1 | // $Id: standard.lib,v 1.32 1999-06-02 16:21:25 obachman Exp $ |
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2 | ////////////////////////////////////////////////////////////////////////////// |
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3 | |
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4 | version="$Id: standard.lib,v 1.32 1999-06-02 16:21:25 obachman Exp $"; |
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5 | info=" |
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6 | LIBRARY: standard.lib PROCEDURES WHICH ARE ALWAYS LOADED AT START-UP |
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7 | |
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8 | stdfglm(ideal[,ord]) standard basis of the ideal via fglm [and ordering ord] |
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9 | stdhilb(ideal) standard basis of the ideal using the Hilbert function |
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10 | groebner(ideal/module) standard basis of ideal or module using a |
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11 | heuristically choosen method |
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12 | quot(any,any[,n]) a general quotient procedure calling several algorithms |
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13 | allows module/module, ideal/ideal, module/ideal and a |
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14 | pre-definition of the algorithm by the parameter n |
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15 | quotient1(m1,m2) computes quotients by every vector of m2 and intersects them |
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16 | quotient2(m1,m2) a heuristic variant: the quotient is just defined by a |
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17 | (not really) general element of m2 which has to be proved |
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18 | quotient3(m1,m2) the homogeneous variant of quotient5(m1,m2) |
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19 | quotient4(m1,m2) the same as quotient5(m1,m2) using the modulo-command |
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20 | instead of the quotient-command from the kernel |
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21 | quotient5(m1,m2) computes with a real general element of m2 by adjoining |
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22 | a new variable |
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23 | sprintf(fmt,...) returns fomatted string |
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24 | fprintf(link,fmt,..) writes formatted string to link |
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25 | printf(fmt,...) displays formatted string |
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26 | "; |
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27 | |
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28 | ////////////////////////////////////////////////////////////////////////////// |
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29 | |
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30 | proc stdfglm (ideal i, list #) |
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31 | "USAGE: stdfglm(i[,s]); i ideal, s string (any allowed ordstr of a ring) |
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32 | RETURN: stdfglm(i): standard basis of i in the basering, calculated via fglm |
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33 | from ordering \"dp\" to the ordering of the basering. |
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34 | stdfglm(i,s): standard basis of i in the basering, calculated via |
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35 | fglm from ordering s to the ordering of the basering. |
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36 | EXAMPLE: example stdfglm; shows an example" |
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37 | { |
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38 | string os; |
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39 | def dr= basering; |
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40 | if( (size(#)==0) or (typeof(#[1]) != "string") ) |
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41 | { |
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42 | os = "dp(" + string( nvars(dr) ) + ")"; |
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43 | if ( (find( ordstr(dr), os ) != 0) and (find( ordstr(dr), "a") == 0) ) |
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44 | { |
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45 | os= "Dp"; |
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46 | } |
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47 | else |
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48 | { |
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49 | os= "dp"; |
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50 | } |
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51 | } |
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52 | else { os = #[1]; } |
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53 | execute "ring sr=("+charstr(dr)+"),("+varstr(dr)+"),"+os+";"; |
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54 | ideal i= fetch(dr,i); |
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55 | intvec opt= option(get); |
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56 | option(redSB); |
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57 | i=std(i); |
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58 | option(set,opt); |
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59 | setring dr; |
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60 | return (fglm(sr,i)); |
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61 | } |
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62 | example |
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63 | { "EXAMPLE:"; echo = 2; |
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64 | ring r = 0,(x,y,z),lp; |
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65 | ideal i = y3+x2, x2y+x2, x3-x2, z4-x2-y; |
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66 | ideal i1= stdfglm(i); //uses fglm from "dp" to "lp" |
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67 | i1; |
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68 | ideal i2= stdfglm(i,"Dp"); //uses fglm from "Dp" to "lp" |
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69 | i2; |
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70 | } |
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71 | ///////////////////////////////////////////////////////////////////////////// |
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72 | |
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73 | proc stdhilb(ideal i,list #) |
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74 | "USAGE: stdhilb(i); i ideal |
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75 | stdhilb(i,v); i homogeneous ideal, v intvec (the Hilbert function) |
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76 | RETURN: stdhilb(i): a standard basis of i (computing v internally) |
