Hi Peter, On 2018-12-30, Peter Luschny <peter.lusc...@gmail.com> wrote: > With Sage 8.4: > LargeSchroeder = SR((1 - x - sqrt(1 - 6*x + x^2))/(2*x))
Putting "SR" around the expression probably isn't needed, as by default x is a symbolic variable (of course this doesn't hold if you have defined x to be something else). > print(LargeSchroeder.taylor(x, 0, 6).list()) > print(LargeSchroeder.series(x, 6).list()) Why "print" (assuming that you are in an interactive session)? > Bug or feature? Moreover > > taylor? .. gives hints > series? .. Object `series` not found. It seems that you are confusing functions and methods. If you do LargeSchroeder.taylor? and LargeSchroeder.series?, you'll see documentation of both. Explanation: In addition to "taylor" being a method of symbolic expressions, it also is a function defined in Sage's global name space; this is not the case for "series", that's why "series?" doesn't give you an answer. Now for the differences of both methods: Unfortunately, the documentation of LargeSchroeder.series? isn't very clear. Apparently .taylor(x,0,6) returns a polynomial (or to be precise: A symbolic expression that looks like a polynomial but is not implemented as an element of a polynomial ring, which from my experience is a difference that is not sufficiently appreciated by most calculus students using computer algebra systems), whereas LargeSchroeder.series(x,6) returns a Laurent series, i.e., it contains negative exponents: sage: LargeSchroeder.series(x,6) (-1/2)*x^(-1) + 3/2 + 2*x + 6*x^2 + 22*x^3 + 90*x^4 + 394*x^5 + Order(x^6) sage: LargeSchroeder.taylor(x,0,6) 1806*x^6 + 394*x^5 + 90*x^4 + 22*x^3 + 6*x^2 + 2*x + 1 It surprises me that .series(x,6) has a pole (after all, LargeSchroeder's discontinuity in x=0 seems removable), so perhaps it's a bug, but perhaps it's a feature after all --- I cannot tell from the documentation if it is intended or not. Best regards, Simon -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at https://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
