Cited By
View all- Costa ESertöz E(2021)Effective Obstruction to Lifting Tate Classes from Positive CharacteristicArithmetic Geometry, Number Theory, and Computation10.1007/978-3-030-80914-0_9(293-333)Online publication date: 16-Jul-2021
ZpL: a p-adic Precision Package
Abstract
We present a new package ZpL for the mathematical software system SageMath. It implements a sharp tracking of precision on p-adic numbers, following the theory of ultrametric precision introduced in a previous paper by the same authors. The underlying algorithms are mostly based on automatic differentiation techniques. We introduce them, study their complexity and discuss our design choices. We illustrate the benefits of our package (in comparison with previous implementations) with a large sample of examples coming from linear algebra, commutative algebra and differential equations.
References
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Xavier Caruso. Computations with p -adic numbers. pages 1--83, 2017.
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Xavier Caruso. Numerical stability of euclide algorithm over ultrametric fields. J. Number Theor. Bordeaux, 29:503--534, 2017.
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Xavier Caruso, David Roe, and Tristan Vaccon. Tracking p -adic precision. LMS Journal of Computation and Mathematics, 17(A):274--294, 2014.
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Xavier Caruso, David Roe, and Tristan Vaccon. p-Adic Stability In Linear Algebra. In Proceedings of the 2015 ACM on International Symposium on Symbolic and Algebraic Computation, ISSAC '15, pages 101--108, New York, NY, USA, 2015. ACM.
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Xavier Caruso, David Roe, and Tristan Vaccon. Division and Slope Factorization of p-Adic Polynomials. In Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation, ISSAC '16, pages 159--166, New York, NY, USA, 2016. ACM.
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Xavier Caruso, David Roe, and Tristan Vaccon. Characteristic Polynomials of P-adic Matrices. In Proceedings of the 2017 ACM on International Symposium on Symbolic and Algebraic Computation, ISSAC '17, pages 389--396, New York, NY, USA, 2017. ACM.
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Nicholas Higham. Accuracy and Stability of Numerical Algorithms. SIAM, Philadelphia, 2nd ed. edition, 2002.
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Pierre Lairez and Tristan Vaccon. On p-adic differential equations with separation of variables. In Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation, ISSAC 2016, Waterloo, ON, Canada, July 19--22, 2016, pages 319--323, 2016.
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Louis Rall. Automatic Differentiation: Techniques and Applications, volume 120 of Lecture Notes in Computer Science. Springer, Berlin, 1981.
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The Sage Developers. SageMath, the Sage Mathematics Software System (Version 8.1), 2018. http://www.sagemath.org.
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Trac #23505: Lattice precision for p-adics. http://trac.sagemath.org/ticket/23505, 2018.
Index Terms
- ZpL: a p-adic Precision Package
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Published In
July 2018
418 pages
ISBN:9781450355506
DOI:10.1145/3208976
- Editor:
- Carlos Arreche,
- General Chairs:
- Manuel Kauers,
- Alexey Ovchinnikov,
- Program Chair:
- Éric Schost
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Published: 11 July 2018
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ISSAC '18
ISSAC '18: International Symposium on Symbolic and Algebraic Computation
July 16 - 19, 2018
NY, New York, USA
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Cited By
View all- Costa ESertöz E(2021)Effective Obstruction to Lifting Tate Classes from Positive CharacteristicArithmetic Geometry, Number Theory, and Computation10.1007/978-3-030-80914-0_9(293-333)Online publication date: 16-Jul-2021
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