Doctest: Add more logic flags to more functions

[rwst]

Some functions are handled with some flags in https://github.com/pynac/pynac/blob/master/ginac/function.cpp#L1581

This should be extended (in Pynac) and doctests added (here). This ticket should list which questions can be answered definitely to the positive. To start:

• f(real).is_real() for f in sin/cos/tan/cot/sec/csc

Depends on #22219

CC: @videlec

Component: symbolics

Author: Ralf Stephan

Branch/Commit: 350580a

Reviewer: Vincent Delecroix

Issue created by migration from https://trac.sagemath.org/ticket/22155

[videlec]

comment:2

The gamma function

sage: gamma(pi).is_real()
False

You might also want to deal with is_positive which would be easily handled for analytic functions whose power series have non-negative coefficients.

Are there flags in ginac for properties like: "power series with non-negative coefficients", "power series with integer coefficients", etc?

[videlec]

comment:3

Hyperbolic trigonometric functions cosh/sinh/tanh and inverses arccosh/arcsinh/arctanh

sage: cosh(-3).is_real()
False
sage: cosh(-3).is_positive()
False

[videlec]

comment:4

But instead of hardcoding all these informations in functions, it would be better to actually deduce it from some other properties (like Taylor series as I suggested before).

[videlec]

comment:5

Will this approach be recursive, namely cos(exp(-3) + log(2)).is_real()?

[rwst]

comment:6

Replying to @videlec:

it would be better to actually deduce it from some other properties (like Taylor series as I suggested before).

Not possible. Taylor series are determined in general by differentiation. There is no builtin formula which we can inspect.

Will this approach be recursive, namely cos(exp(-3) + log(2)).is_real()?

Yes.

[dimpase]

comment:7

as discussed on sage-develop, the best way IMHO would be to be able to return
"Unknown" instead of false "False"...

[rwst]

comment:8

Replying to @dimpase:

as discussed on sage-develop, the best way IMHO would be to be able to return
"Unknown" instead of false "False"...

See #22162.

[rwst]

Dependencies: pynac-0.7.4

[rwst]

comment:9

Improvements in pynac/pynac@acec861

[rwst]

Branch: u/rws/add_more_logic_flags_to_more_functions

[videlec]

Commit: 4a7499b