Make arith versions of some functions default, dispatching to symbolic

[rwst]

Of many functions there are two versions with the same name---in sage/arith and in sage/functions, examples are binomial and factorial. On startup the latter versions overwrite the former because of order of import. That creates problems both with documentation, different interface, and different behavior expected. For example in #14723 the problem of binomial(Qp(5)(8),2) could not be resolved with the sage/functions version (because there the arguments have restrictions), although the sage/arith version would have worked perfectly. OTOH the arith version can not handle binomial(x,y) but the symbolic function version can.

The logical solution would be for all cases to

• make the arith version the default by removing the import in sage/functions/all.py; the arith version will no longer be overwritten
• dispatch calls to the arith version with symbolic arguments to the symbolic function version
• copy some symbolic documentation to arith because that docstring will be shown now

The issues #22314, #17489 depend on this.

CC: @jdemeyer @videlec

Component: basic arithmetic

Author: Ralf Stephan

Branch/Commit: u/rws/make_arith_versions_of_some_functions_default__dispatching_to_symbolic @ 4bc93d0

Issue created by migration from https://trac.sagemath.org/ticket/24178

[jdemeyer]

comment:1

Why should there even be two versions of every function in the first place? Shouldn't we be able to support all use cases in one function?

[rwst]

comment:2

I wanted to have the code completely in functions but #14723 had its problems. See also #17489.

[rwst]

comment:3

I could also naively ask, if everything coerces into SR why can't symbolic functions by default coerce every argument?

[rwst]

comment:4

I mean you implemented the symbolic function machinery, and it's fine if you step back and say, let others go ahead now. But you could at least review attempts to fix your design decisions.

[rwst]

comment:5

Alternatively, if NOT everything coerces into SR then the symbolic binomial interface is more restricted than the arith binomial interface, and thus the arith version should be default, calling the symbolic version.

[rwst]

Description changed:

--- 
+++ 
@@ -4,3 +4,5 @@
 - make the arith version the default by removing the alias in `sage/function`; the arith version will no longer be overwritten
 - dispatch calls to the arith version with symbolic arguments to the symbolic function version
 - copy some symbolic documentation to arith because that docstring will be shown now 
+
+The issues #22314, #17489 depend on this.

[rwst]

comment:7

See also #19461 comment:9

[rwst]

Description changed:

--- 
+++ 
@@ -1,7 +1,7 @@
 Of many functions there are two versions with the same name---in `sage/arith` and in `sage/functions`, examples are `binomial` and `factorial`. On startup the latter versions overwrite the former because of order of import. That creates problems both with documentation, different interface, and different behavior expected. For example in #14723 the problem of `binomial(Qp(5)(8),2)` could not be resolved with the `sage/functions` version (because there the arguments have restrictions), although the `sage/arith` version would have worked perfectly. OTOH the arith version can not handle `binomial(x,y)` but the symbolic function version can.
 
 The logical solution would be for all cases to
-- make the arith version the default by removing the alias in `sage/function`; the arith version will no longer be overwritten
+- make the arith version the default by removing the import in `sage/functions/all.py`; the arith version will no longer be overwritten
 - dispatch calls to the arith version with symbolic arguments to the symbolic function version
 - copy some symbolic documentation to arith because that docstring will be shown now 
 

[rwst]

Branch: u/rws/make_arith_versions_of_some_functions_default__dispatching_to_symbolic

[sagetrac-git]

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

669cfff

24178: changes to arith and doctests