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77 | stdhilb(i,v): standard basis of i, using the given Hilbert function |
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78 | EXAMPLE: example stdhilb; shows an example" |
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79 | { |
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80 | def R=basering; |
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81 | |
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82 | if((homog(i)==1)||(ordstr(basering)[1]=="d")) |
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83 | { |
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84 | if ((size(#)!=0)&&(homog(i)==1)) |
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85 | { |
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86 | return(std(i,#[1])); |
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87 | } |
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88 | return(std(i)); |
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89 | } |
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90 | |
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91 | execute "ring S = ("+charstr(R)+"),("+varstr(R)+",@t),dp;"; |
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92 | ideal i=homog(imap(R,i),@t); |
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93 | intvec v=hilb(std(i),1); |
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94 | execute "ring T = ("+charstr(R)+"),("+varstr(R)+",@t),("+ordstr(R)+");"; |
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95 | ideal i=fetch(S,i); |
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96 | ideal a=std(i,v); |
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97 | setring R; |
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98 | map phi=T,maxideal(1),1; |
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99 | ideal a=phi(a); |
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100 | |
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101 | int k,j; |
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102 | poly m; |
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103 | int c=size(i); |
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104 | |
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105 | for(j=1;j<c;j++) |
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106 | { |
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107 | if(deg(a[j])==0) |
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108 | { |
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109 | a=ideal(1); |
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110 | attrib(a,"isSB",1); |
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111 | return(a); |
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112 | } |
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113 | if(deg(a[j])>0) |
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114 | { |
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115 | m=lead(a[j]); |
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116 | for(k=j+1;k<=c;k++) |
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117 | { |
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118 | if(size(lead(a[k])/m)>0) |
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119 | { |
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120 | a[k]=0; |
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121 | } |
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122 | } |
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123 | } |
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124 | } |
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125 | a=simplify(a,2); |
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126 | attrib(a,"isSB",1); |
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127 | return(a); |
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128 | } |
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129 | example |
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130 | { "EXAMPLE:"; echo = 2; |
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131 | ring r = 0,(x,y,z),lp; |
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132 | ideal i = y3+x2, x2y+x2, x3-x2, z4-x2-y; |
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133 | ideal i1= stdhilb(i); i1; |
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134 | // is in this case equivalent to: |
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135 | intvec v=1,0,0,-3,0,1,0,3,-1,-1; |
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136 | ideal i2=stdhilb(i,v); |
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137 | } |
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138 | ////////////////////////////////////////////////////////////////////////// |
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139 | |
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140 | proc groebner(def i, list #) |
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141 | "USAGE: groebner(i[, wait]) i -- ideal/module; wait -- int |
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142 | RETURNS: Standard basis of ideal or module which is computed using a |
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143 | heuristically choosen method: |
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144 | If the ordering of the current ring is a local ordering, or |
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145 | if it is a non-block ordering and the current ring has no |
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146 | parameters, then std(i) is returned. |
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147 | Otherwise, i is mapped into a ring with no parameters and |
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148 | ordering dp, where its Hilbert series is computed. This is |
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149 | followed by a Hilbert-series based std computation in the |
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150 | original ring. |
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151 | NOTE: If a 2nd argument 'wait' is given, then the computation proceeds |
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152 | at most 'wait' seconds. That is, if no result could be computed in |
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153 | 'wait' seconds, then the computation is interrupted, 0 is returned, |
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154 | a warning message is displayed, and the global variable |
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155 | 'groebner_error' is defined. |
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156 | EXAMPLE: example groebner; shows an example" |
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157 | { |
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158 | def P=basering; |
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159 | |
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160 | // we have two arguments -- try to use MPfork links |
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161 | if (size(#) > 0) |
