (number)0L; |
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[35aab3] | 435 | } |
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| 436 | else if (i==1) |
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| 437 | { |
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| 438 | *result = a; |
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| 439 | } |
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| 440 | else |
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| 441 | { |
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| 442 | nfPower(a,i-1,result); |
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| 443 | *result = nfMult(a,*result); |
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| 444 | } |
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| 445 | #ifdef LDEBUG |
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| 446 | nfTest(*result); |
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| 447 | #endif |
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| 448 | } |
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| 449 | |
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| 450 | /*4 |
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| 451 | * read an integer (with reduction mod p) |
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| 452 | */ |
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[85e68dd] | 453 | static const char* nfEati(const char *s, int *i) |
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[35aab3] | 454 | { |
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| 455 | if (*s >= '0' && *s <= '9') |
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| 456 | { |
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| 457 | *i = 0; |
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| 458 | do |
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| 459 | { |
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| 460 | *i *= 10; |
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| 461 | *i += *s++ - '0'; |
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| 462 | if (*i > (MAX_INT_VAL / 10)) *i = *i % nfCharP; |
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| 463 | } |
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| 464 | while (*s >= '0' && *s <= '9'); |
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| 465 | if (*i >= nfCharP) *i = *i % nfCharP; |
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| 466 | } |
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| 467 | else *i = 1; |
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| 468 | return s; |
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| 469 | } |
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| 470 | |
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| 471 | /*2 |
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| 472 | * read a number |
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| 473 | */ |
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[85e68dd] | 474 | const char * nfRead (const char *s, number *a) |
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[35aab3] | 475 | { |
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| 476 | int i; |
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| 477 | number z; |
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| 478 | number n; |
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| 479 | |
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| 480 | s = nfEati(s, &i); |
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| 481 | z=nfInit(i); |
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| 482 | *a=z; |
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| 483 | if (*s == '/') |
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| 484 | { |
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| 485 | s++; |
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| 486 | s = nfEati(s, &i); |
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| 487 | n=nfInit(i); |
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| 488 | *a = nfDiv(z,n); |
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| 489 | } |
