#11934 closed defect (fixed)
Symbolic simplification error
Reported by: | mjo | Owned by: | burcin |
---|---|---|---|
Priority: | major | Milestone: | sage-5.13 |
Component: | symbolics | Keywords: | |
Cc: | Merged in: | sage-5.13.rc0 | |
Authors: | Michael Orlitzky | Reviewers: | Jeroen Demeyer |
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description (last modified by )
I ran into this today with a real function. Sorry I don't have a shorter test case. The attached file should show a simplification which, as far as I can tell, is invalid.
sage: f = QQ(0.25)*(sqrt(2) - 2)*(x + 1)*x**3 - QQ(3)/QQ(8)*(sqrt(2) - 2)*(x + 1)*x**2 - QQ(0.25)*(sqrt(2) - 2)*(2*(3*sqrt(2) - 2)*x**2 - 2*(sqrt(2) - 1)*x + sqrt(-8*(4*sqrt(2) - 7)*x**4 + 16*(3*sqrt(2) - 5)*x**3 - 8*(2*sqrt(2) - 3)*x - 4*x**2 + 4) - 4*sqrt(2) + 2)*x**3/(sqrt(2)*x**2 + sqrt(2)*x - 2*sqrt(2)) - 1/24*(x + 1)**3*(x**3 - 3*x + 2) + QQ(3)/QQ(8)*(sqrt(2) - 2)*(2*(3*sqrt(2) - 2)*x**2 - 2*(sqrt(2) - 1)*x + sqrt(-8*(4*sqrt(2) - 7)*x**4 + 16*(3*sqrt(2) - 5)*x**3 - 8*(2*sqrt(2) - 3)*x - 4*x**2 + 4) - 4*sqrt(2) + 2)*x**2/(sqrt(2)*x**2 + sqrt(2)*x - 2*sqrt(2)) - QQ(1)/QQ(16)*(x + 1)**2*(2*(sqrt(2) - 3)*x**3 - (3*sqrt(2) - 8)*x**2 + 2*x + sqrt(2) - 4) + QQ(1)/QQ(8)*(x + 1)*sqrt(2) + QQ(1)/QQ(96)*(x**3 - 3*x + 2)*(2*(3*sqrt(2) - 2)*x**2 - 2*(sqrt(2) - 1)*x + sqrt(-8* (4*sqrt(2) - 7)*x**4 + 16*(3*sqrt(2) - 5)*x**3 - 8*(2*sqrt(2) - 3)*x - 4*x**2 + 4) - 4*sqrt(2) + 2)**3/(sqrt(2)*x**2 + sqrt(2)*x - 2*sqrt(2))**3 + 1/32*(2*(3*sqrt(2) - 2)*x**2 - 2*(sqrt(2) - 1)*x + sqrt(-8*(4*sqrt(2) - 7)*x**4 + 16*(3*sqrt(2) - 5)*x**3 - 8* (2*sqrt(2) - 3)*x - 4*x**2 + 4) - 4*sqrt(2) + 2)**2*(2*(sqrt(2) - 3)*x**3 - (3*sqrt(2) - 8)*x**2 + 2*x + sqrt(2) - 4)/(sqrt(2)*x**2 + sqrt(2)*x - 2*sqrt(2))**2 - QQ(0.25)*x - QQ(1)/QQ(8)*(2*(3*sqrt(2) - 2)*x**2 - 2*(sqrt(2) - 1)*x + sqrt(-8*(4*sqrt(2) - 7)*x**4 + 16*(3*sqrt(2) - 5)*x**3 - 8*(2*sqrt(2) - 3)*x - 4*x**2 + 4) - 4*sqrt(2) + 2)*sqrt(2)/(sqrt(2)*x**2 + sqrt(2)*x - 2*sqrt(2)) + QQ(0.25)*(2*(3*sqrt(2) - 2)*x**2 - 2* (sqrt(2) - 1)*x + sqrt(-8*(4*sqrt(2) - 7)*x**4 + 16*(3*sqrt(2) - 5)*x**3 - 8*(2*sqrt(2) - 3)*x - 4*x**2 + 4) - 4*sqrt(2) + 2)/(sqrt(2)*x**2 + sqrt(2)*x - 2*sqrt(2)) - QQ(0.25) sage: f.full_simplify() -1/24*(sqrt(2)*x^8 - 2*(sqrt(2) - 3)*x^7 - (14*sqrt(2) - 15)*x^6 + 10*(9*sqrt(2) - 13)*x^5 - (93*sqrt(2) - 128)*x^4 - 4*(9*sqrt(2) - 14)*x^3 + (58*sqrt(2) - 77)*x^2 + 4* (sqrt(2) - 2)*x - sqrt(2*(4*sqrt(2) - 7)*x^2 + 4*(sqrt(2) - 2)*x - 1)*((16*I*sqrt(2) - 28*I)*x^4 + (-24*I*sqrt(2) + 40*I)*x^3 + (8*I*sqrt(2) - 12*I)*x + 2*I*x^2 - 2*I) - 8*sqrt(2) + 10)/(sqrt(2)*x^2 + 4*sqrt(2)*x + 4*sqrt(2))
Attachments (2)
Change History (13)
Changed 9 years ago by
comment:1 follow-up: ↓ 3 Changed 9 years ago by
- Description modified (diff)
Can you be more specific about the invalidity? I think the plot errors are because of the imaginary pieces. Remember, these simplifications are not supposed to be 100 percent valid at all times; especially with roots there are branch issues, unfortunately. The f
in question is pretty long - any sense as to where it might simplify in an unusual way?
