version 1.11, 2003/07/27 13:18:46 |
version 1.14, 2004/03/05 15:30:50 |
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/*$OpenXM: OpenXM/src/asir-contrib/packages/doc/sm1.oxweave,v 1.10 2003/05/20 23:25:28 takayama Exp $ */ |
/*$OpenXM: OpenXM/src/asir-contrib/packages/doc/sm1.oxweave,v 1.13 2003/07/28 01:36:36 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 |
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@node SM1 Functions,,, Top |
@node SM1 Functions,,, Top |
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*/ |
*/ |
/*&jp-texi |
/*&ja |
@chapter SM1 $BH!?t(B |
@chapter SM1 $BH!?t(B |
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$B$3$N@a$G$O(B sm1 $B$N(B ox $B%5!<%P(B @code{ox_sm1_forAsir} |
$B$3$N@a$G$O(B sm1 $B$N(B ox $B%5!<%P(B @code{ox_sm1_forAsir} |
Line 33 $X$ $B$OJ?LL$KFs$D$N7j$r$"$1$?6u4V$G$"$k$N$G(B, $BE |
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Line 33 $X$ $B$OJ?LL$KFs$D$N7j$r$"$1$?6u4V$G$"$k$N$G(B, $BE |
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$B<!85$rEz$($k(B. |
$B<!85$rEz$($k(B. |
@end tex |
@end tex |
*/ |
*/ |
/*&eg-texi |
/*&en |
@chapter SM1 Functions |
@chapter SM1 Functions |
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This chapter describes interface functions for |
This chapter describes interface functions for |
Line 109 See the appendix. |
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Line 109 See the appendix. |
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* sm1.rank:: |
* sm1.rank:: |
* sm1.auto_reduce:: |
* sm1.auto_reduce:: |
* sm1.slope:: |
* sm1.slope:: |
* sm1.gb_d:: |
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* sm1.syz_d:: |
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* sm1.ahg:: |
* sm1.ahg:: |
* sm1.bfunction:: |
* sm1.bfunction:: |
* sm1.generalized_bfunction:: |
* sm1.generalized_bfunction:: |
Line 119 See the appendix. |
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Line 117 See the appendix. |
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@end menu |
@end menu |
*/ |
*/ |
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/*&jp-texi |
/*&ja |
@section @code{ox_sm1_forAsir} $B%5!<%P(B |
@section @code{ox_sm1_forAsir} $B%5!<%P(B |
*/ |
*/ |
/*&eg-texi |
/*&en |
@section @code{ox_sm1_forAsir} Server |
@section @code{ox_sm1_forAsir} Server |
*/ |
*/ |
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/*&eg-texi |
/*&en |
@node ox_sm1_forAsir,,, SM1 Functions |
@node ox_sm1_forAsir,,, SM1 Functions |
@subsection @code{ox_sm1_forAsir} |
@subsection @code{ox_sm1_forAsir} |
@findex ox_sm1_forAsir |
@findex ox_sm1_forAsir |
Line 157 See the appendix. |
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Line 155 See the appendix. |
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to build your own server by reading @code{sm1} macros. |
to build your own server by reading @code{sm1} macros. |
@end itemize |
@end itemize |
*/ |
*/ |
/*&jp-texi |
/*&ja |
@node ox_sm1_forAsir,,, SM1 Functions |
@node ox_sm1_forAsir,,, SM1 Functions |
@subsection @code{ox_sm1_forAsir} |
@subsection @code{ox_sm1_forAsir} |
@findex ox_sm1_forAsir |
@findex ox_sm1_forAsir |
Line 191 to build your own server by reading @code{sm1} macros. |
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Line 189 to build your own server by reading @code{sm1} macros. |
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*/ |
*/ |
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/*&jp-texi |
/*&ja |
@section $BH!?t0lMw(B |
@section $BH!?t0lMw(B |
*/ |
*/ |
/*&eg-texi |
/*&en |
@section Functions |
@section Functions |
*/ |
*/ |
