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7.7.3.0. sa_reduce
Procedure from library central.lib (see central_lib).
- Usage:
- sa_reduce(V); V ideal
- Return:
- ideal, generated by computed elements
- Purpose:
- compute a subalgebra basis of an algebra generated by the elements of V
- Note:
- At the moment the usage of this procedure is limited to G-algebras
Example:
| | LIB "central.lib";
ring AA = 0,(x,y,z),dp;
matrix D[3][3]=0;
D[1,2]=-z; D[1,3]=2*x; D[2,3]=-2*y;
def A = nc_algebra(1,D); setring A; // this algebra is U(sl_2)
poly f = 4*x*y+z^2-2*z; // a central polynomial
ideal I = f, f*f, f*f*f - 10*f*f, f+3*z^3; I;
==> I[1]=4xy+z2-2z
==> I[2]=16x2y2+8xyz2+z4-32xyz-4z3+32xy+4z2
==> I[3]=64x3y3+48x2y2z2+12xyz4+z6-288x2y2z-96xyz3-6z5+352x2y2+224xyz2+2z4-12\
8xyz+32z3-64xy-40z2
==> I[4]=3z3+4xy+z2-2z
sa_reduce(I); // should be just f and z^3
==> _[1]=4xy+z2-2z
==> _[2]=z3
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See also:
sa_poly_reduce.
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