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D.4.32.5 algebraicDependence
Procedure from library sagbi.lib (see sagbi_lib).
- Usage:
- algebraicDependence(I,it); I an an ideal, it is an integer
- Return:
- ring
- Assume:
- basering is not a qring
- Purpose:
- Returns a ring containing the ideal
algDep, which contains possibly
some algebraic dependencies of the elements of I obtained through it
iterations of the SAGBI construction algorithms. See the example on how
to access these objects.
Example:
| | LIB "sagbi.lib";
ring r= 0,(x,y),dp;
//The following algebra does not have a finite SAGBI basis.
ideal I=x^2, xy-y2, xy2;
//---------------------------------------------------
//Call with two iterations
def DI = algebraicDependence(I,2);
==> //AlgDep-1- initialisation and precomputation
==> //AlgDep-2- call of SAGBI construction algorithm
==> //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.
==> //AlgDep-3- postprocessing of results
setring DI; algDep;
==> algDep[1]=0
// we see that no dependency has been seen so far
//---------------------------------------------------
//Call with two iterations
setring r; kill DI;
def DI = algebraicDependence(I,3);
==> //AlgDep-1- initialisation and precomputation
==> //AlgDep-2- call of SAGBI construction algorithm
==> //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.
==> //AlgDep-3- postprocessing of results
setring DI; algDep;
==> algDep[1]=0
map F = DI,x,y,x^2, xy-y2, xy2;
F(algDep); // we see that it is a dependence indeed
==> _[1]=0
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