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More signatures for quotient_ring_as_module and ideal_as_module #4174

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Oct 4, 2024
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More signatures for quotient_ring_as_module and ideal_as_module #4174

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81a801a
More signatures for `quotient_ring_as_module` and `ideal_as_module`
wdecker Oct 3, 2024
7191d4c
add test
wdecker Oct 4, 2024
9ee4c56
extend doctest
wdecker Oct 4, 2024
8823360
correction
wdecker Oct 4, 2024
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1 change: 1 addition & 0 deletions docs/doc.main
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Expand Up @@ -133,6 +133,7 @@
"CommutativeAlgebra/ModulesOverMultivariateRings/intro.md",
"CommutativeAlgebra/ModulesOverMultivariateRings/free_modules.md",
"CommutativeAlgebra/ModulesOverMultivariateRings/subquotients.md",
"CommutativeAlgebra/ModulesOverMultivariateRings/ideals_quorings_as_modules.md",
"CommutativeAlgebra/ModulesOverMultivariateRings/module_operations.md",
"CommutativeAlgebra/ModulesOverMultivariateRings/hom_operations.md",
"CommutativeAlgebra/ModulesOverMultivariateRings/complexes.md",
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20 changes: 20 additions & 0 deletions ...c/CommutativeAlgebra/ModulesOverMultivariateRings/ideals_quorings_as_modules.md
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@@ -0,0 +1,20 @@
```@meta
CurrentModule = Oscar
```

# Ideals and Quotient Rings as Modules

## Ideals as Modules

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

# Quotient Rings as Modules

```@docs
quotient_ring_as_module(A::MPolyQuoRing)
```



6 changes: 0 additions & 6 deletions docs/src/CommutativeAlgebra/affine_algebras.md
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Expand Up @@ -672,9 +672,3 @@ multi_hilbert_series(A::MPolyQuoRing; algorithm::Symbol=:BayerStillmanA)
multi_hilbert_series_reduced(A::MPolyQuoRing; algorithm::Symbol=:BayerStillmanA)
multi_hilbert_function(A::MPolyQuoRing, g::FinGenAbGroupElem)
```

## Affine Algebras as Modules

```@docs
quotient_ring_as_module(A::MPolyQuoRing)
```
7 changes: 0 additions & 7 deletions docs/src/CommutativeAlgebra/ideals.md
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Expand Up @@ -285,13 +285,6 @@ julia> DH(Ih) == I # dehomogenization of Ih
true
```


## Ideals as Modules

```@docs
ideal_as_module(I::MPolyIdeal)
```

## Generating Special Ideals

### Katsura-n
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37 changes: 28 additions & 9 deletions src/Modules/ModulesGraded.jl
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Expand Up @@ -2879,25 +2879,44 @@ end

Return `A` considered as an object of type `SubquoModule`.

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

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

# Examples
```jldoctest
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> IR = ideal(R, [x^2, y^3]);

julia> quotient_ring_as_module(I)
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)

```
```jldoctest
julia> S, (x, y) = graded_polynomial_ring(QQ, [:x, :y]);
Expand All @@ -2920,7 +2939,7 @@ function quotient_ring_as_module(A::MPolyQuoRing)
return quotient_ring_as_module(modulus(A))
end

function quotient_ring_as_module(I::MPolyIdeal)
function quotient_ring_as_module(I::Union{MPolyIdeal, MPolyQuoIdeal, MPolyLocalizedIdeal, MPolyQuoLocalizedIdeal})
R = base_ring(I)
F = is_graded(R) ? graded_free_module(R, 1) : free_module(R, 1)
e1 = F[1]
Expand All @@ -2930,7 +2949,7 @@ end
#####ideals as modules#####

@doc raw"""
ideal_as_module(I::MPolyIdeal)
ideal_as_module(I::Union{MPolyIdeal, MPolyQuoIdeal, MPolyLocalizedIdeal, MPolyQuoLocalizedIdeal})

Return `I` considered as an object of type `SubquoModule`.

Expand Down Expand Up @@ -2964,7 +2983,7 @@ Graded submodule of S^1
represented as subquotient with no relations
```
"""
function ideal_as_module(I::MPolyIdeal)
function ideal_as_module(I::Union{MPolyIdeal, MPolyQuoIdeal, MPolyLocalizedIdeal, MPolyQuoLocalizedIdeal})
R = base_ring(I)
F = is_graded(R) ? graded_free_module(R, 1) : free_module(R, 1)
e1 = F[1]
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