1 | /**************************************** |
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2 | * Computer Algebra System SINGULAR * |
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3 | ****************************************/ |
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4 | /* $Id: spolys0.cc,v 1.16 2000-02-14 17:15:03 Singular Exp $ */ |
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5 | |
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6 | /* |
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7 | * ABSTRACT - s-polynomials and reduction in general |
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8 | */ |
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9 | |
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10 | #include <string.h> |
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11 | #include "mod2.h" |
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12 | #include "tok.h" |
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13 | #include "mmemory.h" |
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14 | #include "numbers.h" |
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15 | #include "polys.h" |
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16 | #include "spolys0.h" |
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17 | |
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18 | /*0 implementation*/ |
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19 | |
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20 | /* |
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21 | * input - output: a, b |
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22 | * returns: |
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23 | * a := a/gcd(a,b), b := b/gcd(a,b) |
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24 | * and return value |
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25 | * 0 -> a != 1, b != 1 |
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26 | * 1 -> a == 1, b != 1 |
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27 | * 2 -> a != 1, b == 1 |
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28 | * 3 -> a == 1, b == 1 |
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29 | * this value is used to control the spolys |
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30 | */ |
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31 | int spCheckCoeff(number *a, number *b) |
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32 | { |
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33 | int c = 0; |
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34 | number an = *a, bn = *b; |
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35 | nTest(an); |
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36 | nTest(bn); |
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37 | number cn = nGcd(an, bn); |
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38 | |
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39 | if(nIsOne(cn)) |
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40 | { |
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41 | an = nCopy(an); |
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42 | bn = nCopy(bn); |
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43 | } |
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44 | else |
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45 | { |
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46 | an = nIntDiv(an, cn); |
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47 | bn = nIntDiv(bn, cn); |
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48 | } |
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49 | nDelete(&cn); |
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50 | if (nIsOne(an)) |
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51 | { |
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52 | c = 1; |
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53 | } |
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54 | if (nIsOne(bn)) |
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55 | { |
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56 | c += 2; |
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57 | } |
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58 | *a = an; |
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59 | *b = bn; |
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60 | return c; |
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61 | } |
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62 | |
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63 | /*2 |
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64 | * transforms a1 to a polynomial |
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65 | */ |
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66 | void spModuleToPoly(poly a1) |
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67 | { |
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68 | #ifdef PDEBUG |
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69 | poly t=a1; |
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70 | pTest(t); |
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71 | #endif |
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72 | do |
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73 | { |
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74 | pSetComp(a1,0); |
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75 | pIter(a1); |
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76 | } while (a1!=NULL); |
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77 | #ifdef PDEBUG |
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78 | pTest(t); |
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79 | #endif |
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80 | } |
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81 | |
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82 | /*2 |
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83 | * assume m = L(m) and Lc(m) = 1 |
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84 | * pNext(m) = result = p*m |
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85 | * do not destroy p |
