| | LIB "autgradalg.lib";
//////////////////
// example: fano 15:
intmat Q[1][5] = 3,3,2,2,1;
ring R = 0,T(1..5),dp;
// attach degree matrix Q to R:
setBaseMultigrading(Q);
ideal I = T(1)*T(2) + T(3)^2*T(4) + T(5)^6;
def RR = stabilizer(I);
==> // coefficients: QQ
==> // number of vars : 50
==> // block 1 : ordering dp
==> // : names T(1) T(2) T(3) T(4) T(5) Y(1) Y(2) Y(3) Y(\
4) Y(5) Y(6) Y(7) Y(8) Y(9) Y(10) Y(11) Y(12) Y(13) Y(14) Y(15) Y(16) Y(1\
7) Y(18) Y(19) Y(20) Y(21) Y(22) Y(23) Y(24) Y(25) Y(26) Y(27) Y(28) Y(29\
) Y(30) Y(31) Y(32) Y(33) Y(34) Y(35) Y(36) Y(37) Y(38) Y(39) Y(40) Y(41)\
Y(42) Y(43) Y(44) Y(45)
==> // block 2 : ordering C
setring RR;
RR;
==> // coefficients: QQ
==> // number of vars : 46
==> // block 1 : ordering dp
==> // : names Y(1) Y(2) Y(3) Y(4) Y(5) Y(6) Y(7) Y(8) Y(\
9) Y(10) Y(11) Y(12) Y(13) Y(14) Y(15) Y(16) Y(17) Y(18) Y(19) Y(20) Y(21\
) Y(22) Y(23) Y(24) Y(25) Y(26) Y(27) Y(28) Y(29) Y(30) Y(31) Y(32) Y(33)\
Y(34) Y(35) Y(36) Y(37) Y(38) Y(39) Y(40) Y(41) Y(42) Y(43) Y(44) Y(45)
==> // block 2 : ordering dp
==> // : names Z
==> // block 3 : ordering C
Jexported;
==> Jexported[1]=Y(3)
==> Jexported[2]=Y(4)
==> Jexported[3]=Y(5)
==> Jexported[4]=Y(8)
==> Jexported[5]=Y(12)
==> Jexported[6]=Y(13)
==> Jexported[7]=Y(14)
==> Jexported[8]=Y(17)
==> Jexported[9]=Y(19)
==> Jexported[10]=Y(20)
==> Jexported[11]=Y(23)
==> Jexported[12]=Y(24)
==> Jexported[13]=Y(25)
==> Jexported[14]=Y(27)
==> Jexported[15]=Y(28)
==> Jexported[16]=Y(29)
==> Jexported[17]=Y(32)
==> Jexported[18]=Y(33)
==> Jexported[19]=Y(34)
==> Jexported[20]=Y(36)
==> Jexported[21]=Y(37)
==> Jexported[22]=Y(38)
==> Jexported[23]=Y(39)
==> Jexported[24]=Y(40)
==> Jexported[25]=Y(42)
==> Jexported[26]=Y(43)
==> Jexported[27]=Y(44)
==> Jexported[28]=Y(45)
==> Jexported[29]=-Y(2)*Y(10)*Y(22)^2*Y(30)^2*Y(41)^8*Z+Y(1)*Y(11)*Y(22)^2*Y(\
30)^2*Y(41)^8*Z+2*Y(2)*Y(10)*Y(21)*Y(22)*Y(30)*Y(31)*Y(41)^8*Z-2*Y(1)*Y(1\
1)*Y(21)*Y(22)*Y(30)*Y(31)*Y(41)^8*Z-Y(2)*Y(10)*Y(21)^2*Y(31)^2*Y(41)^8*Z\
+Y(1)*Y(11)*Y(21)^2*Y(31)^2*Y(41)^8*Z-1
==> Jexported[30]=Y(26)^2*Y(31)+2*Y(22)*Y(26)*Y(35)+Y(9)*Y(16)+Y(7)*Y(18)
==> Jexported[31]=2*Y(22)*Y(26)*Y(31)+Y(22)^2*Y(35)+Y(7)*Y(16)
==> Jexported[32]=Y(22)^2*Y(31)
==> Jexported[33]=Y(26)^2*Y(30)+2*Y(21)*Y(26)*Y(35)+Y(9)*Y(15)+Y(6)*Y(18)
