
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,h34*h;
I = twostd(I); // twosided ideal generated by I
vdim(I); // it is finitedimensional
==> 10
ideal Cn = 4*e*f+h^22*h; // the only central element
list T = CenCharDec(I,Cn);
T;
==> [1]:
==> [1]:
==> _[1]=4ef+h22h8
==> [2]:
==> _[1]=h
==> _[2]=f
==> _[3]=e
==> [3]:
==> 1
==> [2]:
==> [1]:
==> _[1]=4ef+h22h
==> [2]:
==> _[1]=4ef+h22h8
==> _[2]=h34h
==> _[3]=fh22fh
==> _[4]=eh2+2eh
==> _[5]=f2h2f2
==> _[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.
