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MonomialAlgebras :: findMonomialSubalgebra

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

Synopsis

Description

Denote by C(B) the cone in ℝd 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 , x , x ]
     101  0   1   2   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)