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 25 articles , 2 standard articles )

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  1. Beliakov, Gleb; Matiyasevich, Yuri: A parallel algorithm for calculation of determinants and minors using arbitrary precision arithmetic (2016)
  2. Harvey, David; van der Hoeven, Joris; Lecerf, Grégoire: Even faster integer multiplication (2016)
  3. van der Hoeven, Joris: On the complexity of skew arithmetic (2016)
  4. Bank, Bernd; Giusti, Marc; Heintz, Joos; Lecerf, Grégoire; Matera, Guillermo; Solernó, Pablo: Degeneracy loci and polynomial equation solving (2015)
  5. Grenet, Bruno; van der Hoeven, Joris; Lecerf, Grégoire: Randomized root finding over finite FFT-fields using tangent Graeffe transforms (2015)
  6. Lebreton, Romain: Relaxed Hensel lifting of triangular sets (2015)
  7. van der Hoeven, Joris: Overview of the Mathemagix type system (2014)
  8. Berthomieu, Jérémy; Lecerf, Grégoire; Quintin, Guillaume: Polynomial root finding over local rings and application to error correcting codes (2013)
  9. Hodorog, Mădălina; Schicho, Josef: A regularization approach for estimating the type of a plane curve singularity (2013)
  10. van der Hoeven, Joris: Guessing singular dependencies (2013)
  11. Berthomieu, Jérémy; Lebreton, Romain: Relaxed $p$-adic Hensel lifting for algebraic systems (2012)
  12. Diatta, Daouda Niang; Mourrain, Bernard; Ruatta, Olivier: On the isotopic meshing of an algebraic implicit surface (2012)
  13. Berthomieu, Jérémy; van der Hoeven, Joris; Lecerf, Grégoire: Relaxed algorithms for $p$-adic numbers (2011)
  14. DeVries, Timothy; van der Hoeven, Joris; Pemantle, Robin: Automatic asymptotics for coefficients of smooth, bivariate rational functions (2011)
  15. van der Hoeven, Joris: Meta-expansion of transseries (2011)
  16. van der Hoeven, Joris; Lecerf, Grégoire; Mourrain, Bernard; Trébuchet, Philippe; Berthomieu, Jérémy; Diatta, Daouda Niang; Mantzaflaris, Angelos: Mathemagix: the quest of modularity and efficiency for symbolic and certified numeric computation? (2011)
  17. Fukuda, Komei (ed.); van der Hoeven, Joris (ed.); Joswig, Michael (ed.); Takayama, Nobuki (ed.): Mathematical software -- ICMS 2010. Third international congress on mathematical software, Kobe, Japan, September 13--17, 2010. Proceedings (2010)
  18. Lecerf, Grégoire: Mathemagix: towards large scale programming for symbolic and certified numeric computations (2010)
  19. van der Hoeven, Joris: Newton’s method and FFT trading (2010)
  20. van der Hoeven, Joris: On asymptotic extrapolation (2009)

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