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162 | { |
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163 | if (system("with", "MP")) |
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164 | { |
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165 | if (typeof(#[1]) == "int") |
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166 | { |
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167 | int wait = #[1]; |
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168 | int j = 10; |
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169 | |
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170 | string bs = nameof(basering); |
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171 | link l_fork = "MPtcp:fork"; |
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172 | open(l_fork); |
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173 | write(l_fork, quote(system("pid"))); |
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174 | int pid = read(l_fork); |
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175 | write(l_fork, quote(groebner(eval(i)))); |
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176 | |
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177 | // sleep in small intervalls for appr. one second |
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178 | if (wait > 0) |
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179 | { |
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180 | while(j < 1000000) |
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181 | { |
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182 | if (status(l_fork, "read", "ready", j)) {break;} |
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183 | j = j + j; |
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184 | } |
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185 | } |
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186 | |
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187 | // sleep in intervalls of one second from now on |
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188 | j = 1; |
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189 | while (j < wait) |
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190 | { |
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191 | if (status(l_fork, "read", "ready", 1000000)) {break;} |
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192 | j = j + 1; |
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193 | } |
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194 | |
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195 | if (status(l_fork, "read", "ready")) |
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196 | { |
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197 | def result = read(l_fork); |
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198 | if (bs != nameof(basering)) |
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199 | { |
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200 | def PP = basering; |
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201 | setring P; |
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202 | def result = imap(PP, result); |
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203 | kill PP; |
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204 | } |
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205 | if (defined(groebner_error)) |
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206 | { |
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207 | kill(groebner_error); |
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208 | } |
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209 | kill (l_fork); |
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210 | } |
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211 | else |
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212 | { |
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213 | ideal result; |
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214 | if (! defined(groebner_error)) |
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215 | { |
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216 | int groebner_error = 1; |
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217 | export groebner_error; |
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218 | } |
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219 | "// ** groebner did not finish"; |
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220 | j = system("sh", "kill " + string(pid)); |
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221 | } |
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222 | return (result); |
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223 | } |
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224 | else |
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225 | { |
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226 | "// ** groebner needs int as 2nd arg"; |
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227 | } |
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228 | } |
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229 | else |
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230 | { |
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231 | "// ** groebner with two args is not supported in this configuration"; |
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232 | } |
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233 | } |
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234 | |
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235 | // we are still here -- do the actual computation |
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236 | string ordstr_P = ordstr(P); |
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237 | if (find(ordstr_P,"s") > 0) |
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238 | { |
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239 | //spaeter den lokalen fall ueber lp oder aehnlich behandeln |
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240 | return(std(i)); |
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241 | } |
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242 | |
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243 | int IsSimple_P; |
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244 | if (system("nblocks") <= 2) |
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245 | { |
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246 | if (find(ordstr_P, "M") <= 0) |
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247 | { |
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248 | IsSimple_P = 1; |
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249 | } |
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250 | } |
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251 | int npars_P = npars(P); |
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252 | |
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253 | // return std if no parameters and (dp or wp) |
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254 | if ((npars_P <= 1) && IsSimple_P) |
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255 | { |
