From 3707f3ab06032110c7539e4d2d5b2a45d202bb98 Mon Sep 17 00:00:00 2001 From: "Documenter.jl" Date: Mon, 9 Dec 2024 03:23:55 +0000 Subject: [PATCH] build based on 9d9b975 --- dev/.documenter-siteinfo.json | 2 +- dev/GF/index.html | 2 +- dev/alghom/index.html | 2 +- dev/caller/index.html | 2 +- dev/ideal/index.html | 2 +- dev/index.html | 2 +- dev/integer/index.html | 2 +- dev/matrix/index.html | 2 +- dev/modn/index.html | 2 +- dev/modp/index.html | 2 +- dev/module/index.html | 2 +- dev/nemo/index.html | 2 +- dev/noncommutative/index.html | 2 +- dev/polynomial/index.html | 2 +- dev/qring/index.html | 2 +- dev/rational/index.html | 2 +- dev/resolution/index.html | 2 +- dev/transExt/index.html | 2 +- dev/vector/index.html | 2 +- 19 files changed, 19 insertions(+), 19 deletions(-) diff --git a/dev/.documenter-siteinfo.json b/dev/.documenter-siteinfo.json index 50ab36b6a..aaefbb9d0 100644 --- a/dev/.documenter-siteinfo.json +++ b/dev/.documenter-siteinfo.json @@ -1 +1 @@ -{"documenter":{"julia_version":"1.10.7","generation_timestamp":"2024-12-08T03:23:12","documenter_version":"1.8.0"}} \ No newline at end of file +{"documenter":{"julia_version":"1.10.7","generation_timestamp":"2024-12-09T03:23:49","documenter_version":"1.8.0"}} \ No newline at end of file diff --git a/dev/GF/index.html b/dev/GF/index.html index 0d6d54b4b..a9284eb02 100644 --- a/dev/GF/index.html +++ b/dev/GF/index.html @@ -15,4 +15,4 @@ 7 julia> d = degree(R) -2 +2 diff --git a/dev/alghom/index.html b/dev/alghom/index.html index aa6c4dd27..0b8fa774e 100644 --- a/dev/alghom/index.html +++ b/dev/alghom/index.html @@ -135,4 +135,4 @@ Singular ideal over Singular polynomial ring (QQ),(x,y,z,w),(ds(4),C) with generators (4*x - 4*y + z^2 + 2*z*w + w^2) julia> K2 = kernel(idS) -Singular ideal over Singular polynomial ring (QQ),(a,b,c),(dp(3),C) with generators (0) +Singular ideal over Singular polynomial ring (QQ),(a,b,c),(dp(3),C) with generators (0) diff --git a/dev/caller/index.html b/dev/caller/index.html index dd2486d7e..335bb4b27 100644 --- a/dev/caller/index.html +++ b/dev/caller/index.html @@ -73,4 +73,4 @@ julia> with_prot(true) do; return std(Ideal(R, x^5 - y*x + 1, y^6*x + x^2 + y^3)); end [4294967295:2]5s7s11s1214-s15 product criterion:1 chain criterion:1 -Singular ideal over Singular polynomial ring (QQ),(x,y),(dp(2),C) with generators (x^5 - x*y + 1, x*y^6 + y^3 + x^2, x^4*y^3 - y^6 - y^4 - x, y^9 + y^7 + x^3*y^3 + x*y^3 + x*y - 1) +Singular ideal over Singular polynomial ring (QQ),(x,y),(dp(2),C) with generators (x^5 - x*y + 1, x*y^6 + y^3 + x^2, x^4*y^3 - y^6 - y^4 - x, y^9 + y^7 + x^3*y^3 + x*y^3 + x*y - 1) diff --git a/dev/ideal/index.html b/dev/ideal/index.html index c97adc5b0..9ea8cec48 100644 --- a/dev/ideal/index.html +++ b/dev/ideal/index.html @@ -252,4 +252,4 @@ [x, y, u] [y, u, v] [x, u, w] - [u, v, w] + [u, v, w] diff --git a/dev/index.html b/dev/index.html index dc8af30de..7efd607a7 100644 --- a/dev/index.html +++ b/dev/index.html @@ -16,4 +16,4 @@ Singular resolution: R^1 <- R^2 <- R^1 julia> F[1] -Singular ideal over Singular polynomial ring (QQ),(x,y),(dp(2),C) with generators (x - y, y^2 + 1) +Singular ideal over Singular polynomial ring (QQ),(x,y),(dp(2),C) with generators (x - y, y^2 + 1) diff --git a/dev/integer/index.html b/dev/integer/index.html index 3d9ac8e23..f169238ac 100644 --- a/dev/integer/index.html +++ b/dev/integer/index.html @@ -41,4 +41,4 @@ true julia> 5 <= b -false +false diff --git a/dev/matrix/index.html b/dev/matrix/index.html index a04da8775..1d8302af7 100644 --- a/dev/matrix/index.html +++ b/dev/matrix/index.html @@ -38,4 +38,4 @@ 0, 0, x*y + 5*u*w, 1] julia> N[4, 3] -x*y + 5*u*w +x*y + 5*u*w diff --git a/dev/modn/index.html b/dev/modn/index.html index 0e563b2e5..16fc4540d 100644 --- a/dev/modn/index.html +++ b/dev/modn/index.html @@ -9,4 +9,4 @@ true julia> c = characteristic(R) -26 +26 diff --git a/dev/modp/index.html b/dev/modp/index.html index 657c16005..9e2ca0de0 100644 --- a/dev/modp/index.html +++ b/dev/modp/index.html @@ -17,4 +17,4 @@ 5 julia> b = Int(a) -5 +5 diff --git a/dev/module/index.html b/dev/module/index.html index ddd0d35ee..161b3c602 100644 --- a/dev/module/index.html +++ b/dev/module/index.html @@ -176,4 +176,4 @@ julia> min = minimal_generating_set(M) 2-element Vector{svector{spoly{n_Q}}}: y*gen(2)+y*gen(1) - x*gen(1)-y*gen(2)-y*gen(1)+y^2*gen(2) + x*gen(1)-y*gen(2)-y*gen(1)+y^2*gen(2) diff --git a/dev/nemo/index.html b/dev/nemo/index.html index 55a0ee3ba..6548775d8 100644 --- a/dev/nemo/index.html +++ b/dev/nemo/index.html @@ -2,4 +2,4 @@ Nemo rings and fields · Singular.jl
GitHub

