[{"data":1,"prerenderedAt":449},["ShallowReactive",2],{"project:zero-sum-sequences":3,"catalog":32},{"slug":4,"name":4,"nameHtml":4,"summary":5,"summaryHtml":5,"authors":6,"searchText":10,"facets":11,"source":25,"docs":27,"descriptionHtml":28,"bibliographyHtml":29,"funding":30,"affiliations":31},"zero-sum-sequences","Python tools for factoring finite additive sequences into minimal zero-sum sequences and exploring factorization lengths, relations, and automorphism orbits.",[7],{"name":8,"orcid":9,"html":8},"Benjamin Hackl","https:\u002F\u002Forcid.org\u002F0000-0003-2998-9599","zero-sum-sequences python tools for factoring finite additive sequences into minimal zero-sum sequences and exploring factorization lengths, relations, and automorphism orbits. benjamin hackl zero-sum-sequences provides immutable finite additive sequences and algorithms for factoring them into minimal zero-sum sequences. it runs in ordinary python with networkx and optionally integrates with additive groups supplied by sagemath. for a sequence over an additive group g , the zero-sum condition is g_1 + \\cdots + g_m = 0. the package computes sets of factorization lengths, minimum and maximum lengths, witnesses, and complete factorizations. it also supports atom catalogues, factorization relations, and automorphism orbits. the ambient group and an upper bound for its davenport constant are supplied explicitly by the caller. for example, over c_3 , the minimal zero-sum sequences a=1^3 , b=2^3 , and p=1\\cdot 2 satisfy the factorization relation ab=p^3 . an executable tutorial introduces the api with small examples; the repository also includes benchmarks.",{"tags":12,"audiences":16,"affiliations":18,"license":19,"maintenance":21,"resources":23},[13,14,15],"additive combinatorics","factorization theory","symbolic computation",[17],"research",[],[20],"MIT",[22],"active",[24],"documentation",{"url":26},"https:\u002F\u002Fgithub.com\u002Fbehackl\u002Fzero-sum-sequences","https:\u002F\u002Fgithub.com\u002Fbehackl\u002Fzero-sum-sequences\u002Fblob\u002Fmain\u002FREADME.md","\u003Cp>\u003Ccode>zero-sum-sequences\u003C\u002Fcode> provides immutable finite additive sequences and algorithms\nfor factoring them into minimal zero-sum sequences. It runs in ordinary Python\nwith NetworkX and optionally integrates with additive groups supplied by SageMath.\u003C\u002Fp>\n\u003Cp>For a sequence over an additive group \u003Cmjx-container class=\"MathJax\" jax=\"SVG\" overflow=\"overflow\">\u003Csvg aria-label=\"G\" style=\"vertical-align: -0.05ex;\" xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"1.778ex\" height=\"1.645ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -705 786 727\">\u003Cg stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"scale(1,-1)\">\u003Cg data-mml-node=\"math\" data-latex=\"G\">\u003Cg data-mml-node=\"mi\" data-latex=\"G\">\u003Cpath data-c=\"1D43A\" d=\"M324-22C412-22 481 5 532 59C538 46 564 1 578 1C583 1 586 4 588 8C590 12 597 32 606 68L624 144C630 167 634 184 637 195C648 239 648 238 702 239C715 239 721 247 721 263C721 273 716 278 705 278C686 278 620 274 601 275L462 278C446 278 438 270 438 254C438 245 444 241 456 240C513 237 543 235 546 233C549 231 550 227 550 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distributed as cyclic-group-zerosum-factor , carries out exhaustive computational experiments on zero-sum sequences in cyclic groups of even order c_{2n} . for selected generators a,b,c , it investigates whether a sequence of the form u = a^{2n}b^{2n}c^{2n} = u_1u_2u_3u_4 admits a factorization into four non-empty minimal zero-sum sequences. candidate factorizations are enumerated through products of weak integer compositions, with batches of candidates distributed to worker threads. the zenodo archive includes the rust source, cargo metadata, and a readme with the mathematical formulation, implementation notes, and experimental results. the command cargo run --release -- \u003Cn> selects the group order 2n . this is a standalone program, separate from the zero-sum-sequences python package. the