The function computes a hypersurface H4,6 of bidegree (4,6) in ℙ3 ×ℙ5 which is the image of the model of F(Q) in ℙ3 ×ℙ3 ×ℙ3 ×ℙ3 under a rational map. The fibers of the map are Gm-orbits.
i1 : kk = QQ o1 = QQ o1 : Ring |
i2 : I1=precomputedModelInP3xP3xP3xP3(kk);
o2 : Ideal of QQ[b , b , b , b , b , b , b , b , b , b , b , b , b , b , b , b ]
0,0 0,1 0,2 0,3 1,0 1,1 1,2 1,3 2,0 2,1 2,2 2,3 3,0 3,1 3,2 3,3
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i3 : isHomogeneous I1 o3 = true |
i4 : "--H=collapsingOneCStar I1;" o4 = --H=collapsingOneCStar I1; |
Since the function takes about 150 secends we use the precomputed equations.
i5 : H = precomputedModelInP3xP5(QQ);
1 1
o5 : Matrix (QQ[w , w , w , w , z , z , z , z , z , z ]) <--- (QQ[w , w , w , w , z , z , z , z , z , z ])
0 1 2 3 0 1 2 3 4 5 0 1 2 3 0 1 2 3 4 5
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i6 : degrees ring H
o6 = {{1, 0}, {1, 0}, {1, 0}, {1, 0}, {0, 1}, {0, 1}, {0, 1}, {0, 1}, {0, 1},
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{0, 1}}
o6 : List
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i7 : degrees source H
o7 = {{4, 6}}
o7 : List
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i8 : sum degrees ring H
o8 = {4, 6}
o8 : List
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i9 : betti H
0 1
o9 = total: 1 1
0: 1 .
1: . .
2: . .
3: . .
4: . .
5: . .
6: . .
7: . .
8: . .
9: . 1
o9 : BettiTally
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i10 : tH=terms H_(0,0); |
i11 : #tH o11 = 128 |
i12 : lcmTH=lcm tH
3 2 4 2 3 3 3 3 3 3
o12 = 13209037701120w w w w z z z z z z
0 1 2 3 0 1 2 3 4 5
o12 : QQ[w , w , w , w , z , z , z , z , z , z ]
0 1 2 3 0 1 2 3 4 5
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i13 : factor sub((coefficients lcmTH)_1_(0,0),ZZ)
27 9
o13 = 2 3 5
o13 : Expression of class Product
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