Opened 3 years ago
Closed 16 months ago
#21201 closed enhancement (wontfix)
Add a global is_trivial_zero function
Reported by:  arminstraub  Owned by:  

Priority:  major  Milestone:  sageduplicate/invalid/wontfix 
Component:  symbolics  Keywords:  
Cc:  nbruin, vdelecroix, mmezzarobba  Merged in:  
Authors:  Ralf Stephan  Reviewers:  
Report Upstream:  N/A  Work issues:  
Branch:  u/rws/add_a_global_is_trivial_zero_function (Commits)  Commit:  7241f8e926fc2349c2d62e0911975db4f75f46db 
Dependencies:  Stopgaps: 
Description (last modified by )
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
.
Change History (14)
comment:1 Changed 3 years ago by
comment:2 Changed 18 months ago by
 Branch set to u/rws/add_a_global_is_trivial_zero_function
comment:3 Changed 18 months ago by
 Cc nbruin vdelecroix added
 Commit set to 7241f8e926fc2349c2d62e0911975db4f75f46db
 Description modified (diff)
 Milestone set to sage8.2
 Status changed from new to needs_review
New commits:
7241f8e  21201: global is_trivial_zero

comment:4 Changed 18 months ago by
 Cc mmezzarobba added
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.
comment:5 followup: ↓ 6 Changed 18 months ago by
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.
comment:6 in reply to: ↑ 5 Changed 18 months ago by
Replying to rws:
FYI, about 320 files under
src/sage
have doctests that, directly or indirectly, callExpression.__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...
comment:7 Changed 18 months ago by
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.
comment:8 Changed 18 months ago by
So in every case (e.g. in polynomial_element.pyx) the code has to check for expression, and call that member function?
comment:9 in reply to: ↑ description ; followup: ↓ 10 Changed 18 months ago by
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 globalis_trivial_zero
that explicity requests the object'sis_trivial_zero
member if it exists, otherwise checksobj==0
.
Just to be sure: what do you mean by "check if numeric zero": check if something seems to be zero based on it numerical evaluation, or check if is syntactically zero? If the latter: yes, this is a very useful feature to have, for many, many types of objects. But in the case of SR
, is there any strong reason to have ==
do more than check for syntactic equality?
comment:10 in reply to: ↑ 9 ; followup: ↓ 11 Changed 18 months ago by
Replying to mmezzarobba:
Just to be sure: what do you mean by "check if numeric zero": check if something seems to be zero based on it numerical evaluation, or check if is syntactically zero? If the latter: yes, this is a very useful feature to have, for many, many types of objects. But in the case of
SR
, is there any strong reason to have==
do more than check for syntactic equality?
Clearly not but unfortunately bool()
with symbolic arguments does more by default. Please see https://trac.sagemath.org/wiki/symbolics/nonzero for a summary. The goal is to design a better interface to the existing functionality.
comment:11 in reply to: ↑ 10 Changed 18 months ago by
Replying to rws:
Clearly not but unfortunately
bool()
with symbolic arguments does more by default.
Well, IMO (though I haven't really thought it through):
bool(expr)
should returnFalse
iffexpr
is exactlySR(0)
, without any simplification, even trivial ones,expr == 0
should returnTrue
whenbool(expr)
returnsFalse
, and may returnTrue
in some cases where trivial simplifications show thatexpr
is zero, but shouldn't perform any nontrivial computation (I would say simplifyingx  x
to zero is okay, attempting to expand a polynomial is not—but this is of course debatable), there should be methods
expr.foo()
that attempt to prove thatexpr
is zero (e.g. by simplifying it), thatexpr
is nonzero (e.g. by substituting values for the variable and performing interval evaluation), thatexpr
could be zero (for some values of the variables), and probably more. At least some variants of these methods should take into account assumptions on the variables. I'm not sure what exact set of such methods would be needed, whether they should return plain booleans or useUnknown
, nor how they should be named (and in particular, whether using the namesis_zero()
andis_nonzero()
would conflict with their semantics elsewhere in Sage).
comment:12 Changed 18 months ago by
That is pretty much in line with #19162, and I find William Stein's suggestion of expr.is_zero(simplify=False/True)
an especially good idea.
comment:13 Changed 18 months ago by
 Milestone changed from sage8.2 to sageduplicate/invalid/wontfix
 Status changed from needs_review to positive_review
The original ticket will not be implemented.
comment:14 Changed 16 months ago by
 Resolution set to wontfix
 Status changed from positive_review to closed
closing positively reviewed duplicates
A plan would be in symbolics to use a fast zero comparison like the one in
comparison.pyx:mixed order
inis_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 booleanis_zero
and therefore should have a new name. Having a globalis_trivial_zero
would fit with this.