| version 1.14, 2004/03/05 15:30:50 |
version 1.15, 2004/03/05 15:56:40 |
|
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| /*$OpenXM: OpenXM/src/asir-contrib/packages/doc/sm1.oxweave,v 1.13 2003/07/28 01:36:36 takayama Exp $ */ |
/*$OpenXM: OpenXM/src/asir-contrib/packages/doc/sm1.oxweave,v 1.14 2004/03/05 15:30:50 ohara Exp $ */ |
| |
|
| /*&C-texi |
/*&C |
| @c DO NOT EDIT THIS FILE oxphc.texi |
@c DO NOT EDIT THIS FILE oxphc.texi |
| */ |
*/ |
| /*&C-texi |
/*&C |
| @node SM1 Functions,,, Top |
@node SM1 Functions,,, Top |
| |
|
| */ |
*/ |
| Line 68 Hence, the dimension of the first de Rham cohomology g |
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| Line 68 Hence, the dimension of the first de Rham cohomology g |
|
| cohomology groups. |
cohomology groups. |
| @end tex |
@end tex |
| */ |
*/ |
| /*&C-texi |
/*&C |
| @example |
@example |
| |
|
| @include opening.texi |
@include opening.texi |
| Line 77 cohomology groups. |
|
| Line 77 cohomology groups. |
|
| [1,2] |
[1,2] |
| @end example |
@end example |
| */ |
*/ |
| /*&C-texi |
/*&C |
| @noindent |
@noindent |
| The author of @code{sm1} : Nobuki Takayama, @code{takayama@@math.sci.kobe-u.ac.jp} @* |
The author of @code{sm1} : Nobuki Takayama, @code{takayama@@math.sci.kobe-u.ac.jp} @* |
| The author of sm1 packages : Toshinori Oaku, @code{oaku@@twcu.ac.jp} @* |
The author of sm1 packages : Toshinori Oaku, @code{oaku@@twcu.ac.jp} @* |
| Line 87 Grobner Deformations of Hypergeometric Differential Eq |
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| Line 87 Grobner Deformations of Hypergeometric Differential Eq |
|
| See the appendix. |
See the appendix. |
| */ |
*/ |
| |
|
| /*&C-texi |
/*&C |
| @menu |
@menu |
| * ox_sm1_forAsir:: |
* ox_sm1_forAsir:: |
| * sm1.start:: |
* sm1.start:: |
| Line 279 The descriptor can be obtained by the function |
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| Line 279 The descriptor can be obtained by the function |
|
| $B$3$N<1JLHV9f$O4X?t(B @code{sm1.get_Sm1_proc()} $B$G$H$j$@$9$3$H$,$G$-$k(B. |
$B$3$N<1JLHV9f$O4X?t(B @code{sm1.get_Sm1_proc()} $B$G$H$j$@$9$3$H$,$G$-$k(B. |
| @end itemize |
@end itemize |
| */ |
*/ |
| /*&C-texi |
/*&C |
| @example |
@example |
| [260] ord([da,a,db,b]); |
[260] ord([da,a,db,b]); |
| [da,a,db,b,dx,dy,dz,x,y,z,dt,ds,t,s,u,v,w, |
[da,a,db,b,dx,dy,dz,x,y,z,dt,ds,t,s,u,v,w, |
| Line 361 to execute the command string @var{s}. |
|
| Line 361 to execute the command string @var{s}. |
|
| ($B<!$NNc$G$O(B, $B<1JLHV9f(B 0) |
($B<!$NNc$G$O(B, $B<1JLHV9f(B 0) |
| @end itemize |
@end itemize |
| */ |
*/ |
| /*&C-texi |
/*&C |
| @example |
@example |
| [261] sm1.sm1(0," ( (x-1)^2 ) . "); |
[261] sm1.sm1(0," ( (x-1)^2 ) . "); |
| 0 |
0 |
|
|
| $BLa$jB?9`<0$O(B dehomogenize $B$5$l$k(B ($B$9$J$o$A(B h $B$K(B 1 $B$,BeF~$5$l$k(B). |
$BLa$jB?9`<0$O(B dehomogenize $B$5$l$k(B ($B$9$J$o$A(B h $B$K(B 1 $B$,BeF~$5$l$k(B). |
| @end itemize |
@end itemize |
| */ |
*/ |
| /*&C-texi |
/*&C |
| @example |
@example |
| [293] sm1.gb([[x*dx+y*dy-1,x*y*dx*dy-2],[x,y]]); |
[293] sm1.gb([[x*dx+y*dy-1,x*y*dx*dy-2],[x,y]]); |
| [[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]] |
