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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.


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            User manual for Singular version 2-1-99, August 2004, generated by texi2html.