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5.1.108 reduce
Syntax:
reduce ( poly_expression, ideal_expression )
reduce ( poly_expression, ideal_expression, int_expression )
reduce ( poly_expression, poly_expression, ideal_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 ( vector_expression, poly_expression, module_expression )
reduce ( ideal_expression, ideal_expression )
reduce ( ideal_expression, ideal_expression, int_expression )
reduce ( ideal_expression, matrix_expression, ideal_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 )
reduce ( module_expression, matrix_expression, module_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 standard 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 standard basis.
The third (optional) argument 1 of type int forces a reduction which considers only the leading term and does no tail reduction.
If a second argument u of type poly or matrix is given, the first argument p is replaced by p/u .
This works only for zero dimensional ideals (resp. modules) in the third argument and gives, even in a local ring, a reduced normal form which is the projection to the quotient by the ideal (resp. module).
One may give a degree bound in the fourth argument with respect to a weight vector in the fifth argument in order in order to make the third argument zero dimensional.
If some of the weights are zero, the procedure may not terminate!
Note:
- The commands
reduce and NF are synonymous.
Example:
| ring r1 = 0,(z,y,x),ds;
poly s1=2x5y+7x2y4+3x2yz3;
poly s2=1x2y2z2+3z8;
poly s3=4xy5+2x2y2z3+11x10;
ideal i=s1,s2,s3;
ideal j=std(i);
reduce(3z3yx2+7y4x2+yx5+z12y2x2,j);
==> -yx5+2401/81y14x2+2744/81y11x5+392/27y8x8+224/81y5x11+16/81y2x14
reduce(3z3yx2+7y4x2+yx5+z12y2x2,j,1);
==> -yx5+z12y2x2
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See
ideal;
module;
std;
vector.
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