Nemo rings and fields

Any type that satisfies AbstractAlgebra.jl Ring or Field interface, such as all Nemo ring and field types, can be used as coefficient rings in Singular.jl. These are implemented via the Singular n_RingElem{T} and n_FieldElem{T} types, parameterised by the given Nemo/AbstractAlgebra element type.

The associated parent object of type N_Ring{T} or N_Field{T} can be constructed by a call to the CoefficientRing constructor. In practice, however, this constructor is only used internally, and Nemo rings and fields work directly as Singular coefficient rings, and all the coercions and ad hoc functions that one would expect to be present are implemented.

The Singular.jl n_RingElem (resp. n_FieldElem) types belong directly to the abstract type RingElem (resp. FieldElem) and their parent object types belong to the abstract type Ring (resp. Field). We also have the following type definitions for compatibility with previous version of Singular.jl.

const N_unknown{T} = Union{N_Ring{T}, N_Field{T}}
 const n_unknown{T} = Union{n_RingElem{T}, n_FieldElem{T}}

All of the Singular polynomial arithmetic should work for any Nemo ring and everything, including ideals, modules, standard basis, syzygies, resolutions, etc., should work with any Nemo field.

Specialised efficient wrappers exist for certain Nemo coefficient ring types.

Nemo ring functionality

Singular.jl foreign ring types provide all of the AbstractAlgebra defined ring and some field functionality.

https://nemocas.github.io/AbstractAlgebra.jl/latest/ring

https://nemocas.github.io/AbstractAlgebra.jl/latest/field

Parts of the Euclidean Ring interface may also be implemented, though Singular will report an error if division is meaningless (even after cancelling zero divisors).

https://nemocas.github.io/AbstractAlgebra.jl/latest/euclidean_interface

Below, we describe the functionality that is specific to the Singular foreign ring interface that is not already listed at the given links.

