Functions Module **************** .. module:: sympy.functions Elementary ========== This module implements elementary functions (abs, max, etc.) abs --- Returns the absolute value of the argument. Examples:: >>> from sympy.functions import abs >>> abs(-1) 1 .. autoclass:: sympy.functions.elementary.abs arg --- Returns the argument (in radians) of a complex number. For a real number, the argument is always 0. Examples:: >>> from sympy.functions import arg >>> from sympy import I, sqrt >>> arg(2.0) 0 >>> arg(I) pi/2 >>> arg(sqrt(2) + I*sqrt(2)) pi/4 .. autoclass:: sympy.functions.elementary.arg conjugate --------- Returns the 'complex conjugate '_ of an argument. In mathematics, the complex conjugate of a complex number is given by changing the sign of the imaginary part. Thus, the conjugate of the complex number a + ib (where a and b are real numbers) is a - ib Examples:: >>> from sympy.functions import conjugate >>> from sympy import I >>> conjugate(2) 2 >>> conjugate(I) -I .. autoclass:: sympy.functions.elementary.conjugate min_ ---- Returns the minimum of two (comparable) expressions. Examples:: >>> from sympy.functions import min_ >>> min_(1,2) 1 >>> from sympy import Symbol >>> x = Symbol('x') >>> min_(1,x) min_(1, x) It is named min_ and not min to avoid conflicts with built-in function min. .. autoclass:: sympy.functions.elementary.min_ max_ ---- Returns the maximum of two (comparable) expressions It is named max_ and not max to avoid conflicts with built-in function min. .. autoclass:: sympy.functions.elementary.max_ re -- Return the real part of an expression Examples:: >>> from sympy.functions import re >>> from sympy import I >>> re(2+3*I) 2 .. autoclass:: sympy.functions.elementary.re sqrt ---- Returns the square root of an expression. It is equivalent to raise to Rational(1,2) >>> from sympy.functions import sqrt >>> from sympy import Rational >>> sqrt(2) == 2**Rational(1,2) True .. autoclass:: sympy.functions.elementary.sqrt sign ---- Returns the sign of an expression, that is: -1 if expr is negative 0 if expr is zero 1 if expr is positive >>> from sympy.functions import sign >>> sign(-1) -1 >>> sign(0) 0 .. autoclass:: sympy.functions.elementary.sign Combinatorial ============= This module implements various combinatorial functions. Binomial -------- .. autoclass:: sympy.functions.combinatorial.factorials.Binomial Factorial --------- .. autoclass:: sympy.functions.combinatorial.factorials.Factorial FallingFactorial ---------------- .. autoclass:: sympy.functions.combinatorial.factorials.FallingFactorial MultiFactorial -------------- .. autoclass:: sympy.functions.combinatorial.factorials.MultiFactorial RisingFactorial --------------- .. autoclass:: sympy.functions.combinatorial.factorials.RisingFactorial Special ======= DiracDelta ---------- .. autoclass:: sympy.functions.special.delta_functions.DiracDelta Heaviside --------- .. autoclass:: sympy.functions.special.delta_functions.Heaviside gamma ----- .. autoclass:: sympy.functions.special.gamma_functions.gamma loggamma -------- .. autoclass:: sympy.functions.special.gamma_functions.loggamma polygamma --------- .. autoclass:: sympy.functions.special.gamma_functions.polygamma uppergamma ---------- .. autoclass:: sympy.functions.special.gamma_functions.uppergamma