OpenXM/src/asir-contrib/packages/doc/sm1.oxweave - diff

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version 1.6, 2002/08/23 08:16:13

version 1.7, 2003/05/04 08:37:40

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/*$OpenXM: OpenXM/src/asir-contrib/packages/doc/sm1.oxweave,v 1.5 2002/08/11 08:39:47 takayama Exp $ */

/*$OpenXM: OpenXM/src/asir-contrib/packages/doc/sm1.oxweave,v 1.6 2002/08/23 08:16:13 takayama Exp $ */

/*&C-texi

@c DO NOT EDIT THIS FILE oxphc.texi

Line 1591 division algorithm to @var{f}. The set of variables is

@code{sm1_reduction_noH} is for the Weyl algebra.

@item The return value is of the form

[r,c0,[c1,...,cm],[g1,...gm]] where @var{g}=[g1, ..., gm] and

r/c0 + c1 g1 + ... + cm gm = 0.

c0 f + c1 g1 + ... + cm gm = r.

r/c0 is the normal form.

@item The function reduction reduces reducible terms that appear

in lower order terms.

Line 1629 are for distributed polynomials.

$B>JN,$7$F$b$h$$(B.

@code{sm1_reduction_noH} $B$O(B, Weyl algebra $BMQ(B.

@item $BLa$jCM$O<!$N7A$r$7$F$$$k(B:

[r,c0,[c1,...,cm],[g1,...gm]] $B$3$3$G(B @var{g}=[g1, ..., gm] $B$G$"$j(B,

[r,c0,[c1,...,cm],g] $B$3$3$G(B @var{g}=[g1, ..., gm] $B$G$"$j(B,

r/c0 + c1 g1 + ... + cm gm = 0

c0 f + c1 g1 + ... + cm gm = r

$B$,$J$j$?$D(B.

r/c0 $B$,(B normal form $B$G$"$k(B.

@item $B$3$NH!?t$O(B, $BDc<!9`$K$"$i$o$l$k(B reducible $B$J9`$b4JC12=$9$k(B.

Line 1642 sm1_reduction_d(P,F,G) $B$*$h$S(B sm1_reduction_noH_

/*&C-texi

@example

[259] sm1_reduction([x^2+y^2-4,[y^4-4*y^2+1,x+y^3-4*y],[x,y]]);

[x^2+y^2-4,1,[0,0],[x+y^3-4*y,y^4-4*y^2+1]]

[x^2+y^2-4,1,[0,0],[y^4-4*y^2+1,x+y^3-4*y]]

[260] sm1_reduction([x^2+y^2-4,[y^4-4*y^2+1,x+y^3-4*y],[x,y],[[x,1]]]);

[0,1,[-y^2+4,-x+y^3-4*y],[x+y^3-4*y,y^4-4*y^2+1]]

[0,1,[-y^2+4,-x+y^3-4*y],[y^4-4*y^2+1,x+y^3-4*y]]

@end example

/*&eg-texi