Titlebook: Mathematical Software – ICMS 2024; 8th International Co Kevin Buzzard,Alicia Dickenstein,Yue Ren Conference proceedings 2024 The Editor(s)

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The Reformation of?SageThe monolithic open-source mathematical software system Sage, developed since 2005, is being transformed into a modular system of Python libraries with a renewed focus on collaboration and vertical integration. This paper is the author’s personal account of this modularization project, led by him since 2020.

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Formalization of?the?Existence of?Frobenius ElementsWe use Lean 4 to formalize a proof of the existence of Frobenius elements for finite Galois extensions of number fields.

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Computing the?Determinant of?a?Dense Matrix over?ical efficiency, which is always at least as good as currently known methods. The algorithm uses randomness internally, but the result is guaranteed correct. The main new idea is to use a modular HNF in cases where the Pauderis–Storjohann HCOL method performs poorly. The algorithm is implemented in OSCAR?1.0.

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Computer Classification of?Linear Codes Based on?Lattice Point Enumerationorithmic framework for the classification of linear codes over finite fields with restricted sets of weights. The underlying algorithms are based on lattice point enumeration and integer linear programming. We present new enumeration and non-existence results for projective two-weight codes, divisible codes, and additive .-codes.

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