[6f2edc] | 1 | // $Id: ring.lib,v 1.2 1997-04-28 19:27:25 obachman Exp $ |
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| 2 | //(GMG, last modified 03.11.95) |
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[3d124a7] | 3 | /////////////////////////////////////////////////////////////////////////////// |
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| 4 | |
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[6f2edc] | 5 | LIBRARY: ring.lib PROCEDURES FOR MANIPULATING RINGS AND MAPS |
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[3d124a7] | 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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[6f2edc] | 27 | an existing ring [default: r=basering]. |
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[3d124a7] | 28 | The new ring differs from the old ring only in the characteristic. |
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[6f2edc] | 29 | If, say, (newr,c) = ("R","0,A") and the ring r exists, the new |
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[3d124a7] | 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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[6f2edc] | 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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[3d124a7] | 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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[6f2edc] | 42 | if( @q!=0 ) |
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[3d124a7] | 43 | { string @s = "@newr1"; } |
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[6f2edc] | 44 | else |
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[3d124a7] | 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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[6f2edc] | 53 | execute("qring "+newr+"=i;"); |
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[3d124a7] | 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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[6f2edc] | 72 | an existing ring/qring [default: r=basering]. |
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[3d124a7] | 73 | The new ring differs from the old ring only in the ordering. If, say, |
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[6f2edc] | 74 | (newr,o) = ("R","wp(2,3),dp") and the ring r exists and has >=3 |
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[3d124a7] | 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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[6f2edc] | 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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[3d124a7] | 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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[6f2edc] | 86 | if( @q!=0 ) |
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[3d124a7] | 87 | { string @s = "@newr1"; } |
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[6f2edc] | 88 | else |
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[3d124a7] | 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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[6f2edc] | 97 | execute("qring "+newr+"=i;"); |
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[3d124a7] | 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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[6f2edc] | 118 | is an existing ring/qring [default: r=basering]. |
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[3d124a7] | 119 | The new ring differs from the old ring only in the variables. If, |
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[6f2edc] | 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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[3d124a7] | 122 | t(1),...,t(n). |
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[6f2edc] | 123 | If vars = "a,b,c,d", the new ring will have the variables a,b,c,d. |
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[3d124a7] | 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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[6f2edc] | 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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[3d124a7] | 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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[6f2edc] | 136 | if( @q!=0 ) |
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[3d124a7] | 137 | { string @s = "@newr1"; } |
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[6f2edc] | 138 | else |
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[3d124a7] | 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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[6f2edc] | 142 | { |
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| 143 | @newring = @newring+vars[1,size(vars)-2]+"(1.."+string(nvars(@r))+")"; |
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[3d124a7] | 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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[6f2edc] | 153 | execute("qring "+newr+"=i;"); |
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[3d124a7] | 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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[6f2edc] | 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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[3d124a7] | 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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[6f2edc] | 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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[3d124a7] | 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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[6f2edc] | 260 | if (voice==2) { "// basering is now:",s; } |