| Line 633 graded reverse lexicographic order $B$K4X$9$k%0%l%V%J |
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| Line 633 graded reverse lexicographic order $B$K4X$9$k%0%l%V%J |
|
| $BBP$9$k(B leading monomial (initial monomial) $B$G$"$k(B. |
$BBP$9$k(B leading monomial (initial monomial) $B$G$"$k(B. |
| @end tex |
@end tex |
| */ |
*/ |
| /*&C-texi |
/*&C |
| @example |
@example |
| [294] sm1.gb([[dx^2+dy^2-4,dx*dy-1],[x,y],[[dx,50,dy,2,x,1]]]); |
[294] sm1.gb([[dx^2+dy^2-4,dx*dy-1],[x,y],[[dx,50,dy,2,x,1]]]); |
| [[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]] |
| Line 666 $m' = x^{a'} y^{b'} \partial_x^{c'} \partial_y^{d'}$ |
|
| Line 666 $m' = x^{a'} y^{b'} \partial_x^{c'} \partial_y^{d'}$ |
|
| $B$5$l$k(B). |
$B$5$l$k(B). |
| @end tex |
@end tex |
| */ |
*/ |
| /*&C-texi |
/*&C |
| @example |
@example |
| [294] F=sm1.gb([[dx^2+dy^2-4,dx*dy-1],[x,y],[[dx,50,dy,2,x,1]]]|sorted=1); |
[294] F=sm1.gb([[dx^2+dy^2-4,dx*dy-1],[x,y],[[dx,50,dy,2,x,1]]]|sorted=1); |
| map(print,F[2][0])$ |
map(print,F[2][0])$ |
| map(print,F[2][1])$ |
map(print,F[2][1])$ |
| @end example |
@end example |
| */ |
*/ |
| /*&C-texi |
/*&C |
| @example |
@example |
| [595] |
[595] |
| sm1.gb([["dx*(x*dx +y*dy-2)-1","dy*(x*dx + y*dy -2)-1"], |
sm1.gb([["dx*(x*dx +y*dy-2)-1","dy*(x*dx + y*dy -2)-1"], |
| Line 804 mode. So, it is strongly recommended to execute the co |
|
| Line 804 mode. So, it is strongly recommended to execute the co |
|
| $B$r0l;~(B shutdown $B$7$F%j%9%?!<%H$7$?J}$,0BA4$G$"$k(B. |
$B$r0l;~(B shutdown $B$7$F%j%9%?!<%H$7$?J}$,0BA4$G$"$k(B. |
| @end itemize |
@end itemize |
| */ |
*/ |
| /*&C-texi |
/*&C |
| @example |
@example |
| [332] sm1.deRham([x^3-y^2,[x,y]]); |
[332] sm1.deRham([x^3-y^2,[x,y]]); |
| [1,1,0] |
[1,1,0] |
|
|
| @end itemize |
@end itemize |
| */ |
*/ |
| |
|
| /*&C-texi |
/*&C |
| @example |
@example |
| |
|
| [346] load("katsura")$ |
[346] load("katsura")$ |
|
|
| @var{f} $B$OJQ?t(B @code{rest}(@var{v}) $B>e$NB?9`<0$G$"$k(B. |
@var{f} $B$OJQ?t(B @code{rest}(@var{v}) $B>e$NB?9`<0$G$"$k(B. |
| @end itemize |
@end itemize |
| */ |
*/ |
| /*&C-texi |
/*&C |
| @example |
@example |
| [595] sm1.genericAnn([x^3+y^3+z^3,[s,x,y,z]]); |
[595] sm1.genericAnn([x^3+y^3+z^3,[s,x,y,z]]); |
| [-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] |
| Line 1122 the inputs @var{f} and @var{g} are left ideals of D. |
|
| Line 1122 the inputs @var{f} and @var{g} are left ideals of D. |
|
| $B0lHL$K(B, $B=PNO$O<+M32C72(B D^r $B$NItJ,2C72$G$"$k(B. |
$B0lHL$K(B, $B=PNO$O<+M32C72(B D^r $B$NItJ,2C72$G$"$k(B. |
| @end itemize |
@end itemize |
| */ |
*/ |
| /*&C-texi |
/*&C |
| @example |
@example |
| [258] sm1.wTensor0([[x*dx -1, y*dy -4],[dx+dy,dx-dy^2],[x,y],[1,2]]); |
[258] sm1.wTensor0([[x*dx -1, y*dy -4],[dx+dy,dx-dy^2],[x,y],[1,2]]); |
| [[-y*x*dx-y*x*dy+4*x+y],[5*x*dx^2+5*x*dx+2*y*dy^2+(-2*y-6)*dy+3], |
[[-y*x*dx-y*x*dy+4*x+y],[5*x*dx^2+5*x*dx+2*y*dy^2+(-2*y-6)*dy+3], |
| Line 1210 sm1.reduction_d(P,F,G) $B$*$h$S(B sm1.reduction_noH_ |
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| Line 1210 sm1.reduction_d(P,F,G) $B$*$h$S(B sm1.reduction_noH_ |
|
| $B$O(B, $BJ,;6B?9`<0MQ$G$"$k(B. |
$B$O(B, $BJ,;6B?9`<0MQ$G$"$k(B. |
