A.3.12 Algebraic dependence
Let
We want to check whether
-
are algebraically dependent.
Let
Then
are the algebraic relations between
-
if and only if the normal form of
with respect to
and a
block ordering with respect to
is in
.
Both questions can be answered using the following procedure. If the
second argument is zero, it checks for algebraic dependence and returns
the ideal of relations between the generators of the given ideal.
Otherwise it checks for subring membership and returns the normal form
of the second argument with respect to the ideal I.
|