[f34c37c] | 1 | // $Id: deform.lib,v 1.15 1999-07-06 11:32:46 obachman Exp $ |
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[f0c6f4] | 2 | // author: Bernd Martin email: martin@math.tu-cottbus.de |
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[82716e] | 3 | //(bm, last modified 4/98) |
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[3d124a7] | 4 | /////////////////////////////////////////////////////////////////////////////// |
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[f34c37c] | 5 | version="$Id: deform.lib,v 1.15 1999-07-06 11:32:46 obachman Exp $"; |
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[5480da] | 6 | info=" |
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[f1201a] | 7 | LIBRARY: deform.lib PROCEDURES FOR COMPUTING MINIVERSAL DEFORMATION |
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[f0c6f4] | 8 | |
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[f34c37c] | 9 | AUTHOR: Bernd Martin (martin@math.tu-cottbus.de) |
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| 10 | |
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| 11 | PROCEDURES: |
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[f0c6f4] | 12 | versal(Fo[,d,any]) miniversal deformation of isolated singularity Fo |
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| 13 | mod_versal(Mo,I,[,d,any]) miniversal deformation of module Mo modulo ideal I |
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[82716e] | 14 | lift_kbase(N,M); lifting N into standard kbase of M |
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[f0c6f4] | 15 | lift_rel_kb(N,M[,kbM,p]) relative lifting N into a kbase of M |
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[f34c37c] | 16 | kill_rings([\"prefix\"]) kills the exported rings from above |
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[5480da] | 17 | "; |
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[f0c6f4] | 18 | /////////////////////////////////////////////////////////////////////////////// |
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[f1201a] | 19 | LIB "inout.lib"; |
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| 20 | LIB "general.lib"; |
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| 21 | LIB "matrix.lib"; |
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| 22 | LIB "homolog.lib"; |
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[6f2edc] | 23 | LIB "sing.lib"; |
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[3d124a7] | 24 | /////////////////////////////////////////////////////////////////////////////// |
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[f1201a] | 25 | proc versal (ideal Fo,list #) |
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[d2b2a7] | 26 | "USAGE: versal(Fo[,d,any]); Fo=ideal, d=int, any=list |
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[f1201a] | 27 | COMUPTE: miniversal deformation of Fo up to degree d (default d=100), |
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| 28 | CREATE: Rings (exported): |
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[82716e] | 29 | 'my'Px = extending the basering Po by new variables given by \"A,B,..\" |
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[f1201a] | 30 | (deformation parameters), returns as basering, |
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| 31 | the new variables come before the old ones, |
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[d2b2a7] | 32 | the ordering is the product between \"ls\" and \"ord(Po)\", |
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[f1201a] | 33 | 'my'Qx = Px/Fo extending Qo=Po/Fo, |
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| 34 | 'my'So = being the embedding-ring of the versal base space, |
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[d2b2a7] | 35 | 'my'Ox = Px/Js extending So/Js. (default my=\"\") |
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[82716e] | 36 | Matrices (in Px, exported): |
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[f1201a] | 37 | Js = giving the versal base space (obstructions), |
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| 38 | Fs = giving the versal family of Fo, |
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| 39 | Rs = giving the lifting of Ro=syz(Fo). |
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| 40 | If d is defined (!=0), it computes up to degree d. |
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| 41 | If 'any' is defined and any[1] is no string, interactive version. |
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[d2b2a7] | 42 | Otherwise 'any' gives predefined strings: \"my\",\"param\",\"order\",\"out\" |
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| 43 | (\"my\" prefix-string, \"param\" is a letter (e.g. \"A\") for the name of |
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[82716e] | 44 | first parameter or (e.g. \"A(\") for index parameter variables, \"order\" |
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[d2b2a7] | 45 | ordering string for ring extension), \"out\" name of output-file). |
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[f1201a] | 46 | NOTE: printlevel < 0 no output at all, |
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[82716e] | 47 | printlevel >=0,1,2,.. informs you, what is going on; |
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[f1201a] | 48 | this proc uses 'execute'. |
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| 49 | EXAMPLE:example versal; shows an example |
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[d2b2a7] | 50 | " |
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[3d124a7] | 51 | { |
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[f1201a] | 52 | //------- prepare ------------------------------------------------------------- |
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| 53 | string str,@param,@order,@my,@out,@degrees; |
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| 54 | int @d,d_max,@t1,t1',@t2,@colR,ok_ann,@smooth,@noObstr,@size,@j; |
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| 55 | int p = printlevel-voice+3; |
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| 56 | int time = timer; |
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| 57 | intvec @iv,@jv,@is_qh,@degr; |
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[82716e] | 58 | d_max = 100; |
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[f1201a] | 59 | @my = ""; @param="A"; @order="ds"; @out="no"; |
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| 60 | @size = size(#); |
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| 61 | if( @size>0 ) { d_max = #[1]; } |
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[82716e] | 62 | if( @size>1 ) |
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| 63 | { if(typeof(#[2])!="string") |
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[f1201a] | 64 | { string @active; |
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| 65 | @my,@param,@order,@out = interact1(); |
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| 66 | } |
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| 67 | else |
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| 68 | { @my = #[2]; |
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| 69 | if (@size>2) {@param = #[3];} |
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| 70 | if (@size>3) {@order = #[4];} |
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| 71 | if (@size>4) {@out = #[5];} |
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| 72 | } |
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| 73 | } |
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| 74 | string myPx = @my+"Px"; |
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| 75 | string myQx = @my+"Qx"; |
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| 76 | string myOx = @my+"Ox"; |
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| 77 | string mySo = @my+"So"; |
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| 78 | Fo = simplify(Fo,10); |
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| 79 | @is_qh = qhweight(Fo); |
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| 80 | int @rowR= size(Fo); |
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| 81 | def Po = basering; |
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[82716e] | 82 | setring Po; |
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[f1201a] | 83 | poly X_s = product(maxideal(1)); |
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| 84 | //------- reproduce T12 ------------------------------------------------------ |
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| 85 | list Ls = T12(Fo,1); |
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| 86 | matrix Ro = Ls[6]; // syz(i) |
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| 87 | matrix InfD = Ls[5]; // matrix of inf. deformations |
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| 88 | matrix PreO = Ls[7]; // representation of (Syz/Kos)* |
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| 89 | module PreO'= std(PreO); |
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| 90 | module PreT = Ls[2]; // representation of modT2 (sb) |
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| 91 | if(dim(PreT)==0) |
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| 92 | { |
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| 93 | matrix kbT2 = kbase(PreT); // kbase of T2 |
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| 94 | } |
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| 95 | else |
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| 96 | { |
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| 97 | matrix kbT2 ; // kbase of T2 : empty |
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| 98 | } |
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| 99 | @t1 = Ls[3]; // vdim of T1 |
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| 100 | @t2 = Ls[4]; // vdim of T2 |
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| 101 | kill Ls; |
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[82716e] | 102 | t1' = @t1; |
