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Diff for /OpenXM/doc/Papers/Attic/dag-noro-proc.tex between version 1.7 and 1.8

version 1.7, 2001/11/30 02:02:09 version 1.8, 2001/11/30 02:08:46
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 % $OpenXM: OpenXM/doc/Papers/dag-noro-proc.tex,v 1.6 2001/11/28 09:05:57 noro Exp $  % $OpenXM: OpenXM/doc/Papers/dag-noro-proc.tex,v 1.7 2001/11/30 02:02:09 noro Exp $
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 % This is a sample input file for your contribution to a multi-  % This is a sample input file for your contribution to a multi-
 % author book to be published by Springer Verlag.  % author book to be published by Springer Verlag.
Line 268  case we can apply a simple modular method to compute t
Line 268  case we can apply a simple modular method to compute t
 polynomial.  polynomial.
 \begin{tabbing}  \begin{tabbing}
 Input : a Groebner basis $G$ of $I$, a variable $x_i$\\  Input : a Groebner basis $G$ of $I$, a variable $x_i$\\
 Output : the minimal polynomial of $x$ in $R/I$\\  Output : the minimal polynomial of $x_i$ in $R/I$\\
 do \= \\  do \= \\
 \> $p \leftarrow$ a new prime such that $p \not{|} HC(g)$ for all $g \in G$\\  \> $p \leftarrow$ a new prime such that $p \not{|} HC(g)$ for all $g \in G$\\
 \> $m_p \leftarrow$ the minimal polynomial of $x_i$ in $GF(p)[x_1,\ldots,x_n]/Id(\phi_p(G))$\\  \> $m_p \leftarrow$ the minimal polynomial of $x_i$ in $GF(p)[x_1,\ldots,x_n]/Id(\phi_p(G))$\\
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