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86 | */ |
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87 | static void spGMultCopy0(poly p, poly m, poly spNoether) |
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88 | { |
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89 | poly a, b; |
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90 | |
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91 | a = m; |
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92 | if (spNoether==NULL) |
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93 | { |
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94 | do |
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95 | { |
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96 | a = pNext(a) = pNew(); |
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97 | pCopyAddFast(a,p,m); |
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98 | pSetCoeff0(a,nCopy(pGetCoeff(a))); |
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99 | pIter(p); |
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100 | } |
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101 | while (p!=NULL); |
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102 | pNext(a) = NULL; |
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103 | return; |
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104 | } |
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105 | else |
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106 | { |
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107 | do |
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108 | { |
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109 | b = pNext(a) = pNew(); |
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110 | spMemcpy(b,p); |
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111 | spMonAdd(b,m); |
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112 | if (pComp0(b, spNoether) == -1) |
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113 | { |
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114 | pFree1(b); |
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115 | pNext(a) = NULL; |
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116 | return; |
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117 | } |
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118 | a = b; |
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119 | pSetCoeff0(a,nCopy(pGetCoeff(a))); |
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120 | pIter(p); |
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121 | } while (p!=NULL); |
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122 | pNext(a) = NULL; |
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123 | } |
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124 | } |
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125 | |
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126 | /*2 |
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127 | * assume m = L(m) and Lc(m) = -1 |
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128 | * pNext(n) = result = p*m |
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129 | * do not destroy p |
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130 | */ |
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131 | static void spGMultCopy1(poly p, poly m, poly n,poly spNoether) |
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132 | { |
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133 | poly a, b; |
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134 | |
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135 | a = n; |
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136 | if (spNoether==NULL) |
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137 | { |
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138 | do |
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139 | { |
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140 | number tmp; |
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141 | a = pNext(a) = pNew(); |
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142 | spMemcpy(a,p); |
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143 | spMonAdd(a,m); |
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144 | tmp=nCopy(pGetCoeff(a)); |
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145 | tmp=nNeg(tmp); |
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146 | pSetCoeff0(a,tmp); |
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147 | pIter(p); |
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148 | } |
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149 | while (p!=NULL); |
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150 | pNext(a) = NULL; |
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151 | return; |
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152 | } |
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153 | else |
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154 | { |
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155 | do |
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156 | { |
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157 | b = pNext(a) = pNew(); |
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158 | spMemcpy(b,p); |
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159 | spMonAdd(b,m); |
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160 | if (pComp(b, spNoether) == -1) |
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161 | { |
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162 | pFree1(b); |
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163 | pNext(a) = NULL; |
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164 | return; |
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165 | } |
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166 | a = b; |
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167 | number tmp; |
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168 | tmp=nCopy(pGetCoeff(a)); |
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169 | tmp=nNeg(tmp); |
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170 | pSetCoeff0(a,tmp); |
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171 | pIter(p); |
