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On 05/11/2011 02:08 PM, Arnold Neumaier wrote:
A computer algebra system will indeed see h=g in your case but there are many cases (e.g. involving sine,cosine) for which you will need to help it...If you want to be sure check with the computer the correctness of your formula and then let the computer write the essential part of your functions. Never write a piece of function code by hand..John Pryce wrote:Point A. -------- Interval implementations have to trust the user to get (*) right. Consider Arnold's example below, which can be written g(x)= (x1-x2)/(x1+x2) h(x) = 2/(1+x2/x1) - 1 where x = (x1,x2). A computer algebra system can easily see h is a rearrangement of g, so (*) holds; but no practical implementation will check this at run time--if I suggested such a thing, Nate would flatten me, and rightly so. So if there is a typo in the code, how will this be revealed?
JPM