i1 : R=QQ[x_0..x_1, x_3, x_5..x_6, z, Degrees => {7..8, 17, 19..20, 1}]
o1 = R
o1 : PolynomialRing
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i2 : J=ideal(x_1^3-x_0*x_3+x_1*z^16+x_0*z^17,x_1*x_5-x_0*x_6+x_0^2*z^13+x_1*z^19-x_0*z^20,x_0^4-x_1*x_6+x_0*x_1*z^13
+x_0^2*z^14-x_1*z^20,x_1^2*x_3-x_0^2*x_5-x_5*z^14+x_3*z^16+x_1^2*z^17+x_0*x_1*z^18+x_0^2*z^19,x_3^2-x_0^2*x_6
+x_0^3*z^13-x_6*z^14+x_1^2*z^18+2*x_0*x_1*z^19-x_0^2*z^20+x_0*z^27-2*z^34,x_3*x_5-x_1^2*x_6+x_0*x_1^2*z^13-x_
6*z^16-x_5*z^17+x_3*z^19-x_1^2*z^20+x_0*z^29-2*z^36,x_0^3*x_1^2-x_3*x_6+x_0*x_3*z^13+x_0*x_1^2*z^14+x_0^3*z^
16+x_6*z^17-x_3*z^20+z^37,x_0^3*x_3-x_5^2+x_0^2*x_1*z^16+x_0^3*z^17+x_6*z^18-x_0*z^31+2*z^38,x_0^2*x_1*x_3-x_
5*x_6+x_0*x_5*z^13+x_0*x_1^2*z^16+x_0^2*x_1*z^17+x_0^3*z^18+x_6*z^19-x_5*z^20+z^39,x_0^3*x_5-x_6^2+2*x_0*x_6*
z^13+x_0*x_5*z^14+x_0^3*z^19-2*x_6*z^20-x_0^2*z^26+3*x_0*z^33-z^40)
3 16 17 2 13 19 20
o2 = ideal (x - x x + x z + x z , x x - x x + x z + x z - x z ,
1 0 3 1 0 1 5 0 6 0 1 0
4 13 2 14 20 2 2 14 16 2 17
x - x x + x x z + x z - x z , x x - x x - x z + x z + x z
0 1 6 0 1 0 1 1 3 0 5 5 3 1
18 2 19 2 2 3 13 14 2 18 19 2 20
+ x x z + x z , x - x x + x z - x z + x z + 2x x z - x z
0 1 0 3 0 6 0 6 1 0 1 0
27 34 2 2 13 16 17 19 2 20
+ x z - 2z , x x - x x + x x z - x z - x z + x z - x z +
0 3 5 1 6 0 1 6 5 3 1
29 36 3 2 13 2 14 3 16 17 20
x z - 2z , x x - x x + x x z + x x z + x z + x z - x z +
0 0 1 3 6 0 3 0 1 0 6 3
37 3 2 2 16 3 17 18 31 38 2
z , x x - x + x x z + x z + x z - x z + 2z , x x x - x x +
0 3 5 0 1 0 6 0 0 1 3 5 6
13 2 16 2 17 3 18 19 20 39 3 2
x x z + x x z + x x z + x z + x z - x z + z , x x - x +
0 5 0 1 0 1 0 6 5 0 5 6
13 14 3 19 20 2 26 33 40
2x x z + x x z + x z - 2x z - x z + 3x z - z )
0 6 0 5 0 6 0 0
o2 : Ideal of R
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i3 : L=flatten drop(degrees R,-1)
o3 = {7, 8, 17, 19, 20}
o3 : List
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i4 : (base,family)=getParameterFamily J;
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i5 : numgens base
o5 = 4
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i6 : cbase=decompose base
o6 = {ideal (a , a , a ), ideal (a a - a a
{1, 3} {2, 3} {0, 2} {0, 2} {2, 3} {0, 1} {1,
2
, a a - a a , a - a a , a
3} {3, 4} {2, 3} {1, 2} {1, 3} {0, 2} {1, 2} {1, 3} {0,
a - a a , a a - a a )}
1} {0, 2} {1, 2} {2, 3} {3, 4} {0, 1} {1, 2} {0, 2}
o6 : List
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i7 : J_0
3 16 17
o7 = x - x x + x z + x z
1 0 3 1 0
o7 : R
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i8 : family_(0,0)
3
o8 = x - x x + x a + x a
1 0 3 0 {0, 1} 1 {0, 2}
o8 : 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}
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i9 : J_*/size
o9 = {4, 5, 5, 7, 9, 9, 8, 7, 9, 9}
o9 : List
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i10 : (ideal family)_*/size
o10 = {4, 5, 5, 7, 10, 10, 8, 8, 9, 10}
o10 : List
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i11 : J_4
2 2 3 13 14 2 18 19 2 20 27 34
o11 = x - x x + x z - x z + x z + 2x x z - x z + x z - 2z
3 0 6 0 6 1 0 1 0 0
o11 : R
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i12 : family_(0,4)
2 2 2 2 2
o12 = x - x x + x a + 2x x a + x a - a - x a
3 0 6 0 {1, 1} 0 1 {1, 2} 1 {3, 4} {0, 1} 6 {2, 3}
3
+ a a + x a + x a a
{1, 1} {2, 3} 0 {1, 3} 0 {2, 3} {1, 3}
o12 : 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}
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i13 : support family
o13 = {x , x , x , x , x , a , a , a , a , a , a
0 1 3 5 6 {1, 1} {1, 2} {3, 4} {0, 1} {0, 2} {2,
, a }
3} {1, 3}
o13 : List
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i14 : support family/degree
o14 = {{7}, {8}, {17}, {19}, {20}, {20}, {19}, {18}, {17}, {16}, {14}, {13}}
o14 : List
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