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

version 1.3, 2000/07/31 07:26:12

Line 1

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

% $OpenXM: OpenXM/doc/calc2000p/func1.tex,v 1.2 2000/07/22 08:11:09 noro Exp $

\documentclass[twocolumn]{article}

\pagestyle{empty}

Line 21 on our servers and libraries}

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),

{\color{red} random} (random number generator by the Mersenne twister algorithm).

Line 94 for a zero-dimensional ideal),

quadratic 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

\noindent