SINGULAR                                 /
 A Computer Algebra System for Polynomial Computations       /   version 3-1-6
                                                           0<
 by: W. Decker, G.-M. Greuel, G. Pfister, H. Schoenemann     \   Dec 2012
FB Mathematik der Universitaet, D-67653 Kaiserslautern        \
STDIN   1> //
STDIN   2. // version 2013
STDIN   3. //
STDIN   4. timer=1;
STDIN   5> ring r=(integer,204),(u,v,a),dp;
STDIN   6> int b=0;
STDIN   7> matrix Z[5][5]; Z=Z+1;
STDIN   8> execute(read("fu_dataL.sing"));
STDIN   9> matrix tauL[1][5]; tauL=gen(1)*(1, b*v-a+u, 1, 1, a*u-b+v);
STDIN  10> matrix Z[315][315]; Z=Z+1;
// ** redefining Z **
STDIN  11> execute(read("fu_data0.sing"));
//used time: 2.19 sec
//used time: 0.64 sec
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//used time: 7.79 sec
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//used time: 2.36 sec
STDIN  12> matrix t = matrix(rho(0),315,315);
STDIN  13> matrix t2=t*t;
STDIN  14> matrix t3=t2*t;
STDIN  15> module m=t3;
STDIN  16> matrix tau=m;
STDIN  17> vector vec=transpose(tau)[1];
STDIN  18> matrix tau[1][315]=vec;
// ** redefining tau **
STDIN  19> matrix mJ40 = matrix(J40,315,size(J40));
STDIN  20> 
STDIN  21. ideal IL; ideal I;
STDIN  22> IL=tauL*matrix(L0,5,size(L0)); IL=std(IL);
STDIN  23> 
STDIN  24. I=tau*matrix(J40,315,size(J40));
STDIN  25> I=std(I);
//used time: 1.49 sec
STDIN  26> 
STDIN  27. I=reduce(I,IL);
STDIN  28> I=I,IL; I=std(I);
STDIN  29> 
STDIN  30. ideal I1=I; ideal I2; int change=1; int i; int j; poly f; int count=0;
STDIN  31> while(change){change=0; count++;
STDIN  33.   for(i=1; i<=size(I1); i++){I2=0; 
STDIN  35.     for(j=1; j<=size(I1); j++){ if(j!=i){I2=I2,I1[j];}}
STDIN  37.     f=reduce(I1[i],I2);
STDIN  39.     if(f!=I1[i]){change=1; I1=I2,f; I1=std(I1); break;}
STDIN  41.   }
STDIN  43. }
// ** I2 is no standard basis
// ** I2 is no standard basis
// ** I2 is no standard basis
// ** I2 is no standard basis
// ** I2 is no standard basis
// ** I2 is no standard basis
// ** I2 is no standard basis
// ** I2 is no standard basis
// ** I2 is no standard basis
// ** I2 is no standard basis
// ** I2 is no standard basis
// ** I2 is no standard basis
// ** I2 is no standard basis
// ** I2 is no standard basis
// ** I2 is no standard basis
// ** I2 is no standard basis
// ** I2 is no standard basis
// ** I2 is no standard basis
// ** I2 is no standard basis
// ** I2 is no standard basis
// ** I2 is no standard basis
