Returns the monomial algebra K[B]=P/binomialIdeal(P) associated to the degree monoid of the polynomial ring 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 : affineAlgebra S
S
o4 = ----------------------------------------------
3 2 6 2 3 4 3 2 5 4
(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 : QuotientRing
|
i5 : affineAlgebra B
kk[x ..x ]
0 3
o5 = ----------------------------------------------
3 2 6 2 3 4 3 2 5 4
(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
o5 : QuotientRing
|
i6 : M = monomialAlgebra B
o6 = kk[x ..x ]
0 3
o6 : MonomialAlgebra generated by {{1, 2}, {3, 0}, {0, 4}, {0, 5}}
|
i7 : affineAlgebra M
kk[x ..x ]
0 3
o7 = ----------------------------------------------
3 2 6 2 3 4 3 2 5 4
(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
o7 : QuotientRing
|
The object affineAlgebra is a method function with options.