Mathemagix

Mathemagix: Towards large scale programming for symbolic and certified numeric computations Coordinated by Joris van der Hoeven from the 90’s, the Mathemagix project aims at the design of a scientific programming language for symbolic and certified numeric algorithms. This language can be compiled and interpreted, and it features a strong type system with classes and categories. Several C++ libraries are also being developed, mainly with Bernard Mourrain and Philippe Trébuchet, for the elementary operations with polynomials, power series and matrices, with a special care towards efficiency and numeric stability. In my talk I will give an overview of the language, of the design and the contents of the C++ libraries, and I will illustrate possibilities offered for certified numeric computations with balls and intervals


References in zbMATH (referenced in 37 articles , 3 standard articles )

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  1. Lecerf, Grégoire: On the complexity of the Lickteig-Roy subresultant algorithm (2019-2019)
  2. Harvey, David; van der Hoeven, Joris: On the complexity of integer matrix multiplication (2018)
  3. Barkatou, Moulay A.; Jaroschek, Maximilian; Maddah, Suzy S.: Formal solutions of completely integrable Pfaffian systems with normal crossings (2017)
  4. Minimair, Manfred: Collaborative computer algebra (2017)
  5. van der Hoeven, Joris; Larrieu, Robin; Lecerf, Grégoire: Implementing fast carryless multiplication (2017)
  6. Beliakov, Gleb; Matiyasevich, Yuri: A parallel algorithm for calculation of determinants and minors using arbitrary precision arithmetic (2016)
  7. Groves, A. Whitman; Roche, Daniel S.: Sparse polynomials in FLINT (2016)
  8. Harvey, David; van der Hoeven, Joris; Lecerf, Grégoire: Even faster integer multiplication (2016)
  9. Harvey, David; van der Hoeven, Joris; Lecerf, Grégoire: Fast polynomial multiplication over (\mathbbF_2^60) (2016)
  10. van der Hoeven, Joris: On the complexity of skew arithmetic (2016)
  11. Van Der Hoeven, Joris; Lecerf, Grégoire; Quintin, Guillaume: Modular SIMD arithmetic in \textscMathemagix (2016)
  12. Bank, Bernd; Giusti, Marc; Heintz, Joos; Lecerf, Grégoire; Matera, Guillermo; Solernó, Pablo: Degeneracy loci and polynomial equation solving (2015)
  13. Bruno Grenet: Lacunaryx: Computing bounded-degree factors of lacunary polynomials (2015) arXiv
  14. Grenet, Bruno: Lacunaryx: computing bounded-degree factors of lacunary polynomials (2015)
  15. Grenet, Bruno; van der Hoeven, Joris; Lecerf, Grégoire: Randomized root finding over finite FFT-fields using tangent Graeffe transforms (2015)
  16. Lebreton, Romain: Relaxed Hensel lifting of triangular sets (2015)
  17. van der Hoeven, Joris: Overview of the Mathemagix type system (2014)
  18. Berthomieu, Jérémy; Lecerf, Grégoire; Quintin, Guillaume: Polynomial root finding over local rings and application to error correcting codes (2013)
  19. Hodorog, Mădălina; Schicho, Josef: A regularization approach for estimating the type of a plane curve singularity (2013)
  20. Jolly, Raphaël: Categories as type classes in the Scala algebra system (2013)

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