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 |
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 |
i6 : degrees ring H o6 = {{1, 0}, {1, 0}, {1, 0}, {1, 0}, {0, 1}, {0, 1}, {0, 1}, {0, 1}, {0, 1}, ------------------------------------------------------------------------ {0, 1}} o6 : List |
i7 : degrees source H o7 = {{4, 6}} o7 : List |
i8 : sum degrees ring H o8 = {4, 6} o8 : List |
i9 : betti H 0 1 o9 = total: 1 1 0: 1 . 1: . . 2: . . 3: . . 4: . . 5: . . 6: . . 7: . . 8: . . 9: . 1 o9 : BettiTally |
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 |
i13 : factor sub((coefficients lcmTH)_1_(0,0),ZZ) 27 9 o13 = 2 3 5 o13 : Expression of class Product |