license recorded for the deposited software is cc by 4.0.",{"tags":124,"audiences":126,"affiliations":127,"license":128,"maintenance":130,"resources":131},[13,14,125],"exhaustive search",[17],[],[129],"CC-BY-4.0",[60],[],{"slug":133,"name":134,"nameHtml":134,"summary":135,"summaryHtml":135,"authors":136,"searchText":138,"facets":139},"dependent-bterms","dependent_bterms","SageMath tools for asymptotic expansions with explicit error bounds and a secondary variable whose growth depends on the main variable.",[137],{"name":8,"orcid":9,"html":8},"dependent_bterms sagemath tools for asymptotic expansions with explicit error bounds and a secondary variable whose growth depends on the main variable. benjamin hackl dependent_bterms extends sagemath's asymptoticring framework with a secondary symbolic variable whose growth is bounded by powers of the main asymptotic variable. this supports computations in which, for example, 1 \\leq k \\leq n^{1\u002F2} while n tends to infinity. the toolbox combines asymptotic expansions with explicit error bounds. it provides operations for simplifying expansions, rounding error-bound coefficients, changing the range of validity of bounds, and constructing taylor expansions with explicit remainders. a demonstration notebook introduces the package's capabilities. the individual functions include sagemath examples in their docstrings.",{"tags":140,"audiences":142,"affiliations":143,"license":144,"maintenance":146,"resources":147},[141,15],"asymptotic analysis",[17],[],[145],"GPL-3.0-or-later",[22],[24],{"slug":149,"name":150,"nameHtml":150,"summary":151,"summaryHtml":151,"authors":152,"searchText":160,"facets":161},"gpdps","GPDPS.jl","A Julia reference implementation of generalized primal-dual proximal splitting for nonsmooth, nonconvex optimization.",[153,156,158],{"name":154,"orcid":155,"html":154},"Christian Clason","https:\u002F\u002Forcid.org\u002F0000-0002-9948-8426",{"name":157,"html":157},"Stanislav Mazurenko",{"name":159,"html":159},"Tuomo Valkonen","gpdps.jl a julia reference implementation of generalized primal-dual proximal splitting for nonsmooth, nonconvex optimization. christian clason stanislav mazurenko tuomo valkonen gpdps.jl provides the reference implementation of a generalized primal-dual proximal splitting approach based on generalized conjugation. it accompanies research on nonsmooth, nonconvex optimization. the package includes examples for an elliptic nash equilibrium problem and a huber–potts image segmentation model. the latter supports isotropic and anisotropic variants and configurable images and regularization parameters. the documented test environment uses julia 1.0–1.2 on macos and linux. the repository supplies a project environment and instructions for instantiating its dependencies; compatibility with newer julia versions should be checked before use.",{"tags":162,"audiences":165,"affiliations":166,"license":167,"maintenance":168,"resources":169},[163,164,54],"numerical optimization","nonsmooth 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Python.",[194,195,196],{"name":48,"orcid":49,"html":48},{"name":176,"orcid":177,"html":176},{"name":8,"orcid":9,"html":8},"gratopy opencl-accelerated radon and fanbeam projections, backprojections, and iterative tomographic reconstruction methods for python. kristian bredies richard huber benjamin hackl gratopy — graz accelerated tomographic projections for python provides radon transforms, fanbeam transforms, and their associated backprojections. its pixel-driven projection operators are implemented with opencl for efficient gpu execution and integration with other pyopencl code. the toolbox is intended for developing iterative tomographic reconstruction methods, including optimization-based approaches. it includes landweber, conjugate-gradient, and total-variation reconstruction schemes, together with examples and test data. an experimental radon operator interface supports adjoints and compositions such as r^\\ast r . fanbeam execution remains available through the established projection