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findMonomialSubalgebra -- Find monomial subalgebra corresponding to the convex hull.

Synopsis

• Usage:
findMonomialSubalgebra M
• Inputs:
• Outputs:

Description

Denote by C(B) the cone in \mathbb{R}^d spanned by B. This function computes on each ray of C(B) one element of B which has minimal coordinate sum, and returns the multigraded polynomial ring with the corresponding variables.

If a monomial algebra is specified the function returns a monomial algebra.

 i1 : a=3 o1 = 3 i2 : B={{a, 0}, {0, a}, {1, a-1}, {a-1, 1}} o2 = {{3, 0}, {0, 3}, {1, 2}, {2, 1}} o2 : List i3 : R=QQ[x_0..x_3, Degrees=> B] o3 = R o3 : PolynomialRing i4 : findMonomialSubalgebra R o4 = QQ[x ..x ] 0 1 o4 : PolynomialRing

 i5 : a=3 o5 = 3 i6 : B={{a, 0}, {0, a}, {1, a-1}, {a-1, 1}} o6 = {{3, 0}, {0, 3}, {1, 2}, {2, 1}} o6 : List i7 : M=monomialAlgebra B ZZ o7 = ---[x ..x ] 101 0 3 o7 : MonomialAlgebra generated by {{3, 0}, {0, 3}, {1, 2}, {2, 1}} i8 : findMonomialSubalgebra M ZZ o8 = ---[x ..x ] 101 0 1 o8 : MonomialAlgebra generated by {{3, 0}, {0, 3}}

Ways to use findMonomialSubalgebra :

• findMonomialSubalgebra(MonomialAlgebra)
• findMonomialSubalgebra(PolynomialRing)

For the programmer

The object findMonomialSubalgebra is .