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 $ */ |
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/*&C-texi |
/*&C-texi |
@c DO NOT EDIT THIS FILE oxphc.texi |
@c DO NOT EDIT THIS FILE oxphc.texi |
Line 1591 division algorithm to @var{f}. The set of variables is |
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Line 1591 division algorithm to @var{f}. The set of variables is |
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@code{sm1_reduction_noH} is for the Weyl algebra. |
@code{sm1_reduction_noH} is for the Weyl algebra. |
@item The return value is of the form |
@item The return value is of the form |
[r,c0,[c1,...,cm],[g1,...gm]] where @var{g}=[g1, ..., gm] and |
[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. |
r/c0 is the normal form. |
@item The function reduction reduces reducible terms that appear |
@item The function reduction reduces reducible terms that appear |
in lower order terms. |
in lower order terms. |
Line 1629 are for distributed polynomials. |
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Line 1629 are for distributed polynomials. |
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$B>JN,$7$F$b$h$$(B. |
$B>JN,$7$F$b$h$$(B. |
@code{sm1_reduction_noH} $B$O(B, Weyl algebra $BMQ(B. |
@code{sm1_reduction_noH} $B$O(B, Weyl algebra $BMQ(B. |
@item $BLa$jCM$O<!$N7A$r$7$F$$$k(B: |
@item $BLa$jCM$O<!$N7A$r$7$F$$$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. |
$B$,$J$j$?$D(B. |
r/c0 $B$,(B normal form $B$G$"$k(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. |
@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_ |
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Line 1642 sm1_reduction_d(P,F,G) $B$*$h$S(B sm1_reduction_noH_ |
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/*&C-texi |
/*&C-texi |
@example |
@example |
[259] sm1_reduction([x^2+y^2-4,[y^4-4*y^2+1,x+y^3-4*y],[x,y]]); |
[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]]]); |
[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 |
@end example |
*/ |
*/ |
/*&eg-texi |
/*&eg-texi |