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Annotation of OpenXM/src/k097/lib/minimal/minimal-note-ja.txt, Revision 1.1

1.1     ! takayama    1: $OpenXM$
        !             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: