Opened 7 years ago
Closed 4 years ago
#14326 closed defect (duplicate)
Substituting numeric one in symbolic expression gives symbolic one
Reported by: | zimmerma | Owned by: | AlexGhitza |
---|---|---|---|
Priority: | major | Milestone: | sage-duplicate/invalid/wontfix |
Component: | basic arithmetic | Keywords: | |
Cc: | mmezzarobba, burcin | Merged in: | |
Authors: | Reviewers: | ||
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description
consider the following in Sage 5.8:
sage: u(n) = n^100 / 100^n; u(1.) 1/100
This is inconsistent with:
sage: n=1.; n^100 / 100^n 0.0100000000000000
and with:
sage: v = lambda(n): n^100 / 100^n; v(1.) 0.0100000000000000
and:
sage: def w(n): return n^100 / 100^n sage: w(1.) 0.0100000000000000
Change History (17)
comment:1 Changed 7 years ago by
- Cc mmezzarobba added
comment:2 Changed 7 years ago by
comment:3 Changed 6 years ago by
- Milestone changed from sage-5.11 to sage-5.12
comment:4 Changed 6 years ago by
- Milestone changed from sage-6.1 to sage-6.2
comment:5 Changed 6 years ago by
- Milestone changed from sage-6.2 to sage-6.3
comment:6 Changed 5 years ago by
- Milestone changed from sage-6.3 to sage-6.4
comment:7 Changed 5 years ago by
- Cc burcin added
- Summary changed from function gives symbolic output for numeric input to Substituting numeric one in symbolic expression gives symbolic one
Wow, this is weird. Here is a much simpler example.
sage: w(n) = n sage: w(1.) 1.00000000000000 sage: w(n) = n^2 sage: w(1.) 1
In fact, even
sage: (x^2).subs(x=1.) 1
works. Yuck.
Somehow the custom power method is not doing its job when you substitute . But I don't see an obvious place in Ginac where this would get screwed up...
Aha.
sage: z = x^2 sage: z.subs(x=1.) 1 sage: z.subs(x=2.) 4.00000000000000
Because one does get treated differently. Though
sage: z = x sage: z.subs(x=1.) 1.00000000000000
so it also has something to do with the coercion that happens in the power method for symbolic expressions.
comment:8 Changed 5 years ago by
Okay, I think this might be a bug in Ginac, or possibly in how we use Ginac. In the Ginac definition of automatic rewriting of power::eval, we have
00399 // ^(x,1) -> x 00400 if (eexponent.is_equal(_ex1)) 00401 return basis; ... 00413 // ^(1,x) -> 1 00414 if (ebasis.is_equal(_ex1)) 00415 return _ex1;
The other rewriting rules are probably harmless, though if
sage: z x^n sage: z.subs(x=0.) 0.000000000000000^n sage: z.subs(x=0) 0^n sage: z.subs(n=0) 1 sage: z.subs(n=0.) 1
where the 0^n
business is because Ginac checks if the exponent is numerical because it doesn't want to evaluate something that could, in principle, still become 0^0
.
Unfortunately, I'm not sure how to monkey-patch Pynac into recognizing this situation, and I certainly don't want to do a catch in the symbolic expression code, that is really the wrong place. Here's hoping someone really intimately familiar with our back-and-forth to Pynac sees an easy fix.
comment:9 Changed 5 years ago by
The problem looks similar to #17130, but that's about __call__
.
comment:10 Changed 5 years ago by
do the patches from #17130 solve this ticket?
Paul
comment:11 follow-up: ↓ 12 Changed 5 years ago by
Dear Karl-Dieter,
I think this might be a bug in Ginac, or possibly in how we use Ginac.
please could you ask the Ginac developers if this is a bug in Ginac?
And if not, how to replace _ex1
to get the correct "one"?
Paul
comment:12 in reply to: ↑ 11 Changed 5 years ago by
I think this might be a bug in Ginac, or possibly in how we use Ginac.
please could you ask the Ginac developers if this is a bug in Ginac? And if not, how to replace
_ex1
to get the correct "one"?
I am really not familiar enough with Ginac proper to do either of these with any technical knowledge, unfortunately. And the Ginac developer(s) are not particularly responsive right now to any but the most informed pieces of information, apparently. If someone can figured out how to replicate this in Ginac that would be great, but again it could be us misusing it, I'm not sure.
I would be surprised if #17130 fixed this, based on my experiments above.
comment:13 follow-up: ↓ 14 Changed 5 years ago by
Looking at the code snippet from comment:8 only, I don't think this is a bug in Ginac. The intended behavior is just different in Pynac, so we have to patch Pynac.
Ginac wants to keep unique reference counted expression objects for expressions that are equal. That is why they return _ex1
on line 415. In Pynac, we do not have a unique "one", we should just return ebasis
in this line to keep the precision/type of the base.
comment:14 in reply to: ↑ 13 Changed 5 years ago by
Replying to burcin:
Thanks for replying!
Looking at the code snippet from comment:8 only, I don't think this is a bug in Ginac. The intended behavior is just different in Pynac, so we have to patch Pynac.
Ginac wants to keep unique reference counted expression objects for expressions that are equal. That is why they return
_ex1
on line 415. In Pynac, we do not have a unique "one", we should just returnebasis
in this line to keep the precision/type of the base.
Of course! That makes perfect sense - once you say it, before it was murky :(
What about for the other case, of x^1.0
? We have
sage: (x^2).subs(x=1.) 1 sage: (2^x).subs(x=1.) 2 sage: (x^2).subs(x=2.) 4.00000000000000 sage: (2^x).subs(x=2.) 4.00000000000000
so it would seem that if the exponent is not exact, we want the whole thing to be numerical. I guess we could just strip out that simplification completely, but I don't know if that would give us anything useful either.
comment:15 Changed 5 years ago by
- Milestone changed from sage-6.4 to sage-duplicate/invalid/wontfix
- Status changed from new to needs_review
comment:16 Changed 5 years ago by
- Status changed from needs_review to positive_review
comment:17 Changed 4 years ago by
- Resolution set to duplicate
- Status changed from positive_review to closed
Jeroen, do you have an idea who to include in cc to help isolate this?
Paul