// ** I2 is no standard basis
// ** I2 is no standard basis
// ** I2 is no standard basis
// ** I2 is no standard basis
// ** I2 is no standard basis
// ** I2 is no standard basis
// ** I2 is no standard basis
// ** I2 is no standard basis
// ** I2 is no standard basis
STDIN  44> I=I1;
STDIN  45> 
STDIN  46. matrix Z5[5][5]; Z5=Z5+1;
STDIN  47> 
STDIN  48. int i;
// ** redefining i **
STDIN  49> module mL=L0;
STDIN  50> for(i=1; i<=size(I); i++){mL=mL,module(I[i]*Z5);}
STDIN  51> mL=std(mL);
STDIN  52> 
STDIN  53. module m1L=mL;
STDIN  54> for( int i=0; i<9; i++ ){mL=mL,matrix(rhoL(i),5,5)*matrix(m1L,5,size(m1L));}
// ** redefining i **
STDIN  55> mL=groebner(mL);
//used time: 0.82 sec
STDIN  56> ideal I1L;
STDIN  57> I1L=tauL*matrix(mL,5,size(mL)); I1L=std(I1L);
STDIN  58> I1L=reduce(I1L,I);
STDIN  59> I1L;
I1L[1]=0
I1L[2]=0
I1L[3]=0
I1L[4]=0
I1L[5]=0
I1L[6]=0
I1L[7]=0
I1L[8]=0
I1L[9]=17uv3a+187v3a2+153ua4+153u3v+17v4+153va3+17uv2+119v2a+153v
I1L[10]=17u2v2a+85v2a3+153u4+17uv3+34u3a+68v3a+153ua3+51a4+17u2v+187uva+153va2+68v2+17u+170a
I1L[11]=17u3va+51v4a+102uv2a+17v2a2+119u3+187v3+102ua2+153a3+51uv+34va+51
I1L[12]=u4a+65uv3a+88v3a2+153ua4+153a5+202u3v+74v4+103u2va+54va3+78uv2+74v2a+105ua+48a2+198v
I1L[13]=0
I1L[14]=0
I1L[15]=ua5+188u4v+184uv4+44u3va+80v4a+20u2v2+25uv2a+196v2a2+137u3+181v3+10u2a+5ua2+104a3+149uv+133va+101
I1L[16]=3ua5+20u4v+144uv4+200u3va+36v4a+196u2v2+143uv2a+180v2a2+139u3+203v3+166u2a+15ua2+108a3+175uv+127va+99
I1L[17]=v4a2+12u3v2+168v5+52u2v2a+110u4+130uv3+135u3a+41v3a+132ua3+109a4+82u2v+57uva+175va2+188v2+46u+159a
I1L[18]=v5a+141u5+145u2v3+64uv3a+32v3a2+149ua4+142a5+26u3v+161v4+195u2va+50va3+189uv2+124v2a+93u2+76ua+152a2+45v
I1L[19]=uv4a+203v4a2+45u3v2+49v5+56u2v2a+184u4+145uv3+102u3a+57v3a+153ua3+12u2v+190uva+116va2+9v2+28u+190a
I1L[20]=u2v3a+145a6+121u4v+9uv4+56u3va+26v4a+173u2v2+88uv2a+22v2a2+103u3+7v3+32ua2+65a3+176uv+25va+83
I1L[21]=u3v2a+35v5a+164u2v3+90uv3a+109v3a2+64ua4+176a5+139u3v+79v4+84u2va+127va3+3uv2+14v2a+8u2+68ua+58a2+95v
I1L[22]=0
I1L[23]=0
I1L[24]=0
I1L[25]=0
I1L[26]=0
I1L[27]=u6+103v6+108u4v+6uv4+32u3va+88v4a+59u2v2+175uv2a+86v2a2+49u3+159v3+102u2a+49ua2+128a3+19uv+23va+44
I1L[28]=0
STDIN  60> 
STDIN  61. I=I,I1L; I=std(I);
STDIN  62> 
STDIN  63. module m1L=mL;
// ** redefining m1L **
STDIN  64> module m2L=m1L;
STDIN  65> 
STDIN  66. for( i=0; i<9; i++ ){print(i);
STDIN  68.   mL=matrix(rhoL(i),5,5)*matrix(m1L,5,size(m1L));
STDIN  70.   mL=reduce(mL,m2L);
STDIN  72.   m2L=m2L,mL;
STDIN  74.   m2L=groebner(m2L);
