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\title{\huge \color{blue} 4252 functions are available
on our servers and libraries}
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\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
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\noindent
\rightline{ {\color{red} {\tt http://www.openxm.org} }}

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