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| 261 | } |
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[3d124a7] | 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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[6f2edc] | 271 | USAGE: extendring(na,n,va,o[iv,i,r]); na,va,o=strings, |
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[3d124a7] | 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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[6f2edc] | 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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[3d124a7] | 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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[6f2edc] | 284 | - If o contains a 'c' or a 'C' in front resp. at the end this is |
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[3d124a7] | 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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[6f2edc] | 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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[3d124a7] | 292 | - If an intvec iv !=0 is given, iv[1],iv[2],... is taken for the 1st, |
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[6f2edc] | 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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[3d124a7] | 297 | iv[1] values of iv are taken as weights and the remaining values of |
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[6f2edc] | 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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[3d124a7] | 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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[6f2edc] | 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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[3d124a7] | 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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[6f2edc] | 309 | string @o1,@o2,@ro,@wstr,@v,@newring; |
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[3d124a7] | 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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[6f2edc] | 333 | if( @ro[1]=="c" or @ro[1]=="C" ) |
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[3d124a7] | 334 | { @v=@ro[1,2]; @ro=@ro[3..size(@ro)]; } |
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[6f2edc] | 335 | else |
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[3d124a7] | 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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[6f2edc] | 343 | if( @w!=0 ) |
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| 344 | { |
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| 345 | @wstr=o[@w..@w+1]; |
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[3d124a7] | 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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[6f2edc] | 349 | @k=@k-@iv[1]; |
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[3d124a7] | 350 | @iv=@iv[@iv[1]+2..size(@iv)]; |
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| 351 | @w=0; |
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| 352 | } |
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[6f2edc] | 353 | for( @ii=1; @ii<=size(@iv); @ii=@ii+1 ) |
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[3d124a7] | 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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[6f2edc] | 359 | { |
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| 360 | o=o[1,@w-1]+"("+string(@iv[@ii])+")"+o[@w,size(o)]; |
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[3d124a7] | 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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[6f2edc] | 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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[3d124a7] | 379 | } |
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[6f2edc] | 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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[3d124a7] | 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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[6f2edc] | 396 | show(r);""; |
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[3d124a7] | 397 | //no intvec given, no blocksize given: blocksize is derived from no of vars |
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[6f2edc] | 398 | int t=5; |
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[3d124a7] | 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 |
---|
| 411 | //the remaining variables, if intvec has too many components, the last |
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| 412 | //ones are ignored |
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[6f2edc] | 413 | intvec v=3,2,3,4,1,3; |
---|
| 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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[3d124a7] | 416 | //next v[1] values (=v[2..4]) give weights |
---|
| 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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[6f2edc] | 423 | proc fetchall (R, list #) |
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[3d124a7] | 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/ |
---|
| 426 | matrix) into the basering. |
---|
| 427 | If no 3rd argument is present, the names are the same as in R. If, |
---|
| 428 | say, f is a poly in R and the 3rd argument is the string "R", then f |
