On Friday, December 20, 2013 2:58:51 AM UTC-10, maldun wrote: > > Another more careful approach would be to start at the field of rational > functions and extend it step by step with algebraic and transcendental > functions, till we reach a field which is maximal under the available > symbolic expressions. > I hope you realize that you're going through the same steps as the mathematicians who have been involved in developing axiom, macsyma, maple, mathematica etc. before they settled for the mess that we have now? It may well be possible to come up with a better way of dealing with things, but you'll probably need a fundamentally new computational/representational insight to get it. And you'll probably not get something that is more appealing to beginners than the apparent simplicity of the pen-and-paper approach that SR takes to representing its elements (at least not at first).
If you're interested in taking an algebraic approach to the functions that arise from ordinary linear differential equations (and that includes a lot of the functions relevant for calculus) you should read up on Picard-Vessiot extensions. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/groups/opt_out.
