Singular Manual: CenCharDec

| ##### 7.5.11.0. CenCharDec Procedure from library `ncdecomp.lib` (see ncdecomp_lib). Usage: CenCharDec(I, C); I a module, C an ideal Assume: C consists of generators of the center of the base ring Return: a list L, where each entry consists of three records (if a finite decomposition exists) L[*][1] ('ideal' type), the central character as a maximal ideal in the center, L[*][2] ('module' type), the Groebner basis of the weight module, corresponding to the character in L[*][1], L[*][3] ('int' type) is the vector space dimension of the weight module (-1 in case of infinite dimension); Purpose: compute a finite decomposition of C into central characters or determine that there is no finite decomposition Note: actual decomposition is the sum of L[i][2] above; some modules have no finite decomposition (in such case one gets warning message) The function `central` in `central.lib` may be used to obtain C, when needed. Example:
    LIB "ncdecomp.lib";
    printlevel=0;
    option(returnSB);
    def a = makeUsl2(); // U(sl_2) in characteristic 0
    setring a;
    ideal I = e3,f3,h3-4*h;
    I = twostd(I);           // two-sided ideal generated by I
    vdim(I);                 // it is finite-dimensional
    ==> 10
    ideal Cn = 4*e*f+h^2-2*h; // the only central element
    list T = CenCharDec(I,Cn);
    T;
    ==> [1]:
    ==>    [1]:
    ==>       _[1]=4ef+h2-2h-8
    ==>    [2]:
    ==>       _[1]=h
    ==>       _[2]=f
    ==>       _[3]=e
    ==>    [3]:
    ==>       1
    ==> [2]:
    ==>    [1]:
    ==>       _[1]=4ef+h2-2h
    ==>    [2]:
    ==>       _[1]=4ef+h2-2h-8
    ==>       _[2]=h3-4h
    ==>       _[3]=fh2-2fh
    ==>       _[4]=eh2+2eh
    ==>       _[5]=f2h-2f2
    ==>       _[6]=e2h+2e2
    ==>       _[7]=f3
    ==>       _[8]=e3
    ==>    [3]:
    ==>       9
    // consider another example
    ideal J = e*f*h;
    CenCharDec(J,Cn);
    ==> There is no finite decomposition
    ==> 0
See also: CentralQuot; CentralSaturation.

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