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A.3.12 Algebraic dependence

Let We want to check whether

  1. are algebraically dependent.

    Let Then are the algebraic relations between

  2. 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.

 


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