### SageAlpha

 AboutEnhanced 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.Featuresinvestigations   descriptive investigation of a real-valued functiongeneral 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)Versionsv1.0.0   (Sep 2012)tested on Sage 5.1, Sage 5.0 and Sage 4.8mostly working (known exceptions: `monotonicity``(myfunc7)` ; `investigations(x^5-x^3-x^2+x+1)` )download here or on https://github.com/mathemage/SageAlphaTodoundefined   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 definedinflection_points   dttoasymptotes   verify proper functionality of periodical (vertical) asymptotes - e. g. in tan(x)monotonicityeither improve splitting points by adding `stationary_points` where 1st derivative is undefinedor find better way to locate these intervals (preferably using `solve` that will find intervals of positive/negative 1st derivative)curvature   dttoinvestigationssimplify complex formulae of points for rendering in the plot (see TODO example in the docstring via `investigations?`)beta-tests of periodical (vertical) asymptotes' renderingmore comprehensible comments/documentation for autozoom featuretex_list  line-wrapping of long formulae (or when there are simply too many of them, as well)tex_investigationsmore 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 filetexie  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, ...)...
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SageAlpha.sage
(51k)
Karel Ha,
Sep 24, 2012, 1:40 PM
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Karel Ha,
Sep 23, 2012, 5:46 AM