ideal_as_module(I::Union{MPolyIdeal, MPolyQuoIdeal, MPolyLocalizedIdeal, MPolyQuoLocalizedIdeal})

Return I considered as an object of type SubquoModule.

Examples

julia> R, (x, y) = polynomial_ring(QQ, [:x, :y]);

julia> I = ideal(R, [x^2, y^3])
Ideal generated by
  x^2
  y^3

julia> ideal_as_module(I)
Submodule with 2 generators
  1: x^2*e[1]
  2: y^3*e[1]
represented as subquotient with no relations

julia> S, (x, y) = graded_polynomial_ring(QQ, [:x, :y]);

julia> I = ideal(S, [x^2, y^3])
Ideal generated by
  x^2
  y^3

julia> ideal_as_module(I)
Graded submodule of S^1 with 2 generators
  1: x^2*e[1]
  2: y^3*e[1]
represented as subquotient with no relations

quotient_ring_as_module(A::MPolyQuoRing)

Return A considered as an object of type SubquoModule.

quotient_ring_as_module(I::Union{MPolyIdeal, MPolyQuoIdeal, MPolyLocalizedIdeal, MPolyQuoLocalizedIdeal})

As above, where A is the quotient of base_ring(I) modulo I.

Examples

julia> R, (x, y) = polynomial_ring(QQ, [:x, :y]);

julia> IR = ideal(R, [x^2, y^3]);

julia> quotient_ring_as_module(IR)
Subquotient of submodule with 1 generator
  1: e[1]
by submodule with 2 generators
  1: x^2*e[1]
  2: y^3*e[1]

julia> base_ring(ans)
Multivariate polynomial ring in 2 variables x, y
  over rational field

julia> A, _ = quo(R, ideal(R,[x*y]));

julia> AI = ideal(A, [x^2, y^3]);

julia> quotient_ring_as_module(AI)
Subquotient of submodule with 1 generator
  1: e[1]
by submodule with 2 generators
  1: x^2*e[1]
  2: y^3*e[1]

julia> base_ring(ans)
Quotient
  of multivariate polynomial ring in 2 variables x, y
    over rational field
  by ideal (x*y)

julia> S, (x, y) = graded_polynomial_ring(QQ, [:x, :y]);

julia> I = ideal(S, [x^2, y^3])
Ideal generated by
  x^2
  y^3

julia> quotient_ring_as_module(I)
Graded subquotient of graded submodule of S^1 with 1 generator
  1: e[1]
by graded submodule of S^1 with 2 generators
  1: x^2*e[1]
  2: y^3*e[1]