| @end itemize |
@end itemize |
| */ |
*/ |
| /*&C-texi |
/*&C |
| @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],[y^4-4*y^2+1,x+y^3-4*y]] |
[x^2+y^2-4,1,[0,0],[y^4-4*y^2+1,x+y^3-4*y]] |
|
|
| ($B$?$H$($P(B, /usr/local/jdk1.1.8/bin $B$r%3%^%s%I%5!<%A%Q%9$KF~$l$k$J$I(B.) |
($B$?$H$($P(B, /usr/local/jdk1.1.8/bin $B$r%3%^%s%I%5!<%A%Q%9$KF~$l$k$J$I(B.) |
| @end itemize |
@end itemize |
| */ |
*/ |
| /*&C-texi |
/*&C |
| @example |
@example |
| [263] load("om"); |
[263] load("om"); |
| 1 |
1 |
| Line 1405 syzygy $B$G$"$k(B. |
|
| Line 1405 syzygy $B$G$"$k(B. |
|
| $BF1<!2=JQ?t(B @code{h} $B$,7k2L$K2C$o$k(B. |
$BF1<!2=JQ?t(B @code{h} $B$,7k2L$K2C$o$k(B. |
| @end itemize |
@end itemize |
| */ |
*/ |
| /*&C-texi |
/*&C |
| @example |
@example |
| [293] sm1.syz([[x*dx+y*dy-1,x*y*dx*dy-2],[x,y]]); |
[293] sm1.syz([[x*dx+y*dy-1,x*y*dx*dy-2],[x,y]]); |
| [[[y*x*dy*dx-2,-x*dx-y*dy+1]], generators of the syzygy |
[[[y*x*dy*dx-2,-x*dx-y*dy+1]], generators of the syzygy |
| Line 1414 syzygy $B$G$"$k(B. |
|
| Line 1414 syzygy $B$G$"$k(B. |
|
| [[y*x*dy*dx-2,-x*dx-y*dy+1]]]] |
[[y*x*dy*dx-2,-x*dx-y*dy+1]]]] |
| @end example |
@end example |
| */ |
*/ |
| /*&C-texi |
/*&C |
| @example |
@example |
| [294]sm1.syz([[x^2*dx^2+x*dx+y^2*dy^2+y*dy-4,x*y*dx*dy-1],[x,y],[[dx,-1,x,1]]]); |
[294]sm1.syz([[x^2*dx^2+x*dx+y^2*dy^2+y*dy-4,x*y*dx*dy-1],[x,y],[[dx,-1,x,1]]]); |
| [[[y*x*dy*dx-1,-x^2*dx^2-x*dx-y^2*dy^2-y*dy+4]], generators of the syzygy |
[[[y*x*dy*dx-1,-x^2*dx^2-x*dx-y^2*dy^2-y*dy+4]], generators of the syzygy |
|
|
| @end itemize |
@end itemize |
| */ |
*/ |
| |
|
| /*&C-texi |
/*&C |
| |
|
| @example |
@example |
| [277] sm1.mul(dx,x,[x]); |
[277] sm1.mul(dx,x,[x]); |
| Line 1559 See Saito, Sturmfels, Takayama : Grobner Deformations |
|
| Line 1559 See Saito, Sturmfels, Takayama : Grobner Deformations |
|
| @end itemize |
@end itemize |
| */ |
*/ |
| |
|
| /*&C-texi |
/*&C |
| |
|
| @example |
@example |
| [280] sm1.distraction([x*dx,[x],[x],[dx],[x]]); |
[280] sm1.distraction([x*dx,[x],[x],[dx],[x]]); |
|
|
| @end itemize |
@end itemize |
| */ |
*/ |
| |
|
| /*&C-texi |
/*&C |
| |
|
| @example |
@example |
| |
|
| Line 1709 F_D(a,b1,b2,...,bn,c;x1,...,xn) |
|
| Line 1709 F_D(a,b1,b2,...,bn,c;x1,...,xn) |
|
| @end itemize |
@end itemize |
| */ |
*/ |
| |
|
| /*&C-texi |
/*&C |
| |
|
| @example |
@example |
| |
|
| Line 1793 F_C(a,b,c1,c2,...,cn;x1,...,xn) |
|
| Line 1793 F_C(a,b,c1,c2,...,cn;x1,...,xn) |
|
| @end itemize |
@end itemize |
| */ |
*/ |
| |
|
| /*&C-texi |
/*&C |
| |
|
| @example |
@example |
| |
|
| Line 1870 holonomic. It is generally faster than @code{sm1.rank} |
|
| Line 1870 holonomic. It is generally faster than @code{sm1.rank} |
|
| @end itemize |
@end itemize |
| */ |
*/ |
| |
|
| /*&C-texi |
/*&C |
| |
|
| @example |
@example |
| |
|
| Line 2035 Slope $B$NK\Mh$NDj5A$G$O(B, $BId9f$,Ii$H$J$k$,(B, |
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| Line 2035 Slope $B$NK\Mh$NDj5A$G$O(B, $BId9f$,Ii$H$J$k$,(B, |
|
| Slope $B$N@dBPCM$rLa$9(B. |
Slope $B$N@dBPCM$rLa$9(B. |
| */ |
*/ |
| |
|
| /*&C-texi |
/*&C |
| |
|
| @example |
@example |
| |
|
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