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| 103 | if( @t1==0) { dbprint(p,"// rigit!"); return();} |
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| 104 | if( @t2==0) { @smooth=1; dbprint(p,"// smooth base space");} |
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[f1201a] | 105 | dbprint(p,"// ready: T1 and T2"); |
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| 106 | @colR = ncols(Ro); |
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| 107 | //----- test: quasi-homogeneous, choice of inf. def.-------------------------- |
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| 108 | @degrees = homog_test(@is_qh,matrix(Fo),InfD); |
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| 109 | @jv = 1..@t1; |
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[82716e] | 110 | if (@degrees!="") |
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[f1201a] | 111 | { dbprint(p-1,"// T1 is quasi-homogeneous represented with weight-vector", |
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| 112 | @degrees); |
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| 113 | } |
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| 114 | if (defined(@active)) |
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[82716e] | 115 | { "// matrix of infinitesimal deformations:";print(InfD); |
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[f1201a] | 116 | "// weights of infinitesimal deformations ( emty ='not qhomog'):"; |
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| 117 | @degrees; |
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| 118 | matrix dummy; |
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| 119 | InfD,dummy,t1' = interact2(InfD,@jv);kill dummy; |
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[82716e] | 120 | } |
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[f1201a] | 121 | //---- create new rings and objects ------------------------------------------ |
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| 122 | get_rings(Fo,t1',1,@my,@order,@param); |
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| 123 | setring `myPx`; |
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[82716e] | 124 | @jv=0; @jv[t1']=0; @jv=@jv+1; @jv[nvars(basering)]=0; |
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[f1201a] | 125 | //weight-vector for calculating |
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| 126 | //rel-jet with resp to def-para |
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[82716e] | 127 | ideal Io = imap(Po,Fo); |
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[f1201a] | 128 | ideal J,m_J,tid; attrib(J,"isSB",1); |
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| 129 | matrix Fo = matrix(Io); //initial equations |
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| 130 | matrix homF = kohom(Fo,@colR); |
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| 131 | matrix Ro = imap(Po,Ro); |
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| 132 | matrix homR = transpose(Ro); |
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| 133 | matrix homFR= concat(homR,homF); |
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| 134 | module hom' = std(homFR); |
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[82716e] | 135 | matrix Js[1][@t2]; |
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| 136 | matrix F_R,Fs,Rs,Fn,Rn; |
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| 137 | export Js,Fs,Rs; |
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| 138 | matrix Mon[t1'][1]=maxideal(1); |
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[f1201a] | 139 | Fn = transpose(imap(Po,InfD)*Mon); //infinitesimal deformations |
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[82716e] | 140 | Fs = Fo + Fn; |
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[f1201a] | 141 | dbprint(p-1,"// infinitesimal deformation: Fs: ",Fs); |
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| 142 | Rn = (-1)*lift(Fo,Fs*Ro); //infinit. relations |
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| 143 | Rs = Ro + Rn; |
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| 144 | F_R = Fs*Rs; |
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| 145 | tid = 0 + ideal(F_R); |
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| 146 | if (tid[1]==0) {d_max=1;} //finished ? |
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[82716e] | 147 | setring `myOx`; |
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[f1201a] | 148 | matrix Fs,Rs,Cup,Cup',F_R,homFR,New,Rn,Fn; |
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| 149 | module hom'; |
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[82716e] | 150 | ideal null,tid; attrib(null,"isSB",1); |
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| 151 | setring `myQx`; |
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| 152 | poly X_s = imap(Po,X_s); |
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| 153 | matrix Cup,Cup',MASS; |
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[f1201a] | 154 | ideal tid,null; attrib(null,"isSB",1); |
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[82716e] | 155 | ideal J,m_J; attrib(J,"isSB",1); |
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[f1201a] | 156 | attrib(m_J,"isSB",1); |
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[82716e] | 157 | matrix PreO = imap(Po,PreO); |
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[f1201a] | 158 | module PreO'= imap(Po,PreO'); attrib(PreO',"isSB",1); |
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| 159 | module PreT = imap(Po,PreT); attrib(PreT,"isSB",1); |
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| 160 | matrix kbT2 = imap(Po,kbT2); |
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| 161 | matrix Mon = fetch(`myPx`,Mon); |
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| 162 | matrix F_R = fetch(`myPx`,F_R); |
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| 163 | matrix Js[1][@t2]; |
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[3d124a7] | 164 | //------- start the loop ------------------------------------------------------ |
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[f1201a] | 165 | for (@d=2;@d<=d_max;@d=@d+1) |
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[3d124a7] | 166 | { |
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[f1201a] | 167 | if( @t1==0) {break}; |
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[82716e] | 168 | dbprint(p,"// start computation in degree "+string(@d)+"."); |
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[f0c6f4] | 169 | dbprint(p-3,">>> TIME = "+string(timer-time)); |
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| 170 | dbprint(p-3,"==> memory = "+string(kmemory())+"k"); |
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[f1201a] | 171 | //------- compute obstruction-vector ----------------------------------------- |
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| 172 | if (@smooth) { @noObstr=1;} |
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| 173 | else |
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[82716e] | 174 | { Cup = jet(F_R,@d,@jv); |
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| 175 | Cup = matrix(reduce(ideal(Cup),m_J),@colR,1); |
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| 176 | Cup = jet(Cup,@d,@jv); |
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| 177 | } |
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[3d124a7] | 178 | //------- express obstructions in kbase of T2 -------------------------------- |
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[f1201a] | 179 | if ( @noObstr==0 ) |
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| 180 | { Cup' = reduce(Cup,PreO'); |
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| 181 | tid = simplify(ideal(Cup'),10); |
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| 182 | if(tid[1]!=0) |
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| 183 | { dbprint(p-4,"// *"); |
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| 184 | Cup=Cup-Cup'; |
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| 185 | } |
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| 186 | Cup = lift(PreO,Cup); |
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[82716e] | 187 | MASS = lift_rel_kb(Cup,PreT,kbT2,X_s); |
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| 188 | dbprint(p-3,"// next MASSEY-products:",MASS-jet(MASS,@d-1,@jv)); |
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[f1201a] | 189 | if (MASS==transpose(Js)) |
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[82716e] | 190 | { @noObstr=1;dbprint(p-1,"// no obstruction"); } |
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[f1201a] | 191 | else { @noObstr=0; } |
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[6f2edc] | 192 | } |
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[f1201a] | 193 | //------- obtain equations of base space -------------------------------------- |
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| 194 | if ( @noObstr==0 ) |
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| 195 | { Js = transpose(MASS); |
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| 196 | dbprint(p-2,"// next equation of base space:", |
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| 197 | simplify(ideal(Js),10)); |
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| 198 | setring `myPx`; |
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| 199 | Js = imap(`myQx`,Js); |
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[82716e] | 200 | degBound = @d+1; |
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[f1201a] | 201 | J = std(ideal(Js)); |
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| 202 | m_J = std(J*ideal(Mon)); |
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| 203 | degBound = 0; |
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| 204 | //--------------- obtain new base-ring ---------------------------------------- |
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| 205 | kill `myOx`; |
