Dear All, I fear I definitively misunderstand the algebra code, and I'm always bored with the asin sin x = x for usual mathematics. But am I a little right in this knowledge :
So when I grep asin in algebra directory, I find 3 interesting files : efstruc.spad, elemntry.spad and trigcat.spad. You correct a bug in trigcat.spad and axiom becomes a little better... // A // I understand that trigcat.spad file and this patch describe the category of a ring with /, sqrt, pi and atan. This ring can be formal or numeric. In this case we can compute asin from atan without divide by 0. It's the case for asin (1::Complex Float). // B // The algebra transforms of asin in Expression R are in elementry.spad, and uses iasin or iiasin. If there is a asin function in R then axiom tries this asin in R in iiasin function, by example in Expression Complex Float. For others basic rings as Integer axiom uses the iasin function with the tips asin sin x = x. This is coded in a package but this code can be used by every ExpressionS domains not only the only one existing Expression R. This code uses the test x=+/-1 and not the better? test one? x or one? (-x). The patch bellow allows asin (1::Expression Complex Float). // C // The efstruc.* files and its EFSTRUC package are inner packages for Rish algorithms. The only arcTrigonometric functions for Rish quadrature is the atan function. The Risch algorithm is almost magic for me, I don't analyse this code. ---- What errors can appear if the asin sin x test and others are removed ? The expand functions are in manip.spad : they use that expressions look like Fraction Polynomial Kernel, but only recursive polynomial are possibles, not developped polynomial. Many thanks if you read until this line. François --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To post to this group, send email to [email protected] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/fricas-devel?hl=en -~----------~----~----~----~------~----~------~--~---