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/*&eg-texi |
/*&en |
@c sort-sm1.start |
@c sort-sm1.start |
@node sm1.start,,, SM1 Functions |
@node sm1.start,,, SM1 Functions |
@subsection @code{sm1.start} |
@subsection @code{sm1.start} |
Line 240 The descriptor can be obtained by the function |
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Line 238 The descriptor can be obtained by the function |
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@code{sm1.get_Sm1_proc()}. |
@code{sm1.get_Sm1_proc()}. |
@end itemize |
@end itemize |
*/ |
*/ |
/*&jp-texi |
/*&ja |
@c sort-sm1.start |
@c sort-sm1.start |
@node sm1.start,,, SM1 Functions |
@node sm1.start,,, SM1 Functions |
@subsection @code{sm1.start} |
@subsection @code{sm1.start} |
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a*da |
a*da |
@end example |
@end example |
*/ |
*/ |
/*&eg-texi |
/*&en |
@table @t |
@table @t |
@item Reference |
@item Reference |
@code{ox_launch}, @code{sm1.push_int0}, @code{sm1.push_poly0}, |
@code{ox_launch}, @code{sm1.push_int0}, @code{sm1.push_poly0}, |
@code{ord} |
@code{ord} |
@end table |
@end table |
*/ |
*/ |
/*&jp-texi |
/*&ja |
@table @t |
@table @t |
@item $B;2>H(B |
@item $B;2>H(B |
@code{ox_launch}, @code{sm1.push_int0}, @code{sm1.push_poly0}, |
@code{ox_launch}, @code{sm1.push_int0}, @code{sm1.push_poly0}, |
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/*&eg-texi |
/*&en |
@c sort-sm1 |
@c sort-sm1 |
@node sm1.sm1,,, SM1 Functions |
@node sm1.sm1,,, SM1 Functions |
@subsection @code{sm1.sm1} |
@subsection @code{sm1.sm1} |
Line 339 to execute the command string @var{s}. |
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Line 337 to execute the command string @var{s}. |
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(In the next example, the descriptor number is 0.) |
(In the next example, the descriptor number is 0.) |
@end itemize |
@end itemize |
*/ |
*/ |
/*&jp-texi |
/*&ja |
@node sm1.sm1,,, SM1 Functions |
@node sm1.sm1,,, SM1 Functions |
@subsection @code{sm1.sm1} |
@subsection @code{sm1.sm1} |
@findex sm1.sm1 |
@findex sm1.sm1 |
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@end example |
@end example |
*/ |
*/ |
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/*&jp-texi |
/*&ja |
@table @t |
@table @t |
@item $B;2>H(B |
@item $B;2>H(B |
@code{sm1.start}, @code{ox_push_int0}, @code{sm1.push_poly0}, @code{sm1.get_Sm1_proc()}. |
@code{sm1.start}, @code{ox_push_int0}, @code{sm1.push_poly0}, @code{sm1.get_Sm1_proc()}. |
@end table |
@end table |
*/ |
*/ |
/*&eg-texi |
/*&en |
@table @t |
@table @t |
@item Reference |
@item Reference |
@code{sm1.start}, @code{ox_push_int0}, @code{sm1.push_poly0}, @code{sm1.get_Sm1_proc()}. |
@code{sm1.start}, @code{ox_push_int0}, @code{sm1.push_poly0}, @code{sm1.get_Sm1_proc()}. |
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*/ |
*/ |
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/*&eg-texi |
/*&en |
@c sort-sm1.push_int0 |
@c sort-sm1.push_int0 |
@node sm1.push_int0,,, SM1 Functions |
@node sm1.push_int0,,, SM1 Functions |
@subsection @code{sm1.push_int0} |
@subsection @code{sm1.push_int0} |
Line 428 Note that @code{ox_push_cmo(@var{p},1234)} send the bi |
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Line 426 Note that @code{ox_push_cmo(@var{p},1234)} send the bi |
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@item In other cases, @code{ox_push_cmo} is called without data conversion. |
@item In other cases, @code{ox_push_cmo} is called without data conversion. |
@end itemize |
@end itemize |
*/ |
*/ |
/*&jp-texi |
/*&ja |
@c sort-sm1.push_int0 |
