1 | // $Id: ring.lib,v 1.4 1997-09-12 08:18:04 Singular Exp $ |
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2 | //(GMG, last modified 03.11.95) |
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3 | /////////////////////////////////////////////////////////////////////////////// |
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4 | |
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5 | LIBRARY: ring.lib PROCEDURES FOR MANIPULATING RINGS AND MAPS |
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6 | |
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7 | changechar("R",c[,r]); make a copy R of basering [ring r] with new char c |
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8 | changeord("R",o[,r]); make a copy R of basering [ring r] with new ord o |
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9 | changevar("R",v[,r]); make a copy R of basering [ring r] with new vars v |
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10 | defring("R",c,n,v,o); define a ring R in specified char c, n vars v, ord o |
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11 | defrings(n[,p]); define ring Sn in n vars, char 32003 [p], ord ds |
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12 | defringp(n[,p]); define ring Pn in n vars, char 32003 [p], ord dp |
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13 | extendring("R",n,v,o); extend given ring by n vars v, ord o and name it R |
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14 | fetchall(R[,str]); fetch all objects of ring R to basering |
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15 | imapall(R[,str]); imap all objects of ring R to basering |
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16 | mapall(R,i[,str]); map all objects of ring R via ideal i to basering |
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17 | ringtensor("R",s,t,..);create ring R, tensor product of rings s,t,... |
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18 | (parameters in square brackets [] are optional) |
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19 | |
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20 | LIB "inout.lib"; |
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21 | LIB "general.lib"; |
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22 | /////////////////////////////////////////////////////////////////////////////// |
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23 | |
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24 | proc changechar (string newr, string c, list #) |
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25 | USAGE: changechar(newr,c[,r]); newr,c=strings, r=ring |
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26 | CREATE: create a new ring with name `newr` and make it the basering if r is |
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27 | an existing ring [default: r=basering]. |
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28 | The new ring differs from the old ring only in the characteristic. |
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29 | If, say, (newr,c) = ("R","0,A") and the ring r exists, the new |
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30 | basering will have name R characteristic 0 and one parameter A. |
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31 | RETURN: No return value |
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32 | NOTE: Works for qrings if map from old_char to new_char is implemented |
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33 | This proc uses 'execute' or calls a procedure using 'execute'. |
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34 | If you use it in your own proc, let the local names of your proc |
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35 | start with @ (see the file HelpForProc) |
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36 | EXAMPLE: example changechar; shows an example |
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37 | { |
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38 | if( size(#)==0 ) { def @r=basering; } |
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39 | if( size(#)==1 ) { def @r=#[1]; } |
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40 | setring @r; |
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41 | ideal i = ideal(@r); int @q = size(i); |
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42 | if( @q!=0 ) |
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43 | { string @s = "@newr1"; } |
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44 | else |
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45 | { string @s = newr; } |
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46 | string @newring = @s+"=("+c+"),("+varstr(@r)+"),("+ordstr(@r)+");"; |
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47 | execute("ring "+@newring); |
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48 | if( @q!=0 ) |
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49 | { |
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50 | map phi = @r,maxideal(1); |
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51 | ideal i = phi(i); |
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52 | attrib(i,"isSB",1); //*** attrib funktioniert ? |
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53 | execute("qring "+newr+"=i;"); |
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54 | } |
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55 | export(`newr`); |
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56 | keepring(`newr`); |
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57 | if (voice==2) { "// basering is now",newr; } |
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58 | return(); |
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59 | } |
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60 | example |
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61 | { "EXAMPLE:"; echo = 2; |
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62 | ring r=0,(x,y,u,v),(dp(2),ds); |
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63 | changechar("R","2,A"); R;""; |
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64 | changechar("R1","32003",R); R1; |
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65 | kill R,R1; |
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66 | } |
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67 | /////////////////////////////////////////////////////////////////////////////// |
