# \#algebra

**URL:** https://discourse.julialang.org/tag/algebra/328.md

[Latest](https://discourse.julialang.org/latest.md) · [Categories](https://discourse.julialang.org/categories.md) · [Tags](https://discourse.julialang.org/tags.md)

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## [Hemiplex numbers and factoring symmetric indefinite matrices](https://discourse.julialang.org/t/hemiplex-numbers-and-factoring-symmetric-indefinite-matrices/138501)

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**Author:** [@tim.holy](https://discourse.julialang.org/u/tim.holy)\
**Replies:** 3\
**Last updated:** [July 29, 2026, 1:01pm UTC](https://discourse.julialang.org/t/hemiplex-numbers-and-factoring-symmetric-indefinite-matrices/138501 "2026-07-29T13:01:18Z")

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I’m pleased to announce the release of two new numeric packages, HemiplexNumbers and HemiplexFactorizations, and their accompanying manuscript Jordan algebras, hemiplex numbers, and the Cholesky decomposition of arbitrar…

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## [GroupFunctions.jl - Computing individual d-functions of the unitary group U(d)](https://discourse.julialang.org/t/groupfunctions-jl-computing-individual-d-functions-of-the-unitary-group-u-d/136828)

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**Author:** [@damaro](https://discourse.julialang.org/u/damaro)\
**Replies:** 0\
**Last updated:** [April 22, 2026, 1:26pm UTC](https://discourse.julialang.org/t/groupfunctions-jl-computing-individual-d-functions-of-the-unitary-group-u-d/136828 "2026-04-22T13:26:54Z")

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GroupFunctions.jl Hello everyone. I would like to share a project I have been developing for more than five years: GroupFunctions.jl, a registered Julia package for symbolic and numerical computation of individual group…

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## [Solving A·u = b over a Laurent polynomial ring](https://discourse.julialang.org/t/solving-a-u-b-over-a-laurent-polynomial-ring/134428)

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**Author:** [@nzy1997](https://discourse.julialang.org/u/nzy1997)\
**Replies:** 0\
**Last updated:** [December 8, 2025, 10:05am UTC](https://discourse.julialang.org/t/solving-a-u-b-over-a-laurent-polynomial-ring/134428 "2025-12-08T10:05:32Z")

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Hi, I am trying to solve linear equations over a Laurent polynomial ring in Oscar/Julia. Given a matrix A and a right-hand side b over R = GF(p)\[x₁^{±1}, …, xₙ^{±1}\], I want to compute a vector u such that A \* u = b. M…

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## [Getting Catalyst and Oscar to work together](https://discourse.julialang.org/t/getting-catalyst-and-oscar-to-work-together/121299)

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**Author:** [@adhalanay](https://discourse.julialang.org/u/adhalanay)\
**Replies:** 10\
**Last updated:** [November 20, 2024, 9:34pm UTC](https://discourse.julialang.org/t/getting-catalyst-and-oscar-to-work-together/121299 "2024-11-20T21:34:06Z")

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This more of an extension of the previous topic https://discourse.julialang.org/t/finding-steady-states-symbolicaly/119545/18. First some background: commutative algebra is of great use for studying mass-action chemical…

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## [Polynomial manipulation](https://discourse.julialang.org/t/polynomial-manipulation/114313)

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**Author:** [@BLI](https://discourse.julialang.org/u/BLI)\
**Replies:** 45\
**Last updated:** [July 8, 2024, 9:02am UTC](https://discourse.julialang.org/t/polynomial-manipulation/114313 "2024-07-08T09:02:36Z")

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This is not my field of expertise, but I’m curious about whether Julia has some package that can solve my problem… I have some fraction f(x) of polynomials consisting of a numerator polynomial n(x) and a denominator pol…

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## [Details about the blocks after symmetry reduction or Wedderburn decomposition](https://discourse.julialang.org/t/details-about-the-blocks-after-symmetry-reduction-or-wedderburn-decomposition/116687)

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**Author:** [@Khashayar-Neshat](https://discourse.julialang.org/u/Khashayar-Neshat)\
**Replies:** 3\
**Last updated:** [July 7, 2024, 6:49am UTC](https://discourse.julialang.org/t/details-about-the-blocks-after-symmetry-reduction-or-wedderburn-decomposition/116687 "2024-07-07T06:49:01Z")