@c sort-sm1.push_int0 |
@node sm1.push_int0,,, SM1 Functions |
@node sm1.push_int0,,, SM1 Functions |
@subsection @code{sm1.push_int0} |
@subsection @code{sm1.push_int0} |
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[1,2] |
[1,2] |
@end example |
@end example |
*/ |
*/ |
/*&eg-texi |
/*&en |
@table @t |
@table @t |
@item Reference |
@item Reference |
@code{ox_push_cmo} |
@code{ox_push_cmo} |
@end table |
@end table |
*/ |
*/ |
/*&jp-texi |
/*&ja |
@table @t |
@table @t |
@item Reference |
@item Reference |
@code{ox_push_cmo} |
@code{ox_push_cmo} |
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/*&eg-texi |
/*&en |
@c sort-sm1.gb |
@c sort-sm1.gb |
@node sm1.gb,,, SM1 Functions |
@node sm1.gb,,, SM1 Functions |
@node sm1.gb_d,,, SM1 Functions |
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@subsection @code{sm1.gb} |
@subsection @code{sm1.gb} |
@findex sm1.gb |
@findex sm1.gb |
@findex sm1.gb_d |
@findex sm1.gb_d |
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the polynomials are dehomogenized (,i.e., h is set to 1). |
the polynomials are dehomogenized (,i.e., h is set to 1). |
@end itemize |
@end itemize |
*/ |
*/ |
/*&jp-texi |
/*&ja |
@c sort-sm1.gb |
@c sort-sm1.gb |
@node sm1.gb,,, SM1 Functions |
@node sm1.gb,,, SM1 Functions |
@node sm1.gb_d,,, SM1 Functions |
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@subsection @code{sm1.gb} |
@subsection @code{sm1.gb} |
@findex sm1.gb |
@findex sm1.gb |
@findex sm1.gb_d |
@findex sm1.gb_d |
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[[x*dx+y*dy-1,y^2*dy^2+2],[x*dx,y^2*dy^2]] |
[[x*dx+y*dy-1,y^2*dy^2+2],[x*dx,y^2*dy^2]] |
@end example |
@end example |
*/ |
*/ |
/*&eg-texi |
/*&en |
In the example above, |
In the example above, |
@tex the set $\{ x \partial_x + y \partial_y -1, |
@tex the set $\{ x \partial_x + y \partial_y -1, |
y^2 \partial_y^2+2\}$ |
y^2 \partial_y^2+2\}$ |
Line 625 The set $\{x \partial_x, y^2 \partial_y\}$ is the lead |
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Line 621 The set $\{x \partial_x, y^2 \partial_y\}$ is the lead |
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(the initial monominals) of the Gr\"obner basis. |
(the initial monominals) of the Gr\"obner basis. |
@end tex |
@end tex |
*/ |
*/ |
/*&jp-texi |
/*&ja |
$B>e$NNc$K$*$$$F(B, |
$B>e$NNc$K$*$$$F(B, |
@tex $B=89g(B $\{ x \partial_x + y \partial_y -1, |
@tex $B=89g(B $\{ x \partial_x + y \partial_y -1, |
y^2 \partial_y^2+2\}$ |
y^2 \partial_y^2+2\}$ |
Line 643 graded reverse lexicographic order $B$K4X$9$k%0%l%V%J |
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Line 639 graded reverse lexicographic order $B$K4X$9$k%0%l%V%J |
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[[dx+dy^3-4*dy,-dy^4+4*dy^2-1],[dx,-dy^4]] |
[[dx+dy^3-4*dy,-dy^4+4*dy^2-1],[dx,-dy^4]] |
@end example |
@end example |
*/ |
*/ |
/*&eg-texi |
/*&en |
In the example above, two monomials |
In the example above, two monomials |
@tex |
@tex |
$m = x^a y^b \partial_x^c \partial_y^d$ and |
$m = x^a y^b \partial_x^c \partial_y^d$ and |
Line 656 compared by the reverse lexicographic order |
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Line 652 compared by the reverse lexicographic order |
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(i.e., if $50c+2d+a = 50c'+2d'+a'$, then use the reverse lexicogrpahic order). |
(i.e., if $50c+2d+a = 50c'+2d'+a'$, then use the reverse lexicogrpahic order). |
@end tex |
@end tex |
*/ |
*/ |
/*&jp-texi |
/*&ja |
$B>e$NNc$K$*$$$FFs$D$N%b%N%_%"%k(B |
$B>e$NNc$K$*$$$FFs$D$N%b%N%_%"%k(B |
@tex |
@tex |
$m = x^a y^b \partial_x^c \partial_y^d$ $B$*$h$S(B |