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68 | |
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69 | proc changeord (string newr, string o, list #) |
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70 | USAGE: changeord(newr,o[,r]); newr,o=strings, r=ring/qring |
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71 | CREATE: create a new ring with name `newr` and make it the basering if r is |
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72 | an existing ring/qring [default: r=basering]. |
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73 | The new ring differs from the old ring only in the ordering. If, say, |
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74 | (newr,o) = ("R","wp(2,3),dp") and the ring r exists and has >=3 |
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75 | variables, the new basering will have name R and ordering wp(2,3),dp. |
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76 | RETURN: No return value |
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77 | NOTE: This proc uses 'execute' or calls a procedure using 'execute'. |
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78 | If you use it in your own proc, let the local names of your proc |
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79 | start with @ (see the file HelpForProc) |
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80 | EXAMPLE: example changeord; shows an example |
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81 | { |
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82 | if( size(#)==0 ) { def @r=basering; } |
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83 | if( size(#)==1 ) { def @r=#[1]; } |
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84 | setring @r; |
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85 | ideal i = ideal(@r); int @q = size(i); |
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86 | if( @q!=0 ) |
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87 | { string @s = "@newr1"; } |
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88 | else |
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89 | { string @s = newr; } |
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90 | string @newring = @s+"=("+charstr(@r)+"),("+varstr(@r)+"),("+o+");"; |
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91 | execute("ring "+@newring); |
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92 | if( @q!=0 ) |
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93 | { |
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94 | map phi = @r,maxideal(1); |
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95 | ideal i = phi(i); |
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96 | attrib(i,"isSB",1); //*** attrib funktioniert ? |
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97 | execute("qring "+newr+"=i;"); |
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98 | } |
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99 | export(`newr`); |
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100 | keepring(`newr`); |
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101 | if (voice==2) { "// basering is now",newr; } |
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102 | return(); |
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103 | } |
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104 | example |
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105 | { "EXAMPLE:"; echo = 2; |
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106 | ring r=0,(x,y,u,v),(dp(2),ds); |
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107 | changeord("R","wp(2,3),dp"); R; ""; |
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108 | ideal i = x^2,y^2-u^3,v; |
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109 | qring Q = std(i); |
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110 | changeord("Q'","lp",Q); Q'; |
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111 | kill R,Q,Q'; |
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112 | } |
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113 | /////////////////////////////////////////////////////////////////////////////// |
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114 | |
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115 | proc changevar (string newr, string vars, list #) |
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116 | USAGE: changevar(newr,vars[,r]); newr,vars=strings, r=ring/qring |
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117 | CREATE: creates a new ring with name `newr` and makes it the basering if r |
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118 | is an existing ring/qring [default: r=basering]. |
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119 | The new ring differs from the old ring only in the variables. If, |
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120 | say, (newr,vars) = ("R","t()") and the ring r exists and has n |
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121 | variables, the new basering will have name R and variables |
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122 | t(1),...,t(n). |
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123 | If vars = "a,b,c,d", the new ring will have the variables a,b,c,d. |
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124 | RETURN: No return value |
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125 | NOTE: This procedure is useful in connection with the procedure ringtensor, |
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126 | when a conflict between variable names must be avoided. |
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127 | This proc uses 'execute' or calls a procedure using 'execute'. |
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128 | If you use it in your own proc, let the local names of your proc |
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129 | start with @ (see the file HelpForProc) |
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130 | EXAMPLE: example changevar; shows an example |
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131 | { |
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132 | if( size(#)==0 ) { def @r=basering; } |
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133 | if( size(#)==1 ) { def @r=#[1]; } |
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134 | setring @r; |
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135 | ideal i = ideal(@r); int @q = size(i); |
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136 | if( @q!=0 ) |
