File: [local] / OpenXM / doc / calc2000p / func1.tex (download)
Revision 1.2, Sat Jul 22 08:11:09 2000 UTC (23 years, 11 months ago) by noro
Branch: MAIN
Changes since 1.1: +7 -4
lines
Added speedups by non-collective version of Shoup multiplication.
Created rgb.sty (color database for latex color package).
Several new colors are used but ...
reliable.tex contains "we are reliable" poster.
Modified efficient.tex.
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% $OpenXM: OpenXM/doc/calc2000p/func1.tex,v 1.2 2000/07/22 08:11:09 noro Exp $
\documentclass[twocolumn]{article}
\pagestyle{empty}
%\markright{ {\tt http://www.openxm.org} }
\usepackage{color}
\usepackage{epsfig}
\title{\huge \color{blue} 4252 functions are available
on our servers and libraries}
\author{} \date{}
\begin{document}
\maketitle
\noindent
\fbox{\huge {\color{green}Operations on Integers}}
\noindent
{\color{red} idiv},{\color{red} irem} (division with remainder),
{\color{red} ishift} (bit shifting),
{\color{red} iand},{\color{red} ior},{\color{red} ixor} (logical operations),
{\color{red} igcd},(GCD by various methods such as Euclid's algorithm and
the accelerated GCD algorithm),
{\color{red} fac} (factorial),
{\color{red} inv} (inverse modulo an integer),
{\color{red} random} (random number generator by the Mersenne twister algorithm),
\medbreak
\noindent
\fbox{\huge {\color{green}Ground Fields}}
\noindent
Arithmetics on various fields: the rationals,
${\bf Q}(\alpha_1,\alpha_2,\ldots,\alpha_n)$
($\alpha_i$ is algebraic over ${\bf Q}(\alpha_1,\ldots,\alpha_{i-1})$),
$GF(p)$ ($p$ is a prime of arbitrary size), $GF(2^n)$.
\medbreak
\noindent
\fbox{\huge {\color{green}Operations on Polynomials}}
\noindent
{\color{red} sdiv }, {\color{red} srem } (division with remainder),
{\color{red} ptozp } (removal of the integer content),
{\color{red} diff } (differentiation),
{\color{red} gcd } (GCD over the rationals),
{\color{red} res } (resultant),
{\color{red} subst } (substitution),
{\color{red} umul} (fast multiplication of dense univariate polynomials
by a hybrid method with Karatsuba and FFT+Chinese remainder),
{\color{red} urembymul\_precomp} (fast dense univariate polynomial
division with remainder by the fast multiplication and
the precomputed inverse of a divisor),
\noindent
\fbox{\huge {\color{green}Polynomial Factorization}}
{\color{red} fctr } (factorization over the rationals),
{\color{red} fctr\_ff } (univariate factorization over finite fields),
{\color{red} af } (univariate factorization over algebraic number fields),
{\color{red} sp} (splitting field computation).
\medbreak
\noindent
\fbox{\huge {\color{green} Groebner basis}}
\noindent
{\color{red} dp\_gr\_main } (Groebner basis computation of a polynomial ideal
over the rationals by the trace lifting),
{\color{red} dp\_gr\_mod\_main } (Groebner basis over small finite fields),
{\color{red} tolex } (Modular change of ordering for a zero-dimensional ideal),
{\color{red} tolex\_gsl } (Modular rational univariate representation
for a zero-dimensional ideal),
{\color{red} dp\_f4\_main } ($F_4$ over the rationals),
{\color{red} dp\_f4\_mod\_main } ($F_4$ over small finite fields).
\medbreak
\noindent
\fbox{\huge {\color{green} Ideal Decomposition}}
\noindent
{\color{red} primedec} (Prime decomposition of the radical),
{\color{red} primadec} (Primary decomposition of ideals by Shimoyama/Yokoyama algorithm).
\medbreak
\noindent
\fbox{\huge {\color{green} Quantifier Elimination}}
\noindent
{\color{red} qe} (real quantifier elimination in a linear and
quadratic first-order formula),
{\color{red} simpl} (heuristic simplification of a first-order formula).
\medbreak
\noindent
\fbox{\huge {\color{green} Visualization of curves}}
\noindent
{\color{red} plot} (plotting of a univariate function),
{\color{red} ifplot} (plotting zeros of a bivariate polynomial),
{\color{red} conplot} (contour plotting of a bivariate polynomial function).
\medbreak
\noindent
\fbox{\huge {\color{green} Miscellaneous functions}}
\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
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).
\medbreak
\vfill
\noindent
\rightline{ {\color{red} {\tt http://www.openxm.org} }}
\end{document}