$m = x^a y^b \partial_x^c \partial_y^d$ $B$*$h$S(B |
Line 704 $m' = x^{a'} y^{b'} \partial_x^{c'} \partial_y^{d'}$ |
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Line 700 $m' = x^{a'} y^{b'} \partial_x^{c'} \partial_y^{d'}$ |
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@end example |
@end example |
*/ |
*/ |
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/*&eg-texi |
/*&en |
@table @t |
@table @t |
@item Reference |
@item Reference |
@code{sm1.reduction}, @code{sm1.rat_to_p} |
@code{sm1.reduction}, @code{sm1.rat_to_p} |
@end table |
@end table |
*/ |
*/ |
/*&jp-texi |
/*&ja |
@table @t |
@table @t |
@item $B;2>H(B |
@item $B;2>H(B |
@code{sm1.reduction}, @code{sm1.rat_to_p} |
@code{sm1.reduction}, @code{sm1.rat_to_p} |
Line 719 $m' = x^{a'} y^{b'} \partial_x^{c'} \partial_y^{d'}$ |
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Line 715 $m' = x^{a'} y^{b'} \partial_x^{c'} \partial_y^{d'}$ |
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/*&eg-texi |
/*&en |
@c sort-sm1.deRham |
@c sort-sm1.deRham |
@node sm1.deRham,,, SM1 Functions |
@node sm1.deRham,,, SM1 Functions |
@subsection @code{sm1.deRham} |
@subsection @code{sm1.deRham} |
Line 764 mode. So, it is strongly recommended to execute the co |
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Line 760 mode. So, it is strongly recommended to execute the co |
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@code{ox_shutdown(sm1.get_Sm1_proc());} to interrupt and restart the server. |
@code{ox_shutdown(sm1.get_Sm1_proc());} to interrupt and restart the server. |
@end itemize |
@end itemize |
*/ |
*/ |
/*&jp-texi |
/*&ja |
@c sort-sm1.deRham |
@c sort-sm1.deRham |
@node sm1.deRham,,, SM1 Functions |
@node sm1.deRham,,, SM1 Functions |
@subsection @code{sm1.deRham} |
@subsection @code{sm1.deRham} |
Line 816 mode. So, it is strongly recommended to execute the co |
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Line 812 mode. So, it is strongly recommended to execute the co |
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[1,2] |
[1,2] |
@end example |
@end example |
*/ |
*/ |
/*&eg-texi |
/*&en |
@table @t |
@table @t |
@item Reference |
@item Reference |
@code{sm1.start}, @code{deRham} (sm1 command) |
@code{sm1.start}, @code{deRham} (sm1 command) |
Line 826 mode. So, it is strongly recommended to execute the co |
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Line 822 mode. So, it is strongly recommended to execute the co |
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Journal of pure and applied algebra 139 (1999), 201--233. |
Journal of pure and applied algebra 139 (1999), 201--233. |
@end table |
@end table |
*/ |
*/ |
/*&jp-texi |
/*&ja |
@table @t |
@table @t |
@item $B;2>H(B |
@item $B;2>H(B |
@code{sm1.start}, @code{deRham} (sm1 command) |
@code{sm1.start}, @code{deRham} (sm1 command) |
Line 840 mode. So, it is strongly recommended to execute the co |
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Line 836 mode. So, it is strongly recommended to execute the co |
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/*&eg-texi |
/*&en |
@c sort-sm1.hilbert |
@c sort-sm1.hilbert |
@node sm1.hilbert,,, SM1 Functions |
@node sm1.hilbert,,, SM1 Functions |
@subsection @code{sm1.hilbert} |
@subsection @code{sm1.hilbert} |
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polynomials in @code{sm1} is slower than in @code{asir}. |
polynomials in @code{sm1} is slower than in @code{asir}. |
@end itemize |
@end itemize |
*/ |
*/ |
/*&jp-texi |
/*&ja |
@c sort-sm1.hilbert |
@c sort-sm1.hilbert |
