rhbartels@watcgl.UUCP (Richard Bartels) (02/20/86)
For those of you who kindly replied, this is the state of the experience to date in plotting infinite ranges. The "Maple" system referred to is a symbolic algebra system under development here at Waterloo... ---------------------------------------------------------------------------- I am now using the latest transformation adopted as follows -1-1/x -inf .. -2 x/4 -2 .. 2 1-1/x 2 .. inf I note that at the joints (x = -2,2) this transformation is C1 continuous only. But it is much cheaper to compute relative to computing arctan(x) in Maple. Also that asymptotically, the above looks the same as arctan(x) which is Pi/2 -1/x + O(1/x^3) . Compare these with tanh(x) and x/sqrt(1-x^2) which do not have an O(1/x) term in their assymptotic expansions, and hence converge "too fast" to the limits +-1 as x ==> +-infinity. Tanh(x) converges so fast ( ~= 1 - 2 exp(-2*x) + ...) that one might as well display the range -3..3 and be done with it cause the rest gets squashed into the last pixel width.