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256 | if (find(ordstr_P, "d") > 0) |
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257 | { |
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258 | return (std(i)); |
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259 | } |
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260 | if (find(ordstr_P,"w") > 0) |
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261 | { |
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262 | return (std(i)); |
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263 | } |
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264 | } |
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265 | |
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266 | // reset options |
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267 | intvec opt=option(get); |
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268 | int p_opt; |
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269 | string s_opt = option(); |
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270 | option(none); |
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271 | // turn on option(prot) and/or option(mem), if previously set |
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272 | if (find(s_opt, "prot")) |
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273 | { |
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274 | option(prot); |
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275 | p_opt = 1; |
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276 | } |
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277 | if (find(s_opt, "mem")) |
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278 | { |
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279 | option(mem); |
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280 | } |
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281 | |
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282 | // construct ring in which first std computation is done |
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283 | string varstr_P = varstr(P); |
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284 | string parstr_P = parstr(P); |
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285 | int is_homog = (homog(i) && (npars_P <= 1)); |
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286 | int add_vars = 0; |
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287 | string ri = "ring Phelp ="; |
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288 | |
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289 | // more than one parameters are converted to ring variables |
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290 | if (npars_P > 1) |
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291 | { |
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292 | ri = ri + string(char(P)) + ",(" + varstr_P + "," + parstr_P; |
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293 | add_vars = npars_P; |
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294 | } |
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295 | else |
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296 | { |
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297 | ri = ri + "(" + charstr(P) + "),(" + varstr_P; |
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298 | } |
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299 | |
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300 | // a homogenizing variable is added, if necessary |
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301 | if (! is_homog) |
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302 | { |
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303 | ri = ri + ",@t"; |
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304 | add_vars = add_vars + 1; |
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305 | } |
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306 | // ordering is set to (dp, C) |
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307 | ri = ri + "),(dp,C);"; |
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308 | |
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309 | // change the ring |
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310 | execute(ri); |
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311 | |
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312 | // get ideal from previous ring |
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313 | if (is_homog) |
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314 | { |
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315 | ideal qh = imap(P, i); |
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316 | } |
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317 | else |
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318 | { |
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319 | // and homogenize |
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320 | ideal qh=homog(imap(P,i),@t); |
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321 | } |
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322 | |
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323 | // compute std and hilbert series |
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324 | if (p_opt) |
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325 | { |
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326 | "std in " + ri[13, size(ri) - 13]; |
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327 | } |
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328 | ideal qh1=std(qh); |
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329 | intvec hi=hilb(qh1,1); |
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330 | |
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331 | if (add_vars == 0) |
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332 | { |
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333 | // no additional variables were introduced |
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334 | setring P; // can immediately change to original ring |
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335 | // simply compute std with hilbert series in original ring |
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336 | if (p_opt) |
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337 | { |
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338 | "std with hilb in basering"; |
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339 | } |
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340 | i = std(i, hi); |
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341 | } |
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342 | else |
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343 | { |
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344 | // additional variables were introduced |
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345 | // need another intermediate ring |
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346 | ri = "ring Phelp1 = (" + charstr(Phelp) |
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347 | + "),(" + varstr(Phelp) + "),(" + ordstr_P; |