@node sm1.hilbert,,, SM1 Functions |
@node sm1.hilbert,,, SM1 Functions |
@subsection @code{sm1.hilbert} |
@subsection @code{sm1.hilbert} |
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@end example |
@end example |
*/ |
*/ |
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/*&eg-texi |
/*&en |
@table @t |
@table @t |
@item Reference |
@item Reference |
@code{sm1.start}, @code{sm1.gb}, @code{longname} |
@code{sm1.start}, @code{sm1.gb}, @code{longname} |
@end table |
@end table |
*/ |
*/ |
/*&jp-texi |
/*&ja |
@table @t |
@table @t |
@item $B;2>H(B |
@item $B;2>H(B |
@code{sm1.start}, @code{sm1.gb}, @code{longname} |
@code{sm1.start}, @code{sm1.gb}, @code{longname} |
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*/ |
*/ |
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/*&eg-texi |
/*&en |
@c sort-sm1.genericAnn |
@c sort-sm1.genericAnn |
@node sm1.genericAnn,,, SM1 Functions |
@node sm1.genericAnn,,, SM1 Functions |
@subsection @code{sm1.genericAnn} |
@subsection @code{sm1.genericAnn} |
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@var{f} is a polynomial in the variables @code{rest}(@var{v}). |
@var{f} is a polynomial in the variables @code{rest}(@var{v}). |
@end itemize |
@end itemize |
*/ |
*/ |
/*&jp-texi |
/*&ja |
@c sort-sm1.genericAnn |
@c sort-sm1.genericAnn |
@node sm1.genericAnn,,, SM1 Functions |
@node sm1.genericAnn,,, SM1 Functions |
@subsection @code{sm1.genericAnn} |
@subsection @code{sm1.genericAnn} |
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[-x*dx-y*dy-z*dz+3*s,z^2*dy-y^2*dz,z^2*dx-x^2*dz,y^2*dx-x^2*dy] |
[-x*dx-y*dy-z*dz+3*s,z^2*dy-y^2*dz,z^2*dx-x^2*dz,y^2*dx-x^2*dy] |
@end example |
@end example |
*/ |
*/ |
/*&eg-texi |
/*&en |
@table @t |
@table @t |
@item Reference |
@item Reference |
@code{sm1.start} |
@code{sm1.start} |
@end table |
@end table |
*/ |
*/ |
/*&jp-texi |
/*&ja |
@table @t |
@table @t |
@item $B;2>H(B |
@item $B;2>H(B |
@code{sm1.start} |
@code{sm1.start} |
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/*&eg-texi |
/*&en |
@c sort-sm1.wTensor0 |
@c sort-sm1.wTensor0 |
@node sm1.wTensor0,,, SM1 Functions |
@node sm1.wTensor0,,, SM1 Functions |
@subsection @code{sm1.wTensor0} |
@subsection @code{sm1.wTensor0} |
Line 1086 the inputs @var{f} and @var{g} are left ideals of D. |
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Line 1082 the inputs @var{f} and @var{g} are left ideals of D. |
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@end itemize |
@end itemize |
*/ |
*/ |
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/*&jp-texi |
/*&ja |
@c sort-sm1.wTensor0 |
@c sort-sm1.wTensor0 |
@node sm1.wTensor0,,, SM1 Functions |
@node sm1.wTensor0,,, SM1 Functions |
@subsection @code{sm1.wTensor0} |
@subsection @code{sm1.wTensor0} |
Line 1137 the inputs @var{f} and @var{g} are left ideals of D. |
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Line 1133 the inputs @var{f} and @var{g} are left ideals of D. |
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/*&eg-texi |
/*&en |
@c sort-sm1.reduction |
@c sort-sm1.reduction |
@node sm1.reduction,,, SM1 Functions |
@node sm1.reduction,,, SM1 Functions |
@subsection @code{sm1.reduction} |
@subsection @code{sm1.reduction} |
Line 1175 sm1.reduction_d(P,F,G) and sm1.reduction_noH_d(P,F,G) |
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Line 1171 sm1.reduction_d(P,F,G) and sm1.reduction_noH_d(P,F,G) |
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are for distributed polynomials. |
are for distributed polynomials. |
@end itemize |
@end itemize |
*/ |
*/ |
/*&jp-texi |
/*&ja |
@node sm1.reduction,,, SM1 Functions |
