5.12 Predefined mathematical functions

5.12.1 Overview

GiNaC contains the following predefined mathematical functions:

Name Function abs(x) absolute value step(x) step function csgn(x) complex sign conjugate(x) complex conjugation real_part(x) real part imag_part(x) imaginary part sqrt(x) square root (not a GiNaC function, rather an alias for pow(x, numeric(1, 2))) sin(x) sine cos(x) cosine tan(x) tangent asin(x) inverse sine acos(x) inverse cosine atan(x) inverse tangent atan2(y, x) inverse tangent with two arguments sinh(x) hyperbolic sine cosh(x) hyperbolic cosine tanh(x) hyperbolic tangent asinh(x) inverse hyperbolic sine acosh(x) inverse hyperbolic cosine atanh(x) inverse hyperbolic tangent exp(x) exponential function log(x) natural logarithm Li2(x) dilogarithm Li(m, x) classical polylogarithm as well as multiple polylogarithm G(a, y) multiple polylogarithm G(a, s, y) multiple polylogarithm with explicit signs for the imaginary parts S(n, p, x) Nielsen's generalized polylogarithm H(m, x) harmonic polylogarithm zeta(m) Riemann's zeta function as well as multiple zeta value zeta(m, s) alternating Euler sum zetaderiv(n, x) derivatives of Riemann's zeta function tgamma(x) gamma function lgamma(x) logarithm of gamma function beta(x, y) beta function (tgamma(x)*tgamma(y)/tgamma(x+y)) psi(x) psi (digamma) function psi(n, x) derivatives of psi function (polygamma functions) factorial(n) factorial function n! binomial(n, k) binomial coefficients Order(x) order term function in truncated power series

For functions that have a branch cut in the complex plane GiNaC follows the conventions for C++ as defined in the ANSI standard as far as possible. In particular: the natural logarithm (log) and the square root (sqrt) both have their branch cuts running along the negative real axis where the points on the axis itself belong to the upper part (i.e. continuous with quadrant II). The inverse trigonometric and hyperbolic functions are not defined for complex arguments by the C++ standard, however. In GiNaC we follow the conventions used by CLN, which in turn follow the carefully designed definitions in the Common Lisp standard. It should be noted that this convention is identical to the one used by the C99 standard and by most serious CAS. It is to be expected that future revisions of the C++ standard incorporate these functions in the complex domain in a manner compatible with C99.