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348 | |
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349 | // for lp wit at most one parameter, we do not need a block ordering |
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350 | if ( ! (IsSimple_P && (add_vars <2) && find(ordstr_P, "l"))) |
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351 | { |
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352 | // need block ordering |
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353 | ri = ri + ", dp(" + string(add_vars) + ")"; |
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354 | } |
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355 | ri = ri + ");"; |
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356 | |
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357 | // change to intermediate ring |
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358 | execute(ri); |
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359 | ideal qh = imap(Phelp, qh); |
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360 | kill Phelp; |
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361 | if (p_opt) |
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362 | { |
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363 | "std with hilb in " + ri[14,size(ri)-14]; |
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364 | } |
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365 | // compute std with Hilbert series |
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366 | qh = std(qh, hi); |
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367 | // subst 1 for homogenizing var |
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368 | if (!is_homog) |
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369 | { |
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370 | if (p_opt) |
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371 | { |
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372 | "dehomogenization"; |
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373 | } |
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374 | qh = subst(qh, @t, 1); |
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375 | } |
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376 | |
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377 | // go back to original ring |
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378 | setring P; |
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379 | // get ideal, delete zeros and clean SB |
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380 | if (p_opt) |
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381 | { |
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382 | "imap to original ring"; |
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383 | } |
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384 | i = imap(Phelp1,qh); |
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385 | if (p_opt) |
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386 | { |
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387 | "simplification"; |
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388 | } |
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389 | i = simplify(i, 34); |
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390 | kill Phelp1; |
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391 | } |
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392 | |
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393 | // clean-up time |
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394 | option(set, opt); |
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395 | if (find(s_opt, "redSB") > 0) |
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396 | { |
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397 | if (p_opt) |
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398 | { |
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399 | "interreduction"; |
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400 | } |
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401 | i=interred(i); |
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402 | } |
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403 | attrib(i, "isSB", 1); |
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404 | return (i); |
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405 | } |
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406 | example |
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407 | { |
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408 | "EXAMPLE: "; echo = 2; |
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409 | ring r = 0, (a,b,c,d), lp; |
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410 | option(prot); |
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411 | ideal i = a+b+c+d, ab+ad+bc+cd, abc+abd+acd+bcd, abcd-1; // cyclic 4 |
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412 | groebner(i); |
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413 | ring rp = (0, a, b), (c,d), lp; |
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414 | ideal i = imap(r, i); |
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415 | ideal j = groebner(i); |
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416 | option(noprot); |
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417 | j; simplify(j, 1); std(i); |
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418 | if (system("with", "MP")) {groebner(i, 0);} |
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419 | defined(groebner_error); |
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420 | } |
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421 | |
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422 | |
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423 | ////////////////////////////////////////////////////////////////////////// |
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424 | proc res(list #) |
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425 | { |
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426 | def P=basering; |
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427 | def m=#[1]; //the ideal or module |
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428 | |
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429 | int i=#[2]; //the length of the resolution |
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430 | //if size(#)>2 a minimal resolution is computed |
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431 | |
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432 | string varstr_P = varstr(P); |
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433 | |
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434 | //LaScala for the homogeneous case |
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435 | if(homog(m)==1) |
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436 | { |
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437 | resolution re; |
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438 | if ((i==0) or (i>=nvars(basering))) |
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439 | { |