@node sm1.reduction,,, SM1 Functions |
@subsection @code{sm1.reduction} |
@subsection @code{sm1.reduction} |
@findex sm1.reduction |
@findex sm1.reduction |
Line 1222 sm1.reduction_d(P,F,G) $B$*$h$S(B sm1.reduction_noH_ |
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Line 1218 sm1.reduction_d(P,F,G) $B$*$h$S(B sm1.reduction_noH_ |
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[0,1,[-y^2+4,-x+y^3-4*y],[y^4-4*y^2+1,x+y^3-4*y]] |
[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 |
/*&en |
@table @t |
@table @t |
@item Reference |
@item Reference |
@code{sm1.start}, @code{d_true_nf} |
@code{sm1.start}, @code{d_true_nf} |
@end table |
@end table |
*/ |
*/ |
/*&jp-texi |
/*&ja |
@table @t |
@table @t |
@item $B;2>H(B |
@item $B;2>H(B |
@code{sm1.start}, @code{d_true_nf} |
@code{sm1.start}, @code{d_true_nf} |
Line 1236 sm1.reduction_d(P,F,G) $B$*$h$S(B sm1.reduction_noH_ |
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Line 1232 sm1.reduction_d(P,F,G) $B$*$h$S(B sm1.reduction_noH_ |
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*/ |
*/ |
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/*&eg-texi |
/*&en |
@node sm1.xml_tree_to_prefix_string,,, SM1 Functions |
@node sm1.xml_tree_to_prefix_string,,, SM1 Functions |
@subsection @code{sm1.xml_tree_to_prefix_string} |
@subsection @code{sm1.xml_tree_to_prefix_string} |
@findex sm1.xml_tree_to_prefix_string |
@findex sm1.xml_tree_to_prefix_string |
Line 1264 asir has not yet understood this CMO. |
|
Line 1260 asir has not yet understood this CMO. |
|
command search path.) |
command search path.) |
@end itemize |
@end itemize |
*/ |
*/ |
/*&jp-texi |
/*&ja |
@node sm1.xml_tree_to_prefix_string,,, SM1 Functions |
@node sm1.xml_tree_to_prefix_string,,, SM1 Functions |
@subsection @code{sm1.xml_tree_to_prefix_string} |
@subsection @code{sm1.xml_tree_to_prefix_string} |
@findex sm1.xml_tree_to_prefix_string |
@findex sm1.xml_tree_to_prefix_string |
Line 1308 Trying to connect to the server... Done. |
|
Line 1304 Trying to connect to the server... Done. |
|
basic_plus(basic_times(basic_power(x,4),1),basic_times(basic_power(x,0),-1)) |
basic_plus(basic_times(basic_power(x,4),1),basic_times(basic_power(x,0),-1)) |
@end example |
@end example |
*/ |
*/ |
/*&eg-texi |
/*&en |
@table @t |
@table @t |
@item Reference |
@item Reference |
@code{om_*}, @code{OpenXM/src/OpenMath}, @code{eval_str} |
@code{om_*}, @code{OpenXM/src/OpenMath}, @code{eval_str} |
@end table |
@end table |
*/ |
*/ |
/*&jp-texi |
/*&ja |
@table @t |
@table @t |
@item $B;2>H(B |
@item $B;2>H(B |
@code{om_*}, @code{OpenXM/src/OpenMath}, @code{eval_str} |
@code{om_*}, @code{OpenXM/src/OpenMath}, @code{eval_str} |
Line 1324 basic_plus(basic_times(basic_power(x,4),1),basic_times |
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Line 1320 basic_plus(basic_times(basic_power(x,4),1),basic_times |
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|
|
|
|
|
|
/*&eg-texi |
/*&en |
@c sort-sm1.syz |
@c sort-sm1.syz |
@node sm1.syz,,, SM1 Functions |
@node sm1.syz,,, SM1 Functions |
@node sm1.syz_d,,, SM1 Functions |
|
@subsection @code{sm1.syz} |
@subsection @code{sm1.syz} |
@findex sm1.syz |
@findex sm1.syz |
@findex sm1.syz_d |
@findex sm1.syz_d |
Line 1354 Here @var{s} is the syzygy of @var{f} in the ring of d |
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Line 1349 Here @var{s} is the syzygy of @var{f} in the ring of d |
|
operators with the variable @var{v}. |
operators with the variable @var{v}. |
@var{g} is a Groebner basis of @var{f} with the weight vector @var{w}, |
@var{g} is a Groebner basis of @var{f} with the weight vector @var{w}, |
