#ComputerAlgebra

Arif Solmaz

@arifsolmaz.bsky.social

2 weeks ago

Woxi reimplements Wolfram Language in Rust - runs mathematical computations and symbolic math faster

Woxi reimplements Wolfram Language in Rust - runs mathematical computations and symbolic math faster than WolframScript without kernel overhead or license checks

https://github.com/ad-si/Woxi

#Rust #Mathematics #ComputerAlgebra

Bob Lynn

@boblynn.bsky.social

4 months ago

Sister Mary Celine Fasenmyer: She Wrote the Algorithm Before Computers Existed to Run It Sister Mary Celine Fasenmyer shares how a quiet nun in mid-century Pennsylvania conceived the algorithm behind today’s computer algebra, decades before computers arrived – her method’s erasur…

Sister Mary Celine Fasenmyer: She Wrote the Algorithm Before Computers Existed to Run It
voxmeditantis.com/2025/10/27/s...

#WomenInSTEM #STEM #Combinatorics #Hypergeometric #ComputerAlgebra

Daniel Lakeland

@dlakelan.mastodon.sdf.org.ap.brid.gy

5 months ago

Look guys, in 1999 Bill Schelter released the DOE version of Macsyma he'd been solo maintaining for 20 years called Maxima, and in the 26 years since a small band of maintainers many of whom were contributors to the original thing at MIT have been maintaining and enhancing it. And Y'ALL just […]

Alexander Kasprzyk

@amkasprzyk.bsky.social

6 months ago

Minkowski Polynomials and Mutations Given a Laurent polynomial f, one can form the period of f: this is a function of one complex variable that plays an important role in mirror symmetry for Fano manifolds. Mutations are a particular class of birational transformations acting on Laurent polynomials in two variables; they preserve the period and are closely connected with cluster algebras. We propose a higher-dimensional analog of mutation acting on Laurent polynomials f in n variables. In particular we give a combinatorial description of mutation acting on the Newton polytope P of f, and use this to establish many basic facts about mutations. Mutations can be understood combinatorially in terms of Minkowski rearrangements of slices of P, or in terms of piecewise-linear transformations acting on the dual polytope P* (much like cluster transformations). Mutations map Fano polytopes to Fano polytopes, preserve the Ehrhart series of the dual polytope, and preserve the period of f. Finally we use our results to show that Minkowski polynomials, which are a family of Laurent polynomials that give mirror partners to many three-dimensional Fano manifolds, are connected by a sequence of mutations if and only if they have the same period.

"Minkowski Polynomials and Mutations" by Mohammad Akhtar, Tom Coates, Sergey Galkin, and Alexander Kasprzyk. In SIGMA. #AlgebraicGeometry #LatticePolytope #ComputerAlgebra

Alexander Kasprzyk

@amkasprzyk.bsky.social

6 months ago

Fano 3-folds in format, Tom and Jerry - European Journal of Mathematics We study $${\mathbb {Q}}$$ Q -factorial terminal Fano 3-folds whose equations are modelled on those of the Segre embedding of . These lie in codimension 4 in their total anticanonical embedding and…

"Fano 3-folds in P^1 x P^1 format, Tom and Jerry" by Gavin Brown, Alexander Kasprzyk, and Imran Qureshi. In the European Journal of Mathematics. #AlgebraicGeometry #ComputerAlgebra

Alexander Kasprzyk

@amkasprzyk.bsky.social

7 months ago

Four-dimensional Fano toric complete intersections We find at least 527 new four-dimensional Fano manifolds, each of which is a complete intersection in a smooth toric Fano manifold.

"Four-dimensional Fano toric complete intersections" by Tom Coates, Alexander Kasprzyk, and Thomas Prince. In Proceedings of the Royal Society A. #AlgebraicGeometry #HPC #ComputerAlgebra #Combinatorics

Georgy Scholten

@georgysch.bsky.social

7 months ago

🔍 New algorithm finds ALL local minimizers of functions on tensorized domains using only noisy function evaluations!

Combines approximation theory + computer algebra.

Implemented in Julia package GlobTim

#optimization #mathematics #Julia #computeralgebra

Alexander Kasprzyk

@amkasprzyk.bsky.social

7 months ago

Passagemath is a really interesting project to, as I understand it, streamline the process of using Sage (starting with simple installation via pip, but also easing integration into your own #Python projects) and making it a part of the lively scientific Python community. #computeralgebra #mathsky

Alexander Kasprzyk

@amkasprzyk.bsky.social

7 months ago

Quantum periods for 3-dimensional Fano manifolds The quantum period of a variety X is a generating function for certain Gromov–Witten invariants of X which plays an important role in mirror symmetry. We compute the quantum periods of all 3–dimensional Fano manifolds. In particular we show that 3–dimensional Fano manifolds with very ample anticanonical bundle have mirrors given by a collection of Laurent polynomials called Minkowski polynomials. This was conjectured in joint work with Golyshev. It suggests a new approach to the classification of Fano manifolds: by proving an appropriate mirror theorem and then classifying Fano mirrors. Our methods are likely to be of independent interest. We rework the Mori–Mukai classification of 3–dimensional Fano manifolds, showing that each of them can be expressed as the zero locus of a section of a homogeneous vector bundle over a GIT quotient V//G, where G is a product of groups of the form GL_n(C) and V is a representation of G. When G=GL_1(C)^r, this expresses the Fano 3–fold as a toric complete intersection; in the remaining cases, it expresses the Fano 3–fold as a tautological subvariety of a Grassmannian, partial flag manifold, or projective bundle thereon. We then compute the quantum periods using the quantum Lefschetz hyperplane theorem of Coates and Givental and the abelian/non-abelian correspondence of Bertram, Ciocan-Fontanine, Kim and Sabbah.

