SageAlpha
About
Enhanced solving of easier exercises from mathematical analysis (aimed at the difficulty level of freshmen students at the Faculty of Mathematics and Physics of the Charles University in Prague, Czech Republic).
Written in Python as a Sagemath's module.
Features
investigations descriptive investigation of a real-valued function
general properties (odd, even, periodic, constant)
properties of 1st derivative (stationary points, increasing/decreasing intervals)
properties of 2nd derivative (inflection points, convex/concave intervals)
asymptotes (horizontal, vertical & oblique, with explained calculation)
rendering the plot (with tangents at inflection points & autozoom option)
two output formats - text-based (console/notebook) & LaTeX-based (pdf document - example)
Versions
v1.0.0 (Sep 2012)
tested on Sage 5.1, Sage 5.0 and Sage 4.8
mostly working (known exceptions: monotonicity(myfunc7) ; investigations(x^5-x^3-x^2+x+1) )
download here or on https://github.com/mathemage/SageAlpha
Todo
undefined further causes of undefinition: negative arguments of square roots (and their fourth, sixth root analogies...), arcsin & arccos arguments...
stationary_points stationary points for x-values where 1st derivative is not defined
inflection_points dtto
asymptotes verify proper functionality of periodical (vertical) asymptotes - e. g. in tan(x)
monotonicity
either improve splitting points by adding stationary_points where 1st derivative is undefined
or find better way to locate these intervals (preferably using solve that will find intervals of positive/negative 1st derivative)
curvature dtto
investigations
simplify complex formulae of points for rendering in the plot (see TODO example in the docstring via investigations?)
beta-tests of periodical (vertical) asymptotes' rendering
more comprehensible comments/documentation for autozoom feature
tex_list line-wrapping of long formulae (or when there are simply too many of them, as well)
tex_investigations
more detailed step-by-step explanations (see TODO part in the docstring via tex_investigations?)
use of temporary files for LaTeX's source code (instead of fixed "/tmp/SageAlphaOut.tex")
option for deleting such a temporary file
texie other altenative versions (e. g. with Acrobat Reader, Evince...)
further functionalities - e. g.:
step-by-step solving of simpler integrals
convergence/divergence of easier power series (with tutorials on which criteria to use)
multidimensional stuff (implicit functions, Hessians, Lagrangians, ...)
...