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440 | re=lres(m,i); |
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441 | if(size(#)>2) |
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442 | { |
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443 | re=minres(re); |
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444 | } |
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445 | } |
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446 | else |
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447 | { |
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448 | if(size(#)>2) |
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449 | { |
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450 | re=mres(m,i); |
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451 | } |
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452 | else |
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453 | { |
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454 | re=sres(std(m),i); |
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455 | } |
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456 | } |
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457 | return(re); |
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458 | } |
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459 | |
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460 | //mres for the global non homogeneous case |
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461 | if(find(ordstr(P),"s")==0) |
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462 | { |
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463 | string ri= "ring Phelp =" |
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464 | +string(char(P))+",("+varstr_P+"),(dp,C);"; |
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465 | execute(ri); |
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466 | def m=imap(P,m); |
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467 | list re=mres(m,i); |
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468 | setring P; |
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469 | resolution result=imap(Phelp,re); |
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470 | return(result); |
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471 | } |
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472 | |
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473 | //sres for the local case and not minimal resolution |
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474 | if(size(#)<=2) |
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475 | { |
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476 | string ri= "ring Phelp =" |
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477 | +string(char(P))+",("+varstr_P+"),(ls,c);"; |
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478 | execute(ri); |
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479 | def m=imap(P,m); |
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480 | m=std(m); |
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481 | list re=sres(m,i); |
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482 | setring P; |
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483 | resolution result=imap(Phelp,re); |
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484 | return(result); |
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485 | } |
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486 | |
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487 | //mres for the local case and minimal resolution |
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488 | string ri= "ring Phelp =" |
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489 | +string(char(P))+",("+varstr_P+"),(ls,C);"; |
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490 | execute(ri); |
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491 | def m=imap(P,m); |
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492 | list re=mres(m,i); |
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493 | setring P; |
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494 | resolution result=imap(Phelp,re); |
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495 | return(result); |
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496 | } |
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497 | |
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498 | proc quot (m1,m2,list #) |
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499 | "USAGE: quot(m1, m2[, n]); m1, m2 two submodules of k^s, |
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500 | n (optional) integer (1<= n <=5) |
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501 | RETURN: the quotient of m1 and m2 |
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502 | EXAMPLE: example quot; shows an example" |
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503 | { |
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504 | if (((typeof(m1)!="ideal") and (typeof(m1)!="module")) |
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505 | or ((typeof(m2)!="ideal") and (typeof(m2)!="module"))) |
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506 | { |
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507 | "USAGE: quot(m1, m2[, n]); m1, m2 two submodules of k^s,"; |
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508 | " n (optional) integer (1<= n <=5)"; |
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509 | "RETURN: the quotient of m1 and m2"; |
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510 | "EXAMPLE: example quot; shows an example"; |
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511 | return(); |
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512 | } |
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513 | if (typeof(m1)!=typeof(m2)) |
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514 | { |
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515 | return(quotient(m1,m2)); |
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516 | } |
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517 | if (size(#)>0) |
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518 | { |
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519 | if (typeof(#[1])=="int" ) |
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520 | { |
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521 | return(quot1(m1,m2,#[1])); |
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522 | } |
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523 | } |
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524 | else |
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525 | { |
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526 | return(quot1(m1,m2,2)); |
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527 | } |
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528 | } |
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529 | example |
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530 | { "EXAMPLE:"; echo = 2; |
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531 | ring r=181,(x,y,z),(c,ls); |
