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Annotation of OpenXM/doc/Papers/ohp-v-minimal.tex, Revision 1.1

1.1     ! takayama    1: %% $OpenXM$
        !             2: \documentclass{slides}
        !             3: \begin{document}
        !             4: V-minimal free resolution
        !             5: of the Laplace transform of
        !             6: the annihilating ideal of $1/(x^3-y^2 z^2)$
        !             7: with $(-w,w) = (-1,-1,-1,1,1,1)$.
        !             8:
        !             9: {\footnotesize
        !            10: \begin{verbatim}
        !            11: In(3)=a=Sannfs3("x^3-y^2*z^2");
        !            12: In(4)=b=a[0];
        !            13: In(5)=sm1_pmat(b);
        !            14:  [
        !            15:   [
        !            16:     [    y*Dy-z*Dz ]
        !            17:     [    -2*x*Dx-3*z*Dz+h^2 ]
        !            18:     [    2*x*Dy*Dz^2-3*y*Dx^2*h ]
        !            19:     [    2*x*Dy^2*Dz-3*z*Dx^2*h ]
        !            20:   ]
        !            21:   [
        !            22:     [    9*z*Dx^2*h , 2*x*Dy^2*Dz-3*z*Dx^2*h ,
        !            23:           3*z*Dy , 2*x*Dx ]
        !            24:     [    2*x*Dx+3*z*Dz-h^2 , y*Dy-z*Dz , 0 , 0 ]
        !            25:     [    -6*x*Dy*Dz^2+9*y*Dx^2*h ,
        !            26:          2*x*Dy*Dz^2-3*y*Dx^2*h , 2*x*Dx+3*y*Dy , 0 ]
        !            27:     [    3*Dx^2*h , 0 , Dy , -Dz ]
        !            28:     [    -2*x*Dy*Dz , 0 , -z , y ]
        !            29:     [    2*x*Dx*Dz^2+3*z*Dz^3+5*Dz^2*h^2 ,
        !            30:           y*Dy*Dz^2-z*Dz^3-2*Dz^2*h^2 , 0 , 0 ]
        !            31:   ]
        !            32:   [
        !            33:     [    -y , 2*x*Dy*Dz , z , 0 , 2*x*Dx , 0 ]
        !            34:     [    -Dz , 3*Dx^2*h , Dy , -2*x*Dx-3*y*Dy-3*h^2 ,
        !            35:          -3*Dy*Dz , 0 ]
        !            36:   ]
        !            37:  ]
        !            38: In(6)=Map(a[3],"Length"):
        !            39: [    8 , 17 , 13 , 3 ]
        !            40: In(7)=Map(a[0],"Length"):
        !            41: [    4 , 6 , 2 ]
        !            42: In(8)=sm1_pmat(a[3,2]);
        !            43:  [
        !            44:    [    0 , 1 , 0 , 0 , -1 , 0 , 0 , 0 , 3*z , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 ]
        !            45:    [    -y , 0 , 0 , 1 , 0 , 0 , 0 , 0 , 0 , 0 , 3*z*Dz+3*h^2 , 0 , -2*x , 0 , 0 , 0 , 0 ]
        !            46:    [    z , y , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , -3*z*Dz , 0 , 0 , 2*x , 0 , 0 ]
        !            47:    [    0 , y , 0 , 0 , 0 , 0 , -z , 0 , 3*y*z , 0 , 3*z*Dy , 0 , 0 , 0 , 2*x , 0 , 0 ]
        !            48:    [    -h^2 , 0 , 2*x , Dy , 0 , -3*y*Dx^2*h , z*Dz+h^2 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 ]
        !            49:    [    0 , 0 , 3 , 0 , 0 , 0 , 0 , 3*y , 0 , 0 , 0 , 0 , 3*Dy , 0 , 3*Dz , 0 , 0 ]
        !            50:    [    Dx , 0 , -3 , 0 , 0 , 0 , Dx , 0 , 0 , 0 , 0 , 0 , 0 , 3*Dy , 0 , 3*z*Dz+6*h^2 , 0 ]
        !            51:    [    0 , 0 , -Dy , 0 , 0 , 0 , 0 , z*Dz , 0 , 1 , 0 , 0 , 0 , 0 , 0 , 0 , 0 ]
        !            52:    [    -1 , 0 , 0 , 0 , 0 , 0 , -1 , 0 , 3*y , 0 , 3*Dy , 3*Dz , 0 , 0 , 0 , 0 , 0 ]
        !            53:    [    Dy , 0 , 0 , 0 , Dz , -3*Dx^2*h , 0 , -2*x , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 ]
        !            54:    [    0 , 0 , 0 , 0 , 0 , 0 , 0 , -1 , -Dx , 0 , 0 , 0 , 0 , 0 , 0 , Dy , Dz ]
        !            55:    [    0 , 0 , 0 , 0 , 0 , -Dz^2 , 0 , 0 , 0 , 0 , Dx , 0 , 1 , 1 , 0 , y , 0 ]
        !            56:    [    0 , 0 , 0 , 0 , 0 , Dy*Dz , 0 , 0 , 0 , 0 , 0 , Dx , 0 , 0 , 1 , z , y ]
        !            57:  ]
        !            58: \end{verbatim} }
        !            59:
        !            60:
        !            61:
        !            62:
        !            63: \end{document}
        !            64:
        !            65: {\footnotesize
        !            66: \begin{verbatim}
        !            67:
        !            68:
        !            69:
        !            70: \end{verbatim} }