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version 1.1, 2000/07/21 07:11:52

version 1.2, 2000/07/22 08:11:09

Line 1

% $OpenXM$

% $OpenXM: OpenXM/doc/calc2000p/func1.tex,v 1.1 2000/07/21 07:11:52 noro Exp $

\documentclass[twocolumn]{article}

\pagestyle{empty}

Line 32 the accelerated GCD algorithm),

\noindent

Arithmetics on various fields: the rationals,

$Q(\alpha_1,\alpha_2,\ldots,\alpha_n)$

${\bf Q}(\alpha_1,\alpha_2,\ldots,\alpha_n)$

($\alpha_i$ is algebraic over $Q(\alpha_1,\ldots,\alpha_{i-1})$),

($\alpha_i$ is algebraic over ${\bf Q}(\alpha_1,\ldots,\alpha_{i-1})$),

$GF(p)$ ($p$ is a prime of arbitrary size), $GF(2^n)$.

\medbreak

Line 112 quadratic first-order formula),

\noindent

{\color{red} det} (determinant),

{\color{red} qsort} (sorting of an array by the quick sort algorithm),

{\color{red} eval} (evaluation of a formula containing transcendental functions),

{\color{red} eval} (evaluation of a formula containing transcendental functions

such as

{\color{red} sin}, {\color{red} cos}, {\color{red} tan}, {\color{red} exp},

{\color{red} log})

{\color{red} roots} (finding all roots of a univariate polynomial),

{\color{red} lll} (computation of an LLL-reduced basis of a lattice).