Constant problem
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In mathematics, the constant problem is the problem of deciding whether a given expression is equal to zero.
In mathematics, the constant problem is the problem of deciding whether a given expression is equal to zero. ==The problem== This problem is also referred to as the identity problem or the method of zero estimates. It has no formal statement as such but refers to a general problem prevalent in transcendental number theory. Often proofs in transcendence theory are proofs by contradiction. Specifically, they use some auxiliary function to create an integer n ≥ 0, which is shown to satisfy n 1 , ..., x n are real numbers, then there is an algorithm for deciding whether there are integers a 1 , ..., a n such that a_1 x_1 + \cdots + a_n x_n = 0\,. If the expression we are interested in contains an oscillating function, such as the sine or cosine function, then it has been shown that the problem is undecidable, a result known as Richardson's theorem. In general, methods specific to the expression being studied are required to prove that it cannot be zero. ==See also== Integer relation algorithm ==References==
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