and @var{m} is a matrix that translates the input matrix @var{f} to the Gr\"obner |
and @var{m} is a matrix that translates the input matrix @var{f} to the Gr\"obner |
basis @var {g}. |
basis @var{g}. |
@var{t} is the syzygy of the Gr\"obner basis @var{g}. |
@var{t} is the syzygy of the Gr\"obner basis @var{g}. |
In summary, @var{g} = @var{m} @var{f} and |
In summary, @var{g} = @var{m} @var{f} and |
@var{s} @var{f} = 0 hold as matrices. |
@var{s} @var{f} = 0 hold as matrices. |
Line 1368 In summary, @var{g} = @var{m} @var{f} and |
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Line 1363 In summary, @var{g} = @var{m} @var{f} and |
|
The homogenization variable h is automatically added. |
The homogenization variable h is automatically added. |
@end itemize |
@end itemize |
*/ |
*/ |
/*&jp-texi |
/*&ja |
@c sort-sm1.syz |
@c sort-sm1.syz |
@node sm1.syz,,, SM1 Functions |
@node sm1.syz,,, SM1 Functions |
@node sm1.syz_d,,, SM1 Functions |
|
@subsection @code{sm1.syz} |
@subsection @code{sm1.syz} |
@findex sm1.syz |
@findex sm1.syz |
@findex sm1.syz_d |
@findex sm1.syz_d |
Line 1433 syzygy $B$G$"$k(B. |
|
Line 1427 syzygy $B$G$"$k(B. |
|
|
|
|
|
|
|
/*&eg-texi |
/*&en |
@node sm1.mul,,, SM1 Functions |
@node sm1.mul,,, SM1 Functions |
@subsection @code{sm1.mul} |
@subsection @code{sm1.mul} |
@findex sm1.mul |
@findex sm1.mul |
|
|
@end itemize |
@end itemize |
*/ |
*/ |
|
|
/*&jp-texi |
/*&ja |
@node sm1.mul,,, SM1 Functions |
@node sm1.mul,,, SM1 Functions |
@subsection @code{sm1.mul} |
@subsection @code{sm1.mul} |
@findex sm1.mul |
@findex sm1.mul |
|
|
|
|
|
|
|
|
/*&eg-texi |
/*&en |
@node sm1.distraction,,, SM1 Functions |
@node sm1.distraction,,, SM1 Functions |
@subsection @code{sm1.distraction} |
@subsection @code{sm1.distraction} |
@findex sm1.distraction |
@findex sm1.distraction |
Line 1534 See Saito, Sturmfels, Takayama : Grobner Deformations |
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Line 1528 See Saito, Sturmfels, Takayama : Grobner Deformations |
|
@end itemize |
@end itemize |
*/ |
*/ |
|
|
/*&jp-texi |
/*&ja |
@node sm1.distraction,,, SM1 Functions |
@node sm1.distraction,,, SM1 Functions |
|
|
@subsection @code{sm1.distraction} |
@subsection @code{sm1.distraction} |
|
|
@end example |
@end example |
*/ |
*/ |
|
|
/*&eg-texi |
/*&en |
@table @t |
@table @t |
@item Reference |
@item Reference |
@code{distraction2(sm1)}, |
@code{distraction2(sm1)}, |
@end table |
@end table |
*/ |
*/ |
|
|
/*&jp-texi |
/*&ja |
@table @t |
@table @t |
@item $B;2>H(B |
@item $B;2>H(B |
@code{distraction2(sm1)}, |
@code{distraction2(sm1)}, |
|
|
|
|
|
|
|
|
/*&eg-texi |
/*&en |
@node sm1.gkz,,, SM1 Functions |
@node sm1.gkz,,, SM1 Functions |
@subsection @code{sm1.gkz} |
@subsection @code{sm1.gkz} |
@findex sm1.gkz |
@findex sm1.gkz |
|
|
@end itemize |
@end itemize |
*/ |
*/ |
|
|
/*&jp-texi |
/*&ja |
@node sm1.gkz,,, SM1 Functions |
@node sm1.gkz,,, SM1 Functions |
@subsection @code{sm1.gkz} |
@subsection @code{sm1.gkz} |
@findex sm1.gkz |
@findex sm1.gkz |
|
|
|
|
|
|
|
|
/*&eg-texi |
/*&en |
@node sm1.appell1,,, SM1 Functions |
@node sm1.appell1,,, SM1 Functions |
@subsection @code{sm1.appell1} |
@subsection @code{sm1.appell1} |
@findex sm1.appell1 |
@findex sm1.appell1 |
Line 1688 The parameters a, c, b1, ..., bn may be rational numbe |
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Line 1682 The parameters a, c, b1, ..., bn may be rational numbe |
|
@end itemize |
@end itemize |
*/ |
*/ |
|
|
/*&jp-texi |
/*&ja |
@node sm1.appell1,,, SM1 Functions |
@node sm1.appell1,,, SM1 Functions |