STDIN  76.   print(size(m2L));
STDIN  78. }
0
99
1
99
2
99
3
99
4
99
5
99
6
99
7
99
8
99
STDIN  79> 
STDIN  80. IL=tauL*matrix(m2L,5,size(m2L)); IL=reduce(IL,I); groebner(IL);
_[1]=0
STDIN  81> 
STDIN  82. module m3L=m2L;
STDIN  83> for( i=0; i<9; i++ ){print(i);
STDIN  85.   mL=matrix(rhoL(i),5,5)*matrix(m2L,5,size(m2L));
STDIN  87.   mL=reduce(mL,m3L);
STDIN  89.   m3L=m3L,mL;
STDIN  91.   m3L=groebner(m3L);
STDIN  93.   print(size(m3L));
STDIN  95. }
0
99
1
99
2
99
3
99
4
99
5
99
6
99
7
99
8
99
STDIN  96> 
STDIN  97. reduce(m3L,m2L);
_[1]=0
_[2]=0
_[3]=0
_[4]=0
_[5]=0
_[6]=0
_[7]=0
_[8]=0
_[9]=0
_[10]=0
_[11]=0
_[12]=0
_[13]=0
_[14]=0
_[15]=0
_[16]=0
_[17]=0
_[18]=0
_[19]=0
_[20]=0
_[21]=0
_[22]=0
_[23]=0
_[24]=0
_[25]=0
_[26]=0
_[27]=0
_[28]=0
_[29]=0
_[30]=0
_[31]=0
_[32]=0
_[33]=0
_[34]=0
_[35]=0
_[36]=0
_[37]=0
_[38]=0
_[39]=0
_[40]=0
_[41]=0
_[42]=0
_[43]=0
_[44]=0
_[45]=0
_[46]=0
_[47]=0
_[48]=0
_[49]=0
_[50]=0
_[51]=0
_[52]=0
_[53]=0
_[54]=0
_[55]=0
_[56]=0
_[57]=0
_[58]=0
_[59]=0
_[60]=0
_[61]=0
_[62]=0
_[63]=0
_[64]=0
_[65]=0
_[66]=0
_[67]=0
_[68]=0
_[69]=0
_[70]=0
_[71]=0
_[72]=0
_[73]=0
_[74]=0
_[75]=0
_[76]=0
_[77]=0
_[78]=0
_[79]=0
_[80]=0
_[81]=0
_[82]=0
_[83]=0
_[84]=0
_[85]=0
_[86]=0
_[87]=0
_[88]=0
_[89]=0
_[90]=0
_[91]=0
_[92]=0
_[93]=0
_[94]=0
_[95]=0
_[96]=0
_[97]=0
_[98]=0
_[99]=0
STDIN  98> IL=tauL*matrix(m2L,5,size(m2L)); IL=reduce(IL,I); groebner(IL);
_[1]=0
STDIN  99> 
STDIN 100. ideal I1;
// ** redefining I1 **
STDIN 101> m=matrix(rho(2),315,315)*matrix(J40,315,size(J40));
STDIN 102> I1=tau*matrix(m,315,size(m)); I1=reduce(I1,I);
STDIN 103> I=I,I1; I=std(I);
STDIN 104> print(size(I));
22
STDIN 105> I;
I[1]=68u2+68v
I[2]=34a3+68
I[3]=68uva+136va2+68v2+68u+68a
I[4]=68v3+136ua2+136uv+136va
I[5]=68uv2+136ua+68a2+68v
I[6]=17a4+136a
I[7]=v2a2+102u2a+ua2+25a3+4uv+98va
I[8]=uva2+203va3+202v2a+92u2+202ua+a2+92v
I[9]=u2a2+202uva+3va2+4v2+4u+202a
I[10]=4v3a+116ua3+120a4+96u2v+128uva+68va2+12v2+60u+72a
I[11]=uv2a+69u3+v3+66u2a+ua2+65uv+69va+1
I[12]=u3a+71v3a+60a4+44u2v+59uva+10va2+188v2+76u+201a
I[13]=4v4+28u2va+64va3+128uv2+124v2a+20u2+184ua+136a2+108v
I[14]=4uv3+108u3a+72v3a+96ua3+100a4+164u2v+72uva+84va2+52v2+76u+12a
I[15]=4u2v2+180uv2a+144v2a2+88u3+156v3+172u2a+196ua2+152uv+80va+120
I[16]=4u3v+156u2va+16va3+200uv2+128u2+140ua+4a2+56v
I[17]=4u4+60uv3+192u3a+132v3a+144ua3+60a4+4u2v+72uva+144va2+84v2+12u+168a
I[18]=a5+124u3v+144v4+20u2va+192va3+32uv2+44v2a+96u2+44ua+12a2+88v
I[19]=va4+5v2a2+112u3+4v3+114u2a+ua2+203a3+116uv+110va