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137 | { string @s = "@newr1"; } |
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138 | else |
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139 | { string @s = newr; } |
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140 | string @newring = @s+"=("+charstr(@r)+"),("; |
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141 | if( vars[size(vars)-1]=="(" and vars[size(vars)]==")" ) |
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142 | { |
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143 | @newring = @newring+vars[1,size(vars)-2]+"(1.."+string(nvars(@r))+")"; |
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144 | } |
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145 | else { @newring = @newring+vars; } |
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146 | @newring = @newring+"),("+ordstr(@r)+");"; |
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147 | execute("ring "+@newring); |
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148 | if( @q!=0 ) |
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149 | { |
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150 | map phi = @r,maxideal(1); |
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151 | ideal i = phi(i); |
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152 | attrib(i,"isSB",1); //*** attrib funktioniert ? |
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153 | execute("qring "+newr+"=i;"); |
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154 | } |
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155 | export(`newr`); |
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156 | keepring(`newr`); |
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157 | if (voice==2) { "// basering is now",newr; } |
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158 | return(); |
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159 | } |
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160 | example |
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161 | { "EXAMPLE:"; echo = 2; |
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162 | ring r=0,(x,y,u,v),(dp(2),ds); |
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163 | ideal i = x^2,y^2-u^3,v; |
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164 | qring Q = std(i); |
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165 | setring(r); |
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166 | changevar("R","A()"); R; ""; |
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167 | changevar("Q'","a,b,c,d",Q); Q'; |
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168 | kill R,Q,Q'; |
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169 | } |
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170 | /////////////////////////////////////////////////////////////////////////////// |
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171 | |
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172 | proc defring (string s1, string s2, int n, string s3, string s4) |
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173 | USAGE: defring(s1,s2,n,s3,s4); s1..s4=strings, n=integer |
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174 | CREATE: Define a ring with name 's1', characteristic 's2', ordering 's4' and |
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175 | n variables with names derived from s3 and make it the basering. |
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176 | If s3 is a single letter, say s3="a", and if n<=26 then a and the |
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177 | following n-1 letters from the alphabeth (cyclic order) are taken as |
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178 | variables. If n>26 or if s3 is a single letter followed by (, say |
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179 | s3="T(", the variables are T(1),...,T(n). |
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180 | RETURN: No return value |
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181 | NOTE: This proc is useful for defining a ring in a procedure. |
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182 | This proc uses 'execute' or calls a procedure using 'execute'. |
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183 | If you use it in your own proc, let the local names of your proc |
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184 | start with @ (see the file HelpForProc) |
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185 | EXAMPLE: example defring; shows an example |
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186 | { |
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187 | string @newring = "ring "+s1+"=("+s2+"),("; |
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188 | if( n>26 or s3[2]=="(" ) { string @v = s3[1]+"(1.."+string(n)+")"; } |
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189 | else { string @v = A_Z(s3,n); } |
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190 | @newring=@newring+@v+"),("+s4+");"; |
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191 | execute(@newring); |
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192 | export(basering); |
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193 | keepring(`s1`); |
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194 | if (voice==2) { "// basering is now:",s1; } |
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195 | return(); |
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196 | } |
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197 | example |
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198 | { "EXAMPLE:"; echo = 2; |
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199 | defring("r","0",5,"u","ls"); r; ""; |
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200 | defring("R","2,A",10,"x(","dp(3),ws(1,2,3),ds"); R; |
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201 | kill r,R; |
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202 | } |
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203 | /////////////////////////////////////////////////////////////////////////////// |
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204 | |
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205 | proc defrings (int n, list #) |
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206 | USAGE: defrings(n,[p]); n,p integers |
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207 | CREATE: Defines a ring with name Sn, characteristic p, ordering ds and n |
