Opened 9 years ago
Last modified 3 years ago
#8862 new defect
solve misses some solutions in a certain nonlinear system
Reported by: | casamayou | Owned by: | burcin |
---|---|---|---|
Priority: | major | Milestone: | sage-6.4 |
Component: | calculus | Keywords: | solve |
Cc: | kcrisman, robert.marik, jason | Merged in: | |
Authors: | Reviewers: | ||
Report Upstream: | Reported upstream. No feedback yet. | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: | #12730 |
Description
This function has four critical points : ±(0,1) and ±(1/e,0)
However the function solve can not find any of this.
More, solve returns (0,0) which is not a critical point since f is not differentiable at (0,0) !
sage: var('x y') sage: f(x,y) = (x^2 + y^2)^x sage: solve([diff(f(x,y), x), diff(f(x,y), y)], x, y) [[x == 0, y == 0]]
Change History (12)
comment:1 Changed 9 years ago by
- Milestone changed from sage-4.4.2 to sage-4.4.1
- Priority changed from minor to major
- Type changed from enhancement to defect
comment:2 Changed 9 years ago by
- Cc kcrisman robert.marik jason added
comment:3 follow-up: ↓ 4 Changed 9 years ago by
the issue here is not only that Sage returns undefined points (which indeed duplicates #2617) but that it fails to find the following (trivial) solutions, which is a defect:
sage: sys=[diff(f(x,y), x), diff(f(x,y), y)] sage: map(lambda s: s.subs(x=0,y=1),sys) [0, 0] sage: map(lambda s: s.subs(x=0,y=-1),sys) [0, 0] sage: map(lambda s: s.subs(x=1/e,y=0),sys) [0, 0] sage: map(lambda s: s.subs(x=-1/e,y=0),sys) [0, 0]
For example Maple finds:
> f := (x,y) -> (x^2 + y^2)^x: > solve({diff(f(x,y), x), diff(f(x,y), y)}, {x, y}, Explicit=true); exp(1) exp(1) {x = 0, y = 1}, {x = 0, y = -1}, {x = - ------, y = 0}, {x = ------, y = 0} exp(2) exp(2)
When some solutions are lost, at least a warning should be issued.
comment:4 in reply to: ↑ 3 Changed 9 years ago by
Replying to zimmerma:
the issue here is not only that Sage returns undefined points (which indeed duplicates #2617) but that it fails to find the following (trivial) solutions, which is a defect:
<snip>
When some solutions are lost, at least a warning should be issued.
I don't think we can get that information out of maxima. Can someone more experienced in maxima comment on this? Or ask the maxima developers what they think about this problem?
Another option is to take this as an opportunity to start implementing some native solve()
functionality in Sage. I have no idea how to (more or less algorithmically) find a solution to this system though. I'd appreciate any pointers.
comment:5 Changed 8 years ago by
- Report Upstream changed from N/A to Reported upstream. Little or no feedback.
- Summary changed from failing resolution of a nonlinear system by solve to solve misses some solutions in a certain nonlinear system
Maxima 5.23.2 http://maxima.sourceforge.net using Lisp ECL 11.1.1 Distributed under the GNU Public License. See the file COPYING. Dedicated to the memory of William Schelter. The function bug_report() provides bug reporting information. (%i1) solve([(2*x^2/(x^2 + y^2) + log(x^2 + y^2))*(x^2 + y^2)^x,2*x*y*(x^2 + y^2)^(x - 1)],[x,y]); (%o1) [[x = 0, y = 0]]
So still present in 4.7.alpha1.
This is a pretty straightforward Maxima bug/enhancement need.
The issue about it not being a critical point is irrelevant, since this is exactly equivalent to the uninterpreted
solve([(2*x^2/(x^2 + y^2) + log(x^2 + y^2))*(x^2 + y^2)^x,2*x*y*(x^2 + y^2)^(x - 1)],[x,y])
So the relevant problem is that it's returning something not in the domain of the functions in question, which is indeed a problem. In addition to not finding other solutions.
This is now Maxima bug 3216684.
comment:6 Changed 7 years ago by
- Stopgaps set to #12730
comment:7 Changed 7 years ago by
- Report Upstream changed from Reported upstream. Little or no feedback. to Reported upstream. No feedback yet.
comment:8 Changed 6 years ago by
- Milestone changed from sage-5.11 to sage-5.12
comment:9 Changed 5 years ago by
- Milestone changed from sage-6.1 to sage-6.2
comment:10 Changed 5 years ago by
- Milestone changed from sage-6.2 to sage-6.3
comment:11 Changed 5 years ago by
- Milestone changed from sage-6.3 to sage-6.4
comment:12 Changed 3 years ago by
Just a random comment: sympy can solve this. I tested it in the 'live shell' in their webpage:
solve([(x**2 + y**2)**x*(2*x**2/(x**2 + y**2) + log(x**2 + y**2)),2*(x**2 + y**2)**(x - 1)*x*y],x,y) [(0,−1),(0,1),(−1/e,0),(1/e,0)]
(I edited the output because copy&paste mangled it).
It would be nice to have an 'algorithm=sympy' option to solve(). It seems that nobody is working in the Maxima bug.
What is the expected improvement in this ticket?
The
solve()
function in Sage is just a wrapper around maxima for now. In this case we just return the result from maxima.There are two problems here:
If this ticket is about improving the capabilities of solve to handle the given input properly, this is an enhancement request. Do we know of any algorithm that will help with this?
Otherwise, this ticket is a duplicate of #2617.
Comments?