I[20]=ua4+139a5+104u3v+164v4+152u2va+28va3+124uv2+164v2a+124u2+20a2+164v
I[21]=v5a+73u5+101u2v3+50u3v+125v4+131u2va+62va3+45uv2+92v2a+133u2+148ua+140a2+93v
I[22]=u6+95v6+18uv4+155u2v2+198u3+92v3+176u2a+72ua2+30a3+156uv+136va+101
STDIN 106> 
STDIN 107. module m1=J40;
STDIN 108> for( i=1; i<=size(I); i++){print(i);
STDIN 110.   m=module(I[i]*Z); m=std(m); m1=reduce(m1,m); print(size(m1));
STDIN 112.   m1=m,m1; m1=groebner(m1); print(size(m1));
STDIN 114. }
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STDIN 115> 
STDIN 116. module mm;
STDIN 117> module m2=m1; int j;
// ** redefining j **
STDIN 118> for( i=0; i<31; i++ ){print("--------");print(i);
STDIN 120.   m=matrix(rho(i),315,315)*matrix(J40,315,size(J40));
STDIN 122.   mm=t*m; m=m,mm; mm=t*m; m=m,mm;
STDIN 124.   m=reduce(m,m2); m2=m2,m; print(size(m));
STDIN 126.   if( size(m)>0 ){
STDIN 128.     I1=tau*matrix(m,315,size(m)); I1=reduce(I1,I);
STDIN 130.     I1=groebner(I1); print(I1);
STDIN 132.     if( size(I1)>1 | I1[1]!=0 ){
STDIN 134.       I=reduce(I,I1); I=I,I1; I=std(I); print("I=");print(I);print("----");
STDIN 136.       for( j=1; j<=size(I1); j++ ){m=module(I1[j]*Z); m2=m2,m;}
STDIN 138.     }
STDIN 140.   }
STDIN 142.   m2=groebner(m2);
STDIN 144.   print(size(m2));
STDIN 146. }
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0
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6874
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3340
--------
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0
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3340
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1996
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0
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1996
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24
0
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STDIN 147> 
STDIN 148. module m3=m2; int j;
// ** redefining j **
STDIN 149> for( i=0; i<31; i++ ){print("--------");print(i);
STDIN 151.   m=matrix(rho(i),315,315)*matrix(m2,315,size(m2));
STDIN 153.   mm=t*m; m=m,mm; mm=t*m; m=m,mm;
STDIN 155.   m=reduce(m,m3); m3=m3,m; print(size(m));
STDIN 157.   if( size(m)>0 ){
STDIN 159.     I1=tau*matrix(m,315,size(m)); I1=reduce(I1,I);
STDIN 161.     I1=groebner(I1); print(I1);
STDIN 163.     if( size(I1)>1 | I1[1]!=0 ){
STDIN 165.       I=reduce(I,I1); I=I,I1; I=std(I); print("I=");print(I);print("----");
STDIN 167.       for( j=1; j<=size(I1); j++ ){m=module(I1[j]*Z); m3=m3,m;}
STDIN 169.     }
STDIN 171.   }
