#13836: Fix variable dependence in PiecewisePolynomial
----------------------------------------------+-----------------------------
Reporter: christiankuper | Owner: burcin
Type: defect | Status: needs_review
Priority: major | Milestone: sage-5.9
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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Changes (by afleckenstein):
* status: needs_work => needs_review
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()
> []
> }}}
>
> A variable besides default_variable() is also used (to varying effects)
> in the functions trapezoid(), derivative(), tangent_line() and
> convolution(). The fourier series functions that find coefficients use a
> variable other than default_variable() in the code, but it doesn't affect
> output, and probably doesn't need to be changed. However, the
> _fourier_series_helper() function probably should be changed.
> {{{
> sage: y = var('y')
> sage: f(y) = y^2
> sage: f = Piecewise([[(-1, 1),f]])
> sage: f._fourier_series_helper(3, 1, lambda n: 1)
> -4*cos(pi*x)/pi^2 + cos(2*pi*x)/pi^2 + 1/3
> }}}
>
> It should be possible to obtain consistent results no matter what the
> name of the variable is.
>
> Reviewers: The final patch is trac_13836_piecewise_var_fix.patch. This is
> the only patch that needs to be reviewed, all other patches were works in
> progress.
>
> Apply :
> * [attachment:trac_13836_piecewise_var_fix.patch]
> * [attachment:trac_13836-rev.patch]
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()
[]
}}}
A variable besides default_variable() is also used (to varying effects) in
the functions trapezoid(), derivative(), tangent_line() and convolution().
The fourier series functions that find coefficients use a variable other
than default_variable() in the code, but it doesn't affect output, and
probably doesn't need to be changed. However, the _fourier_series_helper()
function probably should be changed.
{{{
sage: y = var('y')
sage: f(y) = y^2
sage: f = Piecewise([[(-1, 1),f]])
sage: f._fourier_series_helper(3, 1, lambda n: 1)
-4*cos(pi*x)/pi^2 + cos(2*pi*x)/pi^2 + 1/3
}}}
It should be possible to obtain consistent results no matter what the name
of the variable is.
Reviewers: The final patch is trac_13836_piecewise_var_fix.patch. This is
the only patch that needs to be reviewed, all other patches were works in
progress.
Apply :
* [attachment:trac_13836_piecewise_var_fix.patch]
* [attachment:trac_13836-rev-commit.patch]
--
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13836#comment:35>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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