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208 | variables x,y,z,a,b,...if n<=26 (resp. x(1..n) if n>26) and makes it |
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209 | the basering (default: p=32003) |
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210 | RETURN: No return value |
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211 | EXAMPLE: example defrings; shows an example |
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212 | { |
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213 | int p; |
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214 | if (size(#)==0) { p=32003; } |
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215 | else { p=#[1]; } |
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216 | if (n >26) |
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217 | { |
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218 | string s="ring S"+string(n)+"="+string(p)+",x(1.."+string(n)+"),ds;"; |
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219 | } |
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220 | else |
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221 | { |
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222 | string s="ring S"+string(n)+"="+string(p)+",("+A_Z("x",n)+"),ds;"; |
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223 | } |
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224 | execute(s); |
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225 | export basering; |
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226 | execute("keepring S"+string(n)+";"); |
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227 | if (voice==2) { "// basering is now:",s; } |
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228 | } |
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229 | example |
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230 | { "EXAMPLE:"; echo = 2; |
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231 | defrings(5,0); S5; ""; |
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232 | defrings(30); S30; |
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233 | kill S5, S30; |
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234 | } |
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235 | /////////////////////////////////////////////////////////////////////////////// |
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236 | |
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237 | proc defringp (int n,list #) |
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238 | USAGE: defringp(n,[p]); n,p=integers |
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239 | CREATE: defines a ring with name Pn, characteristic p, ordering dp and n |
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240 | variables x,y,z,a,b,...if n<=26 (resp. x(1..n) if n>26) and makes it |
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241 | the basering (default: p=32003) |
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242 | RETURN: No return value |
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243 | EXAMPLE: example defringp; shows an example |
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244 | { |
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245 | int p; |
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246 | if (size(#)==0) { p=32003; } |
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247 | else { p=#[1]; } |
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248 | if (n >26) |
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249 | { |
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250 | string s="ring P"+string(n)+"="+string(p)+",x(1.."+string(n)+"),dp;"; |
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251 | } |
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252 | else |
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253 | { |
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254 | string s="ring P"+string(n)+"="+string(p)+",("+A_Z("x",n)+"),dp;"; |
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255 | } |
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256 | execute(s); |
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257 | export basering; |
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258 | execute("keepring P"+string(n)+";"); |
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259 | //the next comment is only shown if defringp is not called by another proc |
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260 | if (voice==2) { "// basering is now:",s; } |
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261 | } |
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262 | example |
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263 | { "EXAMPLE:"; echo = 2; |
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264 | defringp(5,0); P5; ""; |
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265 | defringp(30); P30; |
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266 | kill P5, P30; |
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267 | } |
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268 | /////////////////////////////////////////////////////////////////////////////// |
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269 | |
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270 | proc extendring (string na, int n, string va, string o, list #) |
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271 | USAGE: extendring(na,n,va,o[iv,i,r]); na,va,o=strings, |
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272 | n,i=integers, r=ring, iv=intvec of positive integers or iv=0 |
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273 | CREATE: Define a ring with name `na` which extends the ring r by adding n new |
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274 | variables in front of [after, if i!=0] the old variables and make it |
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275 | the basering [default: (i,r)=(0,basering)] |
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276 | -- The characteristic is the characteristic of r |
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277 | -- The new vars are derived from va. If va is a single letter, say |
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278 | va="T", and if n<=26 then T and the following n-1 letters from |
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279 | T..Z..T (resp. T(1..n) if n>26) are taken as additional variables. |
