Add a global is_trivial_zero function

[arminstraub]

Some rings have a polymorphic comparison with zero, e.g., comparison in SR can mean 1. "try to prove with certainty" or 2. "check if numeric zero". Other rings may have different features. This ticket implements a global is_trivial_zero that explicity requests the object's is_trivial_zero member if it exists, otherwise checks obj==0.

CC: @nbruin @videlec @mezzarobba

Component: symbolics

Author: Ralf Stephan

Branch/Commit: u/rws/add_a_global_is_trivial_zero_function @ 7241f8e

Issue created by migration from https://trac.sagemath.org/ticket/21201

[rwst]

comment:1

A plan would be in symbolics to use a fast zero comparison like the one in comparison.pyx:mixed order in is_zero and additionally change the expensive symbolic zero comparison (the main code is in __nonzero__, see also #19040) to something being able to return Yes/No/Maybe, which is incompatible with the global boolean is_zero and therefore should have a new name. Having a global is_trivial_zero would fit with this.

[rwst]

Branch: u/rws/add_a_global_is_trivial_zero_function

[rwst]

Commit: 7241f8e

[rwst]

Description changed:

--- 
+++ 
@@ -1,14 +1 @@
-`expr.is_trivial_zero()` is designed as a fast way to check whether an expression `expr` is zero (whereas `expr == 0` can be expensive and may, via `Expression.__nonzero__`, even end up calling Maxima).
-
-A common use case, for instance, in the evaluation of special functions (see #17678 for an example) is to have special code if an argument, say, `x` is zero (or some other fixed value).  In many places, this is done using just `if x == 0:`, which works fine in simple examples but can be expensive is `x` is a complicated expression. To avoid that issue, `if not isinstance(x, Expression) and x == 0:` is sometimes used (in `Hypergeometric_M._eval_`, for instance). Another solution might be `(isinstance(sth, Expression) and sth.is_trivial_zero()) or (not isinstance(sth, Expression) and sth == 0)` but that's not brief and convenient enough to actually use.
-
-Would it be beneficial to have a global function `is_trivial_zero` for such purposes?  So that, in the above example, one could use `is_trivial_zero(x)` without worrying about the type of `x`. One possible implementation could be:
-
-```
-def is_trivial_zero(x):
-    try: return x.is_trivial_zero()
-    except AttributeError: return x == 0
-```
-
-A place for such a function might be `sage/misc/functional.py` which already contains things like `is_even` (which I used as a blueprint here). (But see #17158.)
-
+Some rings have a polymorphic comparison with zero, e.g., comparison in `SR` can mean 1. "try to prove with certainty" or 2. "check if numeric zero". Other rings may have different features. This ticket implements a global `is_trivial_zero` that explicity requests the object's `is_trivial_zero` member if it exists, otherwise checks `obj==0`.

[rwst]

Author: Ralf Stephan

[rwst]

New commits:

7241f8e

21201: global is_trivial_zero

[videlec]

comment:4

I am against such a terrible name in the global namespace that is furthermore almost not specified.

Though it would be good to design a general solution for the different semantics of equality.

[rwst]

comment:5

FYI, about 320 files under src/sage have doctests that, directly or indirectly, call Expression.__nonzero__. A quick glance shows in most cases a simplification/proof of equality is not needed.

[videlec]

comment:6

Replying to @rwst:

FYI, about 320 files under src/sage have doctests that, directly or indirectly, call Expression.__nonzero__. A quick glance shows in most cases a simplification/proof of equality is not needed.

This is a bad measure. And anway, 320 files is 12% of the number of files in the Sage source tree...

[videlec]

comment:7

You aim to introduce a feature that concerns only the symbolic ring. Then simply implement it as a method of SR (or the elements of SR). Ne need to clutter even more the global namespace.