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[c67136] | 206 | if(system("with","Namespaces")==1) { kill Top::`myOx`; } |
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[82716e] | 207 | qring `myOx` = J; |
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[f1201a] | 208 | matrix Fs,Rs,F_R,Cup,Cup',homFR,New,Rn,Fn; |
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| 209 | module hom'; |
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| 210 | ideal null,tid; attrib(null,"isSB",1); |
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[3d124a7] | 211 | } |
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[f1201a] | 212 | //---------------- lift equations F and relations R --------------------------- |
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| 213 | setring `myOx`; |
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[82716e] | 214 | Fs = fetch(`myPx`,Fs); |
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| 215 | Rs = fetch(`myPx`,Rs); |
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| 216 | F_R = Fs*Rs; |
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| 217 | F_R = matrix(reduce(ideal(F_R),null)); |
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[f1201a] | 218 | tid = 0 + ideal(F_R); |
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[82716e] | 219 | if (tid[1]==0) { dbprint(p-1,"// finished"); break;} |
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| 220 | Cup = (-1)*transpose(jet(F_R,@d,@jv)); |
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| 221 | homFR = fetch(`myPx`,homFR); |
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[f1201a] | 222 | hom' = fetch(`myPx`,hom'); attrib(hom',"isSB",1); |
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| 223 | Cup' = simplify(reduce(Cup,hom'),10); |
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| 224 | tid = simplify(ideal(Cup'),10); |
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| 225 | if (tid[1]!=0) |
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| 226 | { dbprint(p-4,"// #"); |
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| 227 | Cup=Cup-Cup'; |
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[6f2edc] | 228 | } |
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[f1201a] | 229 | New = lift(homFR,Cup); |
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| 230 | Rn = matrix(ideal(New[1+@rowR..nrows(New),1]),@rowR,@colR); |
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| 231 | Fn = matrix(ideal(New[1..@rowR,1]),1,@rowR); |
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| 232 | Fs = Fs+Fn; |
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| 233 | Rs = Rs+Rn; |
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| 234 | F_R = Fs*Rs; |
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[82716e] | 235 | tid = 0+reduce(ideal(F_R),null); |
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[f1201a] | 236 | //---------------- fetch results into other rings ----------------------------- |
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| 237 | setring `myPx`; |
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| 238 | Fs = fetch(`myOx`,Fs); |
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| 239 | Rs = fetch(`myOx`,Rs); |
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| 240 | F_R = Fs*Rs; |
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| 241 | setring `myQx`; |
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| 242 | F_R = fetch(`myPx`,F_R); |
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| 243 | m_J = fetch(`myPx`,m_J); attrib(m_J,"isSB",1); |
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| 244 | J = fetch(`myPx`,J); attrib(J,"isSB",1); |
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[82716e] | 245 | Js = fetch(`myPx`,Js); |
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| 246 | tid = fetch(`myOx`,tid); |
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| 247 | if (tid[1]==0) { dbprint(p-1,"// finished");break;} |
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[6f2edc] | 248 | } |
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[f1201a] | 249 | //--------- end loop and final output ---------------------------------------- |
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| 250 | setring `myPx`; |
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| 251 | if (@out!="no") |
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| 252 | { string out = @out+"_"+string(@d); |
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[82716e] | 253 | "// writing file "+out+" with matrix Js, matrix Fs, matrix Rs ready |
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[f1201a] | 254 | for reading in rings "+myPx+" or "+myQx; |
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| 255 | write(out,"matrix Js[1][",@t2,"]=",Js,";matrix Fs[1][",@rowR,"]=",Fs, |
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| 256 | ";matrix Rs[",@rowR,"][",@colR,"]=",Rs,";"); |
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[82716e] | 257 | } |
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[f0c6f4] | 258 | dbprint(p-3,">>> TIME = "+string(timer-time)); |
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[f1201a] | 259 | if (@is_qh != 0) |
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| 260 | { @degr = qhweight(ideal(Js)); |
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| 261 | @degr = @degr[1..t1']; |
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| 262 | dbprint(p-1,"// quasi-homogeneous weights of miniversal base",@degr); |
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[82716e] | 263 | } |
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[f1201a] | 264 | dbprint(p-1, |
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| 265 | "// ___ Equations of miniversal base space ___",Js, |
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| 266 | "// ___ Equations of miniversal total space ___",Fs); |
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| 267 | dbprint(p,"","// Result belongs to ring "+myPx+".", |
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| 268 | "// Equations of total space of miniversal deformation are ", |
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| 269 | "// given by Fs, equations of miniversal base space by Js.", |
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| 270 | "// Make "+myPx+" the basering and list objects defined in " |
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| 271 | +myPx+" by typing:", |
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| 272 | " setring "+myPx+"; show("+myPx+");"," listvar(matrix);", |
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| 273 | "// NOTE: rings "+myQx+", "+myPx+", "+mySo+" are alive!", |
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[82716e] | 274 | "// (use 'kill_rings(\""+@my+"\");' to remove)"); |
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[f1201a] | 275 | return(); |
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[3d124a7] | 276 | } |
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[6f2edc] | 277 | example |
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[3d124a7] | 278 | { "EXAMPLE:"; echo = 2; |
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[6f2edc] | 279 | int p = printlevel; |
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[f1201a] | 280 | printlevel = 0; |
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[6f2edc] | 281 | ring r1 = 0,(x,y,z,u,v),ds; |
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| 282 | matrix m[2][4] = x,y,z,u,y,z,u,v; |
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[82716e] | 283 | ideal Fo = minor(m,2); |
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[f1201a] | 284 | // cone over rational normal curve of degree 4 |
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| 285 | versal(Fo); |
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| 286 | setring Px; |
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[6f2edc] | 287 | // ___ Equations of miniversal base space ___: |
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[f1201a] | 288 | Js;""; |
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[6f2edc] | 289 | // ___ Equations of miniversal total space ___: |
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[f1201a] | 290 | Fs;""; |
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[c67136] | 291 | if(system("with","Namespaces")) { kill Ring::Px,Top::Qx,Ring::So; } |
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[f1201a] | 292 | kill Px,Qx,So; |
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| 293 | ring r2 = 0,(x,y,z),ds; |
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| 294 | ideal Fo = x2,xy,yz,zx; |
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[6f2edc] | 295 | printlevel = 3; |
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[f1201a] | 296 | versal(Fo); |
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[6f2edc] | 297 | printlevel = p; |
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[c67136] | 298 | if(system("with","Namespaces")) { kill Ring::Px,Top::Qx,Ring::So; } |
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[f1201a] | 299 | kill Px,Qx,So; |
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[6f2edc] | 300 | } |
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[3d124a7] | 301 | /////////////////////////////////////////////////////////////////////////////// |
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[f1201a] | 302 | proc mod_versal(matrix Mo, ideal I, list #) |
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[d2b2a7] | 303 | " |
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[82716e] | 304 | USAGE: mod_versal(Mo,I[,d,any]); I=ideal, M=module, d=int, any =list |
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[f1201a] | 305 | COMUPTE: miniversal deformation of coker(Mo) over Qo=Po/Io, Po=basering; |
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| 306 | CREATE: Ringsr (exported): |
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| 307 | 'my'Px = extending the basering by new variables |
