Basic arithmetic in Flint and Nemo

100 Pages·2017·0.47 MB·English

Basic arithmetic in Flint and Nemo
William Hart, Fredrik Johansson
Tommy Hofmann, Claus Fieker
October 23, 2017
WilliamHart BasicarithmeticinFlintandNemo
(cid:73) Univariate polynomials over the above rings
(cid:73) Linear algebra over the above rings
(cid:73) Primality testing and integer factorisation
(cid:73) Polynomial factorisation over Z, Z/nZ, F
q
(cid:73) LLL, HNF, SNF
(cid:73) (Work in progress) multivariate polynomials
Introduction to Flint
(cid:73) Basic rings: Z, Q, Z/nZ, F , Q
q p
WilliamHart BasicarithmeticinFlintandNemo
(cid:73) Linear algebra over the above rings
(cid:73) Primality testing and integer factorisation
(cid:73) Polynomial factorisation over Z, Z/nZ, F
q
(cid:73) LLL, HNF, SNF
(cid:73) (Work in progress) multivariate polynomials
Introduction to Flint
(cid:73) Basic rings: Z, Q, Z/nZ, F , Q
q p
(cid:73) Univariate polynomials over the above rings
WilliamHart BasicarithmeticinFlintandNemo
(cid:73) Primality testing and integer factorisation
(cid:73) Polynomial factorisation over Z, Z/nZ, F
q
(cid:73) LLL, HNF, SNF
(cid:73) (Work in progress) multivariate polynomials
Introduction to Flint
(cid:73) Basic rings: Z, Q, Z/nZ, F , Q
q p
(cid:73) Univariate polynomials over the above rings
(cid:73) Linear algebra over the above rings
WilliamHart BasicarithmeticinFlintandNemo
(cid:73) Polynomial factorisation over Z, Z/nZ, F
q
(cid:73) LLL, HNF, SNF
(cid:73) (Work in progress) multivariate polynomials
Introduction to Flint
(cid:73) Basic rings: Z, Q, Z/nZ, F , Q
q p
(cid:73) Univariate polynomials over the above rings
(cid:73) Linear algebra over the above rings
(cid:73) Primality testing and integer factorisation
WilliamHart BasicarithmeticinFlintandNemo
(cid:73) LLL, HNF, SNF
(cid:73) (Work in progress) multivariate polynomials
Introduction to Flint
(cid:73) Basic rings: Z, Q, Z/nZ, F , Q
q p
(cid:73) Univariate polynomials over the above rings
(cid:73) Linear algebra over the above rings
(cid:73) Primality testing and integer factorisation
(cid:73) Polynomial factorisation over Z, Z/nZ, F
q
WilliamHart BasicarithmeticinFlintandNemo
(cid:73) (Work in progress) multivariate polynomials
Introduction to Flint
(cid:73) Basic rings: Z, Q, Z/nZ, F , Q
q p
(cid:73) Univariate polynomials over the above rings
(cid:73) Linear algebra over the above rings
(cid:73) Primality testing and integer factorisation
(cid:73) Polynomial factorisation over Z, Z/nZ, F
q
(cid:73) LLL, HNF, SNF
WilliamHart BasicarithmeticinFlintandNemo
Introduction to Flint
(cid:73) Basic rings: Z, Q, Z/nZ, F , Q
q p
(cid:73) Univariate polynomials over the above rings
(cid:73) Linear algebra over the above rings
(cid:73) Primality testing and integer factorisation
(cid:73) Polynomial factorisation over Z, Z/nZ, F
q
(cid:73) LLL, HNF, SNF
(cid:73) (Work in progress) multivariate polynomials
WilliamHart BasicarithmeticinFlintandNemo
(cid:73) Elliptic curve integer factorisation
(cid:73) APRCL primality test
(cid:73) Parallelised FFT
(cid:73) Howell form
(cid:73) Characteristic and minimal polynomial
(cid:73) van Hoeij factorisation for Z[x]
(cid:73) Multivariate polynomial arithmetic Z[x,y,z,...]
New features in Flint
(cid:73) Quadratic sieve integer factorisation
WilliamHart BasicarithmeticinFlintandNemo
(cid:73) APRCL primality test
(cid:73) Parallelised FFT
(cid:73) Howell form
(cid:73) Characteristic and minimal polynomial
(cid:73) van Hoeij factorisation for Z[x]
(cid:73) Multivariate polynomial arithmetic Z[x,y,z,...]
New features in Flint
(cid:73) Quadratic sieve integer factorisation
(cid:73) Elliptic curve integer factorisation
WilliamHart BasicarithmeticinFlintandNemo