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172 | } |
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173 | while (p!=NULL); |
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174 | pNext(a) = NULL; |
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175 | } |
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176 | } |
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177 | |
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178 | /*2 |
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179 | * assume m = L(m) and Lc(m) = 1 |
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180 | * pNext(m) = result = a2-a1*m |
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181 | * do not destroy a1, but a2 |
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182 | */ |
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183 | static void spGSpolyLoop1(poly a1, poly a2, poly m, poly spNoether) |
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184 | { |
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185 | poly a, b, s; |
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186 | number tb; |
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187 | int c; |
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188 | |
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189 | if (a2==NULL) |
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190 | { |
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191 | spGMultCopy1(a1, m, m,spNoether); |
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192 | return; |
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193 | } |
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194 | a = m; |
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195 | b = pNew(); |
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196 | spMemcpy(b,a1); |
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197 | spMonAdd(b,m); |
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198 | loop |
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199 | { |
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200 | c = pComp0(b, a2); |
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201 | if (c == 1) |
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202 | { |
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203 | number tmp=nCopy(pGetCoeff(b)); |
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204 | tmp=nNeg(tmp); |
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205 | pSetCoeff0(b,tmp); |
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206 | a = pNext(a) = b; |
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207 | pIter(a1); |
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208 | if (a1!=NULL) |
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209 | { |
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210 | b = pNew(); |
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211 | spMemcpy(b,a1); |
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212 | spMonAdd(b,m); |
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213 | } |
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214 | else |
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215 | { |
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216 | pNext(a) = a2; |
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217 | return; |
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218 | } |
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219 | } |
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220 | else if (c == -1) |
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221 | { |
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222 | a = pNext(a) = a2; |
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223 | pIter(a2); |
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224 | if (a2==NULL) |
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225 | { |
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226 | pFree1(b); |
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227 | spGMultCopy1(a1, m, a,spNoether); |
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228 | return; |
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229 | } |
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230 | } |
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231 | else |
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232 | { |
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233 | tb = pGetCoeff(a2); |
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234 | if (!nEqual(tb,pGetCoeff(a1))) |
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235 | { |
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236 | tb = nSub(tb,pGetCoeff(a1)); |
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237 | pSetCoeff(a2,tb); |
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238 | a = pNext(a) = a2; |
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239 | pIter(a2); |
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240 | } |
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241 | else |
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242 | { |
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243 | s = a2; |
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244 | pIter(a2); |
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245 | nDelete(&tb); |
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246 | pFree1(s); |
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247 | } |
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248 | pIter(a1); |
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249 | if (a1==NULL) |
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250 | { |
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251 | pFree1(b); |
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252 | pNext(a) = a2; |
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253 | return; |
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254 | } |
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255 | if (a2==NULL) |
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256 | { |
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257 | pFree1(b); |
