Returns the toric ideal associated to the degree monoid B of the polynomial ring P as an ideal of P.
i1 : kk=ZZ/101 o1 = kk o1 : QuotientRing |
i2 : B = {{1,2},{3,0},{0,4},{0,5}}
o2 = {{1, 2}, {3, 0}, {0, 4}, {0, 5}}
o2 : List
|
i3 : S = kk[x_0..x_3, Degrees=> B] o3 = S o3 : PolynomialRing |
i4 : binomialIdeal S
3 2 6 2 3 4 3 2 5 4
o4 = ideal (x x - x x , x - x x , x x - x x , x - x )
0 2 1 3 0 1 2 1 2 0 3 2 3
o4 : Ideal of S
|
i5 : C = {{1,2},{0,5}}
o5 = {{1, 2}, {0, 5}}
o5 : List
|
i6 : P = kk[y_0,y_1, Degrees=> C] o6 = P o6 : PolynomialRing |
i7 : binomialIdeal P o7 = ideal () o7 : Ideal of P |
i8 : M = monomialAlgebra B
o8 = kk[x ..x ]
0 3
o8 : MonomialAlgebra generated by {{1, 2}, {3, 0}, {0, 4}, {0, 5}}
|
i9 : binomialIdeal M
3 2 6 2 3 4 3 2 5 4
o9 = ideal (x x - x x , x - x x , x x - x x , x - x )
0 2 1 3 0 1 2 1 2 0 3 2 3
o9 : Ideal of kk[x ..x ]
0 3
|
The object binomialIdeal is a method function with options.