#11934: Symbolic simplification error
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Reporter: mjo | Owner: burcin
Type: defect | Status: new
Priority: major | Milestone: sage-4.7.3
Component: symbolics | Keywords:
Work_issues: | Upstream: N/A
Reviewer: | Author:
Merged: | Dependencies:
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Description changed by kcrisman:
Old description:
> 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))
> }}}
New description:
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))
}}}
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11934#comment:2>
Sage <http://www.sagemath.org>
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