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D.4.25.4 sagbi
Procedure from library sagbi.lib (see sagbi_lib).
- Usage:
- sagbi(id,k[,n]); id ideal, k and n positive integers.
- Return:
- A 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-interreduced SAGBI basis
is returned.
Three algorithm variants are used to perform subalgebra reduction.
The positive interger n determine which variant should be used.
n may take the values (0 or default),1 or 2.
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- Note:
- SAGBI bases computations may be performed in polynomial rings or quotients
thereof.
Example:
| LIB "sagbi.lib";
ring r= 0,(x,y),dp;
ideal I=x2,y2,xy+y;
sagbi(I,1,1);
==> _[1]=x2
==> _[2]=y2
==> _[3]=xy+y
==> _[4]=xy2
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