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258 | spGMultCopy1(a1, m, a,spNoether); |
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259 | return; |
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260 | } |
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261 | spMemcpy(b,a1); |
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262 | spMonAdd(b,m); |
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263 | } |
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264 | } |
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265 | } |
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266 | |
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267 | /*2 |
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268 | * assume m = L(m) and Lc(m) = exp |
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269 | * pNext(n) = result = p*m |
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270 | * do not destroy p |
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271 | */ |
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272 | void spGMultCopyX(poly p, poly m, poly n, number exp, poly spNoether) |
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273 | { |
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274 | poly a, b; |
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275 | |
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276 | a = n; |
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277 | if (spNoether==NULL) |
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278 | { |
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279 | do |
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280 | { |
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281 | a = pNext(a) = pNew(); |
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282 | spMemcpy(a,p); |
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283 | spMonAdd(a,m); |
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284 | pSetCoeff0(a,nMult(pGetCoeff(p),exp)); |
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285 | pIter(p); |
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286 | } while (p!=NULL); |
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287 | pNext(a) = NULL; |
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288 | return; |
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289 | } |
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290 | else |
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291 | { |
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292 | do |
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293 | { |
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294 | b = pNext(a) = pNew(); |
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295 | spMemcpy(b,p); |
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296 | spMonAdd(b,m); |
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297 | if (pComp(b, spNoether) == -1) |
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298 | { |
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299 | pFree1(b); |
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300 | pNext(a) = NULL; |
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301 | return; |
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302 | } |
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303 | a = b; |
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304 | pSetCoeff0(a,nMult(pGetCoeff(p),exp)); |
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305 | pIter(p); |
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306 | } while (p!=NULL); |
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307 | pNext(a) = NULL; |
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308 | } |
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309 | } |
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310 | |
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311 | /*2 |
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312 | * assume m = L(m) |
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313 | * pNext(m) = result = a2-a1*m |
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314 | * do not destroy a1, but a2 |
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315 | */ |
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316 | #if 0 |
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317 | void spGSpolyLoop(poly a1, poly a2, poly m,poly spNoether) |
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318 | { |
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319 | poly a, b, s; |
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320 | number tm = pGetCoeff(m); |
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321 | number tneg,tb,t; |
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322 | int c; |
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323 | |
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324 | tneg = nCopy(tm); |
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325 | tneg = nNeg(tneg); |
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326 | if (a2==NULL) |
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327 | { |
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328 | spGMultCopyX(a1, m, m, tneg,spNoether); |
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329 | nDelete(&tneg); |
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330 | return; |
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331 | } |
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332 | a = m; |
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333 | b = pNew(); |
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334 | spMemcpy(b,a1); |
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335 | spMonAdd(b,m); |
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336 | loop |
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337 | { |
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338 | c = pComp0(b, a2); |
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339 | if (c == 1) |
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340 | { |
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341 | pSetCoeff0(b,nMult(pGetCoeff(a1),tneg)); |
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342 | a = pNext(a) = b; |