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280 | If va is a single letter followed by (, say va="x(", the new |
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281 | variables are x(1),...,x(n) |
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282 | -- The ordering is the product ordering between the ordering of r and |
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283 | an ordering derived from `o` [and iv] |
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284 | - If o contains a 'c' or a 'C' in front resp. at the end this is |
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285 | taken for the whole ordering in front resp. at the end. If o does |
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286 | not contain a 'c' or a 'C' the same rule applies to ordstr(r). |
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287 | - If no intvec iv is given, or if iv=0, o may be any allowed ordstr, |
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288 | like "ds" or "dp(2),wp(1,2,3),Ds(2)" or "ds(a),dp(b),ls" if a and b |
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289 | are globally (!) defined integers and if a+b+1<=n |
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290 | If, however, a and b are local to a proc calling extendring, the |
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291 | intvec iv must be used to let extendring know the values of a and b |
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292 | - If an intvec iv !=0 is given, iv[1],iv[2],... is taken for the 1st, |
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293 | 2nd,... block of o, if o contains no substring "w" or "W" i.e. no |
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294 | weighted ordering (in the above case o="ds,dp,ls" and iv=a,b). |
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295 | If o contains a weighted ordering (only one (!) weighted block is |
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296 | allowed) iv[1] is taken as size for the weight-vector, the next |
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297 | iv[1] values of iv are taken as weights and the remaining values of |
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298 | iv as block-size for the remaining non-weighted blocks. |
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299 | e.g. o="dp,ws,Dp,ds", iv=3,2,3,4,2,5 creates the ordering |
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300 | dp(2),ws(2,3,4),Dp(5),ds |
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301 | RETURN: No return value |
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302 | NOTE: This proc is useful for adding deformation parameters. |
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303 | This proc uses 'execute' or calls a procedure using 'execute'. |
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304 | If you use it in your own proc, let the local names of your proc |
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305 | start with @ (see the file HelpForProc) |
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306 | EXAMPLE: example extendring; shows an example |
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307 | { |
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308 | //--------------- initialization and place c/C of ordering properly ----------- |
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309 | string @o1,@o2,@ro,@wstr,@v,@newring; |
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310 | int @i,@w,@ii,@k; |
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311 | intvec @iv,@iw; |
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312 | if( find(o,"c")+find(o,"C") != 0) |
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313 | { |
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314 | @k=1; |
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315 | if( o[1]=="c" or o[1]=="C" ) { @o1=o[1,2]; o=o[3..size(o)]; } |
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316 | else { @o2=o[size(o)-1,2]; o=o[1..size(o)-2]; } |
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317 | } |
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318 | if( size(#)==0 ) { #[1]=0; } |
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319 | if( typeof(#[1])!="intvec" ) |
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320 | { |
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321 | if( size(#)==1 ) { @i=#[1]; def @r=basering; } |
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322 | if( size(#)==2 ) { @i=#[1]; def @r=#[2]; } |
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323 | if( o[size(o)]!=")" and find(o,",")==0 ) { o=o+"("+string(n)+")"; } |
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324 | } |
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325 | else |
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326 | { |
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327 | @iv=#[1]; |
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328 | if( size(#)==2 ) { @i=#[2]; def @r=basering; } |
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329 | if( size(#)==3 ) { @i=#[2]; def @r=#[3]; } |
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330 | if( @iv==0 && o[size(o)]!=")" && find(o,",")==0 ) {o=o+"("+string(n)+")";} |
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331 | } |
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332 | @ro=ordstr(@r); |
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333 | if( @ro[1]=="c" or @ro[1]=="C" ) |
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334 | { @v=@ro[1,2]; @ro=@ro[3..size(@ro)]; } |
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335 | else |
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336 | { @wstr=@ro[size(@ro)-1,2]; @ro=@ro[1..size(@ro)-2]; } |
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337 | if( @k==0) { @o1=@v; @o2=@wstr; } |
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338 | //----------------- prepare ordering if an intvec is given -------------------- |
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339 | if( typeof(#[1])=="intvec" and #[1]!=0 ) |
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340 | { |
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341 | @k=n; //@k counts no of vars not yet ordered |
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342 | @w=find(o,"w")+find(o,"W");o=o+" "; |
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343 | if( @w!=0 ) |
