i6 : base=last decompose base1
o6 = ideal (a a - a a , a a - a a ,
{0, 2} {2, 3} {0, 1} {1, 3} {3, 4} {2, 3} {1, 2} {1, 3}
2
a - a a , a a - a a , a a
{0, 2} {1, 2} {1, 3} {0, 1} {0, 2} {1, 2} {2, 3} {3, 4} {0,
- a a )
1} {1, 2} {0, 2}
o6 : Ideal of QQ[a , a , a , a , a , a , a ]
{1, 1} {1, 2} {3, 4} {0, 1} {0, 2} {2, 3} {1, 3}
i7 : family=family1%sub(base,ring family1);
1 10
o7 : Matrix (QQ[x ..x , x , x ..x , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a ]) <-- (QQ[x ..x , x , x ..x , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a ])
0 1 3 5 6 {9, 0} {8, 0} {7, 0} {6, 0} {5, 0} {4, 0} {9, 1} {7, 1} {5, 1} {4, 1} {9, 3} {9, 8} {8, 7} {6, 6} {5, 5} {4, 3} {2, 2} {1, 1} {9, 9} {8, 8} {5, 6} {4, 4} {3, 3} {1, 2} {8, 9} {7, 8} {4, 5} {3, 4} {8, 10} {7, 9} {6, 8} {5, 7} {3, 5} {0, 1} {8, 11} {7, 10} {6, 9} {5, 8} {3, 6} {0, 2} {9, 14} {6, 11} {4, 8} {3, 7} {2, 3} {9, 15} {8, 14} {6, 12} {5, 11} {4, 9} {2, 4} {1, 3} 0 1 3 5 6 {9, 0} {8, 0} {7, 0} {6, 0} {5, 0} {4, 0} {9, 1} {7, 1} {5, 1} {4, 1} {9, 3} {9, 8} {8, 7} {6, 6} {5, 5} {4, 3} {2, 2} {1, 1} {9, 9} {8, 8} {5, 6} {4, 4} {3, 3} {1, 2} {8, 9} {7, 8} {4, 5} {3, 4} {8, 10} {7, 9} {6, 8} {5, 7} {3, 5} {0, 1} {8, 11} {7, 10} {6, 9} {5, 8} {3, 6} {0, 2} {9, 14} {6, 11} {4, 8} {3, 7} {2, 3} {9, 15} {8, 14} {6, 12} {5, 11} {4, 9} {2, 4} {1, 3}
i8 : (worked,fiber)=solvingFlatteningRelations(base,family,I);
# of coordinate linear subspace of the base = 2
# of linear subsets which leading to a point =2
i9 : p=nextPrime 10^5
o9 = 100003
i10 : kk=ZZ/p;
i11 : SzFinite=kk[support J, Degrees=>apply(support J,m->degree m)]
o11 = SzFinite
o11 : PolynomialRing
i12 : fibF=sub(fiber,SzFinite);
1 10
o12 : Matrix SzFinite <-- SzFinite
i13 : fiber=fibF*diagonalMatrix({1/2_kk,2/3_kk,1/5_kk,4/3_kk,1/30_kk,2/5_kk,1/2_kk,1/3_kk,1/2_kk,1/3_kk})
o13 = | -50001x_1^3+50001x_0x_3-50001x_1-50001x_0
33335x_1x_5-33335x_0x_6+33335x_0^2+33335x_1-33335x_0
-40001x_0^4+40001x_1x_6-40001x_0x_1-40001x_0^2+40001x_1
-33333x_1^2x_3+33333x_0^2x_5+33333x_5-33333x_3-33333x_1^2-33333x_0x_1-
33333x_0^2 -23334x_3^2+23334x_0^2x_6-23334x_0^3+23334x_6-23334x_1^2-
46668x_0x_1+23334x_0^2-23334x_0+46668
20001x_3x_5-20001x_1^2x_6+20001x_0x_1^2-20001x_6-20001x_5+20001x_3-
20001x_1^2+20001x_0-40002
-50001x_0^3x_1^2+50001x_3x_6-50001x_0x_3-50001x_0x_1^2-50001x_0^3-
50001x_6+50001x_3-50001
-33334x_0^3x_3+33334x_5^2-33334x_0^2x_1-33334x_0^3-33334x_6+33334x_0+
33335 -50001x_0^2x_1x_3+50001x_5x_6-50001x_0x_5-50001x_0x_1^2-50001x_0^
2x_1-50001x_0^3-50001x_6+50001x_5-50001
-33334x_0^3x_5+33334x_6^2+33335x_0x_6-33334x_0x_5-33334x_0^3-33335x_6+
33334x_0^2+x_0+33334 |
1 10
o13 : Matrix SzFinite <-- SzFinite
i14 : (worked,fiber1)=clearDenominators fiber
o14 = (true, | x_1^3-x_0x_3+x_1+x_0 2x_1x_5-2x_0x_6+2x_0^2+2x_1-2x_0
x_0^4-x_1x_6+x_0x_1+x_0^2-x_1
4x_1^2x_3-4x_0^2x_5-4x_5+4x_3+4x_1^2+4x_0x_1+4x_0^2
x_3^2-x_0^2x_6+x_0^3-x_6+x_1^2+2x_0x_1-x_0^2+x_0-2
2x_3x_5-2x_1^2x_6+2x_0x_1^2-2x_6-2x_5+2x_3-2x_1^2+2x_0-4
x_0^3x_1^2-x_3x_6+x_0x_3+x_0x_1^2+x_0^3+x_6-x_3+1
x_0^3x_3-x_5^2+x_0^2x_1+x_0^3+x_6-x_0+2
x_0^2x_1x_3-x_5x_6+x_0x_5+x_0x_1^2+x_0^2x_1+x_0^3+x_6-x_5+1
x_0^3x_5-x_6^2+2x_0x_6+x_0x_5+x_0^3-2x_6-x_0^2+3x_0-1 |)
o14 : Sequence
|