Number identification¶
Most function in mpmath are concerned with producing approximations from exact mathematical formulas. It is also useful to consider the inverse problem: given only a decimal approximation for a number, such as 0.7320508075688772935274463, is it possible to find an exact formula?
Subject to certain restrictions, such “reverse engineering” is indeed possible thanks to the existence of integer relation algorithms. Mpmath implements the PSLQ algorithm (developed by H. Ferguson), which is one such algorithm.
Automated number recognition based on PSLQ is not a silver bullet. Any occurring transcendental constants (
, 
, etc) must be guessed by the user, and the relation between those constants in the formula must be linear (such as 
). More complex formulas can be found by combining PSLQ with functional transformations; however, this is only feasible to a limited extent since the computation time grows exponentially with the number of operations that need to be combined.
The number identification facilities in mpmath are inspired by the Inverse Symbolic Calculator (ISC). The ISC is more powerful than mpmath, as it uses a lookup table of millions of precomputed constants (thereby mitigating the problem with exponential complexity).
