Modular form plotting fails because modular forms (power series) cannot be evaluated at floats

[alexjbest]

If one tries to plot a modular form the plot code tries to evaluate the modular form as a function on floats, which fails. Essentially this boils down to floats not having a .parent() (see traceback at end).

There are two potential fixes, neither of which I had opportunity to test yet, but would like thoughts on:

• Modify the line Q = a.parent() of src/sage/rings/power_series_poly.pyx to something like

         from sage.structure import parent
         Q = parent(a)

which might make power series a bit more resilient to being passed python types as input, this might be a change which should be made across a lot of Sage in that case?

• Or modify plotting code (generate_plot_points) to not use floats, I guess this might come with some performance hit to plotting.

sage: modf = ModularForms(12).basis()[0]
sage: plot(modf)
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
<ipython-input-2-f871686f0b17> in <module>()
----> 1 plot(modf)

/Users/alex/sage/local/lib/python2.7/site-packages/sage/misc/decorators.pyc in wrapper(*args, **kwds)
    565                 options['__original_opts'] = kwds
    566             options.update(kwds)
--> 567             return func(*args, **options)
    568
    569         #Add the options specified by @options to the signature of the wrapped

/Users/alex/sage/local/lib/python2.7/site-packages/sage/plot/plot.pyc in plot(funcs, *args, **kwds)
   1954             xmin = kwds.pop('xmin', -1)
   1955             xmax = kwds.pop('xmax', 1)
-> 1956             G = _plot(funcs, (xmin, xmax), **kwds)
   1957
   1958         # if there is one extra arg, then it had better be a tuple

/Users/alex/sage/local/lib/python2.7/site-packages/sage/plot/plot.pyc in _plot(funcs, xrange, parametric, polar, fill, label, randomize, **options)
   2264         data = generate_plot_points(f, xrange, plot_points,
   2265                                     adaptive_tolerance, adaptive_recursion,
-> 2266                                     randomize)
   2267
   2268

/Users/alex/sage/local/lib/python2.7/site-packages/sage/plot/plot.pyc in generate_plot_points(f, xrange, plot_points, adaptive_tolerance, adaptive_recursion, randomize, initial_points)
   3862
   3863         try:
-> 3864             data[i] = (float(xi), float(f(xi)))
   3865             if str(data[i][1]) in ['nan', 'NaN', 'inf', '-inf']:
   3866                 msg = "Unable to compute f(%s)" % xi

/Users/alex/sage/local/lib/python2.7/site-packages/sage/modular/modform/element.pyc in __call__(self, x, prec)
    174             0
    175         """
--> 176         return self.q_expansion(prec)(x)
    177
    178     @cached_method

/Users/alex/sage/local/lib/python2.7/site-packages/sage/rings/power_series_poly.pyx in sage.rings.power_series_poly.PowerSeries_poly.__call__ (build/cythonized/sage/rings/power_series_poly.c:5702)()
    320             return self.__f(x)
    321
--> 322         Q = a.parent()
    323
    324         from sage.rings.padics.padic_generic import pAdicGeneric

AttributeError: 'float' object has no attribute 'parent'

Component: graphics

Keywords: plotting, modular forms, python types

Issue created by migration from https://trac.sagemath.org/ticket/26317