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| 308 | (deformation parameters), |
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| 309 | the new variables come before the old ones, |
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[d2b2a7] | 310 | the ordering is the product between \"my_ord\" and \"ord(Po)\", |
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[f1201a] | 311 | 'my'Qx = Px/Io extending Qo (returns as basering), |
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| 312 | 'my'Ox = Px/(Io+Js) ring of the versal deformation of coker(Ms), |
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[82716e] | 313 | 'my'So = embedding-ring of the versal base space. (default 'my'=\"\") |
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[f1201a] | 314 | Matrices (in Qx, exported): |
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| 315 | Js = giving the versal base space (obstructions), |
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| 316 | Ms = giving the versal family of Mo, |
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[82716e] | 317 | Ls = giving the lifting of syzygies Lo=syz(Mo), |
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[f1201a] | 318 | If d is defined (!=0), it computes up to degree d. |
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| 319 | If 'any' is defined and any[1] is no string, interactive version. |
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[d2b2a7] | 320 | Otherwise 'any' gives predefined strings:\"my\",\"param\",\"order\",\"out\" |
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| 321 | (\"my\" prefix-string, \"param\" is a letter (e.g. \"A\") for the name of |
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[82716e] | 322 | first parameter or (e.g. \"A(\") for index parameter variables, \"ord\" |
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[d2b2a7] | 323 | ordering string for ringextension), \"out\" name of output-file). |
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[f1201a] | 324 | NOTE: printlevel < 0 no output at all, |
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[82716e] | 325 | printlevel >=0,1,2,.. informs you, what is going on, |
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[f1201a] | 326 | this proc uses 'execute'. |
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| 327 | EXAMPLE:example mod_versal; shows an example |
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[d2b2a7] | 328 | " |
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[3d124a7] | 329 | { |
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[f1201a] | 330 | //------- prepare ------------------------------------------------------------- |
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| 331 | string str,@param,@order,@my,@out,@degrees; |
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| 332 | int @d,d_max,f0,f1,f2,e1,e1',e2,ok_ann,@smooth,@noObstr,@size,@j; |
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| 333 | int p = printlevel-voice+3; |
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| 334 | int time = timer; |
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| 335 | intvec @iv,@jv,@is_qh,@degr; |
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[82716e] | 336 | d_max = 100; |
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[f1201a] | 337 | @my = ""; @param="A"; @order="ds"; @out="no"; |
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| 338 | @size = size(#); |
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| 339 | if( @size>0 ) { d_max = #[1]; } |
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[82716e] | 340 | if( @size>1 ) |
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| 341 | { if(typeof(#[2])!="string") |
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[f1201a] | 342 | { string @active; |
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| 343 | @my,@param,@order,@out = interact1(); |
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| 344 | } |
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| 345 | else |
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| 346 | { @my = #[2]; |
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| 347 | if (@size>2) {@param = #[3];} |
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| 348 | if (@size>3) {@order = #[4];} |
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| 349 | if (@size>4) {@out = #[5];} |
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| 350 | } |
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[82716e] | 351 | } |
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[f1201a] | 352 | string myPx = @my+"Px"; |
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| 353 | string myQx = @my+"Qx"; |
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| 354 | string myOx = @my+"Ox"; |
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| 355 | string mySo = @my+"So"; |
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| 356 | @is_qh = qhweight(I); |
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| 357 | def Po = basering; |
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| 358 | setring Po; |
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| 359 | poly X_s = product(maxideal(1)); |
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| 360 | //-------- compute Ext's ------------------------------------------------------ |
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| 361 | I = std(I); |
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[82716e] | 362 | qring Qo = I; |
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[f1201a] | 363 | matrix Mo = fetch(Po,Mo); |
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[82716e] | 364 | list Lo = compute_ext(Mo,p); |
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[f1201a] | 365 | f0,f1,f2,e1,e2,ok_ann=Lo[1]; |
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| 366 | matrix Ls,kb1,lift1 = Lo[2],Lo[3],Lo[4]; |
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| 367 | matrix kb2,C',D' = Lo[5][2],Lo[5][3],Lo[5][5]; |
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| 368 | module ex2,Co,Do = Lo[5][1],Lo[5][4],Lo[5][6]; |
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| 369 | kill Lo; |
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| 370 | dbprint(p,"// ready: Ext1 and Ext2"); |
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| 371 | //----- test: quasi-homogeneous, choice of inf. def.-------------------------- |
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[82716e] | 372 | @degrees = homog_test(@is_qh,Mo,kb1); |
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[f1201a] | 373 | e1' = e1; @jv = 1..e1; |
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[82716e] | 374 | if (@degrees != "") |
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[f1201a] | 375 | { dbprint(p-1,"// Ext1 is quasi-homogeneous represented: "+@degrees); |
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| 376 | } |
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| 377 | if (defined(@active)) |
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| 378 | { "// kbase of Ext1:"; |
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[82716e] | 379 | print(kb1); |
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[f1201a] | 380 | "// weights of kbase of Ext1 ( empty = 'not qhomog')";@degrees; |
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| 381 | kb1,lift1,e1' = interact2(kb1,@jv,lift1); |
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[82716e] | 382 | } |
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[f1201a] | 383 | //-------- get new rings and objects ------------------------------------------ |
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| 384 | setring Po; |
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| 385 | get_rings(I,e1',0,@my,@order,@param); |
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| 386 | setring `myPx`; |
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| 387 | ideal J,m_J; |
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| 388 | ideal I_J = imap(Po,I); |
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| 389 | ideal Io = I_J; |
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| 390 | matrix Mon[e1'][1] = maxideal(1); |
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[82716e] | 391 | matrix Ms = imap(Qo,Mo); |
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| 392 | matrix Ls = imap(Qo,Ls); |
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| 393 | matrix Js[1][e2]; |
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[f1201a] | 394 | setring `myQx`; |
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| 395 | ideal J,I_J,tet,null; attrib(null,"isSB",1); |
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| 396 | ideal m_J = fetch(`myPx`,m_J); attrib(m_J,"isSB",1); |
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| 397 | @jv=0; @jv[e1] = 0; @jv = @jv+1; @jv[nvars(`myPx`)] = 0; |
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[82716e] | 398 | matrix Ms = imap(Qo,Mo); export(Ms); |
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[f1201a] | 399 | matrix Ls = imap(Qo,Ls); export(Ls); |
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| 400 | matrix Js[e2][1]; export(Js); |
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[82716e] | 401 | matrix MASS; |
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[f1201a] | 402 | matrix Mon = fetch(`myPx`,Mon); |
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| 403 | matrix Mn,Ln,ML,Cup,Cup',Lift; |
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| 404 | matrix C' = imap(Qo,C'); |
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| 405 | module Co = imap(Qo,Co); attrib(Co,"isSB",1); |
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| 406 | module ex2 = imap(Qo,ex2); attrib(ex2,"isSB",1); |
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| 407 | matrix D' = imap(Qo,D'); |
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| 408 | module Do = imap(Qo,Do); attrib(Do,"isSB",1); |
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[82716e] | 409 | matrix kb2 = imap(Qo,kb2); |
