version 1.2, 2000/02/07 04:46:25 |
version 1.3, 2002/08/08 08:56:32 |
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/* $OpenXM: OpenXM/src/asir-contrib/packages/doc/dsolv.oxweave,v 1.1 2000/02/06 06:39:48 takayama Exp $ */ |
/* $OpenXM: OpenXM/src/asir-contrib/packages/doc/dsolv.oxweave,v 1.2 2000/02/07 04:46:25 takayama Exp $ */ |
/* dsolv.oxweave */ |
/* dsolv.oxweave */ |
/*&eg-texi |
/*&eg-texi |
@node DSOLV Functions,,, Top |
@node DSOLV Functions,,, Top |
Line 9 This section is a collection of functions to solve reg |
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Line 9 This section is a collection of functions to solve reg |
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systems in terms of series. |
systems in terms of series. |
Algorithms are explained in the book [SST]. |
Algorithms are explained in the book [SST]. |
You can load this package by the command |
You can load this package by the command |
@code{load("dsolv");} |
@code{load("dsolv")$} |
This package requires @code{Diff} and @code{dmodule}. |
This package requires @code{Diff} and @code{dmodule}. |
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To use the functions of the package @code{dsolv} in OpenXM/Risa/Asir, |
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executing the command @code{load("dsolv")$} |
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is necessary at first. |
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This package uses @code{ox_sm1}, so the variables you can use |
This package uses @code{ox_sm1}, so the variables you can use |
is as same as those you can use in the package @code{sm1}. |
is as same as those you can use in the package @code{sm1}. |
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Line 29 is as same as those you can use in the package @code{s |
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Line 34 is as same as those you can use in the package @code{s |
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$B%"%k%4%j%:%`$K$D$$$F$O(B [SST] $B$K@bL@$,$"$k(B. |
$B%"%k%4%j%:%`$K$D$$$F$O(B [SST] $B$K@bL@$,$"$k(B. |
$B$3$N%Q%C%1!<%8$O<!$N%3%^%s%I(B @code{load("dsolv");} |
$B$3$N%Q%C%1!<%8$O<!$N%3%^%s%I(B @code{load("dsolv");} |
$B$G%m!<%I$G$-$k(B. |
$B$G%m!<%I$G$-$k(B. |
$B$3$N%Q%C%1!<%8$O(B @code{Diff} $B$*$h$S(B @code{dmodule} $B$r;HMQ$9$k(B. |
$B$3$N%Q%C%1!<%8$O(B @code{Diff} $B$*$h$S(B @code{Dmodule} $B$r;HMQ$9$k(B. |
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OpenXM/Risa/Asir $B$G$NMxMQ$K$"$?$C$F$O(B, |
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@example |
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load("dsolv");$ |
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@end example |
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$B$,;O$a$KI,MW(B. |
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$B$3$N%Q%C%1!<%8$O(B @code{ox_sm1} $B$rMxMQ$7$F$$$k(B. |
$B$3$N%Q%C%1!<%8$O(B @code{ox_sm1} $B$rMxMQ$7$F$$$k(B. |
$B$7$?$,$C$F;HMQ$G$-$kJQ?t$O(B @code{sm1} $B%Q%C%1!<%8$HF1MM$NJQ?t$7$+$D$+$($J$$(B. |
$B$7$?$,$C$F;HMQ$G$-$kJQ?t$O(B @code{sm1} $B%Q%C%1!<%8$HF1MM$NJQ?t$7$+$D$+$($J$$(B. |
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Line 64 with variables @var{v}. |
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Line 75 with variables @var{v}. |
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generated by @var{v}. |
generated by @var{v}. |
If it is not primary to the maximal ideal, then this function falls into |
If it is not primary to the maximal ideal, then this function falls into |
