1994 paper by Adam Dingle and Richard Fateman Branch Cuts in Computer Algebra, (ISSAC '94 proceedings. also search online).
When you say things about sqrt(), does it generalize to cuberoot? If it does not, you are in trouble, or will be down the road. What is the principal value of (1)^(1/6) ? Several systems have RootOf( ...) expressions. e.g. RootOf(s^2=x, s). There are 2 values for s. What systems? Maple Macsyma Axiom/Fricas Mathematica probably others. You think you can use sqrt because the quadratic formula says -b+-sqrt(b^2....) etc. So you think you know what sqrt means. But in that formula you can switch the values +- and the formula is still valid. How many other formulas do you expect to fiddle with where that is true? Certainly not this one: sqrt(y^2) = abs(y). So if you go off and do the wrong thing, it is probably prudent to understand that you are doing the wrong thing. Beyond that, you are certainly free to do it. RJF On Sunday, December 7, 2014 2:33:20 AM UTC-8, Joachim Durchholz wrote: > > Am 06.12.2014 um 21:01 schrieb Aaron Meurer: > > Something that I'm not sure about with representing functions as > > multivalued is, how do you represent arbitrary Riemann surfaces. > > > > Another question is computational. How do you compute the surfaces in > > general (say even for a limited class of expressions, like algebraic > > functions), and how do you make cuts in a consistent manner? > > I do not thing that consistent cuts are a well-defined concept in the > first place. > Consider having sin 2x and sin x in the same expression. (Or something > equivalent in log and exp.) > Things become more, er, interesting with more free variables (x, y, z, > ...) > > To catch all equalities: > - Parameterize them all with an integer. > - For n integer parameters, search Z^n (exploiting periods). > > This might turn out to be too slow to be useful. > OTOH it might help with some simplifications. > > > The only thing I can think of is to write everything in terms of exp() > > and log() and parameterized integers, > > Can everything be broken down into this? > I'd have expected that not, since the cardinality of the set of > functions isn't countable, but maybe it's just that all practically > relevant expressions can be broken down that way, or maybe there's some > result that indeed everything multivalued can be written that way. > -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to sympy+unsubscr...@googlegroups.com. To post to this group, send email to sympy@googlegroups.com. Visit this group at http://groups.google.com/group/sympy. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/bfcb90b3-1513-48e9-8ea1-0a942bec52a1%40googlegroups.com. For more options, visit https://groups.google.com/d/optout.
