File: [local] / OpenXM / src / k097 / lib / minimal / minimal-note-ja.txt (download)
Revision 1.3, Thu Jun 8 08:37:53 2000 UTC (24 years, 1 month ago) by takayama
Branch: MAIN
Changes since 1.2: +26 -1
lines
New command:
SisExact_h : it calls sm1 macro isExact_h
Function for debugging:
test10() in minimal-test.k, which is used to check if the Schreyer
resolution constructed Sschreyer (LaScala-Stillman's algorithm) is
exact or not (bug).
|
$OpenXM: OpenXM/src/k097/lib/minimal/minimal-note-ja.txt,v 1.3 2000/06/08 08:37:53 takayama Exp $
SpairAndReduction() :
$BM?$($i$l$?(B pair $B$r(B reduction $B$9$k(B.
V-minimal $B$KI,MW$+$I$&$+$NH=Dj$b$9$k(B.
SpairAndReduction2():
tower2 = StowerOf(tower,level-1);
SsetTower(tower2);
/** sm1(" show_ring "); */
$BM?$($i$l$?(B pair $B$r(B reduction $B$9$k$?$a$N(B schreyer order
$B$r@_Dj$9$k(B. Resolution $B$N?<$5$K1~$8$F(B, tower $B$b?<$/$9$kI,MW$,$"$k(B.
if (IsConstant(t_syz[i])){
Syzygy $B$r$_$F(B, $BDj?t@.J,$,$J$$$+(B check.
t_syz[i] $B$,Dj?t@.J,$G$"$l$P(B, $B0l$DA0$N(B GB $B$N9=@.MWAG$G$"$k(B
g_i $B$,M>J,$J(B GB $B$G$"$k2DG=@-$,$?$+$$(B.
SpairAndReduction() ( LaScala-Stillman $B$NJ}K!(B) $B$H$N@09g@-$r$H$k$?$a(B
g_i $B$r(B tmp[0] $B$KBeF~$7(B ( reduction $B$G$-$J$+$C$?$U$j$r$9$k(B )
g_i $B$N(B V-degree $B$r$7$i$Y$k(B.
Sannfs2_laScala2()
Sannfs3_laScala2() $B$r:n$k(B.
$BFs$D$N%"%k%4%j%:%`$NHf3S(B.
In(11)=sm1_pmat(a1[1]); $B$N=gHV$r$+$($k(B.
[
[ 3*Dx^2*h , 0 , Dy , -Dz ]
[ 6*x*Dy*Dz^2-9*y*Dx^2*h , -2*x*Dy*Dz^2+3*y*Dx^2*h , -2*x*Dx-3*y*Dy , 0]
[ 2*x*Dx+3*z*Dz-h^2 , y*Dy-z*Dz , 0 , 0 ]
[ 2*x*Dy*Dz , 0 , z , -y ]
[ 0 , 2*x*Dy^2*Dz-3*z*Dx^2*h , 0 , 2*x*Dx+3*z*Dz ]
]
In(12)=sm1_pmat(a2[1]);
[
[ 3*Dx^2*h , 0 , Dy , -Dz ]
[ 6*x*Dy*Dz^2-9*y*Dx^2*h , -2*x*Dy*Dz^2+3*y*Dx^2*h , -2*x*Dx-3*y*Dy, 0 ]
[ 2*x*Dx+3*z*Dz-h^2 , y*Dy-z*Dz , 0 , 0 ]
[ 2*x*Dy*Dz , 0 , z , -y ]
[ 9*z*Dx^2*h , 2*x*Dy^2*Dz-3*z*Dx^2*h , 3*z*Dy , 2*x*Dx ]
[ 2*x*Dx*Dz^2+3*z*Dz^3+5*Dz^2*h^2 , y*Dy*Dz^2-z*Dz^3-2*Dz^2*h^2 , 0 , 0 ]
]
In(13)=
----------------------
In(16)=sm1_pmat(a1[2]);
[
[ -2*x*Dx-3*y*Dy-3*z*Dz-6*h^2 , -Dy , -Dz , 3*Dx^2*h , 3*Dy^2 , 3*Dy*Dz , -2*x*Dy , 2*x*Dz , 0 ]
[ 3*y*z , z , y , -2*x*Dy*Dz , -3*z*Dy , 2*x*Dx , 2*x*z , -2*x*y , 0 ]
]
In(17)=sm1_pmat(a2[2]);
[
[ -y , 2*x*Dy*Dz , z , 0 , 2*x*Dx , 0 ]
[ -Dz , 3*Dx^2*h , Dy , -2*x*Dx-3*y*Dy-3*h^2 , -3*Dy*Dz , 0 ]
]
In(18)=
---------------------------
May 22, (Tue), 5:50 (Spain local time, 12:50 JST)
kan96xx/Kan/resol.c $B$G(B,
RemoveRedundantInSchreyerSkelton = 0
$B$KJQ$($F(B ($B$3$N(B option $B$b$"$?$i$7$/2C$($k(B), schreyer $B$,@5$7$/F0$/$+(B
$BD4$Y$k$3$H$K$9$k(B.
( commit $B$O(B kan96xx $B$H(B k097 $BN>J}$9$Y$7(B.)
test8() $B$G(B sm1 $B$G=q$$$?J}$N(B Schreyer $B$r8+$k$H(B,
RemoveRedundantInSchreyerSkelton = 1
$B$G$b(B,
kernel = image
$B$H$J$C$F$$$k$N$G0J8e$3$N(B option $B$O(B 1 $B$N$^$^;H$&$3$H$H$9$k(B.
$BMW$9$k$K(B k0 $B$N%3!<%I$,$I$&$d$i$*$+$7$$$i$7$$(B.
-----------------------------------
June 8, 2000 (Thu), 9:10 (Spain local time)
hol.sm1 : gb_h, syz_h, isSameIdeal, isSameIdeal_h
complex.sm1 : isExact, isExact_h
syzygy $B$r(B homogenization $B$r2p$7$F7W;;$9$k$N$OLdBj$"$j(B.
--> usage of isExact
[(Homogenize_vec) 0] system_variable : vector $B$N(B homogenize $B$r$7$J$$(B.
(grade) (module1v) switch_function : vector $BJQ?t$O(B, total
degree $B$K?t$($J$$(B.
==> $BL58B%k!<%W$KCm0U(B ---> gb_h, syz_h $B$N(B usage.
minimal-test.k $B$N(B ann(x^3-y^2*z^2) $B$N(B laplace $BJQ49$N(B
betti $B?t$,JQ(B, exact $B$G$J$$(B, $B$r(B isExact_h $B$G(B check
$B$7$h$&(B.
minimal-test.k
test10();
LaScala-Stillman $B$NJ}K!$G$D$/$C$?(B, schreyer resol $B$,(B exact $B$+(B
$BD4$Y$k(B.
$BNcBj$O(B, ann(1/(x^3-y^2 z^2)) $B$N(B Laplace $BJQ49(B.