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D.4.2.4 algDependent

Procedure from library algebra.lib (see algebra_lib).

Usage:
algDependent(f[,c]); f ideal (say, f = f1,...,fm), c integer

Return:
 
         a list l  of size 2, l[1] integer, l[2] ring:
         - l[1] = 1 if f1,...,fm are algebraic dependent, 0 if not
         - l[2] is a ring with variables x(1),...,x(n),y(1),...,y(m) if the
           basering has n variables. It contains the ideal 'ker', depending
           only on the y(i) and generating the algebraic relations between the
           f[i], i.e. substituting y(i) by fi yields 0. Of course, ker is
           nothing but the kernel of the ring map
              K[y(1),...,y(m)] ---> basering,  y(i) --> fi.

Note:
Three different algorithms are used depending on c = 1,2,3. If c is not given or c=0, a heuristically best method is chosen. The basering may be a quotient ring.
To access to the ring l[2] and see ker you must give the ring a name, e.g. def S=l[2]; setring S; ker;

Display:
The above comment is displayed if printlevel >= 0 (default).

Example:
 


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