Constructors

Given an AbstractAlgebra compatible ring $R$, e.g. a Nemo ring, we have the following constructor, which returns the associated Singular.jl coefficient ring.

CoefficientRing(R::Ring)

If there are generators to be coerced from Nemo/AbstractAlgebra into corresponding elements, the Singular.jl coefficient ring can be used to coerce them to a Singular n_RingElem or n_FieldElem element.

Examples

R, x = Nemo.polynomial_ring(ZZ, "x")
 S = CoefficientRing(R)
-t = S(x)

Note that it is unlikely that a user directly needs to construct the Singular coefficient ring from a Nemo ring, since the Singular.jl constructors are designed to accept Nemo coefficient rings directly. Singular.jl automatically constructs the required Singular coefficient ring and makes use of it.

+t = S(x)

Note that it is unlikely that a user directly needs to construct the Singular coefficient ring from a Nemo ring, since the Singular.jl constructors are designed to accept Nemo coefficient rings directly. Singular.jl automatically constructs the required Singular coefficient ring and makes use of it.

diff --git a/dev/noncommutative/index.html b/dev/noncommutative/index.html index 950c88835..57ffa18d1 100644 --- a/dev/noncommutative/index.html +++ b/dev/noncommutative/index.html @@ -88,4 +88,4 @@ julia> push_term!(B, QQ(-1), Int[]); julia> finish(B) -2*z*y*x*z - 1 +2*z*y*x*z - 1 diff --git a/dev/polynomial/index.html b/dev/polynomial/index.html index 9cf1f5079..66f1a3100 100644 --- a/dev/polynomial/index.html +++ b/dev/polynomial/index.html @@ -117,4 +117,4 @@ p = x^5 + y^3+1 -p2 change_base_ring(CoefficientRing(Nemo.QQ), p) +p2 change_base_ring(CoefficientRing(Nemo.QQ), p) diff --git a/dev/qring/index.html b/dev/qring/index.html index 642a21f21..15a715537 100644 --- a/dev/qring/index.html +++ b/dev/qring/index.html @@ -18,4 +18,4 @@ Singular ideal over Singular polynomial ring (QQ),(x,y),(dp(2),C) with generators (x*y, y^3, x^2 + y^2) julia> base_ring(quotient_ideal(Q1)) == base_ring(quotient_ideal(Q2)) -true +true diff --git a/dev/rational/index.html b/dev/rational/index.html index 7012e16bb..6eba9d50d 100644 --- a/dev/rational/index.html +++ b/dev/rational/index.html @@ -33,4 +33,4 @@ 1 julia> q2 = reconstruct(ZZ(7), 5) --1//2 +-1//2 diff --git a/dev/resolution/index.html b/dev/resolution/index.html index 8f8bad117..1ca80697b 100644 --- a/dev/resolution/index.html +++ b/dev/resolution/index.html @@ -59,4 +59,4 @@ Singular resolution: R^1 <- R^5 <- R^6 <- R^2 julia> M = minres(F) -Singular resolution: R^1 <- R^5 <- R^5 <- R^1 +Singular resolution: R^1 <- R^5 <- R^5 <- R^1 diff --git a/dev/transExt/index.html b/dev/transExt/index.html index ab8b2576c..85e704883 100644 --- a/dev/transExt/index.html +++ b/dev/transExt/index.html @@ -41,4 +41,4 @@ a1 a2 a3 - a4 + a4 diff --git a/dev/vector/index.html b/dev/vector/index.html index e2ad32015..aec4c4905 100644 --- a/dev/vector/index.html +++ b/dev/vector/index.html @@ -41,4 +41,4 @@ x^5*gen(1)+2*x^3*gen(2)+x^2*gen(3)+3*y^2*gen(2)+gen(1) julia> w = jet(v, 3) -2*x^3*gen(2)+x^2*gen(3)+3*y^2*gen(2)+gen(1) +2*x^3*gen(2)+x^2*gen(3)+3*y^2*gen(2)+gen(1)