comment:2 Changed 9 years ago by
- Description modified (diff)
comment:3 in reply to: ↑ 1 Changed 9 years ago by
Replying to kcrisman:
Can you be more specific about the invalidity?
This seems to be the root of the problem. My function is real, the simplification is not:
sage: n(f(x=-0.5)) 0.0175781250000000 sage: n(f.full_simplify()(x=-0.5)) 0.0175781250000000 - 1.27567374911183e-18*I
I realize that the imaginary part is basically zero, but one of the simplifications has overstepped its bounds somewhere in that the expression is verifiably different pre- and post-simplification.
comment:5 Changed 9 years ago by
- Dependencies set to #12322
- Milestone set to sage-5.0
- Status changed from new to needs_review
comment:6 follow-up: ↓ 7 Changed 7 years ago by
- Status changed from needs_review to needs_info
I'm questioning whether this really is fixing anything. First, it's still there with simplify_radical
.
sage: f = sqrt(-8*(4*sqrt(2) - 7)*x^4 + 16*(3*sqrt(2) - 5)*x^3) sage: f.subs(x=-1/2).n() 1.47861134210963 sage: f.simplify_radical().subs(x=-1/2).n() 1.47861134210963 - 9.05388323648765e-17*I
Secondly, the problem is really this. Notice I'm not simplifying anything at all here.
sage: h = I*x^(1/2) sage: h(x=-1/2) I*sqrt(-1/2) sage: h(x=-1/2).n() -0.707106781186548 + 4.32978028117747e-17*I
Needs work/info, but not because of your patch or #12737, but rather because this doesn't really treat the underlying issue. This could just be some floating point thing that is inherently impossible to avoid once one allows complex numbers (and since your original example is complex sometimes, the answers are going to be complex, unfortunately).
comment:7 in reply to: ↑ 6 Changed 7 years ago by
Replying to kcrisman:
Needs work/info, but not because of your patch or #12737, but rather because this doesn't really treat the underlying issue. This could just be some floating point thing that is inherently impossible to avoid once one allows complex numbers (and since your original example is complex sometimes, the answers are going to be complex, unfortunately).
There aren't any floating point issues if you don't call n()
on anything. The issue is still there with simplify_radical()
, but that's because simplify_radical()
is broken by design: it chooses a branch arbitrarily for the square root. This is what radcan()
in Maxima is documented to do, but if you re-brand it as a simplification, it's a bug.
Plain simplify()
works:
sage: f = sqrt(-8*(4*sqrt(2) - 7)*x^4 + 16*(3*sqrt(2) - 5)*x^3) sage: f.simplify() sqrt(-8*(4*sqrt(2) - 7)*x^4 + 16*(3*sqrt(2) - 5)*x^3)
As does simplify_trig()
:
sage: f.simplify_trig() sqrt(-8*(4*sqrt(2) - 7)*x^4 + 16*(3*sqrt(2) - 5)*x^3)
And simplify_rational()
:
sage: f.simplify_rational() sqrt(-8*(4*sqrt(2) - 7)*x^4 + 16*(3*sqrt(2) - 5)*x^3)
And simplify_log()
:
sage: f.simplify_log() sqrt(-8*(4*sqrt(2) - 7)*x^4 + 16*(3*sqrt(2) - 5)*x^3)
It's only simplify_radical()
that messes everything up (note I haven't called n()
anywhere, so there are no numerical issues):
sage: f.simplify_radical() 2*I*sqrt((4*sqrt(2) - 7)*x - 6*sqrt(2) + 10)*sqrt(2)*x^(3/2)
I don't want a random branch of the square root when I ask for a simplification. I want a simplification, but only if possible! Without more information, you can't simplify that expression. The rest of the simplify functions don't do anything, but that's the correct thing to do here.
comment:8 Changed 7 years ago by
- Milestone changed from sage-5.11 to sage-5.12
comment:9 Changed 7 years ago by
- Status changed from needs_info to needs_review
I just uploaded a slightly better doctest now that this is fixed.
comment:10 follow-up: ↓ 11 Changed 7 years ago by
- Dependencies #12322 deleted
- Merged in set to sage-5.13.rc0
- Resolution set to fixed
- Reviewers set to Jeroen Demeyer
- Status changed from needs_review to closed
This doesn't seem to depend on #12322 at all.
A sage file that displays and attempts to plot the simplification