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.
On Friday, December 20, 2013 9:26:22 AM UTC+1, maldun wrote: > > On Thursday, December 19, 2013 7:47:19 PM UTC+1, Nils Bruin wrote: > >> On Wednesday, December 18, 2013 11:04:22 PM UTC-10, maldun wrote: >>> >>> What I mean is that we should only allow expressions of meromorphic >>> functions in the symbolic field, i.e. we would only allow variables, >>> trigonometric functions and so on. >>> SR should be then a superset where everything else should also be >>> allowed. >>> >> >> I think you'll find that category is a little too small to even just do >> first year calculus: even log(z) isn't meromorphic (at z=0). >> > > Good argument. Is it possible to reasonable relax the condition. E.g. > meromorphic almost everywhere in CC? > Alternatively extend the field of meromorphic functions to the > differential field (M,d/dz) (see > http://en.wikipedia.org/wiki/Differential_algebra#Differential_field) > Such a field can be extended by it's logarithms (so log(z) would be > contained) and all elementary functions also would be contained. > Additionally it's very useful > for symbolic differentiation and integration. > > >> > On Thursday, December 19, 2013 8:05:15 PM UTC+1, vdelecroix wrote: >> >> And meromorphic functions are not stable under composition... >> > > Is this really relevant for symbolic calculus? At least the composition is > closed. > -- 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.