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| 490 | if (strncmp(s,nfParameter,strlen(nfParameter))==0) |
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| 491 | { |
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| 492 | s+=strlen(nfParameter); |
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| 493 | if ((*s >= '0') && (*s <= '9')) |
---|
| 494 | { |
---|
| 495 | s=eati(s,&i); |
---|
| 496 | while (i>=nfCharQ1) i-=nfCharQ1; |
---|
| 497 | } |
---|
| 498 | else |
---|
| 499 | i=1; |
---|
[01a57b] | 500 | z=(number)(long)i; |
---|
[35aab3] | 501 | *a=nfMult(*a,z); |
---|
| 502 | } |
---|
| 503 | #ifdef LDEBUG |
---|
| 504 | nfTest(*a); |
---|
| 505 | #endif |
---|
| 506 | return s; |
---|
| 507 | } |
---|
| 508 | |
---|
| 509 | #ifdef HAVE_FACTORY |
---|
| 510 | int gf_tab_numdigits62 ( int q ); |
---|
| 511 | int convertback62 ( char * p, int n ); |
---|
| 512 | #else |
---|
| 513 | static int gf_tab_numdigits62 ( int q ) |
---|
| 514 | { |
---|
| 515 | if ( q < 62 ) return 1; |
---|
| 516 | else if ( q < 62*62 ) return 2; |
---|
| 517 | /*else*/ return 3; |
---|
| 518 | } |
---|
| 519 | |
---|
| 520 | static int convback62 ( char c ) |
---|
| 521 | { |
---|
| 522 | if ( c >= '0' && c <= '9' ) |
---|
| 523 | return int(c) - int('0'); |
---|
| 524 | else if ( c >= 'A' && c <= 'Z' ) |
---|
| 525 | return int(c) - int('A') + 10; |
---|
| 526 | else |
---|
| 527 | return int(c) - int('a') + 36; |
---|
| 528 | } |
---|
| 529 | |
---|
| 530 | static int convertback62 ( char * p, int n ) |
---|
| 531 | { |
---|
| 532 | int r = 0; |
---|
| 533 | for ( int j = 0; j < n; j++ ) |
---|
| 534 | r = r * 62 + convback62( p[j] ); |
---|
| 535 | return r; |
---|
| 536 | } |
---|
| 537 | #endif |
---|
| 538 | |
---|
| 539 | int nfMinPoly[16]; |
---|
| 540 | |
---|
| 541 | void nfShowMipo() |
---|
| 542 | { |
---|
| 543 | int i=nfMinPoly[0]; |
---|
| 544 | int j=0; |
---|
| 545 | loop |
---|
| 546 | { |
---|
| 547 | j++; |
---|
| 548 | if (nfMinPoly[j]!=0) |
---|
| 549 | StringAppend("%d*%s^%d",nfMinPoly[j],nfParameter,i); |
---|
| 550 | i--; |
---|
| 551 | if(i<0) break; |
---|
| 552 | if (nfMinPoly[j]!=0) |
---|
| 553 | StringAppendS("+"); |
---|
| 554 | } |
---|
| 555 | } |
---|
| 556 | |
---|
| 557 | static void nfReadMipo(char *s) |
---|
| 558 | { |
---|
| 559 | const char *l=strchr(s,';')+1; |
---|
| 560 | char *n; |
---|
| 561 | int i=strtol(l,&n,10); |
---|
| 562 | l=n; |
---|
| 563 | int j=1; |
---|
| 564 | nfMinPoly[0]=i; |
---|
| 565 | while(i>=0) |
---|
| 566 | { |
---|
| 567 | nfMinPoly[j]=strtol(l,&n,10); |
---|
| 568 | if (l==n) break; |
---|
| 569 | l=n; |
---|
| 570 | j++; |
---|
| 571 | i--; |
---|
| 572 | } |
---|
| 573 | if (i>=0) |
---|
| 574 | { |
---|
| 575 | WerrorS("error in reading minpoly from gftables"); |
---|
| 576 | } |
---|
| 577 | } |
---|
| 578 | |
---|
| 579 | /*2 |
---|
| 580 | * init global variables from files 'gftables/%d' |
---|
| 581 | */ |
---|
| 582 | void nfSetChar(int c, char **param) |
---|
| 583 | { |
---|
| 584 | //Print("GF(%d)\n",c); |
---|
| 585 | nfParameter=param[0]; |
---|
| 586 | if ((c==nfCharQ)||(c==-nfCharQ)) |
---|
| 587 | /*this field is already set*/ return; |
---|
| 588 | int i=0; |
---|
| 589 | while ((fftable[i]!=c) && (fftable[i]!=0)) i++; |
---|
| 590 | if (fftable[i]==0) |
---|
| 591 | return; |
---|
| 592 | if (nfCharQ > 1) |
---|
| 593 | { |
---|
| 594 | omFreeSize( (ADDRESS)nfPlus1Table,nfCharQ*sizeof(CARDINAL) ); |
---|
| 595 | nfPlus1Table=NULL; |
---|
| 596 | } |
---|
| 597 | if ((c>1) || (c<0)) |
---|
| 598 | { |
---|
| 599 | if (c>1) nfCharQ = c; |
---|
| 600 | else nfCharQ = -c; |
---|
| 601 | char buf[100]; |
---|
| 602 | sprintf(buf,"gftables/%d",nfCharQ); |
---|
| 603 | FILE * fp = feFopen(buf,"r",NULL,TRUE); |
---|
| 604 | if (fp==NULL) |
---|
| 605 | { |
---|
| 606 | return; |
---|
| 607 | } |
---|
| 608 | if(!fgets( buf, sizeof(buf), fp)) return; |
---|
| 609 | if(strcmp(buf,"@@ factory GF(q) table @@\n")!=0) |
---|
| 610 | { |
---|
| 611 | goto err; |
---|
| 612 | } |
---|
| 613 | if(!fgets( buf, sizeof(buf), fp)) |
---|
| 614 | { |
---|
| 615 | goto err; |
---|
| 616 | } |
---|
| 617 | int q; |
---|
| 618 | sscanf(buf,"%d %d",&nfCharP,&q); |
---|
| 619 | nfReadMipo(buf); |
---|
| 620 | nfCharQ1=nfCharQ-1; |
---|
