#13836: Fix variable dependence in PiecewisePolynomial
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Reporter: christiankuper | Owner: burcin
Type: defect | Status: needs_work
Priority: major | Milestone: sage-5.6
Component: symbolics | Resolution:
Keywords: Piecewise, critical_points | Work issues:
Report Upstream: N/A | Reviewers: Burcin Erocal
Authors: Andrew Fleckenstein | Merged in:
Dependencies: | Stopgaps:
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Description changed by afleckenstein:
Old description:
> When using the example in the documentation of the function the following
> results are displayed for critical points:
>
> {{{
> sage: R.<x> = QQ[]
> sage: f1 = x^0
> sage: f2 = 10*x - x^2
> sage: f3 = 3*x^4 - 156*x^3 + 3036*x^2 - 26208*x
> sage: f = Piecewise([[(0,3),f1],[(3,10),f2],[(10,20),f3]])
> sage: f.critical_points()
> [5.0, 12.000000000000124, 12.999999999999725, 14.000000000000151]
> }}}
>
> When doing the same with y instead of x as a variable an empty list is
> returned as a result:
>
> {{{
> sage: R.<y> = QQ[]
> sage: f1 = y^0
> sage: f2 = 10*y - y^2
> sage: f3 = 3*y^4 - 156*y^3 + 3036*y^2 - 26208*y
> sage: f = Piecewise([[(0,3),f1],[(3,10),f2],[(10,20),f3]])
> sage: f.critical_points()
> []
> }}}
>
> This behavior does not change even if y is explicitly defined as the
> variable:
>
> {{{
> sage: f = Piecewise([[(0,3),f1],[(3,10),f2],[(10,20),f3]],y)
> sage: f.critical_points()
> []
> }}}
>
> IMHO it should be possible to optain correct results no matter what the
> name of the variable is.
New description:
When using the example in the documentation of the function the following
results are displayed for critical points:
{{{
sage: R.<x> = QQ[]
sage: f1 = x^0
sage: f2 = 10*x - x^2
sage: f3 = 3*x^4 - 156*x^3 + 3036*x^2 - 26208*x
sage: f = Piecewise([[(0,3),f1],[(3,10),f2],[(10,20),f3]])
sage: f.critical_points()
[5.0, 12.000000000000124, 12.999999999999725, 14.000000000000151]
}}}
When doing the same with y instead of x as a variable an empty list is
returned as a result:
{{{
sage: R.<y> = QQ[]
sage: f1 = y^0
sage: f2 = 10*y - y^2
sage: f3 = 3*y^4 - 156*y^3 + 3036*y^2 - 26208*y
sage: f = Piecewise([[(0,3),f1],[(3,10),f2],[(10,20),f3]])
sage: f.critical_points()
[]
}}}
This behavior does not change even if y is explicitly defined as the
variable:
{{{
sage: f = Piecewise([[(0,3),f1],[(3,10),f2],[(10,20),f3]],y)
sage: f.critical_points()
[]
}}}
The wrong variable is also used (to varying effects) in the functions
trapezoid() and derivative(). Multiple fourier series functions also use
the wrong variable, but it doesn't affect the result. The Laplace
transform also uses the wrong variable, but only if you aren't explicit
about it.
It should be possible to obtain correct results no matter what the name of
the variable is.
--
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13836#comment:8>
Sage <http://www.sagemath.org>
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and MATLAB
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