STDIN 173.   m3=groebner(m3);
STDIN 175.   print(size(m3));
STDIN 177. }
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STDIN 178> 
STDIN 179. module m4=m3; int j;
// ** redefining j **
STDIN 180> for( i=0; i<31; i++ ){print("--------");print(i);
STDIN 182.   m=matrix(rho(i),315,315)*matrix(m3,315,size(m3));
STDIN 184.   mm=t*m; m=m,mm; mm=t*m; m=m,mm;
STDIN 186.   m=reduce(m,m4); m4=m4,m; print(size(m));
STDIN 188.   if( size(m)>0 ){
STDIN 190.     I1=tau*matrix(m,315,size(m)); I1=reduce(I1,I);
STDIN 192.     I1=groebner(I1); print(I1);
STDIN 194.     if( size(I1)>1 | I1[1]!=0 ){
STDIN 196.       I=reduce(I,I1); I=I,I1; I=std(I); print("I=");print(I);print("----");
STDIN 198.       for( j=1; j<=size(I1); j++ ){m=module(I1[j]*Z); m4=m4,m;}
STDIN 200.     }
STDIN 202.   }
STDIN 204.   m4=groebner(m4);
STDIN 206.   print(size(m4));
STDIN 208. }
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STDIN 209> 
STDIN 210. m=reduce(m4,m3);
STDIN 211> groebner(m);
_[1]=0
STDIN 212> 
STDIN 213. I;
I[1]=68u2+68v
I[2]=34a3+68
I[3]=68uva+136va2+68v2+68u+68a
I[4]=68v3+136ua2+136uv+136va
I[5]=68uv2+136ua+68a2+68v
I[6]=17a4+136a
I[7]=v2a2+102u2a+ua2+25a3+4uv+98va
I[8]=uva2+203va3+202v2a+92u2+202ua+a2+92v
I[9]=u2a2+202uva+3va2+4v2+4u+202a
I[10]=4v3a+116ua3+120a4+96u2v+128uva+68va2+12v2+60u+72a
I[11]=uv2a+69u3+v3+66u2a+ua2+65uv+69va+1
I[12]=u3a+71v3a+60a4+44u2v+59uva+10va2+188v2+76u+201a
I[13]=4v4+28u2va+64va3+128uv2+124v2a+20u2+184ua+136a2+108v
I[14]=4uv3+108u3a+72v3a+96ua3+100a4+164u2v+72uva+84va2+52v2+76u+12a
I[15]=4u2v2+180uv2a+144v2a2+88u3+156v3+172u2a+196ua2+152uv+80va+120
I[16]=4u3v+156u2va+16va3+200uv2+128u2+140ua+4a2+56v
I[17]=4u4+60uv3+192u3a+132v3a+144ua3+60a4+4u2v+72uva+144va2+84v2+12u+168a
I[18]=a5+124u3v+144v4+20u2va+192va3+32uv2+44v2a+96u2+44ua+12a2+88v
I[19]=va4+5v2a2+112u3+4v3+114u2a+ua2+203a3+116uv+110va
I[20]=ua4+139a5+104u3v+164v4+152u2va+28va3+124uv2+164v2a+124u2+20a2+164v
I[21]=v5a+73u5+101u2v3+50u3v+125v4+131u2va+62va3+45uv2+92v2a+133u2+148ua+140a2+93v
I[22]=u6+95v6+18uv4+155u2v2+198u3+92v3+176u2a+72ua2+30a3+156uv+136va+101
STDIN 214> 
STDIN 215. // the gb for Q
STDIN 216. poly g(1)= a3+8;
STDIN 217> poly g(2)=2a3+1;
STDIN 218> poly g(3)=3a3+8;
STDIN 219> poly f(1)=g(1)*g(2)*g(3);
STDIN 220> poly f(2)=g(1)*g(3)*(u-a);
STDIN 221> poly f(3)=g(3)*(6u3-3a2u+a3+2);
STDIN 222> poly f(4)=336u4-792u3a+180u2a5+1272u2a2+846ua3+3264u-114a7-1405a4-3152a;
STDIN 223> poly f(5)=288v+336u3a2+216u2a3+2016u2-432ua4-2112ua-6a8+53a5+472a2;
