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D.4.20.5 sagbiPart

Procedure from library sagbi.lib (see sagbi_lib).

Usage:
sagbi(id,k,c[,n]); id ideal, k, c and n positive integer.

Return:
A partial SAGBI basis for the subalgebra defined by the generators of id.
 
     should stop. k determine 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 which turn Sagbi basis computations 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 either
in polynomial rings or quotient polynomial rings.
- This version of sagbi procedure is interesting in the case of an Subalgebras with infinte SAGBI basis. In this case, by means of this procedure, we may check for example, 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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