Refactoring in Chebyshev functions

[rwst]

While other orthogonal polynomial functions (as well as almost all other symbolic functions) are simply BuiltinFunctions or GinacFunctions this ticket suffers from the fact that the Cheby functions in Sage allow the algorithm keyword (by using a __call__ method in the superclass). The way such polymorphisms are resolved in other functions is by having the interface (the callable global function chebyshev_T()) dispatching on the keyword, especially because doctests involving all kind of Sage objects as function argument are expected to work eternally.

The goal of this ticket is to move the __call__ method out of the Function class (as well as other methods used as interface) into a separate interface class; to 2. make the remaining class inherit from BuiltinFunction and, 3., to remove the ChebyshevFunction superclass as it is then no longer used.

Component: symbolics

Author: Ralf Stephan

Branch/Commit: u/rws/24554 @ 957ce14

Issue created by migration from https://trac.sagemath.org/ticket/24554

[rwst]

Description changed:

--- 
+++ 
@@ -1 +1 @@
-While other orthogonal polynomial functions (as well as almost all other symbolic functions) are simply `BuiltinFunction`s or `GinacFunction`s this ticket suffers from the fact that the Cheby functions in Sage allow the `algorithm` keyword (by using a `__call__` method in the superclass). The way such polymorphisms are resolved in other functions is by having the interface (the callable global function `chebyshev_T()`) dispatching on the keyword.
+While other orthogonal polynomial functions (as well as almost all other symbolic functions) are simply `BuiltinFunction`s or `GinacFunction`s this ticket suffers from the fact that the Cheby functions in Sage allow the `algorithm` keyword (by using a `__call__` method in the superclass). The way such polymorphisms are resolved in other functions is by having the interface (the callable global function `chebyshev_T()`) dispatching on the keyword. OTOH the call `chebyshev_T.eval_algebraic()` is expected to work. The only way this can be resolved and prepared for any deprecations is by having the `chebyshev` class not being a `Function` but creating such an object.

[rwst]

comment:2

The usage chebyshev_T(...algorithm='pari' silently uses normal evaluation because there is no _eval_pari_ member, so Pari was never supported.

[rwst]

Description changed:

--- 
+++ 
@@ -1 +1,3 @@
-While other orthogonal polynomial functions (as well as almost all other symbolic functions) are simply `BuiltinFunction`s or `GinacFunction`s this ticket suffers from the fact that the Cheby functions in Sage allow the `algorithm` keyword (by using a `__call__` method in the superclass). The way such polymorphisms are resolved in other functions is by having the interface (the callable global function `chebyshev_T()`) dispatching on the keyword. OTOH the call `chebyshev_T.eval_algebraic()` is expected to work. The only way this can be resolved and prepared for any deprecations is by having the `chebyshev` class not being a `Function` but creating such an object.
+While other orthogonal polynomial functions (as well as almost all other symbolic functions) are simply `BuiltinFunction`s or `GinacFunction`s this ticket suffers from the fact that the Cheby functions in Sage allow the `algorithm` keyword (by using a `__call__` method in the superclass). The way such polymorphisms are resolved in other functions is by having the interface (the callable global function `chebyshev_T()`) dispatching on the keyword, especially because doctests involving all kind of classes as function argument are expected to work eternally.
+
+The goal of this ticket is to move the `__call__` method out of the `Function` class (as well as other methods used as interface) into a separate interface class; to 2. make the remaining class inherit from `BuiltinFunction` and, 3., to remove the `ChebyshevFunction` superclass as it is then no longer used.

[rwst]

Description changed:

--- 
+++ 
@@ -1,3 +1,3 @@
-While other orthogonal polynomial functions (as well as almost all other symbolic functions) are simply `BuiltinFunction`s or `GinacFunction`s this ticket suffers from the fact that the Cheby functions in Sage allow the `algorithm` keyword (by using a `__call__` method in the superclass). The way such polymorphisms are resolved in other functions is by having the interface (the callable global function `chebyshev_T()`) dispatching on the keyword, especially because doctests involving all kind of classes as function argument are expected to work eternally.
+While other orthogonal polynomial functions (as well as almost all other symbolic functions) are simply `BuiltinFunction`s or `GinacFunction`s this ticket suffers from the fact that the Cheby functions in Sage allow the `algorithm` keyword (by using a `__call__` method in the superclass). The way such polymorphisms are resolved in other functions is by having the interface (the callable global function `chebyshev_T()`) dispatching on the keyword, especially because doctests involving all kind of Sage objects as function argument are expected to work eternally.
 
 The goal of this ticket is to move the `__call__` method out of the `Function` class (as well as other methods used as interface) into a separate interface class; to 2. make the remaining class inherit from `BuiltinFunction` and, 3., to remove the `ChebyshevFunction` superclass as it is then no longer used.

[rwst]

comment:5

Also the usage chebyshev_T(...algorithm='maxima') used normal evaluation. Maxima returns a polynomial in (x-1) which probably is useful so I'm changing doctests. In a later step this could be renamed to a more descriptive name and computed by Sage.

[rwst]

comment:6

Also eval_formula() should become algorithm='hypergeometric'. The Maxima "algorithm" is variant of it, see https://en.wikipedia.org/wiki/Chebyshev_polynomials#Explicit_expressions

[rwst]

Branch: u/rws/remove___call_____usage_in_chebyshev_functions

[sagetrac-git]

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

23190a6	24554: refactor chebyshev_U
2582330	24554: remove ChebyshevFunction

[sagetrac-git]

Commit: 2582330

[rwst]

Author: Ralf Stephan