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343 | pIter(a1); |
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344 | if (a1!=NULL) |
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345 | { |
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346 | b = pNew(); |
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347 | spMemcpy(b,a1); |
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348 | spMonAdd(b,m); |
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349 | } |
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350 | else |
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351 | { |
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352 | pNext(a) = a2; |
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353 | nDelete(&tneg); |
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354 | return; |
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355 | } |
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356 | } |
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357 | else if (c == -1) |
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358 | { |
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359 | a = pNext(a) = a2; |
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360 | pIter(a2); |
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361 | if (a2==NULL) |
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362 | { |
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363 | pFree1(b); |
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364 | spGMultCopyX(a1, m, a, tneg,spNoether); |
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365 | nDelete(&tneg); |
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366 | return; |
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367 | } |
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368 | } |
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369 | else |
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370 | { |
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371 | t = pGetCoeff(a2); |
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372 | tb = nMult(pGetCoeff(a1),tm); |
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373 | if (!nEqual(t,tb)) |
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374 | { |
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375 | t = nSub(t,tb); |
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376 | pSetCoeff(a2,t); |
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377 | a = pNext(a) = a2; |
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378 | pIter(a2); |
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379 | } |
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380 | else |
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381 | { |
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382 | s = a2; |
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383 | pIter(a2); |
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384 | nDelete(&t); |
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385 | pFree1(s); |
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386 | } |
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387 | nDelete(&tb); |
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388 | pIter(a1); |
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389 | if (a1==NULL) |
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390 | { |
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391 | pFree1(b); |
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392 | pNext(a) = a2; |
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393 | nDelete(&tneg); |
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394 | return; |
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395 | } |
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396 | if (a2==NULL) |
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397 | { |
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398 | pFree1(b); |
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399 | spGMultCopyX(a1, m, a, tneg,spNoether); |
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400 | nDelete(&tneg); |
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401 | return; |
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402 | } |
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403 | spMemcpy(b,a1); |
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404 | spMonAdd(b,m); |
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405 | } |
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406 | } |
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407 | } |
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408 | #endif |
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409 | |
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410 | /*2 |
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411 | * reduction of p2 with p1 |
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412 | * do not destroy p1, but p2 |
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413 | */ |
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414 | poly spGSpolyRed(poly p1, poly p2,poly spNoether, spSpolyLoopProc spSpolyLoop) |
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415 | { |
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416 | poly a1 = pNext(p1), a2 = pNext(p2); |
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417 | number an = pGetCoeff(p1), bn = pGetCoeff(p2); |
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418 | int ct = spCheckCoeff(&an, &bn); |
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419 | |
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420 | pSetCoeff(p2,bn); |
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421 | if(a1==NULL) |
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422 | { |
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423 | nDelete(&an); |
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424 | nDelete(&bn); |
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425 | pFree1(p2); |
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426 | return a2; |
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427 | } |