==> Jexported[34]=2*Y(22)*Y(26)*Y(30)+2*Y(21)*Y(26)*Y(31)+2*Y(21)*Y(22)*Y(35)\
+Y(7)*Y(15)+Y(6)*Y(16)
==> Jexported[35]=Y(22)^2*Y(30)+2*Y(21)*Y(22)*Y(31)
==> Jexported[36]=2*Y(21)*Y(26)*Y(30)+Y(21)^2*Y(35)+Y(6)*Y(15)
==> Jexported[37]=-Y(41)^6+2*Y(21)*Y(22)*Y(30)+Y(21)^2*Y(31)-Y(26)^2*Y(35)-Y(\
9)*Y(18)
==> Jexported[38]=Y(21)^2*Y(30)
==> Jexported[39]=Y(9)*Y(11)+Y(2)*Y(18)
==> Jexported[40]=Y(7)*Y(11)+Y(2)*Y(16)
==> Jexported[41]=Y(6)*Y(11)+Y(2)*Y(15)
==> Jexported[42]=Y(2)*Y(11)
==> Jexported[43]=Y(9)*Y(10)+Y(1)*Y(18)
==> Jexported[44]=Y(7)*Y(10)+Y(1)*Y(16)
==> Jexported[45]=Y(6)*Y(10)+Y(1)*Y(15)
==> Jexported[46]=-2*Y(21)*Y(22)*Y(30)-Y(21)^2*Y(31)+Y(2)*Y(10)+Y(1)*Y(11)
==> Jexported[47]=Y(1)*Y(10)
dim(std(Jexported));
==> 3
getVariableWeights();
==> 3,3,2,2,1,3,3,2,3,3,3,2,2,1,3,3,2,3,3,3,2,2,1,3,3,2,3,3,3,2,2,1,3,3,2,3,3\
,3,2,2,1,3,3,2,3,-22
kill RR, Q, R;
/////////////
// example 3.14 from the paper
intmat Q[3][5] =
1,1,1,1,1,
1,-1,0,0,1,
1,1,1,0,0;
list TOR = 2;
ring R = 0,T(1..5),dp;
// attach degree matrix Q to R:
setBaseMultigrading(Q);
ideal I = T(1)*T(2) + T(3)^2 + T(4)^2;
list TOR = 2;
==> // ** redefining TOR (list TOR = 2;) ./examples/stabilizer.sing:27
def RR = stabilizer(I, TOR);
==> // coefficients: QQ
==> // number of vars : 30
==> // block 1 : ordering dp
==> // : names T(1) T(2) T(3) T(4) T(5) Y(1) Y(2) Y(3) Y(\
4) Y(5) Y(6) Y(7) Y(8) Y(9) Y(10) Y(11) Y(12) Y(13) Y(14) Y(15) Y(16) Y(1\
7) Y(18) Y(19) Y(20) Y(21) Y(22) Y(23) Y(24) Y(25)
==> // block 2 : ordering C
==> // ** redefining adMons ( list adMons;) autgradalg.lib::autKS:2324
==> // ** redefining MONexported ( export(MONexported);)
==> // ** redefining k (int k = 1;) autgradalg.lib::stabilizer:1975
setring RR;
RR;
==> // coefficients: QQ
==> // number of vars : 26
==> // block 1 : ordering dp
==> // : names Y(1) Y(2) Y(3) Y(4) Y(5) Y(6) Y(7) Y(8) Y(\
9) Y(10) Y(11) Y(12) Y(13) Y(14) Y(15) Y(16) Y(17) Y(18) Y(19) Y(20) Y(21\
) Y(22) Y(23) Y(24) Y(25)
==> // block 2 : ordering dp
==> // : names Z
==> // block 3 : ordering C
Jexported;
==> Jexported[1]=Y(24)
==> Jexported[2]=Y(23)
==> Jexported[3]=Y(22)
==> Jexported[4]=Y(21)
==> Jexported[5]=Y(20)
==> Jexported[6]=Y(17)
==> Jexported[7]=Y(16)
==> Jexported[8]=Y(15)
==> Jexported[9]=Y(12)
==> Jexported[10]=Y(11)
==> Jexported[11]=Y(10)
==> Jexported[12]=Y(9)
