From 2f971726979f26650abbfe398054627391c5a59a Mon Sep 17 00:00:00 2001 From: "Documenter.jl" Date: Mon, 21 Oct 2024 03:15:16 +0000 Subject: [PATCH] build based on 88c8130 --- 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 c81607178..ddc67c6ac 100644 --- a/dev/.documenter-siteinfo.json +++ b/dev/.documenter-siteinfo.json @@ -1 +1 @@ -{"documenter":{"julia_version":"1.10.5","generation_timestamp":"2024-10-20T03:15:42","documenter_version":"1.7.0"}} \ No newline at end of file +{"documenter":{"julia_version":"1.10.5","generation_timestamp":"2024-10-21T03:15:11","documenter_version":"1.7.0"}} \ No newline at end of file diff --git a/dev/GF/index.html b/dev/GF/index.html index 57545b9ad..d73079b07 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 bd4ac2003..18c849041 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 b0c24ef1e..58b41f4fb 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 b3038fb2f..ceb2b316d 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 f31fe3629..fb76587ef 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 c4528bb10..3c3da1dcd 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 6672bb90a..30ad3eadf 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 a3831dad5..ceb0e1830 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 8a86c1052..17c024add 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 9aee40d40..bbb44e269 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 ddcdb9e10..95748b688 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 107ea2837..7924c7708 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 4a5e7f284..0339a4f91 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 9b87506dc..1f8f014f2 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 9113d1e17..d98f2d552 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 7e027e8bc..54f885529 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 a0dc1b3ee..a2a469773 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 ef41c4697..3aadcdc0a 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)