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D.4.22.5 sagbiPart

Procedure from library sagbi.lib (see sagbi_lib).

Usage:
sagbiPart(id,k,c[,n]); id ideal, k, c and n positive integers

Return:
A partial SAGBI basis for the subalgebra defined by the generators of id.
 
     k determines what kind of s-reduction is performed:
     - if (k=0) no tail s-reduction is performed.
     - if (k=1) tail s-reduction is performed, and S-intereduced SAGBI basis
      is returned.
     c determines, after how many loops the Sagbi basis computation should stop.
     Three algorithm variants are used to perform subalgebra reduction.
     The positive integer n determines which variant should be used.
     n may take the values (0 or default),1 or 2.

Note:
- SAGBI bases computations may be performed in polynomial rings or quotients thereof.
- This version of sagbi is interesting in the case of subalgebras with infinte SAGBI basis. In this case, it may be used to check, if the elements of this basis have a particular form.

Example:
 
LIB "sagbi.lib";
ring r= 0,(x,y),dp;
ideal I=x,xy-y2,xy2;//the corresponding Subalgebra has an infinte SAGBI basis
sagbiPart(I,1,3);// computations should stop after 3 turns.
==> _[1]=x
==> _[2]=xy-y2
==> _[3]=xy2
==> _[4]=xy3-1/2y4
==> _[5]=xy5-1/3y6
==> _[6]=xy4
==> _[7]=xy9-1/5y10
==> _[8]=xy8
==> _[9]=xy7-1/4y8
==> _[10]=xy6
==> _[11]=xy15-1/8y16
==> _[12]=xy16
==> _[13]=xy12
==> _[14]=xy13-1/7y14
==> _[15]=xy11-1/6y12
==> _[16]=xy10
==> _[17]=xy17-1/9y18
==> _[18]=xy14

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