==> Jexported[13]=Y(8)
==> Jexported[14]=Y(6)
==> Jexported[15]=Y(5)
==> Jexported[16]=Y(4)
==> Jexported[17]=Y(3)
==> Jexported[18]=Y(2)
==> Jexported[19]=Y(18)*Y(19)
==> Jexported[20]=Y(14)*Y(19)
==> Jexported[21]=Y(13)*Y(18)
==> Jexported[22]=Y(14)^2-Y(18)^2
==> Jexported[23]=Y(13)*Y(14)
==> Jexported[24]=Y(13)^2-Y(19)^2
==> Jexported[25]=Y(1)*Y(7)-Y(18)^2-Y(19)^2
==> Jexported[26]=Y(14)*Y(18)^3*Y(25)*Z-Y(13)*Y(19)^3*Y(25)*Z+1
==> Jexported[27]=Y(19)^5*Y(25)*Z-Y(13)
==> Jexported[28]=Y(13)*Y(19)^4*Y(25)*Z-Y(19)
==> Jexported[29]=Y(18)^5*Y(25)*Z+Y(14)
dim(std(Jexported));
==> 3
stabExported;
==> [1]:
==> [1]:
==> _[1,1]=Y(1)
==> _[1,2]=0
==> _[1,3]=0
==> _[1,4]=0
==> _[1,5]=0
==> _[2,1]=0
==> _[2,2]=Y(7)
==> _[2,3]=0
==> _[2,4]=0
==> _[2,5]=0
==> _[3,1]=0
==> _[3,2]=0
==> _[3,3]=Y(13)
==> _[3,4]=0
==> _[3,5]=0
==> _[4,1]=0
==> _[4,2]=0
==> _[4,3]=0
==> _[4,4]=Y(19)
==> _[4,5]=0
==> _[5,1]=0
==> _[5,2]=0
==> _[5,3]=0
==> _[5,4]=0
==> _[5,5]=Y(25)
==> [2]:
==> 1,0,0,
==> 0,1,0,
==> 0,0,1
==> [3]:
==> _[1]=Y(2)
==> _[2]=Y(3)
==> _[3]=Y(4)
==> _[4]=Y(5)
==> _[5]=Y(6)
==> _[6]=Y(8)
==> _[7]=Y(9)
==> _[8]=Y(10)
==> _[9]=Y(11)
==> _[10]=Y(12)
==> _[11]=Y(14)
==> _[12]=Y(15)
==> _[13]=Y(16)
==> _[14]=Y(17)
==> _[15]=Y(18)
==> _[16]=Y(20)
==> _[17]=Y(21)
==> _[18]=Y(22)
==> _[19]=Y(23)
==> _[20]=Y(24)
==> _[21]=Y(1)*Y(7)*Y(13)*Y(19)*Y(25)*Z-1
==> _[22]=Y(13)^2-Y(19)^2
==> _[23]=Y(1)*Y(7)-Y(13)^2
==> [2]:
==> [1]:
==> _[1,1]=Y(1)
==> _[1,2]=0
==> _[1,3]=0
==> _[1,4]=0
==> _[1,5]=0
==> _[2,1]=0
==> _[2,2]=Y(7)
==> _[2,3]=0
==> _[2,4]=0
==> _[2,5]=0
==> _[3,1]=0
==> _[3,2]=0
==> _[3,3]=0
==> _[3,4]=Y(14)
==> _[3,5]=0
==> _[4,1]=0
==> _[4,2]=0
==> _[4,3]=Y(18)
==> _[4,4]=0
==> _[4,5]=0
==> _[5,1]=0
==> _[5,2]=0
==> _[5,3]=0
==> _[5,4]=0
==> _[5,5]=Y(25)
==> [2]:
==> 1,0,0,
==> 0,1,0,
==> 1,1,1
==> [3]:
==> _[1]=Y(2)
==> _[2]=Y(3)
==> _[3]=Y(4)
==> _[4]=Y(5)
==> _[5]=Y(6)
==> _[6]=Y(8)
==> _[7]=Y(9)
==> _[8]=Y(10)
==> _[9]=Y(11)
==> _[10]=Y(12)
==> _[11]=Y(13)
==> _[12]=Y(15)
==> _[13]=Y(16)
==> _[14]=Y(17)
==> _[15]=Y(19)
==> _[16]=Y(20)
==> _[17]=Y(21)
==> _[18]=Y(22)
==> _[19]=Y(23)
==> _[20]=Y(24)
==> _[21]=-Y(1)*Y(7)*Y(14)*Y(18)*Y(25)*Z-1
==> _[22]=-Y(14)^2+Y(18)^2
==> _[23]=Y(1)*Y(7)-Y(18)^2
kill RR, Q, R;
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