| 621 | //Print("nfCharQ=%d,nfCharQ1=%d,mipo=>>%s<<\n",nfCharQ,nfCharQ1,buf); |
---|
| 622 | nfPlus1Table= (CARDINAL *)omAlloc( (nfCharQ)*sizeof(CARDINAL) ); |
---|
| 623 | int digs = gf_tab_numdigits62( nfCharQ ); |
---|
| 624 | char * bufptr; |
---|
| 625 | int i = 1; |
---|
| 626 | int k; |
---|
| 627 | while ( i < nfCharQ ) |
---|
| 628 | { |
---|
| 629 | fgets( buf, sizeof(buf), fp); |
---|
| 630 | //( strlen( buffer ) == (size_t)digs * 30, "illegal table" ); |
---|
| 631 | bufptr = buf; |
---|
| 632 | k = 0; |
---|
| 633 | while ( (i < nfCharQ) && (k < 30) ) |
---|
| 634 | { |
---|
| 635 | nfPlus1Table[i] = convertback62( bufptr, digs ); |
---|
| 636 | if(nfPlus1Table[i]>nfCharQ) |
---|
| 637 | { |
---|
| 638 | Print("wrong entry %d: %d(%c%c%c)\n",i,nfPlus1Table[i],bufptr[0],bufptr[1],bufptr[2]); |
---|
| 639 | } |
---|
| 640 | bufptr += digs; |
---|
| 641 | if (nfPlus1Table[i]==nfCharQ) |
---|
| 642 | { |
---|
| 643 | if(i==nfCharQ1) |
---|
| 644 | { |
---|
| 645 | nfM1=0; |
---|
| 646 | } |
---|
| 647 | else |
---|
| 648 | { |
---|
| 649 | nfM1=i; |
---|
| 650 | } |
---|
| 651 | } |
---|
| 652 | i++; k++; |
---|
| 653 | } |
---|
| 654 | } |
---|
| 655 | nfPlus1Table[0]=nfPlus1Table[nfCharQ1]; |
---|
| 656 | } |
---|
| 657 | else |
---|
| 658 | nfCharQ=0; |
---|
| 659 | #ifdef LDEBUG |
---|
| 660 | nfTest((number)0); |
---|
| 661 | #endif |
---|
| 662 | return; |
---|
| 663 | err: |
---|
| 664 | Werror("illegal GF-table %d",nfCharQ); |
---|
| 665 | } |
---|
| 666 | |
---|
| 667 | /*2 |
---|
| 668 | * map Z/p -> GF(p,n) |
---|
| 669 | */ |
---|
| 670 | number nfMapP(number c) |
---|
| 671 | { |
---|
[7447d8] | 672 | return nfInit((int)((long)c)); |
---|
[35aab3] | 673 | } |
---|
| 674 | |
---|
[85e68dd] | 675 | /*2 |
---|
| 676 | * map GF(p,n1) -> GF(p,n2), n1 < n2, n1 | n2 |
---|
| 677 | */ |
---|
| 678 | int nfMapGG_factor; |
---|
| 679 | number nfMapGG(number c) |
---|
| 680 | { |
---|
| 681 | int i=(long)c; |
---|
| 682 | i*= nfMapGG_factor; |
---|
| 683 | while (i >nfCharQ1) i-=nfCharQ1; |
---|
| 684 | return (number)((long)i); |
---|
| 685 | } |
---|
| 686 | /*2 |
---|
| 687 | * map GF(p,n1) -> GF(p,n2), n1 > n2, n2 | n1 |
---|
| 688 | */ |
---|
| 689 | number nfMapGGrev(number c) |
---|
| 690 | { |
---|
| 691 | int ex=(int)((long)c); |
---|
| 692 | if ((ex % nfMapGG_factor)==0) |
---|
| 693 | return (number)(((long)ex) / ((long)nfMapGG_factor)); |
---|
| 694 | else |
---|
| 695 | return (number)(long)nfCharQ; /* 0 */ |
---|
| 696 | } |
---|
| 697 | |
---|
[35aab3] | 698 | /*2 |
---|
| 699 | * set map function nMap ... -> GF(p,n) |
---|
| 700 | */ |
---|
| 701 | nMapFunc nfSetMap(ring src, ring dst) |
---|
| 702 | { |
---|
| 703 | if (rField_is_GF(src,nfCharQ)) |
---|
| 704 | { |
---|
| 705 | return ndCopy; /* GF(p,n) -> GF(p,n) */ |
---|
| 706 | } |
---|
[85e68dd] | 707 | if (rField_is_GF(src)) |
---|
| 708 | { |
---|
| 709 | int q=src->ch; |
---|
| 710 | if ((nfCharQ % q)==0) /* GF(p,n1) -> GF(p,n2), n2 > n1 */ |
---|
| 711 | { |
---|
| 712 | // check if n2 is a multiple of n1 |
---|
| 713 | int n1=1; |
---|
| 714 | int qq=nfCharP; |
---|
| 715 | while(qq!=q) { qq *= nfCharP; n1++; } |
---|
| 716 | int n2=1; |
---|
| 717 | qq=nfCharP; |
---|
| 718 | while(qq!=nfCharQ) { qq *= nfCharP; n2++; } |
---|
| 719 | Print("map %d^%d -> %d^%d\n",nfCharP,n1,nfCharP,n2); |
---|
| 720 | if ((n2 % n1)==0) |
---|
| 721 | { |
---|
| 722 | int save_ch=currRing->ch; |
---|
| 723 | char **save_par=currRing->parameter; |
---|
| 724 | nfSetChar(src->ch,src->parameter); |
---|
| 725 | int nn=nfPlus1Table[0]; |
---|
| 726 | nfSetChar(save_ch,save_par); |
---|
| 727 | nfMapGG_factor= nfPlus1Table[0] / nn; |
---|
| 728 | Print("nfMapGG_factor=%d (%d / %d)\n",nfMapGG_factor, nfPlus1Table[0], nn); |
---|
| 729 | return nfMapGG; |
---|
| 730 | } |
---|
| 731 | else if ((n1 % n2)==0) |
---|
| 732 | { |
---|
| 733 | nfMapGG_factor= (n1/n2); |
---|
| 734 | return nfMapGGrev; |
---|
| 735 | } |
---|
| 736 | else |
---|
| 737 | return NULL; |
---|
| 738 | } |
---|
| 739 | } |
---|
[35aab3] | 740 | if (rField_is_Zp(src,nfCharP)) |
---|
| 741 | { |
---|
| 742 | return nfMapP; /* Z/p -> GF(p,n) */ |
---|
| 743 | } |
---|
| 744 | return NULL; /* default */ |
---|
| 745 | } |
---|