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[f1201a] | 410 | matrix kb1 = imap(Qo,kb1); |
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| 411 | matrix lift1= imap(Qo,lift1); |
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| 412 | poly X_s = imap(Po,X_s); |
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[82716e] | 413 | intvec intv = e1',e1,f0,f1,f2; |
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| 414 | Ms,Ls= get_inf_def(Ms,Ls,kb1,lift1,X_s); |
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[f1201a] | 415 | kill kb1,lift1; |
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| 416 | dbprint(p-1,"// infinitesimal extension",Ms); |
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| 417 | //----------- start the loop -------------------------------------------------- |
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| 418 | for (@d=2;@d<=d_max;@d=@d+1) |
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[82716e] | 419 | { |
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[f0c6f4] | 420 | dbprint(p-3,">>> time = "+string(timer-time)); |
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| 421 | dbprint(p-3,"==> memory = "+string(memory(0)/1000)+ |
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[f1201a] | 422 | ", allocated = "+string(memory(1)/1000)); |
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[82716e] | 423 | dbprint(p,"// start deg = "+string(@d)); |
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[f1201a] | 424 | //-------- get obstruction ---------------------------------------------------- |
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| 425 | Cup = matrix(ideal(Ms*Ls),f0*f2,1); |
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| 426 | Cup = jet(Cup,@d,@jv); |
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| 427 | Cup = reduce(ideal(Cup),m_J); |
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| 428 | Cup = jet(Cup,@d,@jv); |
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| 429 | //-------- express obstruction in kbase --------------------------------------- |
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| 430 | Cup' = reduce(Cup,Do); |
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| 431 | tet = simplify(ideal(Cup'),10); |
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[82716e] | 432 | if (tet[1]!=0) |
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[f1201a] | 433 | { dbprint(p-4,"// *"); |
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| 434 | Cup = Cup-Cup'; |
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| 435 | } |
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| 436 | Cup = lift(D',Cup); |
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| 437 | if (ok_ann) |
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| 438 | { MASS = lift_rel_kb(Cup,ex2,kb2,X_s);} |
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| 439 | else |
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[82716e] | 440 | { MASS = reduce(Cup,ex2);} |
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[f1201a] | 441 | dbprint(p-3,"// next MATRIC-MASSEY-products", |
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| 442 | MASS-jet(MASS,@d-1,@jv)); |
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| 443 | if ( MASS==transpose(Js)) |
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| 444 | { @noObstr = 1;dbprint(p-1,"//no obstruction"); } |
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[82716e] | 445 | else { @noObstr = 0; } |
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[f1201a] | 446 | //-------- obtain equations of base space ------------------------------------- |
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| 447 | if (@noObstr == 0) |
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| 448 | { Js = MASS; |
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| 449 | dbprint(p-2,"// next equation of base space:",simplify(ideal(Js),10)); |
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| 450 | setring `myPx`; |
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| 451 | Js = imap(`myQx`,Js); |
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| 452 | degBound=@d+1; |
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| 453 | J = std(ideal(Js)); |
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| 454 | m_J = std(ideal(Mon)*J); |
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| 455 | degBound=0; |
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| 456 | I_J = Io,J; attrib(I_J,"isSB",1); |
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[82716e] | 457 | //-------- obtain new base ring ----------------------------------------------- |
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[f1201a] | 458 | kill `myOx`; |
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[c67136] | 459 | if(system("with","Namespaces")==1) { |
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| 460 | if(defined(Top::`myOx`)) { kill Top::`myOx`; } |
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| 461 | } |
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[82716e] | 462 | qring `myOx` = I_J; |
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[f1201a] | 463 | ideal null,tet; attrib(null,"isSB",1); |
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| 464 | matrix Ms = imap(`myQx`,Ms); |
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| 465 | matrix Ls = imap(`myQx`,Ls); |
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| 466 | matrix Mn,Ln,ML,Cup,Cup',Lift; |
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[82716e] | 467 | matrix C' = imap(Qo,C'); |
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[f1201a] | 468 | module Co = imap(Qo,Co); attrib(Co,"isSB",1); |
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| 469 | module ex2 = imap(Qo,ex2); attrib(ex2,"isSB",1); |
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| 470 | matrix kb2 = imap(Qo,kb2); |
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| 471 | poly X_s = imap(Po,X_s); |
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[82716e] | 472 | } |
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[f1201a] | 473 | //-------- get lifts ---------------------------------------------------------- |
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| 474 | setring `myOx`; |
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| 475 | ML = matrix(reduce(ideal(Ms*Ls),null),f0,f2); |
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| 476 | Cup = matrix(ideal(ML),f0*f2,1); |
---|
| 477 | Cup = jet(Cup,@d,@jv); |
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| 478 | Cup'= reduce(Cup,Co); |
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[82716e] | 479 | tet = simplify(ideal(Cup'),10); |
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| 480 | if (tet[1]!=0) |
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[f1201a] | 481 | { dbprint(p-4,"// #"); |
---|
| 482 | Cup = Cup-Cup'; |
---|
| 483 | } |
---|
[82716e] | 484 | Lift = lift(C',Cup); |
---|
[f1201a] | 485 | Mn = matrix(ideal(Lift),f0,f1); |
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| 486 | Ln = matrix(ideal(Lift[f0*f1+1..nrows(Lift),1]),f1,f2); |
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| 487 | Ms = Ms-Mn; |
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| 488 | Ls = Ls-Ln; |
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| 489 | dbprint(p-3,"// next extension of Mo",Mn); |
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| 490 | dbprint(p-3,"// next extension of syz(Mo)",Ln); |
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| 491 | ML = reduce(ideal(Ms*Ls),null); |
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[82716e] | 492 | //--------- test: finished ---------------------------------------------------- |
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[f1201a] | 493 | tet = simplify(ideal(ML),10); |
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| 494 | if (tet[1]==0) { dbprint(p-1,"// finished in degree ",@d);} |
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| 495 | //---------fetch results into Qx and Px --------------------------------------- |
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| 496 | setring `myPx`; |
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| 497 | Ms = fetch(`myOx`,Ms); |
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[82716e] | 498 | Ls = fetch(`myOx`,Ls); |
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[f1201a] | 499 | setring `myQx`; |
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| 500 | Ms = fetch(`myOx`,Ms); |
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[82716e] | 501 | Ls = fetch(`myOx`,Ls); |
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[f1201a] | 502 | ML = Ms*Ls; |
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[82716e] | 503 | ML = matrix(reduce(ideal(ML),null),f0,f2); |
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[f1201a] | 504 | tet = imap(`myOx`,tet); |
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| 505 | if (tet[1]==0) { break;} |
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[82716e] | 506 | } |
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| 507 | //------- end of loop, final output ------------------------------------------- |
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[f1201a] | 508 | if (@out != "no") |
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| 509 | { string out = @out+"_"+string(@d); |
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[82716e] | 510 | "// writing file '"+out+"' with matrix Js, matrix Ms, matrix Ls |
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[f1201a] | 511 | ready for reading in rings "+myPx+" or "+myQx; |
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| 512 | write(out,"matrix Js[1][",e2,"]=",Js,";matrix Ms[",f0,"][",f1,"]=",Ms, |
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| 513 | ";matrix Ls[",f1,"][",f2,"]=",Ls,";"); |
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| 514 | } |