an infinite loop. |
an infinite loop. |
@item This is an implementation of Algorithm 2.3.14 of the book [SST]. |
@end itemize |
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@noindent |
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Algorithm: |
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This is an implementation of Algorithm 2.3.14 of the book [SST]. |
If we replace variables x, y, ... in the output by log(x), log(y), ..., |
If we replace variables x, y, ... in the output by log(x), log(y), ..., |
then these polynomials in log are solutions of the system of differential |
then these polynomials in log are solutions of the system of differential |
equations @var{f}@code{_(x->x*dx, y->y*dy, ...)}. |
equations @var{f}@code{_(x->x*dx, y->y*dy, ...)}. |
@end itemize |
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*/ |
*/ |
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/*&jp-texi |
/*&jp-texi |
Line 96 equations @var{f}@code{_(x->x*dx, y->y*dy, ...)}. |
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Line 112 equations @var{f}@code{_(x->x*dx, y->y*dy, ...)}. |
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@item @var{f} $B$G@8@.$5$l$k%$%G%"%k$O(B, @var{v} $B$G@8@.$5$l$k6KBg%$%G%"%k$K(B |
@item @var{f} $B$G@8@.$5$l$k%$%G%"%k$O(B, @var{v} $B$G@8@.$5$l$k6KBg%$%G%"%k$K(B |
$BBP$7$F(B, primary $B$G$J$$$H$$$1$J$$(B. |
$BBP$7$F(B, primary $B$G$J$$$H$$$1$J$$(B. |
primary $B$G$J$$>l9g(B, $B$3$NH!?t$OL58B%k!<%W$K$*$A$$$k(B. |
primary $B$G$J$$>l9g(B, $B$3$NH!?t$OL58B%k!<%W$K$*$A$$$k(B. |
@item $B$3$NH!?t$OK\(B [SST] $B$N(B Algorithm 2.3.14 $B$N<BAu$G$"$k(B. |
@end itemize |
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@noindent |
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Algorithm: |
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$B$3$NH!?t$OK\(B [SST] $B$N(B Algorithm 2.3.14 $B$N<BAu$G$"$k(B. |
$B=PNOCf$NJQ?t(B x, y, ... $B$r$=$l$>$l(B log(x), log(y), ..., $B$G$*$-$+$($k$H(B, |
$B=PNOCf$NJQ?t(B x, y, ... $B$r$=$l$>$l(B log(x), log(y), ..., $B$G$*$-$+$($k$H(B, |
$B$3$l$i$N(B log $BB?9`<0$O(B, |
$B$3$l$i$N(B log $BB?9`<0$O(B, |
@var{f}@code{_(x->x*dx, y->y*dy, ...)} |
@var{f}@code{_(x->x*dx, y->y*dy, ...)} |
$B$G@8@.$5$l$kHyJ,J}Dx<07O(B |
$B$G@8@.$5$l$kHyJ,J}Dx<07O(B |
$B$N2r$H$J$C$F$$$k(B. |
$B$N2r$H$J$C$F$$$k(B. |
@end itemize |
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*/ |
*/ |
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/*&C-texi |
/*&C-texi |
Line 201 Staring terms $B$r7W;;$9$k(B. $B$3$3$G(B, @var{v} |
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Line 220 Staring terms $B$r7W;;$9$k(B. $B$3$3$G(B, @var{v} |
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$B$3$NH!?t$O7W;;$NESCf$K$$$m$$$m$H%a%C%;!<%8$r=PNO$9$k(B. |
$B$3$NH!?t$O7W;;$NESCf$K$$$m$$$m$H%a%C%;!<%8$r=PNO$9$k(B. |
@end itemize |
@end itemize |
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*/ |
*/ |
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/*&C-texi |
/*&C-texi |
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@noindent |
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Algorithm: Saito, Sturmfels, Takayama, Grobner Deformations of Hypergeometric |
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Differential Equations ([SST]), Chapter 2. |
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@example |
@example |
[1076] F = sm1_gkz( [ [[1,1,1,1,1],[1,1,0,-1,0],[0,1,1,-1,0]], [1,0,0]]); |
[1076] F = sm1_gkz( [ [[1,1,1,1,1],[1,1,0,-1,0],[0,1,1,-1,0]], [1,0,0]]); |