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344 | { |
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345 | @wstr=o[@w..@w+1]; |
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346 | o=o[1,@w-1]+"@"+o[@w+2,size(o)]; |
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347 | @iw=@iv[2..@iv[1]+1]; |
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348 | @wstr=@wstr+"("+string(@iw)+")"; |
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349 | @k=@k-@iv[1]; |
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350 | @iv=@iv[@iv[1]+2..size(@iv)]; |
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351 | @w=0; |
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352 | } |
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353 | for( @ii=1; @ii<=size(@iv); @ii=@ii+1 ) |
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354 | { |
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355 | if( find(o,",",@w+1)!=0 ) |
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356 | { |
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357 | @w=find(o,",",@w+1); |
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358 | if( o[@w-1]!="@" ) |
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359 | { |
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360 | o=o[1,@w-1]+"("+string(@iv[@ii])+")"+o[@w,size(o)]; |
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361 | @w=find(o,",",@w+1); |
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362 | @k=@k-@iv[@ii]; |
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363 | } |
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364 | else { @ii=@ii-1; } |
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365 | } |
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366 | } |
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367 | @w=find(o,"@"); |
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368 | if( @w!=0 ) { o=o[1,@w-1] + @wstr + o[@w+1,size(o)]; } |
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369 | if( @k>0 and o[size(o)]!=")" ) { o=o+"("+string(@k)+")"; } |
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370 | } |
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371 | //------------------------ prepare string of new ring ------------------------- |
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372 | @newring = "ring "+na+"=("+charstr(@r)+"),("; |
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373 | if( n>26 or va[2]=="(" ) { @v = va[1]+"(1.."+string(n)+")"; } |
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374 | else { @v = A_Z(va,n); } |
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375 | if( @i==0 ) |
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376 | { |
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377 | @v=@v+","+varstr(@r); |
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378 | o=@o1+o+","+@ro+@o2; |
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379 | } |
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380 | else |
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381 | { |
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382 | @v=varstr(@r)+","+@v; |
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383 | o=@o1+@ro+","+o+@o2; |
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384 | } |
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385 | @newring=@newring+@v+"),("+o+");"; |
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386 | //---------------------------- execute and export ----------------------------- |
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387 | execute(@newring); |
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388 | export(basering); |
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389 | keepring(`na`); |
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390 | if (voice==2) { "// basering is now",na; } |
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391 | return(); |
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392 | } |
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393 | example |
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394 | { "EXAMPLE:"; echo = 2; |
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395 | ring r=0,(x,y,z),ds; |
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396 | show(r);""; |
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397 | //no intvec given, no blocksize given: blocksize is derived from no of vars |
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398 | int t=5; |
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399 | extendring("R1",t,"a","dp"); //t global: "dp" -> "dp(5)" |
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400 | show(R1); ""; |
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401 | extendring("R2",4,"T(","c,dp",1,r); //"dp" -> "c,..,dp(4)" |
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402 | show(R2);""; |
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403 | |
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404 | //no intvec given, blocksize given: given blocksize is used |
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405 | extendring("R3",4,"T(","dp(2)",0,r); // "dp(2)" -> "dp(2)" |
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406 | show(R3);""; |
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407 | |
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408 | //intvec given: weights and blocksize is derived from given intvec |
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409 | //(no specification of a blocksize in the given ordstr is allowed!) |
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410 | //if intvec does not cover all given blocks, the last block is used for |
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411 | //the remaining variables, if intvec has too many components, the last |
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412 | //ones are ignored |
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413 | intvec v=3,2,3,4,1,3; |
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414 | extendring("R4",10,"A","ds,ws,Dp,dp",v,0,r); |
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415 | //v covers 3 blocks: v[1] (=3) : no of components of ws |
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416 | //next v[1] values (=v[2..4]) give weights |
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417 | //remaining components of v are used for the remaining blocks |
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418 | show(R4); |