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[f0c6f4] | 515 | dbprint(p-3,">>> TIME = "+string(timer-time)); |
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[f1201a] | 516 | if (@is_qh != 0) |
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| 517 | { @degr = qhweight(ideal(Js)); |
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| 518 | @degr = @degr[1..e1']; |
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| 519 | dbprint(p-1,"// quasi-homogeneous weights of miniversal base",@degr); |
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[82716e] | 520 | } |
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[f1201a] | 521 | dbprint(p-1,"// Result belongs to qring "+myQx, |
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| 522 | "// Equations of total space of miniversal deformation are in Js", |
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| 523 | simplify(ideal(Js),10), |
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| 524 | "// Matrix of the deformed module is Ms and lifted syzygies are Ls.", |
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| 525 | "// Make "+myQx+" the basering and list objects defined in "+myQx+ |
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| 526 | " by typing:", |
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| 527 | " listvar(ring);setring "+myQx+"; show("+myQx+");listvar(ideal);"+ |
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| 528 | "listvar(matrix);", |
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| 529 | "// NOTE: rings "+myQx+", "+myOx+", "+mySo+" are still alive!", |
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| 530 | "// (use: 'kill_rings("+@my+");' to remove them)"); |
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| 531 | return(); |
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[3d124a7] | 532 | } |
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[6f2edc] | 533 | example |
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[3d124a7] | 534 | { "EXAMPLE:"; echo = 2; |
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[f1201a] | 535 | int p = printlevel; |
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| 536 | printlevel = 1; |
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| 537 | ring Ro = 0,(x,y),wp(3,4); |
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| 538 | ideal Io = x4+y3; |
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| 539 | matrix Mo[2][2] = x2,y,-y2,x2; |
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| 540 | mod_versal(Mo,Io); |
---|
| 541 | printlevel = p; |
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[c67136] | 542 | if(system("with","Namespaces")) { kill Ring::Px,Top::Qx,Ring::So; } |
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[82716e] | 543 | kill Px,Qx,So; |
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[3d124a7] | 544 | } |
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[82716e] | 545 | //============================================================================= |
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[3d124a7] | 546 | /////////////////////////////////////////////////////////////////////////////// |
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[f1201a] | 547 | proc kill_rings(list #) |
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[d2b2a7] | 548 | "USAGE: kill_rings([string]); |
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[82716e] | 549 | Sub-procedure: kills exported rings of 'versal' and |
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[f1201a] | 550 | 'mod_versal' with prefix 'string' |
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[d2b2a7] | 551 | " |
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[3d124a7] | 552 | { |
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[f1201a] | 553 | string my,br; |
---|
| 554 | if (size(#)>0) { my = #[1];} |
---|
| 555 | string na=nameof(basering); |
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| 556 | br = my+"Qx"; |
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| 557 | if (defined(`br`)) { kill `br`;} |
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| 558 | br = my+"Px"; |
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| 559 | if (defined(`br`)) { kill `br`;} |
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| 560 | br = my+"So"; |
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| 561 | if (defined(`br`)) { kill `br`;} |
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| 562 | br = my+"Ox"; |
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| 563 | if (defined(`br`)) { kill `br`;} |
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| 564 | br = my+"Sx"; |
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| 565 | if (defined(`br`)) { kill `br`} |
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[c67136] | 566 | if(system("with","Namespaces")) { |
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| 567 | br = my+"Qx"; |
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| 568 | if (defined(Top::`br`)) { kill Top::`br`;} |
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| 569 | br = my+"Ox"; |
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| 570 | if (defined(Top::`br`)) { kill Top::`br`;} |
---|
| 571 | br = my+"Px"; |
---|
| 572 | if (defined(Ring::`br`)) { kill Ring::`br`;} |
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| 573 | br = my+"So"; |
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| 574 | if (defined(Ring::`br`)) { kill Ring::`br`;} |
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| 575 | } |
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[f1201a] | 576 | if (defined(basering)==0) |
---|
| 577 | { "// choose new basering?"; |
---|
[c67136] | 578 | if(system("with","Namespaces")) { listvar(Top,ring); } |
---|
| 579 | else { listvar(ring); } |
---|
[f1201a] | 580 | } |
---|
| 581 | return(); |
---|
[3d124a7] | 582 | } |
---|
| 583 | /////////////////////////////////////////////////////////////////////////////// |
---|
[f1201a] | 584 | proc compute_ext(matrix Mo,int p) |
---|
[d2b2a7] | 585 | " |
---|
[f1201a] | 586 | Sub-procedure: obtain Ext1 and Ext2 and other objects used by mod_versal |
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[d2b2a7] | 587 | " |
---|
[82716e] | 588 | { |
---|
[f1201a] | 589 | int l,f0,f1,f2,f3,e1,e2,ok_ann; |
---|
| 590 | module Co,Do,ima,ex1,ex2; |
---|
[82716e] | 591 | matrix M0,M1,M2,ker,kb1,lift1,kb2,A,B,C,D; |
---|
[f1201a] | 592 | //------- resM --------------------------------------------------------------- |
---|
[3939bc] | 593 | list resM = nres(Mo,3); |
---|
[f1201a] | 594 | M0 = resM[1]; |
---|
| 595 | M1 = resM[2]; |
---|
| 596 | M2 = resM[3]; kill resM; |
---|
| 597 | f0 = nrows(M0); |
---|
| 598 | f1 = ncols(M0); |
---|
| 599 | f2 = ncols(M1); |
---|
| 600 | f3 = ncols(M2); |
---|
| 601 | //------ compute Ext^2 ------------------------------------------------------ |
---|
[82716e] | 602 | B = kohom(M0,f3); |
---|
[f1201a] | 603 | A = kontrahom(M2,f0); |
---|
[82716e] | 604 | D = modulo(A,B); |
---|
| 605 | Do = std(D); |
---|
[f1201a] | 606 | ima = kohom(M0,f2),kontrahom(M1,f0); |
---|
| 607 | ex2 = modulo(D,ima); |
---|
| 608 | ex2 = std(ex2); |
---|
| 609 | e2 = vdim(ex2); |
---|
| 610 | kb2 = kbase(ex2); |
---|
| 611 | dbprint(p,"// vdim (Ext^2) = "+string(e2)); |
---|
| 612 | //------ test: max = Ann(Ext2) ----------------------------------------------- |
---|
| 613 | for (l=1;l<=e2;l=l+1) |
---|
| 614 | { ok_ann = ok_ann+ord(kb2[l]); |
---|
| 615 | } |
---|
| 616 | if (ok_ann==0) |
---|
[82716e] | 617 | { e2 =nrows(ex2); |
---|
[f1201a] | 618 | dbprint(p,"// Ann(Ext2) is maximal"); |
---|
| 619 | } |
---|
| 620 | //------ compute Ext^1 ------------------------------------------------------- |
---|
[82716e] | 621 | B = kohom(M0,f2); |
---|
[f1201a] | 622 | A = kontrahom(M1,f0); |
---|
| 623 | ker = modulo(A,B); |
---|
[82716e] | 624 | ima = kohom(M0,f1),kontrahom(M0,f0); |
---|
[f1201a] | 625 | ex1 = modulo(ker,ima); |
---|
| 626 | ex1 = std(ex1); |
---|
| 627 | e1 = vdim(ex1); |
---|
| 628 | dbprint(p,"// vdim (Ext^1) = "+string(e1)); |
---|
| 629 | kb1 = kbase(ex1); |
---|
| 630 | kb1 = ker*kb1; |
---|
| 631 | C = concat(A,B); |
---|
| 632 | Co = std(C); |
---|
| 633 | //------ compute the liftings of Ext^1 --------------------------------------- |
---|
| 634 | lift1 = A*kb1; |
---|
[82716e] | 635 | lift1 = lift(B,lift1); |
---|
[f1201a] | 636 | intvec iv = f0,f1,f2,e1,e2,ok_ann; |
---|
| 637 | list L' = ex2,kb2,C,Co,D,Do; |
---|
| 638 | return(iv,M1,kb1,lift1,L'); |
---|
[3d124a7] | 639 | } |
---|
[f1201a] | 640 | ////////////////////////////////////////////////////////////////////////////// |
---|
| 641 | proc get_rings(ideal Io,int e1,int switch, list #) |
---|
[d2b2a7] | 642 | " |
---|
[82716e] | 643 | Sub-procedure: creating ring-extensions |
---|
[d2b2a7] | 644 | " |
---|
[82716e] | 645 | { |
---|
| 646 | def Po = basering; |
---|
[f1201a] | 647 | string my; |
---|
| 648 | string my_ord = "ds"; |
---|
[82716e] | 649 | string my_var = "A"; |
---|
[f1201a] | 650 | if (size(#)>2) |
---|
[3d124a7] | 651 | { |
---|
[f1201a] | 652 | my = #[1]; |
---|
| 653 | my_ord = #[2]; |
---|
| 654 | my_var = #[3]; |
---|
[3d124a7] | 655 | } |
---|
[82716e] | 656 | string my_Px = my+"Px"; |
---|
| 657 | string my_Qx = my+"Qx"; |
---|
| 658 | string my_Ox = my+"Ox"; |
---|
| 659 | string my_So = my+"So"; |
---|
[f1201a] | 660 | extendring(my_Px,e1,my_var,my_ord); |
---|
| 661 | ideal Io = imap(Po,Io); attrib(Io,"isSB",1); |
---|
| 662 | my ="qring "+my_Qx+" = Io; export("+my_Qx+");"; |
---|
| 663 | execute(my); |
---|
| 664 | if (switch) |
---|
[3d124a7] | 665 | { |
---|
[f1201a] | 666 | setring `my_Px`; |
---|
| 667 | my = "qring "+my_Ox+" = std(ideal(0));export("+my_Ox+");"; |
---|
[3d124a7] | 668 | } |
---|
[f1201a] | 669 | else |
---|
[6f2edc] | 670 | { |
---|
[f1201a] | 671 | my = "def "+my_Ox+" = "+my_Qx+";export("+my_Ox+");"; |
---|
[3d124a7] | 672 | } |
---|
[f1201a] | 673 | execute(my); |
---|
| 674 | defring(my_So,charstr(Po),e1,my_var,my_ord); |
---|
| 675 | return(); |
---|
[3d124a7] | 676 | } |
---|
[f1201a] | 677 | ////////////////////////////////////////////////////////////////////////////// |