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532 | ideal id1=maxideal(4); |
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533 | ideal id2=x2+xyz,y2-z3y,z3+y5xz; |
---|
534 | option(prot); |
---|
535 | ideal id6=quotient(id1,id2); |
---|
536 | id6; |
---|
537 | ideal id7=quot(id1,id2,1); |
---|
538 | id7; |
---|
539 | ideal id8=quot(id1,id2,2); |
---|
540 | id8; |
---|
541 | } |
---|
542 | |
---|
543 | static proc quot1 (module m1, module m2,int n) |
---|
544 | "USAGE: quot1(m1, m2, n); m1, m2 two submodules of k^s, |
---|
545 | n integer (1<= n <=5) |
---|
546 | RETURN: the quotient of m1 and m2 |
---|
547 | EXAMPLE: example quot1; shows an example" |
---|
548 | { |
---|
549 | if (n==1) |
---|
550 | { |
---|
551 | return(quotient1(m1,m2)); |
---|
552 | } |
---|
553 | else |
---|
554 | { |
---|
555 | if (n==2) |
---|
556 | { |
---|
557 | return(quotient2(m1,m2)); |
---|
558 | } |
---|
559 | else |
---|
560 | { |
---|
561 | if (n==3) |
---|
562 | { |
---|
563 | return(quotient3(m1,m2)); |
---|
564 | } |
---|
565 | else |
---|
566 | { |
---|
567 | if (n==4) |
---|
568 | { |
---|
569 | return(quotient4(m1,m2)); |
---|
570 | } |
---|
571 | else |
---|
572 | { |
---|
573 | if (n==5) |
---|
574 | { |
---|
575 | return(quotient5(m1,m2)); |
---|
576 | } |
---|
577 | else |
---|
578 | { |
---|
579 | return(quotient(m1,m2)); |
---|
580 | } |
---|
581 | } |
---|
582 | } |
---|
583 | } |
---|
584 | } |
---|
585 | } |
---|
586 | example |
---|
587 | { "EXAMPLE:"; echo = 2; |
---|
588 | ring r=181,(x,y,z),(c,ls); |
---|
589 | ideal id1=maxideal(4); |
---|
590 | ideal id2=x2+xyz,y2-z3y,z3+y5xz; |
---|
591 | option(prot); |
---|
592 | ideal id6=quotient(id1,id2); |
---|
593 | id6; |
---|
594 | ideal id7=quot1(id1,id2,1); |
---|
595 | id7; |
---|
596 | ideal id8=quot1(id1,id2,2); |
---|
597 | id8; |
---|
598 | } |
---|
599 | |
---|
600 | static proc quotient0(module a,module b) |
---|
601 | { |
---|
602 | module mm=b+a; |
---|
603 | resolution rs=lres(mm,0); |
---|
604 | list I=list(rs); |
---|
605 | matrix M=I[2]; |
---|
606 | matrix A[1][nrows(M)]=M[1..nrows(M),1]; |
---|
607 | ideal i=A; |
---|
608 | return (i); |
---|
609 | } |
---|
610 | proc quotient1(module a,module b) //17sec |
---|
611 | "USAGE: quotient1(m1, m2); m1, m2 two submodules of k^s, |
---|
612 | RETURN: the quotient of m1 and m2" |
---|
613 | { |
---|
614 | int i; |
---|
615 | a=std(a); |
---|
616 | module dummy; |
---|
617 | module B=NF(b,a)+dummy; |
---|
618 | ideal re=quotient(a,module(B[1])); |
---|
619 | for(i=2;i<=size(B);i++) |
---|
620 | { |
---|
621 | re=intersect1(re,quotient(a,module(B[i]))); |
---|
622 | } |
---|
623 | return(re); |
---|
624 | } |
---|
625 | proc quotient2(module a,module b) //13sec |
---|
626 | "USAGE: quotient2(m1, m2); m1, m2 two submodules of k^s, |
---|
627 | RETURN: the quotient of m1 and m2" |
---|
628 | { |
---|
629 | a=std(a); |
---|
630 | module dummy; |
---|
631 | module bb=NF(b,a)+dummy; |
---|
632 | int i=size(bb); |
---|
633 | ideal re=quotient(a,module(bb[i])); |
---|
634 | bb[i]=0; |
---|
635 | module temp; |
---|
636 | module temp1; |
---|
637 | module bbb; |
---|
638 | int mx; |
---|
639 | i=i-1; |
---|
640 | while (1) |
---|
641 | { |
---|
642 | if (i==0) break; |
---|
643 | temp = a+bb*re; |
---|
644 | temp1 = lead(interred(temp)); |
---|
645 | mx=ncols(a); |
---|
646 | if (ncols(temp1)>ncols(a)) |
---|
647 | { |
---|
648 | mx=ncols(temp1); |
---|
649 | } |
---|
650 | temp1 = matrix(temp1,1,mx)-matrix(lead(a),1,mx); |
---|
651 | temp1 = dummy+temp1; |
---|
652 | if (deg(temp1[1])<0) break; |
---|
653 | re=intersect1(re,quotient(a,module(bb[i]))); |
---|
654 | bb[i]=0; |
---|
655 | i = i-1; |
---|
656 | } |
---|
657 | return(re); |
---|
658 | } |
---|
659 | proc quotient3(module a,module b) //89sec |
---|
660 | "USAGE: quotient3(m1, m2); m1, m2 two submodules of k^s, |
---|
661 | only for global rings |
---|
662 | RETURN: the quotient of m1 and m2" |
---|
663 | { |
---|
664 | string s="ring @newr=("+charstr(basering)+ |
---|
665 | "),("+varstr(basering)+",@t,@w),dp;"; |
---|
666 | def @newP=basering; |
---|
667 | execute s; |
---|
668 | module b=imap(@newP,b); |
---|
669 | module a=imap(@newP,a); |
---|
670 | int i; |
---|
671 | int j=size(b); |
---|
672 | vector @b; |
---|
673 | for(i=1;i<=j;i++) |
---|
674 | { |
---|
675 | @b=@b+@t^(i-1)*@w^(j-i+1)*b[i]; |
---|
676 | } |
---|
677 | ideal re=quotient(a,module(@b)); |
---|
678 | setring @newP; |
---|
679 | ideal re=imap(@newr,re); |
---|
680 | return(re); |
---|
681 | } |
---|
682 | proc quotient5(module a,module b) //89sec |
---|
683 | "USAGE: quotient5(m1, m2); m1, m2 two submodules of k^s, |
---|
684 | only for global rings |
---|
685 | RETURN: the quotient of m1 and m2" |
---|
686 | { |
---|
687 | string s="ring @newr=("+charstr(basering)+ |
---|
688 | "),("+varstr(basering)+",@t),dp;"; |
---|
689 | def @newP=basering; |
---|
690 | execute s; |
---|
691 | module b=imap(@newP,b); |
---|
692 | module a=imap(@newP,a); |
---|
693 | int i; |
---|
694 | int j=size(b); |
---|
695 | vector @b; |
---|
696 | for(i=1;i<=j;i++) |
---|
697 | { |
---|
698 | @b=@b+@t^(i-1)*b[i]; |
---|
699 | } |
---|
700 | @b=homog(@b,@w); |
---|
701 | ideal re=quotient(a,module(@b)); |
---|
702 | setring @newP; |
---|
703 | ideal re=imap(@newr,re); |
---|
704 | return(re); |
---|
705 | } |
---|
706 | proc quotient4(module a,module b) //95sec |
---|
707 | "USAGE: quotient4(m1, m2); m1, m2 two submodules of k^s, |
---|
708 | only for global rings |
---|
709 | RETURN: the quotient of m1 and m2" |
---|
710 | { |
---|
711 | string s="ring @newr=("+charstr(basering)+ |
---|
712 | "),("+varstr(basering)+",@t),dp;"; |
---|
713 | def @newP=basering; |
---|
714 | execute s; |
---|
715 | module b=imap(@newP,b); |
---|
716 | module a=imap(@newP,a); |
---|
717 | int i; |
---|
718 | vector @b=b[1]; |
---|
719 | for(i=2;i<=size(b);i++) |
---|
720 | { |
---|
721 | @b=@b+@t^(i-1)*b[i]; |
---|
722 | } |
---|
723 | matrix sy=modulo(@b,a); |
---|
724 | ideal re=sy; |
---|
725 | setring @newP; |
---|
726 | ideal re=imap(@newr,re); |
---|
727 | return(re); |
---|
728 | } |
---|
729 | static proc intersect1(ideal i,ideal j) |
---|
730 | { |
---|
731 | def R=basering; |
---|
732 | execute "ring gnir = ("+charstr(basering)+"), |
---|
733 | ("+varstr(basering)+",@t),(C,dp);"; |
---|
734 | ideal i=var(nvars(basering))*imap(R,i)+(var(nvars(basering))-1)*imap(R,j); |
---|
735 | ideal j=eliminate(i,var(nvars(basering))); |
---|
736 | setring R; |
---|
737 | map phi=gnir,maxideal(1); |
---|
738 | return(phi(j)); |
---|
739 | } |
---|
740 | |
---|
741 | ////////////////////////////////////////////////////////////////// |
---|
742 | /// |
---|
743 | /// sprintf, fprintf printf |
---|
744 | /// |
---|
745 | proc sprintf(string fmt, list #) |
---|
746 | "USAGE: sprintf(fmt, ...) fmt string |
---|
747 | RETURN: string |
---|
748 | PURPOSE: sprintf performs output formatting. The first argument is a format |
---|
749 | control string. Additional arguments may be required, depending on |
---|
750 | the contents of the control string. A series of output characters is |
---|
751 | generated as directed by the control string; these characters are |
---|
