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D.4.32.2 sagbiReduce
Procedure from library sagbi.lib (see sagbi_lib).
- Usage:
- sagbiReduce(I, A[, tr, mt]); I, A ideals, tr, mt optional integers
- Return:
- ideal of remainders of I after SAGBI reduction by A
- Assume:
- basering is not a qring
- Purpose:
| | The optional argument tr=tailred determines whether tail reduction will be performed.
- If (tailred=0), no tail reduction is done.
- If (tailred<>0), tail reduction is done.
The other optional argument meth determines which method is
used for Groebner basis computations.
- If mt=0 (default), the procedure std is used.
- If mt=1, the procedure slimgb is used.
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Example:
| | LIB "sagbi.lib";
ring r=0,(x,y,z),dp;
ideal A=x2,2*x2y+y,x3y2;
poly p1=x^5+x2y+y;
poly p2=x^16+x^12*y^5+6*x^8*y^4+x^6+y^4+3;
ideal P=p1,p2;
//---------------------------------------------
//SAGBI reduction of polynomial p1 by algebra A.
//Default call, that is, no tail-reduction is done.
sagbiReduce(p1,A);
==> x5+x2y+y
//---------------------------------------------
//SAGBI reduction of set of polynomials P by algebra A,
//now tail-reduction is done.
sagbiReduce(P,A,1);
==> _[1]=x5+1/2y
==> _[2]=x6y5-8y4
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