---|
[d2b2a7] | 678 | proc get_inf_def(list #) |
---|
| 679 | " |
---|
[82716e] | 680 | Sub-procedure: compute infinitesimal family of a module and its syzygies |
---|
[f1201a] | 681 | from a kbase of Ext1 and its lifts |
---|
[d2b2a7] | 682 | " |
---|
[f1201a] | 683 | { |
---|
| 684 | matrix Ms = #[1]; |
---|
| 685 | matrix Ls = #[2]; |
---|
| 686 | matrix kb1 = #[3]; |
---|
| 687 | matrix li1 = #[4]; |
---|
| 688 | int e1,f0,f1,f2; |
---|
| 689 | poly X_s = #[5]; |
---|
| 690 | e1 = ncols(kb1); |
---|
| 691 | f0 = nrows(Ms); |
---|
| 692 | f1 = nrows(Ls); |
---|
| 693 | f2 = ncols(Ls); |
---|
| 694 | int l; |
---|
| 695 | for (l=1;l<=e1;l=l+1) |
---|
| 696 | { |
---|
| 697 | Ms = Ms + var(l)*matrix(ideal(kb1[l]),f0,f1); |
---|
| 698 | Ls = Ls - var(l)*matrix(ideal(li1[l]),f1,f2); |
---|
| 699 | } |
---|
| 700 | return(Ms,Ls); |
---|
[82716e] | 701 | } |
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[f1201a] | 702 | ////////////////////////////////////////////////////////////////////////////// |
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| 703 | proc lift_rel_kb (module N, module M, list #) |
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[d2b2a7] | 704 | " |
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[f1201a] | 705 | USAGE lift_rel_kb(N,M[,kbaseM,p]); |
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| 706 | ASSUME [p a monomial ] or the product of all variables |
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| 707 | N, M modules of same rank, |
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| 708 | M depending only on variables not in p and vdim(M) finite in this ring, |
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[82716e] | 709 | [ kbaseM the kbase of M in the subring given by variables not in p ] |
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[f1201a] | 710 | warning: check that these assumtions are fulfilled! |
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| 711 | RETURN matrix A, whose j-th columnes present the coeff's of N[j] in kbaseM, |
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| 712 | i.e. kbaseM*A = reduce(N,std(M)) |
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| 713 | EXAMPLE example lift_rel_kb; shows examples |
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[d2b2a7] | 714 | " |
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[f1201a] | 715 | { |
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| 716 | poly p = product(maxideal(1)); |
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| 717 | M = std(M); |
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[82716e] | 718 | matrix A; |
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[f1201a] | 719 | if (size(#)>0) { p=#[2]; module kbaseM=#[1];} |
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[82716e] | 720 | else |
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[f1201a] | 721 | { if (vdim(M)<=0) { "// vdim(M) not finite";return(A);} |
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| 722 | module kbaseM = kbase(M); |
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| 723 | } |
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| 724 | N = reduce(N,M); |
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| 725 | if (simplify(N,10)[1]==[0]) {return(A);} |
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| 726 | A = coeffs(N,kbaseM,p); |
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| 727 | return(A); |
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[82716e] | 728 | } |
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[3d124a7] | 729 | example |
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[f1201a] | 730 | { |
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| 731 | "EXAMPLE"; echo=2; |
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| 732 | ring r=0,(A,B,x,y),dp; |
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| 733 | module M = [x2,xy],[xy,y3],[y2],[0,x]; |
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| 734 | module kbaseM = [1],[x],[xy],[y],[0,1],[0,y],[0,y2]; |
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| 735 | poly f=xy; |
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| 736 | module N = [AB,BBy],[A3xy+x4,AB*(1+y2)]; |
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| 737 | matrix A = lift_rel_kb(N,M,kbaseM,f); |
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| 738 | print(A); |
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| 739 | "TEST:"; |
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| 740 | print(matrix(kbaseM)*A-matrix(reduce(N,std(M)))); |
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| 741 | "2nd EXAMPLE"; |
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| 742 | ring r = 100,(x,y),dp; |
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| 743 | ideal I = x2+y2,x2y; |
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| 744 | module M = jacob(I)+I*freemodule(2); |
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| 745 | module N = [x+y,1+x2+xy]; |
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| 746 | matrix A = lift_rel_kb(N,M); |
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[3d124a7] | 747 | print(A); |
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[f1201a] | 748 | print(kbase(std(M))*A); |
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| 749 | print(reduce(N,std(M))); |
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[82716e] | 750 | } |
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[f0c6f4] | 751 | /////////////////////////////////////////////////////////////////////////////// |
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| 752 | proc lift_kbase (N, M) |
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[d2b2a7] | 753 | "USAGE: lift_kbase(N,M); N,M=poly/ideal/vector/module |
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[f0c6f4] | 754 | RETURN: matrix A, coefficient matrix expressing N as linear combination of |
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| 755 | k-basis of M. Let the k-basis have k elements and size(N)=c columns. |
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| 756 | Then A satisfies: |
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| 757 | matrix(reduce(N,std(M)),k,c) = matrix(kbase(std(M)))*A |
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| 758 | ASSUME: dim(M)=0 and the monomial ordering is a well ordering or the last |
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| 759 | block of the ordering is c or C |
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| 760 | EXAMPLE: example lift_kbase; shows an example |
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[d2b2a7] | 761 | " |
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[f0c6f4] | 762 | { |
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| 763 | return(lift_rel_kb(N,M)); |
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| 764 | } |
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| 765 | example |
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| 766 | {"EXAMPLE:"; echo=2; |
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| 767 | ring R=0,(x,y),ds; |
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| 768 | module M=[x2,xy],[y2,xy],[0,xx],[0,yy]; |
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| 769 | module N=[x3+xy,x],[x,x+y2]; |
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| 770 | print(M); |
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| 771 | module kb=kbase(std(M)); |
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| 772 | print(kb); |
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| 773 | print(N); |
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| 774 | matrix A=lift_kbase(N,M); |
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| 775 | print(A); |
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| 776 | matrix(reduce(N,std(M)),nrows(kb),ncols(A)) - matrix(kbase(std(M)))*A; |
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| 777 | } |
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| 778 | |
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| 779 | |
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[f1201a] | 780 | /////////////////////////////////////////////////////////////////////////////// |
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| 781 | proc interact1 () |
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[d2b2a7] | 782 | " |
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[82716e] | 783 | Sub_procedure: asking for and reading your input-strings |
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[d2b2a7] | 784 | " |
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[f1201a] | 785 | { |
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| 786 | string my = "@"; |
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| 787 | string str,out,my_ord,my_var; |
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| 788 | my_ord = "ds"; |
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[82716e] | 789 | my_var = "A"; |
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[f1201a] | 790 | "INPUT: name of output-file (ENTER = no output, do not use \"my\"!)"; |
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[82716e] | 791 | str = read(""); |
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| 792 | if (size(str)>1) |
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[f1201a] | 793 | { out = str[1..size(str)-1];} |
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| 794 | else |
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| 795 | { out = "no";} |
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| 796 | "INPUT: prefix-string of ring-extension (ENTER = '@')"; |
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[82716e] | 797 | str = read(""); |
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| 798 | if ( size(str) > 1 ) |
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| 799 | { my = str[1..size(str)-1]; } |
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| 800 | "INPUT:parameter-string |
