identity problem

Given an expression involving known constants, integration in finite terms, computation of limits, etc., the constant problem is the determination of if the expression is equal to zero. The constant problem, sometimes also called the identity problem is a very difficult unsolved problem in transcendental number theory. However, it is known that the problem is undecidable if the expression involves oscillatory functions such as sine. However, the Ferguson-Forcade algorithm is a practical algorithm for determining if there exist integers a_i for given real numbers x_i such that a_1 x_1 + a_2 x_2 + ... + a_n x_n = 0, or else establishing bounds within which no relation can exist.

almost integer | almost zero | Ferguson-Forcade algorithm | Hermite-Lindemann theorem | hidden zero | identically zero | integer relation | integration problem | Richardson's theorem | Schanuel's conjecture | uniformity conjecture