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D.4.27.4 sagbiPart
Procedure from library sagbi.lib (see sagbi_lib).
- Usage:
- sagbiPart(A, k,[tr, mt]); A is an ideal, k, tr and mt are integers
- Return:
- ideal
- Assume:
- basering is not a qring
- Purpose:
- Performs k iterations of the SAGBI construction algorithm for the subalgebra given by the generators given by A.
| | The optional argument tr=tailred determines if tail reduction will be performed.
- If (tailred=0), no tail reduction is performed,
- If (tailred<>0), tail reduction is performed.
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;
//The following algebra does not have a finite SAGBI basis.
ideal A=x,xy-y2,xy2;
//---------------------------------------------------
//Call with two iterations, no tail-reduction is done.
sagbiPart(A,2);
==> //SAGBI construction algorithm stopped as it reached the limit of 2 itera\
tions.
==> //In general the returned generators are no SAGBI basis for the given alg\
ebra.
==> _[1]=x
==> _[2]=xy-y2
==> _[3]=xy2
==> _[4]=2xy3-y4
==> _[5]=3xy5-y6
==> _[6]=xy4
//---------------------------------------------------
//Call with three iterations, tail-reduction and method 0.
sagbiPart(A,3,1,0);
==> //SAGBI construction algorithm stopped as it reached the limit of 3 itera\
tions.
==> //In general the returned generators are no SAGBI basis for the given alg\
ebra.
==> _[1]=x
==> _[2]=xy-y2
==> _[3]=xy2
==> _[4]=2xy3-y4
==> _[5]=3xy5-y6
==> _[6]=xy4
==> _[7]=5xy9-y10
==> _[8]=xy8
==> _[9]=4xy7-y8
==> _[10]=xy6
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