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[f1201a] | 801 | (give a letter corresponding to first new variable followed by the next letters, |
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| 802 | or 'T(' - a letter + '(' - getting a string of indexed variables) |
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| 803 | (ENTER = A) :"; |
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[82716e] | 804 | str = read(""); |
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[f1201a] | 805 | if (size(str)>1) { my_var=str[1..size(str)-1]; } |
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| 806 | "INPUT:order-string (local or weighted!) (ENTER = ds) :"; |
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[82716e] | 807 | str = read(""); |
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| 808 | if (size(str)>1) { my_ord=str[1..size(str)-1]; } |
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[f1201a] | 809 | if( find(my_ord,"s")+find(my_ord,"w") == 0 ) |
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| 810 | { "// ordering must be an local! changed into 'ds'"; |
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| 811 | my_ord = "ds"; |
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| 812 | } |
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| 813 | return(my,my_var,my_ord,out); |
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[3d124a7] | 814 | } |
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| 815 | /////////////////////////////////////////////////////////////////////////////// |
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[f1201a] | 816 | proc interact2 (matrix A, intvec col_vec, list #) |
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[d2b2a7] | 817 | " |
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[f1201a] | 818 | Sub-procedure: asking for and reading your input |
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[d2b2a7] | 819 | " |
---|
[3d124a7] | 820 | { |
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[f1201a] | 821 | module B,C; |
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| 822 | matrix D; |
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| 823 | int flag; |
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| 824 | if (size(#)>0) { D=#[1];flag=1;} |
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| 825 | int t1 = ncols(A); |
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| 826 | ">>Do you want all deformations? (ENTER=yes)"; |
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| 827 | string str = read(""); |
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| 828 | if (size(str)>1) |
---|
| 829 | { ">> Choose columnes of the matrix"; |
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[82716e] | 830 | ">> (Enter = all columnes)"; |
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[f1201a] | 831 | "INPUT (number of columnes to use as integer-list 'i_1,i_2,.. ,i_t' ):"; |
---|
| 832 | string columnes = read(""); |
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| 833 | if (size(columnes)<2) {columnes=string(col_vec);} |
---|
| 834 | t1 = size(columnes)/2; |
---|
| 835 | int l,l1; |
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| 836 | for (l=1;l<=t1;l=l+1) |
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[3d124a7] | 837 | { |
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[f1201a] | 838 | execute("l1= "+columnes[2*l-1]+";"); |
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| 839 | B[l] = A[l1]; |
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[82716e] | 840 | if(flag) { C[l]=D[l1];} |
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[3d124a7] | 841 | } |
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[f1201a] | 842 | A = matrix(B,nrows(A),size(B)); |
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| 843 | D = matrix(C,nrows(D),size(C)); |
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[6f2edc] | 844 | } |
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[f1201a] | 845 | return(A,D,t1); |
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[6f2edc] | 846 | } |
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[f1201a] | 847 | /////////////////////////////////////////////////////////////////////////////// |
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| 848 | proc negative_part(intvec iv) |
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[d2b2a7] | 849 | " |
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[82716e] | 850 | RETURNS intvec of indices of jv having negative entries (or iv, if non) |
---|
[d2b2a7] | 851 | " |
---|
[f1201a] | 852 | { |
---|
| 853 | intvec jv; |
---|
| 854 | int l,k; |
---|
| 855 | for (l=1;l<=size(iv);l=l+1) |
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[82716e] | 856 | { if (iv[l]<0) |
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[f1201a] | 857 | { k = k+1; |
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| 858 | jv[k]=l; |
---|
| 859 | } |
---|
| 860 | } |
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[75089b] | 861 | if (jv==0) {jv=1; dbprint(printlevel-1,"// empty negative part, return all ");} |
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[f1201a] | 862 | return(jv); |
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[3d124a7] | 863 | } |
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| 864 | /////////////////////////////////////////////////////////////////////////////// |
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[f1201a] | 865 | proc find_ord(matrix A, intvec w_vec) |
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[d2b2a7] | 866 | " |
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[f1201a] | 867 | Sub-proc: return martix ord(a_ij) with respect to weight_vec, or |
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| 868 | 0 if A non-qh |
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[d2b2a7] | 869 | " |
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[f1201a] | 870 | { |
---|
| 871 | int @r = nrows(A); |
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| 872 | int @c = ncols(A); |
---|
| 873 | int i,j; |
---|
| 874 | string ord_str = "wp("+string(w_vec)+")"; |
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| 875 | def br = basering; |
---|
| 876 | changeord("nr",ord_str); |
---|
| 877 | matrix A = imap(br,A); |
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| 878 | intmat degA[@r][@c]; |
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[82716e] | 879 | if (homog(ideal(A))) |
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[f1201a] | 880 | { for (i=1;i<=@r;i=i+1) |
---|
| 881 | { for(j=1;j<=@c;j=j+1) |
---|
| 882 | { degA[i,j]=ord(A[i,j]); } |
---|
| 883 | } |
---|
| 884 | } |
---|
| 885 | setring br; |
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[c67136] | 886 | if(system("with","Namespaces")) { kill Ring::nr; } |
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[82716e] | 887 | kill nr; |
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[f1201a] | 888 | return(degA); |
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| 889 | } |
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| 890 | ////////////////////////////////////////////////////////////////////////////////// |
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| 891 | proc homog_test(intvec w_vec, matrix Mo, matrix A) |
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[d2b2a7] | 892 | " |
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[82716e] | 893 | Sub proc: return relative weight string of columnes of A with respect |
---|
| 894 | to the given w_vec and to Mo, or \"\" if not qh |
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[f1201a] | 895 | NOTE: * means weight is not determined |
---|
[d2b2a7] | 896 | " |
---|
[f1201a] | 897 | { |
---|
| 898 | int k,l; |
---|
| 899 | intvec tv; |
---|
| 900 | string @nv; |
---|
| 901 | int @r = nrows(A); |
---|
| 902 | int @c = ncols(A); |
---|
[82716e] | 903 | A = concat(matrix(ideal(Mo),@r,1),A); |
---|
| 904 | intmat a = find_ord(A,w_vec); |
---|
[f1201a] | 905 | intmat b[@r][@c]; |
---|
| 906 | for (l=1;l<=@c;l=l+1) |
---|
[82716e] | 907 | { |
---|
[f1201a] | 908 | for (k=1;k<=@r;k=k+1) |
---|
[82716e] | 909 | { if (A[k,l+1]!=0) |
---|
[f1201a] | 910 | { b[k,l] = a[k,l+1]-a[k,1];} |
---|
| 911 | } |
---|
| 912 | tv = 0; |
---|
| 913 | for (k=1;k<=@r;k=k+1) |
---|
[82716e] | 914 | { if (A[k,l+1]*A[k,1]!=0) |
---|
[f1201a] | 915 | {tv = tv,b[k,l];} |
---|
| 916 | } |
---|
| 917 | if (size(tv)>1) |
---|
[82716e] | 918 | { k = tv[2]; |
---|
[f1201a] | 919 | tv = tv[2..size(tv)]; tv = tv -k; |
---|
[82716e] | 920 | if (tv==0) { @nv = @nv+string(-k)+",";} |
---|
[f1201a] | 921 | else {return("");} |
---|
| 922 | } |
---|
| 923 | else { @nv = @nv+"*,";} |
---|
| 924 | } |
---|
| 925 | @nv = @nv[1..size(@nv)-1]; |
---|
| 926 | return(@nv); |
---|
| 927 | } |
---|
| 928 | ////////////////////////////////////////////////////////////////////////////////// |
---|
| 929 | proc homog_t(intvec d_vec, matrix Fo, matrix A) |
---|
[d2b2a7] | 930 | " |
---|
[82716e] | 931 | Sub-procedure: Computing relative (with respect to flatten(Fo)) weight_vec |
---|
[f1201a] | 932 | of columnes of A (return zero if Fo or A not qh) |
---|
[d2b2a7] | 933 | " |
---|
[f1201a] | 934 | { |
---|
| 935 | Fo = matrix(Fo,nrows(A),1); |
---|
| 936 | A = concat(Fo,A); |
---|
| 937 | A = transpose(A); |
---|
| 938 | def br = basering; |
---|
| 939 | string o_str = "wp("+string(d_vec)+")"; |
---|
| 940 | changeord("nr",o_str); |
---|
| 941 | module A = fetch(br,A); |
---|
| 942 | intvec dv; |
---|
| 943 | int l = homog(A) ; |
---|
[c67136] | 944 | if (l==0) { |
---|
| 945 | setring br; |
---|
| 946 | if(system("with","Namespaces")) { kill Ring::nr; } |
---|
| 947 | kill nr; |
---|
| 948 | return(l); |
---|
| 949 | } |
---|
[f1201a] | 950 | dv = attrib(A,"isHomog"); |
---|
| 951 | l = dv[1]; |
---|
| 952 | dv = dv[2..size(dv)]; |
---|
| 953 | dv = dv-l; |
---|
[82716e] | 954 | setring br; |
---|
[c67136] | 955 | if(system("with","Namespaces")) { kill Ring::nr; } |
---|
[f1201a] | 956 | kill nr; |
---|
| 957 | return(dv); |
---|
| 958 | } |
---|
[e7a0fa] | 959 | |
---|