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Open problems with signatures

There are several open problems with signatures. Some we know that are likely to be impossible to solve, as their solution would imply that P=NP. Others are still open and their solution may have a truly profound impact in practical and effective computer algebra.

Signatures of boolean expressions
Signature of $\pi$
Signature of $\Gamma (k)$
Signature of a derivative
Definite integrals
Signatures of sets

Gaston Gonnet
1999-07-04