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For each irreducible representation, I want to know its degree and the number of times it occurs in the Wedderburn decomposition of the underlying algebra of equivariant maps using SymbolicWedderburn.jl . I also want to …

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## [SymbolicWedderburn examples](https://discourse.julialang.org/t/symbolicwedderburn-examples/116682)

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**Author:** [@Khashayar-Neshat](https://discourse.julialang.org/u/Khashayar-Neshat)\
**Replies:** 3\
**Last updated:** [July 6, 2024, 9:24am UTC](https://discourse.julialang.org/t/symbolicwedderburn-examples/116682 "2024-07-06T09:24:53Z")

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Hi @abulak When I run ex\_C2\_linear or runtest in SymbolicWedderburn.jl, I get ERROR: UndefVarError: \`Monomial\` not defined Stacktrace: \[1\] top-level scope @ c:\\Users\\raven\\.julia\\packages\\SymbolicWedderburn\\lbiby\\e…

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## [Oscar and Matlab both call nrows](https://discourse.julialang.org/t/oscar-and-matlab-both-call-nrows/114157)

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**Author:** [@ilovemath](https://discourse.julialang.org/u/ilovemath)\
**Replies:** 9\
**Last updated:** [May 14, 2024, 3:42am UTC](https://discourse.julialang.org/t/oscar-and-matlab-both-call-nrows/114157 "2024-05-14T03:42:46Z")

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Hi there, So, I am calling both Oscar and Matlab packages. Both call nrows in their subroutines under the hood in their often typical function calls. I was able to write the code so that I would not get the warning sa…

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## [\[ANN\] New registered package Chevie](https://discourse.julialang.org/t/ann-new-registered-package-chevie/107683)

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**Author:** [@Jean\_Michel](https://discourse.julialang.org/u/Jean_Michel)\
**Replies:** 1\
**Last updated:** [February 13, 2024, 2:09am UTC](https://discourse.julialang.org/t/ann-new-registered-package-chevie/107683 "2024-02-13T02:09:08Z")

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This to announce a new registered package Chevie dealing with various areas of representation theory. https://github.com/jmichel7/Chevie.jl Here is the README This is my attempt to port the Chevie package from GAP3 to…

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## [Matrix multiplication and type stability](https://discourse.julialang.org/t/matrix-multiplication-and-type-stability/107020)

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**Author:** [@denshd](https://discourse.julialang.org/u/denshd)\
**Replies:** 1\
**Last updated:** [December 4, 2023, 9:32am UTC](https://discourse.julialang.org/t/matrix-multiplication-and-type-stability/107020 "2023-12-04T09:32:06Z")

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Hello! Let’s consider MVE: using LinearAlgebra using AlgebraicNumbers M = AlgebraicNumber.(\[ 1 2 3 4 \]) b = AlgebraicNumber.(\[5; 6\]) println(typeof(M)) println(typeof(b)) x = M \* b println(typeof(x)) Expe…

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## [\[ANN\] ConstraintTrees.jl -- tidy constrained systems for JuMP](https://discourse.julialang.org/t/ann-constrainttrees-jl-tidy-constrained-systems-for-jump/105563)

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**Author:** [@MirekKratochvil](https://discourse.julialang.org/u/MirekKratochvil)\
**Replies:** 0\
**Last updated:** [October 30, 2023, 11:43am UTC](https://discourse.julialang.org/t/ann-constrainttrees-jl-tidy-constrained-systems-for-jump/105563 "2023-10-30T11:43:22Z")

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What is it about? We’ve lately spent quite some time on developing constraint-based modeling software that works with JuMP (first COBREXA.jl, then FBCModelTests.jl, and lately DifferentialMetabolism.jl). A common observ…

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## [Lyapunov + Symmetries = Infeasible, Lyapunov - Symmetries = Feasible](https://discourse.julialang.org/t/lyapunov-symmetries-infeasible-lyapunov-symmetries-feasible/101585)

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**Author:** [@ilovemath](https://discourse.julialang.org/u/ilovemath)\
**Replies:** 9\
**Last updated:** [September 22, 2023, 11:21pm UTC](https://discourse.julialang.org/t/lyapunov-symmetries-infeasible-lyapunov-symmetries-feasible/101585 "2023-09-22T23:21:44Z")

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Hi again @blegat @abulak I am using SOS programming to find a Lyapunov function, obeying some natural symmetry. The time derivative of V also obeys said symmetry. The feasibility of the Lyapunov function is dependent …

