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Annotation of OpenXM/src/k097/lib/minimal/minimal-note-ja.txt, Revision 1.3

1.3     ! takayama    1: $OpenXM: OpenXM/src/k097/lib/minimal/minimal-note-ja.txt,v 1.2 2000/05/24 15:24:54 takayama Exp $
1.1       takayama    2:
                      3: SpairAndReduction() :
                      4:    $BM?$($i$l$?(B pair $B$r(B reduction $B$9$k(B.
                      5:    V-minimal $B$KI,MW$+$I$&$+$NH=Dj$b$9$k(B.
                      6:
                      7: SpairAndReduction2():
                      8:   tower2 = StowerOf(tower,level-1);
                      9:   SsetTower(tower2);
                     10:   /** sm1(" show_ring ");   */
                     11:
                     12:   $BM?$($i$l$?(B pair $B$r(B reduction $B$9$k$?$a$N(B schreyer order
                     13:   $B$r@_Dj$9$k(B.  Resolution $B$N?<$5$K1~$8$F(B, tower $B$b?<$/$9$kI,MW$,$"$k(B.
                     14:
                     15:
                     16:   if (IsConstant(t_syz[i])){
                     17:
                     18:   Syzygy $B$r$_$F(B, $BDj?t@.J,$,$J$$$+(B check.
                     19:   t_syz[i] $B$,Dj?t@.J,$G$"$l$P(B, $B0l$DA0$N(B GB $B$N9=@.MWAG$G$"$k(B
                     20:   g_i $B$,M>J,$J(B GB $B$G$"$k2DG=@-$,$?$+$$(B.
                     21:   SpairAndReduction() ( LaScala-Stillman $B$NJ}K!(B) $B$H$N@09g@-$r$H$k$?$a(B
                     22:   g_i $B$r(B tmp[0] $B$KBeF~$7(B ( reduction $B$G$-$J$+$C$?$U$j$r$9$k(B )
                     23:   g_i $B$N(B V-degree $B$r$7$i$Y$k(B.
                     24:
                     25:
                     26: Sannfs2_laScala2()
                     27: Sannfs3_laScala2()  $B$r:n$k(B.
                     28:
                     29: $BFs$D$N%"%k%4%j%:%`$NHf3S(B.
                     30: In(11)=sm1_pmat(a1[1]); $B$N=gHV$r$+$($k(B.
                     31:  [
                     32:    [    3*Dx^2*h , 0 , Dy , -Dz ]
                     33:    [    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]
                     34:    [    2*x*Dx+3*z*Dz-h^2 , y*Dy-z*Dz , 0 , 0 ]
                     35:    [    2*x*Dy*Dz , 0 , z , -y ]
                     36:
                     37:    [    0 , 2*x*Dy^2*Dz-3*z*Dx^2*h , 0 , 2*x*Dx+3*z*Dz ]
                     38:  ]
                     39: In(12)=sm1_pmat(a2[1]);
                     40:  [
                     41:    [    3*Dx^2*h , 0 , Dy , -Dz ]
                     42:    [    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 ]
                     43:    [    2*x*Dx+3*z*Dz-h^2 , y*Dy-z*Dz , 0 , 0 ]
                     44:    [    2*x*Dy*Dz , 0 , z , -y ]
                     45:
                     46:    [    9*z*Dx^2*h , 2*x*Dy^2*Dz-3*z*Dx^2*h , 3*z*Dy , 2*x*Dx ]
                     47:    [    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 ]
                     48:  ]
                     49: In(13)=
                     50:
                     51: ----------------------
                     52: In(16)=sm1_pmat(a1[2]);
                     53:  [
                     54:    [    -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 ]
                     55:    [    3*y*z , z , y , -2*x*Dy*Dz , -3*z*Dy , 2*x*Dx , 2*x*z , -2*x*y , 0 ]
                     56:  ]
                     57: In(17)=sm1_pmat(a2[2]);
                     58:  [
                     59:    [    -y , 2*x*Dy*Dz , z , 0 , 2*x*Dx , 0 ]
                     60:    [    -Dz , 3*Dx^2*h , Dy , -2*x*Dx-3*y*Dy-3*h^2 , -3*Dy*Dz , 0 ]
                     61:  ]
                     62: In(18)=
                     63:
1.2       takayama   64: ---------------------------
                     65:
                     66: May 22, (Tue),  5:50 (Spain local time, 12:50 JST)
                     67:
                     68: kan96xx/Kan/resol.c $B$G(B,
                     69:    RemoveRedundantInSchreyerSkelton = 0
                     70: $B$KJQ$($F(B ($B$3$N(B option $B$b$"$?$i$7$/2C$($k(B), schreyer $B$,@5$7$/F0$/$+(B
                     71: $BD4$Y$k$3$H$K$9$k(B.
                     72: ( commit $B$O(B kan96xx $B$H(B k097 $BN>J}$9$Y$7(B.)
                     73:
                     74: test8() $B$G(B sm1 $B$G=q$$$?J}$N(B Schreyer $B$r8+$k$H(B,
                     75:    RemoveRedundantInSchreyerSkelton = 1
                     76: $B$G$b(B,
                     77: kernel = image
                     78: $B$H$J$C$F$$$k$N$G0J8e$3$N(B option $B$O(B 1 $B$N$^$^;H$&$3$H$H$9$k(B.
                     79: $BMW$9$k$K(B k0 $B$N%3!<%I$,$I$&$d$i$*$+$7$$$i$7$$(B.
1.3     ! takayama   80:
        !            81: -----------------------------------
        !            82: June 8, 2000 (Thu), 9:10 (Spain local time)
        !            83: hol.sm1 :  gb_h, syz_h, isSameIdeal, isSameIdeal_h
        !            84: complex.sm1 :  isExact, isExact_h
        !            85:
        !            86: syzygy $B$r(B homogenization $B$r2p$7$F7W;;$9$k$N$OLdBj$"$j(B.
        !            87: --> usage of isExact
        !            88:
        !            89: [(Homogenize_vec) 0] system_variable : vector $B$N(B homogenize $B$r$7$J$$(B.
        !            90: (grade) (module1v) switch_function : vector $BJQ?t$O(B, total
        !            91:        degree $B$K?t$($J$$(B.
        !            92: ==> $BL58B%k!<%W$KCm0U(B   ---> gb_h, syz_h  $B$N(B usage.
        !            93:
        !            94: minimal-test.k $B$N(B ann(x^3-y^2*z^2) $B$N(B laplace $BJQ49$N(B
        !            95: betti $B?t$,JQ(B, exact $B$G$J$$(B, $B$r(B isExact_h $B$G(B check
        !            96: $B$7$h$&(B.
        !            97:
        !            98: minimal-test.k
        !            99: test10();
        !           100:   LaScala-Stillman $B$NJ}K!$G$D$/$C$?(B, schreyer resol $B$,(B exact $B$+(B
        !           101:   $BD4$Y$k(B.
        !           102:   $BNcBj$O(B, ann(1/(x^3-y^2 z^2)) $B$N(B Laplace $BJQ49(B.
        !           103:
        !           104: