1 | // $Id: standard.lib,v 1.11 1998-05-18 13:24:50 Singular Exp $ |
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2 | /////////////////////////////////////////////////////////////////////////////// |
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3 | |
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4 | version="$Id: standard.lib,v 1.11 1998-05-18 13:24:50 Singular 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 | "; |
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11 | |
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12 | /////////////////////////////////////////////////////////////////////////////// |
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13 | |
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14 | proc stdfglm (ideal i, list #) |
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15 | "USAGE: stdfglm(i[,s]); i ideal, s string (any allowed ordstr of a ring) |
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16 | RETURN: stdfglm(i): standard basis of i in the basering, calculated via fglm |
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17 | from ordering \"dp\" to the ordering of the basering. |
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18 | stdfglm(i,s): standard basis of i in the basering, calculated via |
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19 | fglm from ordering s to the ordering of the basering. |
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20 | EXAMPLE: example stdfglm; shows an example" |
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21 | { |
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22 | string os; |
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23 | def dr= basering; |
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24 | if( (size(#)==0) or (typeof(#[1]) != "string") ) |
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25 | { |
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26 | os = "dp(" + string( nvars(dr) ) + ")"; |
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27 | if ( (find( ordstr(dr), os ) != 0) and (find( ordstr(dr), "a") == 0) ) |
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28 | { |
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29 | os= "Dp"; |
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30 | } |
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31 | else |
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32 | { |
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33 | os= "dp"; |
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34 | } |
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35 | } |
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36 | else { os = #[1]; } |
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37 | execute "ring sr=("+charstr(dr)+"),("+varstr(dr)+"),"+os+";"; |
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38 | ideal i= fetch(dr,i); |
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39 | intvec opt= option(get); |
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40 | option(redSB); |
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41 | i=std(i); |
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42 | option(set,opt); |
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43 | setring dr; |
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44 | return (fglm(sr,i)); |
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45 | } |
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46 | example |
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47 | { "EXAMPLE:"; echo = 2; |
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48 | ring r = 0,(x,y,z),lp; |
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49 | ideal i = y3+x2, x2y+x2, x3-x2, z4-x2-y; |
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50 | ideal i1= stdfglm(i); //uses fglm from "dp" to "lp" |
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51 | i1; |
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52 | ideal i2= stdfglm(i,"Dp"); //uses fglm from "Dp" to "lp" |
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53 | i2; |
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54 | } |
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55 | /////////////////////////////////////////////////////////////////////////////// |
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56 | |
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57 | proc stdhilb(ideal i,list #) |
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58 | "USAGE: stdhilb(i); i ideal |
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59 | stdhilb(i,v); i homogeneous ideal, v intvec (the Hilbert function) |
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60 | RETURN: stdhilb(i): a standard basis of i (computing v internally) |
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61 | stdhilb(i,v): standard basis of i, using the given Hilbert function |
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62 | EXAMPLE: example stdhilb; shows an example" |
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63 | { |
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64 | def R=basering; |
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65 | |
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66 | if((homog(i)==1)||(ordstr(basering)[1]=="d")) |
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67 | { |
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68 | if ((size(#)!=0)&&(homog(i)==1)) |
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69 | { |
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70 | return(std(i,#[1])); |
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71 | } |
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72 | return(std(i)); |
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73 | } |
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74 | |
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75 | execute "ring S = ("+charstr(R)+"),("+varstr(R)+",@t),dp;"; |
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76 | ideal i=homog(imap(R,i),@t); |
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77 | intvec v=hilb(std(i),1); |
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78 | execute "ring T = ("+charstr(R)+"),("+varstr(R)+",@t),("+ordstr(R)+");"; |
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79 | ideal i=fetch(S,i); |
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80 | ideal a=std(i,v); |
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81 | setring R; |
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82 | map phi=T,maxideal(1),1; |
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83 | ideal a=phi(a); |
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84 | |
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85 | int k,j; |
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86 | poly m; |
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87 | int c=size(i); |
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88 | |
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89 | for(j=1;j<c;j++) |
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90 | { |
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91 | if(deg(a[j])==0) |
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92 | { |
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93 | a=ideal(1); |
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94 | attrib(a,"isSB",1); |
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95 | return(a); |
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96 | } |
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97 | if(deg(a[j])>0) |
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98 | { |
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99 | m=lead(a[j]); |
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100 | for(k=j+1;k<=c;k++) |
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101 | { |
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102 | if(size(lead(a[k])/m)>0) |
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103 | { |
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104 | a[k]=0; |
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105 | } |
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106 | } |
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107 | } |
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108 | } |
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109 | a=simplify(a,2); |
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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 | example |
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114 | { "EXAMPLE:"; echo = 2; |
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115 | ring r = 0,(x,y,z),lp; |
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116 | ideal i = y3+x2, x2y+x2, x3-x2, z4-x2-y; |
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117 | ideal i1= stdhilb(i); i1; |
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118 | // is in this case equivalent to: |
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119 | intvec v=1,0,0,-3,0,1,0,3,-1,-1; |
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120 | ideal i2=stdhilb(i,v); |
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121 | } |
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122 | /////////////////////////////////////////////////////////////////////////////// |
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123 | |
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