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## [Oscar and DynamicaPolynomials: Convert polynomial type for basis of invariant rings](https://discourse.julialang.org/t/oscar-and-dynamicapolynomials-convert-polynomial-type-for-basis-of-invariant-rings/102422)

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**Author:** [@ilovemath](https://discourse.julialang.org/u/ilovemath)\
**Replies:** 6\
**Last updated:** [September 14, 2023, 2:57am UTC](https://discourse.julialang.org/t/oscar-and-dynamicapolynomials-convert-polynomial-type-for-basis-of-invariant-rings/102422 "2023-09-14T02:57:48Z")

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I would like to know if there is a way to convert a type nf\_elem to a polynomial. My goal with this code is to find all minimal monomials of degree d that obey a rotational symmetry, so I can directly construct a polyno…

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## [Symmetry & SOS Optimization Compatibility Issues?](https://discourse.julialang.org/t/symmetry-sos-optimization-compatibility-issues/98057)

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**Author:** [@ilovemath](https://discourse.julialang.org/u/ilovemath)\
**Replies:** 6\
**Last updated:** [June 5, 2023, 8:29pm UTC](https://discourse.julialang.org/t/symmetry-sos-optimization-compatibility-issues/98057 "2023-06-05T20:29:12Z")

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Hello all, I am trying to implement rotational symmetry for an SOS problem. In particular, I followed the example problem here: Dihedral symmetry of the Robinson form · SumOfSquares. My goal is to use a cyclic group i…

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## [\[ANN\] Released GaloisFields v1.0](https://discourse.julialang.org/t/ann-released-galoisfields-v1-0/33071)

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**Author:** [@tkluck](https://discourse.julialang.org/u/tkluck)\
**Replies:** 7\
**Last updated:** [April 18, 2023, 10:29am UTC](https://discourse.julialang.org/t/ann-released-galoisfields-v1-0/33071 "2023-04-18T10:29:28Z")

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I just released v1.0 of GaloisFields.jl. For those people not familiar – a Galois field (or ‘finite field’) is a finite set that supports addition and multiplication, both with their inverses subtraction and division. Th…

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## [DateTime: Time division](https://discourse.julialang.org/t/datetime-time-division/95285)

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**Author:** [@ryofurue](https://discourse.julialang.org/u/ryofurue)\
**Replies:** 9\
**Last updated:** [February 28, 2023, 11:36am UTC](https://discourse.julialang.org/t/datetime-time-division/95285 "2023-02-28T11:36:03Z")

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I was wondering how division works on time intervals. My naïve thought doesn’t work using Dates hr = Dates.Hour(1) t1 = DateTime(2023, 1, 3) r = 7.4 t2 = t1 + hr/r # -\>InexactError: Int64(0.13513513513513511) The foll…

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## [\[ANN\] Quaternions.jl v0.7.0](https://discourse.julialang.org/t/ann-quaternions-jl-v0-7-0/91368)

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**Author:** [@hyrodium](https://discourse.julialang.org/u/hyrodium)\
**Replies:** 4\
**Last updated:** [December 15, 2022, 1:51pm UTC](https://discourse.julialang.org/t/ann-quaternions-jl-v0-7-0/91368 "2022-12-15T13:51:08Z")

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@sethaxen and I have been working on maintaining the Quaternion.jl this year. Today, version v0.7.0 has been released with some breaking changes, and this will likely be the last release before v1.0.0. The changes we w…

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## [Solve Simultaneous Algebraic Equations (x eqns and x unknowns)](https://discourse.julialang.org/t/solve-simultaneous-algebraic-equations-x-eqns-and-x-unknowns/88060)

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**Author:** [@rwalters31](https://discourse.julialang.org/u/rwalters31)\
**Replies:** 2\
**Last updated:** [October 1, 2022, 1:55am UTC](https://discourse.julialang.org/t/solve-simultaneous-algebraic-equations-x-eqns-and-x-unknowns/88060 "2022-10-01T01:55:01Z")

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I have been looking for a Julia package to solve simultaneous algebraic equations. A simple example for two equations and two unknowns might look like: x^{2}+y^{2}=5 y=\\frac{1}{2}x^{3}+3x^{2}-2x-3 Here is a plot of…

