These are very old methods that David Joyner put in Sage when there was virtually nothing for calculus - particularly pedagogical examples - in Sage. I believe they only work with the Piecewise class, and return Piecewise functions (which can't do much). In sage.functions.piecewise.py :
- David Joyner (2006-09): added __eq__, extend_by_zero_to, unextend, convolution, trapezoid, trapezoid_integral_approximation, riemann_sum, riemann_sum_integral_approximation, tangent_line fixed bugs in __mul__, __add__ You'll also notice that the examples in the doctest use polynomial rings - because the "symbolic ring" didn't yet exist at that point. Incidentally, this isn't a slam on the Piecewise stuff - it's just recognition that massive work by people to get Maxima and Pynac/Ginac into Sage properly has vastly improved its capabilities. So my opinion is that we should leave those alone for now. The Piecewise class needs a massive rewrite, because we really need good piecewise support; unfortunately those who have the expertise don't have the motivation and time, and those who have the motivation and time don't have the expertise to do so. This would be a great project for someone wanting to make a lasting impact - giving That doesn't mean we shouldn't have some good pedagogically motivated RS methods for any old functions, but that would be a somewhat bigger job (though certainly tractable for a single ticket). Probably http://wiki.sagemath.org/interact/calculus#Numericalintegralswithvariousrules would be good inspiration for that. @Marshall - I suppose you could write an equivalent RS for trapezoid, yes, but I haven't ever seen a treatment which talks about it that way. Simpson is the same, in my view. - kcrisman On Jan 12, 2:58 am, Francois Maltey <fmal...@nerim.fr> wrote: > Hello, > (and copy to Sage-edu)>>> Currently, both riemann_sum and > riemann_sum_integral_approximation > >>> does not support trapezoid mode. But instead there are separate > >>> function which computes these for trapezoid mode . > > >>> I am added this mode to both riemann_sum and > >>> riemann_sum_integral_approximation and wanted to take a vote on how > >>> many people think trapezoid function should stay, should be deprecated > >>> or completely deleted. > > I prefer very few functions with an optional parameter. > > In this case, I vote for an only one (if possible) function > numerical_integral with a new option in > the parameter algorithm (or method) > > algorithm="Riemann", algorithm="trapezoid" or algorithm="Simpson", > algorithm="GaussLegendre"... > > I don't find any riemann_sum_integral_approximation nor rieman_sum > functions in my 4.6 Sage. > > F. -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
