On 15 February 2016 at 15:01, Andrew Corrigan <andrew.corri...@gmail.com> wrote: > Thank you both for your replies. I'm not sure I follow the discussion to be > honest as to how it applies to my original problem. In particular: >>> >>> Distilling this down you want to compute the integral of the square >>> root of a quadratic > > I'm not sure that is accurate.
It is for the example you showed :). > If you are just referring to that it is > (foo(xi))**2 + (bar(xi))**2, then yes the expression is quadratic in foo > and bar. But in general, foo(xi) and bar(xi) are themselves higher degree > polynomials of xi (and in higher dimensions other coordinates too). This is > a very simple and minimal reproducing example: in this case foo and bar are > linear polynomials so the whole expression is quadratic. The example is not minimal. Much of your expression is a red herring with symbols that are unimportant to people reading on this list. A minimal example would be something like: sqrt(ax^2 + bx + c) > I have expressions > I need to integrate, where foo(xi) and bar(xi) are higher-order polynomials > terms of xi. If you want to do sqrt(P(x)) with P(x) polynomial of degree k then I think you can have general solutions for k=1,2,3 and 4 (assuming P(x) has no repeated roots). Sympy can do k=1 and should be able to do 2 with a bit of help. For 3 and 4 you want the elliptic integrals although maybe sympy doesn't do them yet. For k>4 there may be solutions for certain special cases of the polynomial coefficients. In general for a polynomial with symbolic coefficients I don't think that there exist well-known mathematical functions to represent the results. -- Oscar -- 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 https://groups.google.com/group/sympy. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/CAHVvXxT-s_h6M5AvXPF6mYgXDOD6By1_zXekZ1gynrk3KnGHog%40mail.gmail.com. For more options, visit https://groups.google.com/d/optout.