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## [\[ANN\] CliffordAlgebras.jl](https://discourse.julialang.org/t/ann-cliffordalgebras-jl/71955)

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**Author:** [@atell\_soundtheory](https://discourse.julialang.org/u/atell_soundtheory)\
**Replies:** 19\
**Last updated:** [November 30, 2021, 1:07am UTC](https://discourse.julialang.org/t/ann-cliffordalgebras-jl/71955 "2021-11-30T01:07:35Z")

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I’m pleased to announce the first release of CliffordAlgebras.jl, a package for performing calculations in generic Clifford algebras / geometric algebras. Package registration is still pending. https://github.com/ATell-…

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## [Submodules AbstractAlgebra](https://discourse.julialang.org/t/submodules-abstractalgebra/70308)

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**Author:** [@Gilles\_Dubois](https://discourse.julialang.org/u/Gilles_Dubois)\
**Replies:** 5\
**Last updated:** [October 27, 2021, 8:30pm UTC](https://discourse.julialang.org/t/submodules-abstractalgebra/70308 "2021-10-27T20:30:50Z")

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Hi everybody ! I’m now busy with the submodule concept as described in AbstractAlgebra package documentation. I noticed that, on my point of view, a lot of things are missing in the interface. For example as a minimum…

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## [ModuleElts](https://discourse.julialang.org/t/moduleelts/69675)

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**Author:** [@Jean\_Michel](https://discourse.julialang.org/u/Jean_Michel)\
**Replies:** 0\
**Last updated:** [October 13, 2021, 10:31am UTC](https://discourse.julialang.org/t/moduleelts/69675 "2021-10-13T10:31:21Z")

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This is to announce a new package. Comments/ideas/criticisms are welcome. ModuleElts Module Elements — elements of free modules. A ModuleElt{K,V} represents an element of a free module where basis elements are…

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## [\[ANN\] TensorAlgebra.jl: Taking covariance seriously](https://discourse.julialang.org/t/ann-tensoralgebra-jl-taking-covariance-seriously/43587)

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**Author:** [@anon67531922](https://discourse.julialang.org/u/anon67531922)\
**Replies:** 49\
**Last updated:** [March 22, 2021, 11:52am UTC](https://discourse.julialang.org/t/ann-tensoralgebra-jl-taking-covariance-seriously/43587 "2021-03-22T11:52:06Z")

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TL;DR Vector spaces are first class. Tensors are linear maps from a vector space to an underlying field t: V\\to K Dual spaces are first class with α = Covector(V,\[1,2,3\]) Vectors are degree-1 tensors whose domain is …

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## [\[ANN\] CommutativeRings](https://discourse.julialang.org/t/ann-commutativerings/55268)

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**Author:** [@klacru](https://discourse.julialang.org/u/klacru)\
**Replies:** 0\
**Last updated:** [February 14, 2021, 6:09pm UTC](https://discourse.julialang.org/t/ann-commutativerings/55268 "2021-02-14T18:09:38Z")

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This package CommutativeRings supports processing in discrete commutative algebra. It has Galois fields, univariate and multivariate polynomials, matrices and vector spaces over finite fields.

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## [Weave unable to execute Maxima.jl](https://discourse.julialang.org/t/weave-unable-to-execute-maxima-jl/49560)

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**Author:** [@brett\_knoss](https://discourse.julialang.org/u/brett_knoss)\
**Replies:** 0\
**Last updated:** [November 4, 2020, 2:22am UTC](https://discourse.julialang.org/t/weave-unable-to-execute-maxima-jl/49560 "2020-11-04T02:22:05Z")

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When I try to Weave a Julia Markdown with Maxima.jl, it ends up not starting. using Maxima It just stays on the first block of code.

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## [Generate faa di bruno matrix](https://discourse.julialang.org/t/generate-faa-di-bruno-matrix/38059)

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**Author:** [@Veenty](https://discourse.julialang.org/u/Veenty)\
**Replies:** 9\
**Last updated:** [April 24, 2020, 2:25am UTC](https://discourse.julialang.org/t/generate-faa-di-bruno-matrix/38059 "2020-04-24T02:25:31Z")

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I am trying to implement the funcion A(x1, x2, x3, ..xn) Such that \[A\]\_{m,j} = B\_{m,j} , where B\_{m,j} corresponds to the incomplete bell polynomial. The thing is, that I don’t want to have to construct that matrix ev…