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