"Quantum periods for 3-dimensional Fano manifolds" by Tom Coates, Alessio Corti, Sergey Galkin and Alexander Kasprzyk. In Geometry & Topology. #AlgebraicGeometry #ComputerAlgebra #HPC

Georgy Scholten

@georgysch.bsky.social

7 months ago

New pre-print: Probabilistic algorithm for computing all local minimizers of Morse functions on a compact domain - Archive ouverte HAL

📄 Preprint: hal.science/hal-05160251v1

💻 Julia: github.com/gescholt/Glo...

#Optimization #JuliaLang #ScientificComputing #ComputerAlgebra

Alexander Kasprzyk

@amkasprzyk.bsky.social

7 months ago

This includes the new GIT package by my good friend Jesus Martinez-Garcia and Robert Hanson. #AlgebraicGeometry #ComputerAlgebra

arxiv.org/abs/2506.19431

Alexander Kasprzyk

@amkasprzyk.bsky.social

8 months ago

LMFDB, Computation, and Number Theory (LuCaNT) 2025 This will be a one-week conference broadly focused on the topics of the LMFDB (http://lmfdb.org), mathematical databases, computation, and number theory. The conference will include invited talks, presentations by authors of papers submitted to the conference and selected by the scientific committee following peer-review, as well as time for research and collaboration. We plan to publish a proceedings volume that will include all of the accepted papers. The field of mathematical databases has emerged as an important area of research at the intersection of computer science and mathematics. It seeks to address questions that arise when organizing, storing, and providing access to mathematical knowledge in a structured manner. These databases are intended to be easily searchable and navigable, providing researchers, educators, and students with a convenient way to access mathematical content. There are many challenges in developing and maintaining mathematical databases, ranging from data quality and integration, to standardization, search design, updating and maintenance, and usability. In addition, many algorithmic and theoretical questions emerge naturally when considering systematic computations that must be done on a large scale.

Next week I am delighted to be speaking at the workshop "LMFDB, Computation, and Number Theory" at @icerm.bsky.social , Brown University, USA. #LMFDB #ComputerAlgebra #AlgebraicGeometry #NumberTheory

passagemath

@passagemath.org

8 months ago

Connections to Lean / mathlib · Issue #1025 · passagemath/passagemath #1019 References: leanprover-community/mathlib4#942 (2022) https://leanprover.zulipchat.com/#narrow/channel/270676-lean4/topic/Basic.20unverified.20symbolic.20calculations.20in.20Lean4.20using.20PA...

Visited the #Lean / #mathlib community this past week on their Zulip server to learn about connections between
- the #TheoremProving software/communities and
- #ComputerAlgebra / exact mathematical computing communities.
Findings (sparse) documented in
github.com/passagemath/...
#MathSky

Alexander Kasprzyk

@amkasprzyk.bsky.social

8 months ago

Databases of quantum periods for Fano manifolds - Scientific Data Fano manifolds are basic building blocks in geometry – they are, in a precise sense, atomic pieces of shapes. The classification of Fano manifolds is therefore an important problem in geometry, which has been open since the 1930s. One can think of this as building a Periodic Table for shapes. A recent breakthrough in Fano classification involves a technique from theoretical physics called Mirror Symmetry. From this perspective, a Fano manifold is encoded by a sequence of integers: the coefficients of a power series called the regularized quantum period. Progress to date has been hindered by the fact that quantum periods require specialist expertise to compute, and descriptions of known Fano manifolds and their regularized quantum periods are incomplete and scattered in the literature. We describe databases of regularized quantum periods for Fano manifolds in dimensions up to four. The databases in dimensions one, two, and three are complete; the database in dimension four will be updated as new four-dimensional Fano manifolds are discovered and new regularized quantum periods computed.

"Databases of quantum periods for Fano manifolds" by Tom Coates and Alexander Kasprzyk. In Nature #ScientificData. #AlgebraicGeometry #BigData #ComputerAlgebra

Alexander Kasprzyk

@amkasprzyk.bsky.social

10 months ago

Very happy to see my friends Paolo Cascini, Vanya Cheltsov, Tyler Kelly, and Evgeny Shinder will be visiting @sydmathinst.bsky.social . I must have spent three years on-and-off visiting Sydney Uni (including a 13 month period in the #ComputerAlgebra Group) and I loved every minute. A beautiful city!