interface. opencl drivers and a suitable pyopencl installation are required.",{"tags":199,"audiences":200,"affiliations":201,"license":202,"maintenance":203,"resources":204},[109,53,183,56],[17],[],[145],[22],[24,63],{"slug":206,"name":207,"nameHtml":207,"summary":208,"summaryHtml":208,"authors":209,"authorsNote":211,"authorsNoteHtml":211,"searchText":212,"facets":213},"manim","Manim","A community-developed Python library for creating precise mathematical animations programmatically, for explanatory videos, teaching, and presentations.",[210],{"name":8,"orcid":9,"html":8},"and the Manim community","manim a community-developed python library for creating precise mathematical animations programmatically, for explanatory videos, teaching, and presentations. benjamin hackl and the manim community manim community is a python library for creating mathematical animations programmatically. scenes are defined in python and rendered into videos, making it possible to build precise, 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control",[17],[],[60],[60],[24,63],{"slug":240,"name":241,"nameHtml":241,"summary":242,"summaryHtml":242,"authors":243,"searchText":253,"facets":254},"sage-acsv","sage_acsv","SageMath algorithms for computing asymptotics of multivariate sequences with rational generating functions, using exact algebraic computations.",[244,245,247,249,251],{"name":8,"orcid":9,"html":8},{"name":246,"html":246},"Andrew Luo",{"name":248,"html":248},"Stephen Melczer",{"name":250,"html":250},"Jesse Selover",{"name":252,"html":252},"Elaine Wong","sage_acsv sagemath algorithms for computing asymptotics of multivariate sequences with rational generating functions, using exact algebraic computations. benjamin hackl andrew luo stephen melczer jesse selover elaine wong sage_acsv implements algorithms for analytic combinatorics in several variables in sagemath. it computes asymptotic information about multivariate sequences with rational generating functions, using exact algebraic computations. for generating functions of the form f(\\mathbf{z}) = \\frac{g(\\mathbf{z})}{h(\\mathbf{z})}, the geometry of the singular variety h(\\mathbf{z})=0 is central to the asymptotic analysis. the package's original algorithms treat smooth cases; subsequent work extends the implementation to non-smooth singular varieties under additional geometric assumptions, using whitney stratification. further capabilities include higher-order asymptotic expansions and alternative backends for algebraic computations. documentation and examples are available online, and the package can be explored through binder .",{"tags":255,"audiences":257,"affiliations":258,"license":259,"maintenance":260,"resources":261},[256,141,15],"analytic combinatorics",[17],[],[20],[22],[24,63],{"slug":263,"name":264,"nameHtml":264,"summary":265,"summaryHtml":265,"authors":266,"searchText":272,"facets":273},"sagemath-asymptotic-ring","SageMath Asymptotic Ring","Symbolic arithmetic with univariate and multivariate asymptotic expansions, 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computer algebra system. it is distributed as part of sagemath and is distinct from the separate dependent_bterms extension for explicit error bounds with a dependent secondary variable.",{"tags":274,"audiences":275,"affiliations":276,"license":277,"maintenance":279,"resources":280},[141,15],[17],[],[278],"GPL-2.0-or-later",[22],[24],{"slug":282,"name":283,"nameHtml":283,"summary":284,"summaryHtml":284,"authors":285,"searchText":292,"facets":293},"sagemath-banff-cluster-algebras-and-finite-laurent-intersection-rings","Banff cluster algebras and finite Laurent intersection rings in SageMath","SageMath classes for finite Laurent intersection rings (FLIRs) and Banff cluster algebras, with algorithms for membership testing, divisor\u002Fclass group computation, and factorization.",[286,289],{"name":287,"orcid":288,"html":287},"Mara Pompili","https:\u002F\u002Forcid.org\u002F0000-0003-0681-7241",{"name":290,"orcid":291,"html":290},"Daniel 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