|
3.22 reduce
Syntax:
reduce ( poly_expression, ideal_expression )
reduce ( poly_expression, ideal_expression, int_expression )
reduce ( vector_expression, ideal_expression )
reduce ( vector_expression, ideal_expression, int_expression )
reduce ( vector_expression, module_expression )
reduce ( vector_expression, module_expression, int_expression )
reduce ( ideal_expression, ideal_expression )
reduce ( ideal_expression, ideal_expression, int_expression )
reduce ( module_expression, ideal_expression )
reduce ( module_expression, ideal_expression, int_expression )
reduce ( module_expression, module_expression )
reduce ( module_expression, module_expression, int_expression )
Type:
- the type of the first argument
Purpose:
- reduces a polynomial, vector, ideal or module to its normal form with
respect to an ideal or module represented by a Groebner basis.
Returns 0 if and only if the polynomial (resp. vector, ideal, module)
is an element (resp. subideal, submodule) of the ideal (resp. module).
The result may have no meaning if the second argument is not a Groebner basis.
The third (optional) argument 1 of type int forces a reduction which considers only the leading term and does no tail reduction.
Note:
- The commands
reduce and NF are synonymous.
Example:
| ring r=(0,a),(e,f,h),Dp;
matrix d[3][3];
d[1,2]=-h; d[1,3]=2e; d[2,3]=-2f;
ncalgebra(1,d); // this is parametric U(sl_2)
ideal I=e2,f2,h2-1;
I=std(I);
ideal J=e,h-a;
J=std(J);
poly z=4*e*f+h^2-2*h; // z is the central element of U(sl_2)
// the central character of I:
NF(z,I);
==> 3
// the central character of J:
NF(z,J);
==> (a2+2a)
|
See
ideal;
module;
std.
see also vector in SINGULAR manual.
|