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428 | if ((ct == 0) || (ct == 2)) |
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429 | { |
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430 | pMultN(a2, an); |
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431 | } |
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432 | nDelete(&an); |
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433 | BOOLEAN reset_vec=FALSE; |
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434 | if (pGetComp(p1) != pGetComp(p2)) |
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435 | { |
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436 | pSetCompP(a1,pGetComp(p2)); |
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437 | reset_vec=TRUE; |
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438 | } |
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439 | spMonSub(p2,p1); |
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440 | if (ct < 2) |
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441 | { |
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442 | if (spSpolyLoop != NULL) |
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443 | spSpolyLoop(a1, a2, p2,spNoether); |
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444 | else |
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445 | spSpolyLoop_General(a1, a2, p2,spNoether); |
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446 | } |
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447 | else |
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448 | { |
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449 | spGSpolyLoop1(a1, a2, p2,spNoether); |
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450 | } |
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451 | a2 = pNext(p2); |
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452 | if (reset_vec) |
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453 | { |
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454 | spModuleToPoly(a1); |
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455 | } |
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456 | nDelete(&bn); |
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457 | pFree1(p2); |
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458 | return a2; |
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459 | } |
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460 | |
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461 | /*2 |
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462 | * reduction of tail(q) with p1 |
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463 | * lead(p1) divides lead(pNext(q2)) and pNext(q2) is reduced |
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464 | * do not destroy p1, but tail(q2) |
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465 | */ |
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466 | void spGSpolyTail(poly p1, poly q, poly q2, poly spNoether, |
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467 | spSpolyLoopProc spSpolyLoop) |
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468 | { |
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469 | number t; |
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470 | poly m, h; |
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471 | poly a1 = pNext(p1), p2 = pNext(q2), a2 = pNext(p2); |
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472 | number an = pGetCoeff(p1), bn = pGetCoeff(p2); |
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473 | int ct = spCheckCoeff(&an, &bn); |
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474 | BOOLEAN reset_vec=FALSE; |
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475 | |
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476 | if(a1==NULL) |
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477 | { |
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478 | nDelete(&an); |
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479 | nDelete(&bn); |
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480 | nDelete(&pGetCoeff(p2)); |
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481 | pFree1(p2); |
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482 | pNext(q2) = a2; |
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483 | return; |
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484 | } |
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485 | if (p1 != q) |
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486 | { |
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487 | m = p2; |
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488 | pSetCoeff(m,bn); |
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489 | } |
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490 | else |
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491 | { |
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492 | m = pNew(); |
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493 | spMemcpy(m,p2); |
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494 | pSetCoeff0(m,bn); |
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495 | a2 = pCopy(a2); |
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496 | } |
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497 | if ((ct == 0) || (ct == 2)) |
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498 | { |
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499 | pMultN(a2, an); |
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500 | } |
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501 | if ((pGetComp(p1) != pGetComp(p2)) |
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502 | && (pGetComp(p1)==0)) |
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503 | { |
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504 | pSetCompP(a1,pGetComp(p2)); |
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505 | reset_vec=TRUE; |
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506 | } |
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507 | spMonSub(m,p1); |
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508 | if (ct < 2) |
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509 | { |
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510 | if (spSpolyLoop != NULL) |
