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On 08/17/2011 06:24 PM, Vincent Lefevre wrote:
On 2011-08-17 15:37:05 +0200, Arnold Neumaier wrote:On 08/17/2011 03:43 AM, Vincent Lefevre wrote: [in: Motion 26: NO]5.8.4 and 5.8.5 are very complicated and difficult to understand, and without better explanations, I'm not convinced that they are correct. Moreover 5.8.5 seems to be wrong on the following example: * xx = [-2,-1] * yy = Empty * f(x,y) = sqrt(x) + y One gets: * The decoration of xx from domain(xx) is bnd. * The decoration of yy from domain(yy) is emp. * For zz = sqrt((xx,bnd)), p_emp(sqrt,xx) holds, so that one chooses e = emp. Thus d = min{emp,bnd} = emp. * For zz + yy, if one applies (Eval3) directly as said in 5.8.5: one chooses e = con. Then d = min{con,emp,emp} = emp. But since the box (xx,yy) is empty, according to (8), the decoration of f(xx,yy) must be> emp, leading to a contradiction. So, it seems that (Eval1) was necessary here.Note that (as already discussed last year) before any function evaluation with decorations, domain must be called to set the correct initial decorations, which is designed to take care of situations with some empty input. Thus the specification is OK.This is exactly what I've done above: * The decoration of xx from domain(xx) is bnd. * The decoration of yy from domain(yy) is emp.
If you consider the steps described in 5.8.5, how can ein be generated?
Since you compute a function of two variables, you need to apply domain to the vector consisting of both variables, not to each variable separately!