# Singular

#### D.4.25.5 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 ```