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Diff for /OpenXM/doc/calc2000p/func1.tex between version 1.1 and 1.4

version 1.1, 2000/07/21 07:11:52 version 1.4, 2000/08/03 00:46:13
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 % $OpenXM$  % $OpenXM: OpenXM/doc/calc2000p/func1.tex,v 1.3 2000/07/31 07:26:12 noro Exp $
 \documentclass[twocolumn]{article}  \documentclass[twocolumn]{article}
 \pagestyle{empty}  \pagestyle{empty}
 %\markright{ {\tt http://www.openxm.org} }  %\markright{ {\tt http://www.openxm.org} }
 \usepackage{color}  \usepackage{color}
 \usepackage{epsfig}  \usepackage{epsfig}
 \title{\huge \color{blue} 4252 functions are available  \title{\huge \color{blue} 1077 functions are available
 on our servers and libraries}  on our servers and libraries}
 \author{} \date{}  \author{} \date{}
 \begin{document}  \begin{document}
Line 21  on our servers and libraries}
Line 21  on our servers and libraries}
 the accelerated GCD algorithm),  the accelerated GCD algorithm),
 {\color{red} fac} (factorial),  {\color{red} fac} (factorial),
 {\color{red} inv} (inverse modulo an integer),  {\color{red} inv} (inverse modulo an integer),
 {\color{red} random} (random number generator by the Mersenne twister algorithm),  {\color{red} random} (random number generator by the Mersenne twister algorithm).
   
   
   
Line 32  the accelerated GCD algorithm),
Line 32  the accelerated GCD algorithm),
   
 \noindent  \noindent
 Arithmetics on various fields: the rationals,  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), $GF(2^n)$.  $GF(p)$ ($p$ is a prime of arbitrary size), $GF(2^n)$.
   
 \medbreak  \medbreak
Line 94  for a zero-dimensional ideal),
Line 94  for a zero-dimensional ideal),
 quadratic first-order formula),  quadratic first-order formula),
 {\color{red} simpl} (heuristic simplification of a first-order formula).  {\color{red} simpl} (heuristic simplification of a first-order formula).
   
   {\scriptsize
   \begin{verbatim}
   [0] MTP2 = ex([x11,x12,x13,x21,x22,x23,x31,x32,x33],
   x11+x12+x13 @== a1 @&& x21+x22+x23 @== a2 @&& x31+x32+x33 @== a3
   @&& x11+x21+x31 @== b1 @&& x12+x22+x32 @== b2 @&& x13+x23+x33 @== b3
   @&& 0 @<= x11 @&& 0 @<= x12 @&& 0 @<= x13 @&& 0 @<= x21
   @&& 0 @<= x22 @&& 0 @<= x23 @&& 0 @<= x31 @&& 0 @<= x32 @&& 0 @<= x33)$
   [1] TSOL= a1+a2+a3@=b1+b2+b3 @&& a1@>=0 @&& a2@>=0 @&& a3@>=0
   @&& b1@>=0 @&& b2@>=0 @&& b3@>=0$
   [2] QE_MTP2 = qe(MTP2)$
   [3] qe(all([a1,a2,a3,b1,b2,b3],QE_MTP2 @equiv TSOL));
   @true
   \end{verbatim}}
 \medbreak  \medbreak
   
 \noindent  \noindent
Line 112  quadratic first-order formula),
Line 125  quadratic first-order formula),
 \noindent  \noindent
 {\color{red} det} (determinant),  {\color{red} det} (determinant),
 {\color{red} qsort} (sorting of an array by the quick sort algorithm),  {\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} roots} (finding all roots of a univariate polynomial),
 {\color{red} lll} (computation of an LLL-reduced basis of a lattice).  {\color{red} lll} (computation of an LLL-reduced basis of a lattice).
   
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  Added in v.1.4
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