752 | returned as a string. The control string is simply text to be copied, |
---|
753 | except that the string may contain conversion specifications. Do |
---|
754 | 'help print:' for a listing of valid conversion specifications. |
---|
755 | As an addition to the conversions of 'print', the '%n' and '%2' |
---|
756 | conversion specification does not consume an additional argument, |
---|
757 | but simply generates a newline character. |
---|
758 | NOTE: If one of the additional arguments is a list, then it should be |
---|
759 | enclosed once more into a list() command, since passing a list |
---|
760 | as an argument flattens the list by one level. |
---|
761 | SEE ALSO: fprintf, printf, print, string |
---|
762 | EXAMPLE : example sprintf; shows an example |
---|
763 | " |
---|
764 | { |
---|
765 | int sfmt = size(fmt); |
---|
766 | if (sfmt <= 1) |
---|
767 | { |
---|
768 | return (fmt); |
---|
769 | } |
---|
770 | int next, l, nnext; |
---|
771 | string ret; |
---|
772 | list formats = "%l", "%s", "%2l", "%2s", "%t", "%;", "%p", "%b", "%n", "%2"; |
---|
773 | while (1) |
---|
774 | { |
---|
775 | if (size(#) <= 0) |
---|
776 | { |
---|
777 | return (ret + fmt); |
---|
778 | } |
---|
779 | nnext = 0; |
---|
780 | while (nnext < sfmt) |
---|
781 | { |
---|
782 | nnext = find(fmt, "%", nnext + 1); |
---|
783 | if (nnext == 0) |
---|
784 | { |
---|
785 | next = 0; |
---|
786 | break; |
---|
787 | } |
---|
788 | l = 1; |
---|
789 | while (l <= size(formats)) |
---|
790 | { |
---|
791 | next = find(fmt, formats[l], nnext); |
---|
792 | if (next == nnext) break; |
---|
793 | l++; |
---|
794 | } |
---|
795 | if (next == nnext) break; |
---|
796 | } |
---|
797 | if (next == 0) |
---|
798 | { |
---|
799 | return (ret + fmt); |
---|
800 | } |
---|
801 | if (formats[l] != "%2" && formats[l] != "%n") |
---|
802 | { |
---|
803 | ret = ret + fmt[1, next - 1] + print(#[1], formats[l]); |
---|
804 | # = delete(#, 1); |
---|
805 | } |
---|
806 | else |
---|
807 | { |
---|
808 | ret = ret + fmt[1, next - 1] + print("", "%2s"); |
---|
809 | } |
---|
810 | if (size(fmt) <= (next + size(formats[l]) - 1)) |
---|
811 | { |
---|
812 | return (ret); |
---|
813 | } |
---|
814 | fmt = fmt[next + size(formats[l]), size(fmt)-next-size(formats[l]) + 1]; |
---|
815 | } |
---|
816 | } |
---|
817 | example |
---|
818 | { |
---|
819 | ring r=0,(x,y,z),dp; |
---|
820 | module m=[1,y],[0,x+z]; |
---|
821 | intmat M=betti(mres(m,0)); |
---|
822 | list l = r, m, M; |
---|
823 | string s = sprintf("s:%s,%n l:%l", 1, 2); s; |
---|
824 | s = sprintf("s:%n%s", l); s; |
---|
825 | s = sprintf("s:%2%s", list(l)); s; |
---|
826 | s = sprintf("2l:%n%2l", list(l)); s; |
---|
827 | s = sprintf("%p", list(l)); s; |
---|
828 | s = sprintf("%;", list(l)); s; |
---|
829 | s = sprintf("%b", M); s; |
---|
830 | } |
---|
831 | |
---|
832 | proc printf(string fmt, list #) |
---|
833 | "USAGE: printf(fmt, ...) fmt string |
---|
834 | RETURN: none |
---|
835 | PURPOSE: printf performs output formatting. The first argument is a format |
---|
836 | control string. Additional arguments may be required, depending on |
---|
837 | the contents of the control string. A series of output characters is |
---|
838 | generated as directed by the control string; these characters are |
---|
839 | displayed (i.e. printed to standard out). |
---|
840 | The control string is simply text to be copied, except that the |
---|
841 | string may contain conversion specifications. |
---|
842 | Do 'help print:' for a listing of valid conversion specifications. |
---|
843 | As an addition to the conversions of 'print', the '%n' and '%2' |
---|
844 | conversion specification does not consume an additional argument, |
---|
845 | but simply generates a newline character. |
---|
846 | |
---|
847 | NOTE: If one of the additional arguments is a list, then it should be |
---|
848 | enclosed once more into a list() command, since passing a list |
---|
849 | as an argument flattens the list by one level. |
---|
850 | SEE ALSO: sprintf, fprintf, print, string |
---|
851 | EXAMPLE : example printf; shows an example |
---|
852 | " |
---|
853 | { |
---|
854 | write("", sprintf(fmt, #)); |
---|
855 | } |
---|
856 | example |
---|
857 | { |
---|
858 | ring r=0,(x,y,z),dp; |
---|
859 | module m=[1,y],[0,x+z]; |
---|
860 | intmat M=betti(mres(m,0)); |
---|
861 | list l = r, m, M; |
---|
862 | printf("s:%s, l:%l", 1, 2); |
---|
863 | printf("s:%s", l); |
---|
864 | printf("s:%s", list(l)); |
---|
865 | printf("2l:%2l", list(l)); |
---|
866 | printf("%p", list(l)); |
---|
867 | printf("%;", list(l)); |
---|
868 | printf("%b", M); |
---|
869 | } |
---|
870 | |
---|
871 | |
---|
872 | proc fprintf(link l, string fmt, list #) |
---|
873 | "USAGE: fprintf(l, fmt, ...) l link; fmt string |
---|
874 | RETURN: none |
---|
875 | PURPOSE: fprintf performs output formatting. The second argument is a format |
---|
876 | control string. Additional arguments may be required, depending on |
---|
877 | the contents of the control string. A series of output characters is |
---|
878 | generated as directed by the control string; these characters are |
---|
879 | written to the link l. |
---|
880 | The control string is simply text to be copied, except that the |
---|
881 | string may contain conversion specifications. |
---|
882 | Do 'help print:' for a listing of valid conversion specifications. |
---|
883 | As an addition to the conversions of 'print', the '%n' and '%2' |
---|
884 | conversion specification does not consume an additional argument, |
---|
885 | but simply generates a newline character. |
---|
886 | |
---|
887 | NOTE: If one of the additional arguments is a list, then it should be |
---|
888 | enclosed once more into a list() command, since passing a list |
---|
889 | as an argument flattens the list by one level. |
---|
890 | SEE ALSO: sprintf, printf, print, string |
---|
891 | EXAMPLE : example fprintf; shows an example |
---|
892 | " |
---|
893 | { |
---|
894 | write(l, sprintf(fmt, #)); |
---|
895 | } |
---|
896 | example |
---|
897 | { |
---|
898 | ring r=0,(x,y,z),dp; |
---|
899 | module m=[1,y],[0,x+z]; |
---|
900 | intmat M=betti(mres(m,0)); |
---|
901 | list l = r, m, M; |
---|
902 | link li = ""; // link to stdout |
---|
903 | fprintf(li, "s:%s, l:%l", 1, 2); |
---|
904 | fprintf(li, "s:%s", l); |
---|
905 | fprintf(li, "s:%s", list(l)); |
---|
906 | fprintf(li, "2l:%2l", list(l)); |
---|
907 | fprintf(li, "%p", list(l)); |
---|
908 | fprintf(li, "%;", list(l)); |
---|
909 | fprintf(li, "%b", M); |
---|
910 | } |
---|
911 | |
---|
912 | |
---|
913 | |
---|
914 | |
---|
915 | |
---|
916 | |
---|
917 | /* |
---|
918 | proc minres(list #) |
---|
919 | { |
---|
920 | if (size(#) == 2) |
---|
921 | { |
---|
922 | if (typeof(#[1]) == "ideal" || typeof(#[1]) == "module") |
---|
923 | { |
---|
924 | if (typeof(#[2] == "int")) |
---|
925 | { |
---|
926 | return (res(#[1],#[2],1)); |
---|
927 | } |
---|
928 | } |
---|
929 | } |
---|
930 | |
---|
931 | if (typeof(#[1]) == "resolution") |
---|
932 | { |
---|
933 | return minimizeres(#[1]); |
---|
934 | } |
---|
935 | else |
---|
936 | { |
---|
937 | return minimizeres(#); |
---|
938 | } |
---|
939 | |
---|
940 | } |
---|
941 | |
---|
942 | */ |
---|