@subsection @code{sm1.appell1} |
@subsection @code{sm1.appell1} |
@findex sm1.appell1 |
@findex sm1.appell1 |
Line 1745 F_D(a,b1,b2,...,bn,c;x1,...,xn) |
|
Line 1739 F_D(a,b1,b2,...,bn,c;x1,...,xn) |
|
|
|
*/ |
*/ |
|
|
/*&eg-texi |
/*&en |
@node sm1.appell4,,, SM1 Functions |
@node sm1.appell4,,, SM1 Functions |
@subsection @code{sm1.appell4} |
@subsection @code{sm1.appell4} |
@findex sm1.appell4 |
@findex sm1.appell4 |
Line 1772 The parameters a, b, c1, ..., cn may be rational numbe |
|
Line 1766 The parameters a, b, c1, ..., cn may be rational numbe |
|
@end itemize |
@end itemize |
*/ |
*/ |
|
|
/*&jp-texi |
/*&ja |
@node sm1.appell4,,, SM1 Functions |
@node sm1.appell4,,, SM1 Functions |
@subsection @code{sm1.appell4} |
@subsection @code{sm1.appell4} |
@findex sm1.appell4 |
@findex sm1.appell4 |
Line 1819 F_C(a,b,c1,c2,...,cn;x1,...,xn) |
|
Line 1813 F_C(a,b,c1,c2,...,cn;x1,...,xn) |
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|
|
|
|
|
|
/*&eg-texi |
/*&en |
@node sm1.rank,,, SM1 Functions |
@node sm1.rank,,, SM1 Functions |
@subsection @code{sm1.rank} |
@subsection @code{sm1.rank} |
@findex sm1.rank |
@findex sm1.rank |
Line 1848 holonomic. It is generally faster than @code{sm1.rank} |
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Line 1842 holonomic. It is generally faster than @code{sm1.rank} |
|
@end itemize |
@end itemize |
*/ |
*/ |
|
|
/*&jp-texi |
/*&ja |
@node sm1.rank,,, SM1 Functions |
@node sm1.rank,,, SM1 Functions |
@subsection @code{sm1.rank} |
@subsection @code{sm1.rank} |
@findex sm1.rank |
@findex sm1.rank |
Line 1899 holonomic. It is generally faster than @code{sm1.rank} |
|
Line 1893 holonomic. It is generally faster than @code{sm1.rank} |
|
*/ |
*/ |
|
|
|
|
/*&eg-texi |
/*&en |
@node sm1.auto_reduce,,, SM1 Functions |
@node sm1.auto_reduce,,, SM1 Functions |
@subsection @code{sm1.auto_reduce} |
@subsection @code{sm1.auto_reduce} |
@findex sm1.auto_reduce |
@findex sm1.auto_reduce |
Line 1925 Grobner bases. This is the default. |
|
Line 1919 Grobner bases. This is the default. |
|
@end itemize |
@end itemize |
*/ |
*/ |
|
|
/*&jp-texi |
/*&ja |
@node sm1.auto_reduce,,, SM1 Functions |
@node sm1.auto_reduce,,, SM1 Functions |
@subsection @code{sm1.auto_reduce} |
@subsection @code{sm1.auto_reduce} |
@findex sm1.auto_reduce |
@findex sm1.auto_reduce |
Line 1953 reduced $B%0%l%V%J4pDl$H$O$+$.$i$J$$(B. $B$3$A$i$,% |
|
Line 1947 reduced $B%0%l%V%J4pDl$H$O$+$.$i$J$$(B. $B$3$A$i$,% |
|
|
|
|
|
|
|
/*&eg-texi |
/*&en |
@node sm1.slope,,, SM1 Functions |
@node sm1.slope,,, SM1 Functions |
@subsection @code{sm1.slope} |
@subsection @code{sm1.slope} |
@findex sm1.slope |
@findex sm1.slope |
Line 1998 of the slopes are returned. |
|
Line 1992 of the slopes are returned. |
|
|
|
*/ |
*/ |
|
|
/*&jp-texi |
/*&ja |
@node sm1.slope,,, SM1 Functions |
@node sm1.slope,,, SM1 Functions |
@subsection @code{sm1.slope} |
@subsection @code{sm1.slope} |
@findex sm1.slope |
@findex sm1.slope |
Line 2060 Slope $B$N@dBPCM$rLa$9(B. |
|
Line 2054 Slope $B$N@dBPCM$rLa$9(B. |
|
@end example |
@end example |
|
|
*/ |
*/ |
/*&eg-texi |
/*&en |
@table @t |
@table @t |
@item Reference |
@item Reference |
@code{sm.gb} |
@code{sm.gb} |
@end table |
@end table |
*/ |
*/ |
/*&jp-texi |
/*&ja |
@table @t |
@table @t |
@item $B;2>H(B |
@item $B;2>H(B |
@code{sm.gb} |
@code{sm.gb} |
Line 2074 Slope $B$N@dBPCM$rLa$9(B. |
|
Line 2068 Slope $B$N@dBPCM$rLa$9(B. |
|
*/ |
*/ |
|
|
|
|
/*&eg-texi |
/*&en |
@include sm1-auto-en.texi |
@include sm1-auto-en.texi |
*/ |
*/ |
|
|
/*&jp-texi |
/*&ja |
@include sm1-auto-ja.texi |
@include sm1-auto-ja.texi |
*/ |
*/ |
|
|