Gosper algorithm and Wilf-Zeilberger certificate

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Pynac-0.7.3 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.

Also, the WZ certificate can be computed to prove hypergeometric identities.

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).

Pynac-0.7.5 adds a crucial improvement and a faster implementation.

Depends on #22174
Depends on #22364

Component: symbolics

Author: Ralf Stephan

Branch/Commit: 70462e2

Reviewer: Frédéric Chapoton

Issue created by migration from https://trac.sagemath.org/ticket/22090

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Branch: u/rws/gosper_algorithm

[sagetrac-git]

Commit: 5003327

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

dda7f2d	Merge branch 'develop' into t/22090/gosper_algorithm
5003327	22090: test file

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Description changed:

--- 
+++ 
@@ -1 +1,6 @@
 Pynac-0.7.3 will have Gosper's hypergeometric summation algorithm. The ticket will implement the interface and add an extensive test file. Later tickets may call it before delegating unsolved sums to Maxima.
+
+The test file has three tests marked as known bug. Each of them shows an area where the implementation will have to be approved:
+- expressions with algebraic coefficients (i.e. manipulations of polynomials over algebraic fields)
+- 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.
+- enhancement of GiNaC's resultant implementation

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Author: Ralf Stephan

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Description changed:

--- 
+++ 
@@ -1,6 +1,6 @@
 Pynac-0.7.3 will have Gosper's hypergeometric summation algorithm. The ticket will implement the interface and add an extensive test file. Later tickets may call it before delegating unsolved sums to Maxima.
 
-The test file has three tests marked as known bug. Each of them shows an area where the implementation will have to be approved:
+The test file has three tests marked as known bug. Each of them shows an area where the implementation will have to be improved:
 - expressions with algebraic coefficients (i.e. manipulations of polynomials over algebraic fields)
 - 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.
 - enhancement of GiNaC's resultant implementation

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Changed dependencies from #19461, pynac-0.7.3 to #19461, #22136

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comment:6

I concede that we don't need really need #19461.

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

0e48511	22136: pkg version/chksum
c636059	Merge branch 't/22136/upgrade_to_pynac_0_7_3' into t/22090/gosper_algorithm
17c5e40	22090: fixes

[sagetrac-git]

Changed commit from 5003327 to 17c5e40