STDIN 224> ideal Id; Id=f(1),f(2),f(3),f(4),f(5); Id=std(Id); Id;
Id[1]=68a3+136
Id[2]=34a4+68a
Id[3]=34ua3+187a4+68u+68a
Id[4]=12v2a2+12ua2+96a3+48uv+156va
Id[5]=12uva2+192va3+180v2a+84u2+180ua+12a2+84v
Id[6]=12u2a2+180uva+36va2+48v2+48u+180a
Id[7]=12v3a+108u2a2+144ua3+156a4+84u2v+168uva+120va2+60v2
Id[8]=12uv2a+12u3+12v3+180u2a+12ua2+168uv+12va+12
Id[9]=12u3a+36u2a2+112ua3+150a4+72u2v+96uva+24va2+48v2+176u+60a
Id[10]=12v4+84u2va+192va3+180uv2+168v2a+60u2+144ua+120v
Id[11]=12uv3+12u3a+192v3a+120u2a2+114ua3+117a4+84u2v+144uva+144va2+60u+12a
Id[12]=12u2v2+72uv2a+24u2a+96ua2+12a3+132uv+72va+96
Id[13]=12u3v+60u2va+48va3+192uv2+180u2+12ua+12a2+168v
Id[14]=12u4+96uv3+192u3a+96v3a+84u2a2+46ua3+3a4+36u2v+48uva+12va2+96v2+152u+192a
Id[15]=a5+48u3v+60u2va+156uva2+12va3+192uv2+96v2a+144u2+36ua+92a2+36v
Id[16]=2va4+120u2v2+168uv2a+108v2a2+12u3+144u2a+168ua2+120a3+132uv+64va
Id[17]=2ua4+56a5+72u3v+24u2va+108uva2+96va3+120uv2+144v2a+12u2+172ua+124a2+144v
Id[18]=4v2a3+144u4+120uv3+48u3a+144v3a+72u2a2+36a4+144u2v+108uva+120va2+200v2+132u+48a
Id[19]=2uva3+185va4+108u2v2+36uv2a+108v2a2+60u2a+156ua2+156a3+4uv+112va+48
Id[20]=2u2a3+83ua4+171a5+168u3v+96u2va+192uva2+48va3+60uv2+72v2a+196u2+112ua+84a2+144v
Id[21]=u2a4+52ua5+40a6+108u3+176u2a+188ua2+26a3+60uv+168va+48
STDIN 225> reduce(Id,I);
_[1]=0
_[2]=0
_[3]=0
_[4]=0
_[5]=0
_[6]=0
_[7]=0
_[8]=0
_[9]=0
_[10]=0
_[11]=0
_[12]=0
_[13]=0
_[14]=0
_[15]=0
_[16]=0
_[17]=0
_[18]=0
_[19]=0
_[20]=0
_[21]=0
STDIN 226> reduce(I,Id);
_[1]=68u2+68v
_[2]=34a3+68
_[3]=68uva+136va2+68v2+68u+68a
_[4]=68v3+136ua2+136uv+136va
_[5]=68uv2+136ua+68a2+68v
_[6]=17a4+136a
_[7]=v2a2+102u2a+ua2+25a3+4uv+98va
_[8]=uva2+203va3+202v2a+92u2+202ua+a2+92v
_[9]=u2a2+202uva+3va2+4v2+4u+202a
_[10]=4v3a+116ua3+120a4+96u2v+128uva+68va2+12v2+60u+72a
_[11]=uv2a+69u3+v3+66u2a+ua2+65uv+69va+1
_[12]=u3a+71v3a+60a4+44u2v+59uva+10va2+188v2+76u+201a
_[13]=4v4+28u2va+64va3+128uv2+124v2a+20u2+184ua+136a2+108v
_[14]=4uv3+60ua3+58a4+32u2v+132uva+24va2+88v2+136u+180a
_[15]=4u2v2+112u3+180v3+124u2a+76ua2+72a3+116uv+68va+144
_[16]=4u3v+156u2va+16va3+200uv2+128u2+140ua+4a2+56v
_[17]=4u4+118ua3+21a4+100u2v+156uva+108va2+108v2+104u+120a
_[18]=76u3v+176u2va+168va3+128uv2+68v2a+120u2+8ua+76a2+112v
_[19]=va4+5v2a2+112u3+4v3+114u2a+ua2+203a3+116uv+110va
_[20]=ua4+164u3v+164v4+176u2va+160uv2+164v2a+112u2+180ua+144a2
_[21]=v5a+73u5+101u2v3+50u3v+125v4+131u2va+62va3+45uv2+92v2a+133u2+148ua+140a2+93v
_[22]=u6+95v6+18uv4+155u2v2+198u3+92v3+176u2a+72ua2+30a3+156uv+136va+101
> Auf Wiedersehen.