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419 | kill r,R1,R2,R3,R4; |
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420 | } |
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421 | /////////////////////////////////////////////////////////////////////////////// |
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422 | |
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423 | proc fetchall (R, list #) |
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424 | USAGE: fetchall(R[,s]); R=ring/qring, s=string |
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425 | CREATE: fetch all objects of ring R (of type poly/ideal/vector/module/number/ |
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426 | matrix) into the basering. |
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427 | If no 3rd argument is present, the names are the same as in R. If, |
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428 | say, f is a poly in R and the 3rd argument is the string "R", then f |
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429 | is maped to f_R etc. |
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430 | RETURN: no return value |
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431 | NOTE: As fetch, this procedure maps the 1st, 2nd, ... variable of R to the |
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432 | 1st, 2nd, ... variable of the basering. |
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433 | The 3rd argument is useful in order to avoid conflicts of names, the |
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434 | empty string is allowed |
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435 | CAUTION: fetchall does not work inside a procedure |
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436 | //***at the moment it does not work if R contains a map |
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437 | EXAMPLE: example fetchall; shows an example |
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438 | { |
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439 | list @L@=names(R); |
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440 | int @ii@; string @s@; |
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441 | if( size(#) > 0 ) { @s@=@s@+"_"+#[1]; } |
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442 | for( @ii@=size(@L@); @ii@>0; @ii@=@ii@-1 ) |
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443 | { |
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444 | execute("def "+@L@[@ii@]+@s@+"=fetch(R,`@L@[@ii@]`);"); |
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445 | execute("export "+@L@[@ii@]+@s@+";"); |
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446 | } |
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447 | return(); |
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448 | } |
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449 | example |
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450 | { "EXAMPLE:"; |
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451 | "// This example is not executed since fetchall does not work in a procedure"; |
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452 | "// (and hence not in the example procedure). Just try the following commands:"; |
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453 | " ring R=0,(x,y,z),dp;"; |
---|
454 | " ideal j=x,y2,z2;"; |
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455 | " matrix M[2][3]=1,2,3,x,y,z;"; |
---|
456 | " j; print(M);"; |
---|
457 | " ring S=0,(a,b,c),ds;"; |
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458 | " fetchall(R); // map from R to S: x->a, y->b, z->c"; |
---|
459 | " names(S);"; |
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460 | " j; print(M);"; |
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461 | " fetchall(S,\"1\"); // identity map of S: copy objects, change names"; |
---|
462 | " names(S);"; |
---|
463 | " kill R,S;"; |
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464 | } |
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465 | /////////////////////////////////////////////////////////////////////////////// |
---|
466 | |
---|
467 | proc imapall (R, list #) |
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468 | USAGE: imapall(R[,s]); R=ring/qring, s=string |
---|
469 | CREATE: map all objects of ring R (of type poly/ideal/vector/module/number/ |
---|
470 | matrix) into the basering, by applying imap to all objects of R. |
---|
471 | If no 3rd argument is present, the names are the same as in R. If, |
---|
472 | say, f is a poly in R and the 3rd argument is the string "R", then f |
---|
473 | is maped to f_R etc. |
---|
474 | RETURN: no return value |
---|
475 | NOTE: As imap, this procedure maps the variables of R to the variables with |
---|
476 | the same name in the basering, the other variables are maped to 0. |
---|
477 | The 3rd argument is useful in order to avoid conflicts of names, the |
---|
478 | empty string is allowed |
---|
479 | CAUTION: imapall does not work inside a procedure |
---|
480 | //***at the moment it does not work if R contains a map |
---|
481 | EXAMPLE: example imapall; shows an example |
---|
482 | { |
---|
483 | list @L@=names(R); |
---|
484 | int @ii@; string @s@; |
---|
485 | if( size(#) > 0 ) { @s@=@s@+"_"+#[1]; } |
---|
486 | for( @ii@=size(@L@); @ii@>0; @ii@=@ii@-1 ) |
---|
487 | { |
---|
488 | execute("def "+@L@[@ii@]+@s@+"=imap(R,`@L@[@ii@]`);"); |
---|
489 | execute("export "+@L@[@ii@]+@s@+";"); |
---|
490 | } |
---|
491 | return(); |
---|
492 | } |
---|
493 | example |
---|
494 | { "EXAMPLE:"; |
---|
495 | "// This example is not executed since imapall does not work in a procedure"; |
---|
496 | "// (and hence not in the example procedure). Just try the following commands:"; |
---|
497 | " ring R=0,(x,y,z,u),dp;"; |
---|
498 | " ideal j=x,y,z,u2+ux+z;"; |
---|
499 | " matrix M[2][3]=1,2,3,x,y,uz;"; |
---|
500 | " j; print(M);"; |
---|
501 | " ring S=0,(a,b,c,x,z,y),ds;"; |
---|
502 | " imapall(R); // map from R to S: x->x, y->y, z->z, u->0"; |
---|
503 | " names(S);"; |
---|
504 | " j; print(M);"; |
---|
505 | " imapall(S,\"1\"); // identity map of S: copy objects, change names"; |
---|
506 | " names(S);"; |
---|
507 | " kill R,S;"; |
---|
508 | } |
---|
509 | /////////////////////////////////////////////////////////////////////////////// |
---|
510 | |
---|
511 | proc mapall (R, ideal i, list #) |
---|
512 | USAGE: mapall(R,i[,s]); R=ring/qring, i=ideal of basering, s=string |
---|
