From 65b8024ee64390b56f5bfee2432f33401df9a098 Mon Sep 17 00:00:00 2001 From: "Documenter.jl" Date: Sat, 28 Sep 2024 03:11:21 +0000 Subject: [PATCH] build based on aa9bb52 --- 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 985348bca..949e832d8 100644 --- a/dev/.documenter-siteinfo.json +++ b/dev/.documenter-siteinfo.json @@ -1 +1 @@ -{"documenter":{"julia_version":"1.10.5","generation_timestamp":"2024-09-27T14:47:30","documenter_version":"1.7.0"}} \ No newline at end of file +{"documenter":{"julia_version":"1.10.5","generation_timestamp":"2024-09-28T03:11:16","documenter_version":"1.7.0"}} \ No newline at end of file diff --git a/dev/GF/index.html b/dev/GF/index.html index 28a17cc22..59aa50901 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 a231b9773..2fb726abe 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 e34705e14..75aafdfb9 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 2f717c47a..431eaeafa 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 114942aa4..a599fea1a 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 4dd1867b1..bf626f2bf 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 1199b48e6..2fac0850f 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 57f57713b..fc2a97bbf 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 9b869382c..0e7d4de1b 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 384c226cd..595156eb5 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 5751d5acd..cc871d30a 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 6a47c2792..72e2ab6b2 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 3cdfa0c61..be5671f49 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 da5007beb..4cf403bf7 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 f067e0f27..2d35ac399 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 ed0e0909d..cdeaf7111 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 a19bfa070..b60bc7f2c 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 108b34c6b..b2484bff9 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)