Addendum: I suppose a general query would be how do we incorporate new knowledge into Sage (narrowing this down to things like (a) closed form expressions of integrals (b) well known expressions of finite or infinite sums (c) well known solutions of equations such as the previous message
Is it a matter of identifying the area (e.g. pynac, pari, maxima) and proposing a change to that codebase (possibly in C or Lisp)? On Apr 23, 11:27 am, Ross Kyprianou <ros...@gmail.com> wrote: > Question 1: > Is it possible (and reasonable) to have the error function, erf, > return 0 for "erf(0)"? > Currently it returns the expression: erf(0) > > Question 2 (related): > The standard normal (or Gaussian) curve has half its (unit) area to > the left (and right) of x==0 as we see here... > sage: gaussian = 1/sqrt(2*pi)*exp( -(1/2)*x^2 ) > sage: integrate( gaussian, x, -oo, 0) > 1/2 > > To find the value of t for which the area is 1/2 we might try > sage: solve( integrate(gaussian, x, -oo, t)==1/2, t ) > > Unfortunately we get the expression > [erf(1/2*sqrt(2)*t) == 0] > > which for t==0 reduces to erf(0) which ideally would reduce to 0 hence > Question 1 above ;-) > I suppose Question 2 is: > Although the erf doco suggests this is all done with PARI, is it > possible for [erf(1/2*sqrt(2)*t) == 0] to be made to reduce to > [t==0]? > > -- > 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 athttp://groups.google.com/group/sage-devel > URL:http://www.sagemath.org -- 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