513 | CREATE: map all objects of ring R (of type poly/ideal/vector/module/number/ |
---|
514 | matrix, map) into the basering, by mapping the jth variable of R to |
---|
515 | the jth generator of the ideal i. If no 3rd argument is present, the |
---|
516 | names are the same as in R. If, say, f is a poly in R and the 3rd |
---|
517 | argument is the string "R", then f is maped to f_R etc. |
---|
518 | RETURN: no return value |
---|
519 | NOTE: This procedure has the same effect as defining a map, say psi, by |
---|
520 | map psi=R,i; and then applying psi to all objects of R. In particular, |
---|
521 | maps from R to some ring S are composed with psi, creating thus a map |
---|
522 | from the basering to S. |
---|
523 | mapall may be combined with copyring to change vars for all objects. |
---|
524 | The 3rd argument is useful in order to avoid conflicts of names, the |
---|
525 | empty string is allowed |
---|
526 | CAUTION: mapall does not work inside a procedure |
---|
527 | EXAMPLE: example mapall; shows an example |
---|
528 | { |
---|
529 | list @L@=names(R); map @psi@ = R,i; |
---|
530 | int @ii@; string @s@; |
---|
531 | if( size(#) > 0 ) { @s@=@s@+"_"+#[1]; } |
---|
532 | for( @ii@=size(@L@); @ii@>0; @ii@=@ii@-1 ) |
---|
533 | { |
---|
534 | execute("def "+@L@[@ii@]+@s@+"=@psi@(`@L@[@ii@]`);"); |
---|
535 | execute("export "+@L@[@ii@]+@s@+";"); |
---|
536 | } |
---|
537 | return(); |
---|
538 | } |
---|
539 | example |
---|
540 | { "EXAMPLE:"; |
---|
541 | "// This example is not executed since mapall does not work in a procedure"; |
---|
542 | "// (and hence not in the example procedure). Just try the following commands:"; |
---|
543 | " ring R=0,(x,y,z),dp;"; |
---|
544 | " ideal j=x,y,z;"; |
---|
545 | " matrix M[2][3]=1,2,3,x,y,z;"; |
---|
546 | " map phi=R,x2,y2,z2; "; |
---|
547 | " ring S=0,(a,b,c),ds;"; |
---|
548 | " ideal i=c,a,b;"; |
---|
549 | " mapall(R,i); // map from R to S: x->c, y->a, z->b"; |
---|
550 | " names(S);"; |
---|
551 | " j; print(M); phi; // phi is a map from R to S: x->c2, y->a2, z->b2"; |
---|
552 | " ideal i1=a2,a+b,1;"; |
---|
553 | " mapall(R,i1,\"\"); // map from R to S: x->a2, y->a+b, z->1"; |
---|
554 | " names(S);"; |
---|
555 | " j_; print(M_); phi_;"; |
---|
556 | " changevar(\"T\",\"x()\",R); // change vars in R and call result T"; |
---|
557 | " mapall(R,maxideal(1)); // identity map from R to T"; |
---|
558 | " names(T);"; |
---|
559 | " j; print(M); phi;"; |
---|
560 | " kill R,S,T;"; |
---|
561 | } |
---|
562 | /////////////////////////////////////////////////////////////////////////////// |
---|
563 | |
---|
564 | proc ringtensor (string s, list #) |
---|
565 | USAGE: ringtensor(s,r1,r2,...); s=string, r1,r2,...=rings |
---|
566 | CREATE: A new base ring with name `s` if r1,r2,... are existing rings. |
---|
567 | If, say, s = "R" and the rings r1,r2,... exist, the new ring will |
---|
568 | have name R, variables from all rings r1,r2,... and as monomial |
---|
569 | ordering the block (product) ordering of r1,r2,... . Hence, R |
---|
570 | is the tensor product of the rings r1,r2,... with ordering matrix |
---|
571 | equal to the direct sum of the ordering matrices of r1,r2,... |
---|
572 | RETURN: no return value |
---|
573 | NOTE: The characteristic of the new ring will be that of r1. The names of |
---|
574 | variables in the rings r1,r2,... should differ (if a name, say x, |
---|
575 | occurs in r1 and r2, then, in the new ring r, x always refers to the |
---|
576 | variable with name x in r1, there is no access to x in r2). |
---|
577 | The procedure works also for quotient rings ri, if the characteristic |
---|
578 | of ri is compatible with the characteristic of r1 (i.e. if imap from |
---|
579 | ri to r1 is implemented) |
---|
580 | This proc uses 'execute' or calls a procedure using 'execute'. |
---|
581 | If you use it in your own proc, let the local names of your proc |
---|
582 | start with @ (see the file HelpForProc) |
---|
583 | EXAMPLE: example ringtensor; shows an example |
---|
584 | { |
---|
585 | int @ii,@q; |
---|
586 | int @n = size(#); |
---|
587 | string @vars,@order,@oi,@s1; |
---|
588 | //---- gather variables, orderings and ideals (of qrings) from given rings ---- |
---|
589 | for(@ii=1; @ii<=@n; @ii=@ii+1) |
---|
590 | { |
---|
591 | if( ordstr(#[@ii])[1]=="C" or ordstr(#[@ii])[1]=="c" ) |
---|
592 | { @oi=ordstr(#[@ii])[3,size(ordstr(#[@ii]))-2]; } |
---|
593 | else { @oi=ordstr(#[@ii])[1,size(ordstr(#[@ii]))-2]; } |
---|
594 | @vars = @vars+varstr(#[@ii])+","; |
---|
595 | @order= @order+@oi+","; |
---|
596 | def @r(@ii)=#[@ii]; |
---|
597 | setring @r(@ii); |
---|
598 | ideal i(@ii)=ideal(@r(@ii)); |
---|
599 | int @q(@ii)=size(i(@ii)); |
---|
600 | @q=@q+@q(@ii); |
---|
601 | } |
---|
602 | if( @q!=0 ) { @s1 = "@newr"; } // @q=0 iff none of the rings ri is a qring |
---|
603 | else { @s1 = s; } |
---|
604 | //------------------------------- create new ring ----------------------------- |
---|
605 | string @newring ="=("+charstr(#[1])+"),("+@vars[1,size(@vars)-1]+"),(" |
---|
606 | +@order[1,size(@order)-1]+");"; |
---|
607 | execute("ring "+@s1+@newring); |
---|
608 | //------ create ideal for new ring if one of the given rings is a qring ------- |
---|
609 | if( @q!=0 ) |
---|
610 | { |
---|
611 | ideal i; |
---|
612 | for(@ii=1; @ii<=@n; @ii=@ii+1) |
---|
613 | { |
---|
614 | if( @q(@ii)!=0 ) |
---|
615 | { |
---|
616 | i=i+imap(@r(@ii),i(@ii)); |
---|
617 | } |
---|
618 | } |
---|
619 | i=std(i); |
---|
620 | execute("qring "+s+"=i;"); |
---|
621 | } |
---|
622 | //----------------------- export and keep created ring ------------------------ |
---|
623 | export(`s`); |
---|
624 | keepring(`s`); |
---|
625 | if (voice==2) { "// basering is now",s; } |
---|
626 | return(); |
---|
627 | } |
---|
628 | example |
---|
629 | { "EXAMPLE:"; echo = 2; |
---|
630 | ring r=32003,(x,y,u,v),dp; |
---|
631 | ring s=0,(a,b,c),wp(1,2,3); |
---|
632 | ring t=0,x(1..5),(c,ls); |
---|
633 | ringtensor("R",r,s,t); |
---|
634 | type R;""; |
---|
635 | setring s; |
---|
636 | ideal i = a2+b3+c5; |
---|
637 | changevar("S","x,y,z"); //set S (change vars of s to x,y,z) the basering |
---|
638 | qring qS =std(fetch(s,i)); //create qring of S mod i (maped to S) |
---|
639 | changevar("T","d,e,f,g,h",t); //set T (change vars of t to d..h) the basering |
---|
640 | qring qT=std(d2+e2-f3); //create qring of T mod d2+e2-f3 |
---|
641 | ringtensor("Q",s,qS,t,qT); |
---|
642 | type Q; |
---|
643 | kill R,Q,S,T; |
---|
644 | } |
---|
645 | /////////////////////////////////////////////////////////////////////////////// |
---|