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511 | spSpolyLoop(a1, a2, m,spNoether); |
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512 | else |
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513 | spSpolyLoop_General(a1, a2, m,spNoether); |
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514 | } |
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515 | else |
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516 | { |
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517 | spGSpolyLoop1(a1, a2, m,spNoether); |
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518 | } |
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519 | if ((ct == 0) || (ct == 2)) |
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520 | { |
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521 | h = q; |
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522 | do |
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523 | { |
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524 | t = nMult(pGetCoeff(h),an); |
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525 | pSetCoeff(h,t); |
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526 | pIter(h); |
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527 | } |
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528 | while (h != p2); |
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529 | } |
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530 | h = pNext(m); |
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531 | nDelete(&an); |
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532 | nDelete(&bn); |
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533 | pFree1(m); |
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534 | pNext(q2) = h; |
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535 | if (reset_vec) |
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536 | spModuleToPoly(a1); |
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537 | if (p1 == q) |
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538 | { |
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539 | pDelete(&p2); |
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540 | } |
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541 | } |
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542 | |
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543 | /*2 |
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544 | * reduction of p2 with p1 |
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545 | * do not destroy p1 and p2 |
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546 | */ |
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547 | poly spGSpolyRedNew(poly p1, poly p2,poly spNoether, |
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548 | spSpolyLoopProc spSpolyLoop) |
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549 | { |
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550 | poly m; |
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551 | poly a1 = pNext(p1), a2 = pNext(p2); |
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552 | number an = pGetCoeff(p1), bn = pGetCoeff(p2); |
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553 | int ct = spCheckCoeff(&an, &bn); |
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554 | |
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555 | if(a1==NULL) |
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556 | { |
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557 | nDelete(&an); |
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558 | nDelete(&bn); |
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559 | return pCopy(a2); |
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560 | } |
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561 | if ((ct == 0) || (ct == 2)) |
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562 | { |
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563 | a2 = pMultCopyN(a2,an); |
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564 | } |
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565 | else |
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566 | { |
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567 | a2 = pCopy(a2); |
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568 | } |
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569 | pTest(a2); |
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570 | pTest(p2); |
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571 | nDelete(&an); |
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572 | BOOLEAN reset_vec=FALSE; |
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573 | if (pGetComp(p1) != pGetComp(p2)) |
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574 | { |
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575 | pSetCompP(a1,pGetComp(p2)); |
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576 | reset_vec=TRUE; |
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577 | } |
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578 | m = pNew(); |
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579 | spMemcpy(m,p2); |
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580 | spMonSub(m,p1); |
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581 | if (ct < 2) |
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582 | { |
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583 | pSetCoeff0(m,bn); |
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584 | if (spSpolyLoop != NULL) |
---|
585 | spSpolyLoop(a1, a2, m,spNoether); |
---|
586 | else |
---|
587 | spSpolyLoop_General(a1, a2, m,spNoether); |
---|
588 | } |
---|
589 | else |
---|
590 | { |
---|
591 | spGSpolyLoop1(a1, a2, m,spNoether); |
---|
592 | } |
---|
593 | a2 = pNext(m); |
---|
594 | pTest(a2); |
---|
595 | pTest(p2); |
---|
596 | if (reset_vec) |
---|
597 | { |
---|
598 | spModuleToPoly(a1); |
---|
599 | } |
---|
600 | nDelete(&bn); |
---|
601 | pFree1(m); |
---|
602 | pTest(a2); |
---|
603 | pTest(p2); |
---|
604 | return a2; |
---|
605 | } |
---|
606 | |
---|
607 | /*2 |
---|
608 | * creates the S-polynomial of p1 and p2 |
---|
609 | * do not destroy p1 and p2 |
---|
610 | */ |
---|
