airy Airy functions of the first and second kind, and their derivatives. airy(0,x) = Ai(x), airy(1,x) = Ai'(x), airy(2,x) = Bi(x), airy(3,x) = Bi'(x) besselj Bessel functions of the first kind. bessely Bessel functions of the second kind. besseli Modified Bessel functions of the first kind. besselk Modified Bessel functions of the second kind. besselh Compute Hankel functions of the first (k = 1) or second (k = 2) kind. beta The Beta function, beta (a, b) = gamma (a) * gamma (b) / gamma (a + b). betainc The incomplete Beta function, erf The error function, erfinv The inverse of the error function. gamma The Gamma function, gammainc The incomplete gamma function,
For example,
sage: octave("airy(3,2)") 4.10068 sage: octave("beta(2,2)") 0.166667 sage: octave("betainc(0.2,2,2)") 0.104 sage: octave("besselh(0,2)") (0.223891,0.510376) sage: octave("besselh(0,1)") (0.765198,0.088257) sage: octave("besseli(1,2)") 1.59064 sage: octave("besselj(1,2)") 0.576725 sage: octave("besselk(1,2)") 0.139866 sage: octave("erf(0)") 0 sage: octave("erf(1)") 0.842701 sage: octave("erfinv(0.842)") 0.998315 sage: octave("gamma(1.5)") 0.886227 sage: octave("gammainc(1.5,1)") 0.77687
The Octave interface reads in even very long input (using files) in a robust manner:
sage: t = '"%s"'%10^10000 # ten thousand character string. sage: a = octave.eval(t + ';') # < 1/100th of a second sage: a = octave(t)
Note that actually reading a back out takes forever. This *must* be fixed ASAP - see http://trac.sagemath.org/sage_trac/ticket/940/.
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