Changes between Version 8 and Version 13 of Ticket #22090
 Timestamp:
 01/23/17 08:10:08 (3 years ago)
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Ticket #22090

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Dependencies
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to
pynac0.7.5

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Commit
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17c5e409466c4b258e1eb07fc490cf6828dff9ba
toe74a4141763cec2b68ce5a27fdfe2650c88b07d4

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Summary
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Gosper algorithm
toGosper algorithm and WilfZeilberger certificate

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Ticket #22090 – Description
v8 v13 1 1 Pynac0.7.3 introduces Gosper's hypergeometric summation algorithm. The ticket will implement the interface and add an extensive test file. Later tickets may call the function before delegating unsolved sums to Maxima. 2 2 3 The test file has three tests marked as known bug. Each of them shows an area where the implementation will have to be improved: 4  expressions with algebraic coefficients (i.e. manipulations of polynomials over algebraic fields) 5  the final computation in Gosper's algorithm may result in `NaN` from `0*inf`,`0/0` or such. Here a limit computation will give the result. I didn't want to call Maxima from Pynac however. 6  enhancement of GiNaC's resultant implementation 3 Also, the WZ certificate can be computed to prove hypegeometric identities. 4 5 The test file has one test marked as known bug. Its resolution depends on handling of expressions with algebraic coefficients (i.e. manipulations of polynomials over algebraic fields). 6 7 Pynac0.7.5 adds a crucial improvement and a faster implementation.