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[6f2edc] | 429 | is maped to f_R etc. |
---|
[3d124a7] | 430 | RETURN: no return value |
---|
| 431 | NOTE: As fetch, this procedure maps the 1st, 2nd, ... variable of R to the |
---|
[6f2edc] | 432 | 1st, 2nd, ... variable of the basering. |
---|
[3d124a7] | 433 | The 3rd argument is useful in order to avoid conflicts of names, the |
---|
| 434 | empty string is allowed |
---|
| 435 | CAUTION: fetchall does not work inside a procedure |
---|
[6f2edc] | 436 | //***at the moment it does not work if R contains a map |
---|
[3d124a7] | 437 | EXAMPLE: example fetchall; shows an example |
---|
[6f2edc] | 438 | { |
---|
[3d124a7] | 439 | list @L@=names(R); |
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| 440 | int @ii@; string @s@; |
---|
| 441 | if( size(#) > 0 ) { @s@=@s@+"_"+#[1]; } |
---|
[6f2edc] | 442 | for( @ii@=size(@L@); @ii@>0; @ii@=@ii@-1 ) |
---|
| 443 | { |
---|
[3d124a7] | 444 | execute("def "+@L@[@ii@]+@s@+"=fetch(R,`@L@[@ii@]`);"); |
---|
| 445 | execute("export "+@L@[@ii@]+@s@+";"); |
---|
| 446 | } |
---|
| 447 | return(); |
---|
| 448 | } |
---|
| 449 | example |
---|
| 450 | { "EXAMPLE:"; |
---|
| 451 | "// This example is not executed since fetchall does not work in a procedure"; |
---|
| 452 | "// (and hence not in the example procedure). Just try the following commands:"; |
---|
| 453 | " ring R=0,(x,y,z),dp;"; |
---|
| 454 | " ideal j=x,y2,z2;"; |
---|
| 455 | " matrix M[2][3]=1,2,3,x,y,z;"; |
---|
| 456 | " j; print(M);"; |
---|
| 457 | " ring S=0,(a,b,c),ds;"; |
---|
| 458 | " fetchall(R); // map from R to S: x->a, y->b, z->c"; |
---|
| 459 | " names(S);"; |
---|
| 460 | " j; print(M);"; |
---|
| 461 | " fetchall(S,\"1\"); // identity map of S: copy objects, change names"; |
---|
| 462 | " names(S);"; |
---|
| 463 | " kill R,S;"; |
---|
| 464 | } |
---|
| 465 | /////////////////////////////////////////////////////////////////////////////// |
---|
| 466 | |
---|
[6f2edc] | 467 | proc imapall (R, list #) |
---|
[3d124a7] | 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 |
---|
[6f2edc] | 473 | is maped to f_R etc. |
---|
[3d124a7] | 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 |
---|
[6f2edc] | 480 | //***at the moment it does not work if R contains a map |
---|
[3d124a7] | 481 | EXAMPLE: example imapall; shows an example |
---|
[6f2edc] | 482 | { |
---|
[3d124a7] | 483 | list @L@=names(R); |
---|
| 484 | int @ii@; string @s@; |
---|
| 485 | if( size(#) > 0 ) { @s@=@s@+"_"+#[1]; } |
---|
[6f2edc] | 486 | for( @ii@=size(@L@); @ii@>0; @ii@=@ii@-1 ) |
---|
| 487 | { |
---|
[3d124a7] | 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 | |
---|
[6f2edc] | 511 | proc mapall (R, ideal i, list #) |
---|
[3d124a7] | 512 | USAGE: mapall(R,i[,s]); R=ring/qring, i=ideal of basering, s=string |
---|
[6f2edc] | 513 | CREATE: map all objects of ring R (of type poly/ideal/vector/module/number/ |
---|
[3d124a7] | 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 |
---|
[6f2edc] | 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. |
---|
[3d124a7] | 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 |
---|
[6f2edc] | 522 | from the basering to S. |
---|
[3d124a7] | 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 |
---|
[6f2edc] | 526 | CAUTION: mapall does not work inside a procedure |
---|
[3d124a7] | 527 | EXAMPLE: example mapall; shows an example |
---|
[6f2edc] | 528 | { |
---|
[3d124a7] | 529 | list @L@=names(R); map @psi@ = R,i; |
---|
| 530 | int @ii@; string @s@; |
---|
| 531 | if( size(#) > 0 ) { @s@=@s@+"_"+#[1]; } |
---|
[6f2edc] | 532 | for( @ii@=size(@L@); @ii@>0; @ii@=@ii@-1 ) |
---|
| 533 | { |
---|
[3d124a7] | 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;"; |
---|
[6f2edc] | 546 | " map phi=R,x2,y2,z2; "; |
---|
[3d124a7] | 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. |
---|
[6f2edc] | 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 |
---|
[3d124a7] | 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 |
---|
[6f2edc] | 578 | of ri is compatible with the characteristic of r1 (i.e. if imap from |
---|
[3d124a7] | 579 | ri to r1 is implemented) |
---|
[6f2edc] | 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 |
---|
[3d124a7] | 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 ---- |
---|
[6f2edc] | 589 | for(@ii=1; @ii<=@n; @ii=@ii+1) |
---|
[3d124a7] | 590 | { |
---|
[6f2edc] | 591 | if( ordstr(#[@ii])[1]=="C" or ordstr(#[@ii])[1]=="c" ) |
---|
[3d124a7] | 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); |
---|
[6f2edc] | 598 | ideal i(@ii)=ideal(@r(@ii)); |
---|
[3d124a7] | 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; |
---|
[6f2edc] | 612 | for(@ii=1; @ii<=@n; @ii=@ii+1) |
---|
[3d124a7] | 613 | { |
---|
| 614 | if( @q(@ii)!=0 ) |
---|
| 615 | { |
---|
| 616 | i=i+imap(@r(@ii),i(@ii)); |
---|
| 617 | } |
---|
| 618 | } |
---|
| 619 | i=std(i); |
---|
[6f2edc] | 620 | execute("qring "+s+"=i;"); |
---|
[3d124a7] | 621 | } |
---|
| 622 | //----------------------- export and keep created ring ------------------------ |
---|
| 623 | export(`s`); |
---|
| 624 | keepring(`s`); |
---|
| 625 | if (voice==2) { "// basering is now",s; } |
---|
| 626 | return(); |
---|
| 627 | } |
---|
[6f2edc] | 628 | example |
---|
[3d124a7] | 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); |
---|
[6f2edc] | 633 | ringtensor("R",r,s,t); |
---|
[3d124a7] | 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 |
---|
[6f2edc] | 641 | ringtensor("Q",s,qS,t,qT); |
---|
[3d124a7] | 642 | type Q; |
---|
| 643 | kill R,Q,S,T; |
---|
| 644 | } |
---|
| 645 | /////////////////////////////////////////////////////////////////////////////// |
---|