611 | poly spGSpolyCreate(poly p1, poly p2,poly spNoether, |
---|
612 | spSpolyLoopProc spSpolyLoop) |
---|
613 | { |
---|
614 | Exponent_t x; |
---|
615 | poly m, b; |
---|
616 | poly a1 = pNext(p1), a2 = pNext(p2); |
---|
617 | number an = pGetCoeff(p1), bn = pGetCoeff(p2); |
---|
618 | int co=0, ct = spCheckCoeff(&an, &bn); |
---|
619 | |
---|
620 | if (pGetComp(p1)!=pGetComp(p2)) |
---|
621 | { |
---|
622 | if (pGetComp(p1)==0) |
---|
623 | { |
---|
624 | co=1; |
---|
625 | pSetCompP(p1,pGetComp(p2)); |
---|
626 | } |
---|
627 | else |
---|
628 | { |
---|
629 | co=2; |
---|
630 | pSetCompP(p2,pGetComp(p1)); |
---|
631 | } |
---|
632 | } |
---|
633 | b = pInit(); |
---|
634 | m = pInit(); |
---|
635 | for (int i = pVariables; i; i--) |
---|
636 | { |
---|
637 | x = pGetExp(p1,i) - pGetExp(p2,i); |
---|
638 | if (x > 0) |
---|
639 | { |
---|
640 | pSetExp(b,i,x); |
---|
641 | pSetExp(m,i,0); |
---|
642 | } |
---|
643 | else |
---|
644 | { |
---|
645 | pSetExp(m,i,-x); |
---|
646 | pSetExp(b,i,0); |
---|
647 | } |
---|
648 | } |
---|
649 | pSetm(m); |
---|
650 | pSetm(b); |
---|
651 | if (a2!=NULL) |
---|
652 | { |
---|
653 | if ((ct == 0) || (ct == 2)) |
---|
654 | { |
---|
655 | spGMultCopyX(a2, b, b, an,spNoether); |
---|
656 | } |
---|
657 | else |
---|
658 | { |
---|
659 | spGMultCopy0(a2, b,spNoether); |
---|
660 | } |
---|
661 | a2 = pNext(b); |
---|
662 | } |
---|
663 | nDelete(&an); |
---|
664 | pFree1(b); |
---|
665 | if (a1!=NULL) |
---|
666 | { |
---|
667 | if (ct < 2) |
---|
668 | { |
---|
669 | pSetCoeff0(m,bn); |
---|
670 | if (spSpolyLoop != NULL) |
---|
671 | spSpolyLoop(a1, a2, m,spNoether); |
---|
672 | else |
---|
673 | spSpolyLoop_General(a1, a2, m,spNoether); |
---|
674 | } |
---|
675 | else |
---|
676 | { |
---|
677 | spGSpolyLoop1(a1, a2, m,spNoether); |
---|
678 | } |
---|
679 | a2 = pNext(m); |
---|
680 | } |
---|
681 | nDelete(&bn); |
---|
682 | pFree1(m); |
---|
683 | if (co != 0) |
---|
684 | { |
---|
685 | if (co==1) |
---|
686 | { |
---|
687 | spModuleToPoly(p1); |
---|
688 | } |
---|
689 | else |
---|
690 | { |
---|
691 | spModuleToPoly(p2); |
---|
692 | } |
---|
693 | } |
---|
694 | return a2; |
---|
695 | } |
---|
696 | |
---|
697 | /*2 |
---|
698 | * creates the leading term of the S-polynomial of p1 and p2 |
---|
699 | * do not destroy p1 and p2 |
---|
700 | * remarks: |
---|
701 | * 1. the coefficient is 0 (nNew) |
---|
702 | * 2. pNext is undefined |
---|
703 | */ |
---|
704 | //static void bbb() { int i=0; } |
---|
705 | poly spGSpolyShortBba(poly p1, poly p2) |
---|
706 | { |
---|
707 | poly a1 = pNext(p1), a2 = pNext(p2); |
---|
708 | Exponent_t c1=pGetComp(p1),c2=pGetComp(p2); |
---|
709 | Exponent_t c; |
---|
710 | poly m1,m2; |
---|
711 | number t1,t2; |
---|
712 | int cm,i; |
---|
713 | BOOLEAN equal; |
---|
714 | |
---|
715 | if (a1==NULL) |
---|
716 | { |
---|
717 | if(a2!=NULL) |
---|
718 | { |
---|
719 | m2=pInit(); |
---|
720 | x2: |
---|
721 | for (i = pVariables; i; i--) |
---|
722 | { |
---|
723 | c = pGetExpDiff(p1, p2,i); |
---|
724 | if (c>0) |
---|
725 | { |
---|
726 | pSetExp(m2,i,(c+pGetExp(a2,i))); |
---|
727 | } |
---|
728 | else |
---|
729 | { |
---|
730 | pSetExp(m2,i,pGetExp(a2,i)); |
---|
731 | } |
---|
732 | } |
---|
733 | if ((c1==c2)||(c2!=0)) |
---|
734 | { |
---|
735 | pSetComp(m2,pGetComp(a2)); |
---|
736 | } |
---|
737 | else |
---|
738 | { |
---|
739 | pSetComp(m2,c1); |
---|
740 | } |
---|
741 | pSetm(m2); |
---|
742 | nNew(&(pGetCoeff(m2))); |
---|
743 | return m2; |
---|
744 | } |
---|
745 | else |
---|
746 | return NULL; |
---|
747 | } |
---|
748 | if (a2==NULL) |
---|
749 | { |
---|
750 | m1=pInit(); |
---|
751 | x1: |
---|
752 | for (i = pVariables; i; i--) |
---|
753 | { |
---|
754 | c = pGetExpDiff(p2, p1,i); |
---|
755 | if (c>0) |
---|
756 | { |
---|
757 | pSetExp(m1,i,(c+pGetExp(a1,i))); |
---|
758 | } |
---|
759 | else |
---|
760 | { |
---|
761 | pSetExp(m1,i,pGetExp(a1,i)); |
---|
762 | } |
---|
763 | } |
---|
764 | if ((c1==c2)||(c1!=0)) |
---|
765 | { |
---|
766 | pSetComp(m1,pGetComp(a1)); |
---|
767 | } |
---|
768 | else |
---|
769 | { |
---|
770 | pSetComp(m1,c2); |
---|
771 | } |
---|
772 | pSetm(m1); |
---|
773 | nNew(&(pGetCoeff(m1))); |
---|
774 | return m1; |
---|
775 | } |
---|
776 | m1 = pInit(); |
---|
777 | m2 = pInit(); |
---|
778 | loop |
---|
779 | { |
---|
780 | for (i = pVariables; i; i--) |
---|
781 | { |
---|
782 | c = pGetExpDiff(p1, p2,i); |
---|
783 | if (c > 0) |
---|
784 | { |
---|
785 | pSetExp(m2,i,(c+pGetExp(a2,i))); |
---|
786 | pSetExp(m1,i,pGetExp(a1,i)); |
---|
787 | } |
---|
788 | else |
---|
789 | { |
---|
790 | pSetExp(m1,i,(pGetExp(a1,i)-c)); |
---|
791 | pSetExp(m2,i,pGetExp(a2,i)); |
---|
792 | } |
---|
793 | } |
---|
794 | if(c1==c2) |
---|
795 | { |
---|
796 | pSetComp(m1,pGetComp(a1)); |
---|
797 | pSetComp(m2,pGetComp(a2)); |
---|
798 | } |
---|
799 | else |
---|
800 | { |
---|
801 | if(c1!=0) |
---|
802 | { |
---|
803 | pSetComp(m1,pGetComp(a1)); |
---|
804 | pSetComp(m2,c1); |
---|
805 | } |
---|
806 | else |
---|
807 | { |
---|
808 | pSetComp(m2,pGetComp(a2)); |
---|
809 | pSetComp(m1,c2); |
---|
810 | } |
---|
811 | } |
---|
812 | pSetm(m1); |
---|
813 | pSetm(m2); |
---|
814 | cm = pComp0(m1, m2); |
---|
815 | if (cm!=0) |
---|
816 | { |
---|
817 | if(cm==1) |
---|
818 | { |
---|
819 | pFree1(m2); |
---|
820 | nNew(&(pGetCoeff(m1))); |
---|
821 | return m1; |
---|
822 | } |
---|
823 | else |
---|
824 | { |
---|
825 | pFree1(m1); |
---|
826 | nNew(&(pGetCoeff(m2))); |
---|
827 | return m2; |
---|
828 | } |
---|
829 | } |
---|
830 | t1 = nMult(pGetCoeff(a2),pGetCoeff(p1)); |
---|
831 | t2 = nMult(pGetCoeff(a1),pGetCoeff(p2)); |
---|
832 | equal = nEqual(t1,t2); |
---|
833 | nDelete(&t2); |
---|
834 | nDelete(&t1); |
---|
835 | if (!equal) |
---|
836 | { |
---|
837 | pFree1(m2); |
---|
838 | nNew(&(pGetCoeff(m1))); |
---|
839 | return m1; |
---|
840 | } |
---|
841 | pIter(a1); |
---|
842 | pIter(a2); |
---|
843 | if (a2==NULL) |
---|
844 | { |
---|
845 | pFree1(m2); |
---|
846 | if (a1==NULL) |
---|
847 | { |
---|
848 | pFree1(m1); |
---|
849 | return NULL; |
---|
850 | } |
---|
851 | goto x1; |
---|
852 | } |
---|
853 | if (a1==NULL) |
---|
854 | { |
---|
855 | pFree1(m1); |
---|
856 | goto x2; |
---|
857 | } |
---|
858 | } |
---|
859 | } |
---|
860 | |
---|