Elementary ========== This module implements elementary functions, as well as functions like Abs, Max, etc. Abs --- Returns the absolute value of the argument. Examples:: >>> from sympy.functions import Abs >>> Abs(-1) 1 .. autoclass:: sympy.functions.elementary.complexes.Abs :members: acos ---- .. autoclass:: sympy.functions.elementary.trigonometric.acos :members: acosh ----- .. autoclass:: sympy.functions.elementary.hyperbolic.acosh :members: acot ---- .. autoclass:: sympy.functions.elementary.trigonometric.acot :members: acoth ----- .. autoclass:: sympy.functions.elementary.hyperbolic.acoth :members: 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.complexes.arg :members: asin ---- .. autoclass:: sympy.functions.elementary.trigonometric.asin :members: asinh ----- .. autoclass:: sympy.functions.elementary.hyperbolic.asinh :members: atan ---- .. autoclass:: sympy.functions.elementary.trigonometric.atan :members: atan2 ----- This function is like `atan`, but considers the sign of both arguments in order to correctly determine the quadrant of its result. .. autoclass:: sympy.functions.elementary.trigonometric.atan2 :members: atanh ----- .. autoclass:: sympy.functions.elementary.hyperbolic.atanh :members: ceiling ------- .. autoclass:: sympy.functions.elementary.integers.ceiling :members: 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 :math:`a + ib` (where a and b are real numbers) is :math:`a - ib` Examples:: >>> from sympy.functions import conjugate >>> from sympy import I >>> conjugate(2) 2 >>> conjugate(I) -I .. autoclass:: sympy.functions.elementary.complexes.conjugate :members: cos --- .. autoclass:: sympy.functions.elementary.trigonometric.cos :members: cosh ---- .. autoclass:: sympy.functions.elementary.hyperbolic.cosh :members: cot --- .. autoclass:: sympy.functions.elementary.trigonometric.cot :members: coth ---- .. autoclass:: sympy.functions.elementary.hyperbolic.coth :members: exp --- .. autoclass:: sympy.functions.elementary.exponential.exp :members: .. seealso:: classes :py:class:`sympy.functions.elementary.exponential.log` ExprCondPair ------------ .. autoclass:: sympy.functions.elementary.piecewise.ExprCondPair :members: floor ----- .. autoclass:: sympy.functions.elementary.integers.floor :members: HyperbolicFunction ------------------ .. autoclass:: sympy.functions.elementary.hyperbolic.HyperbolicFunction :members: IdentityFunction ---------------- .. autoclass:: sympy.functions.elementary.miscellaneous.IdentityFunction :members: im -- Returns the imaginary part of an expression. Examples:: >>> from sympy.functions import im >>> from sympy import I >>> im(2+3*I) 3 .. autoclass: sympy.functions.elementary.im :members: .. seealso:: :py:class:`sympy.functions.elementary.complexes.re` LambertW -------- .. autoclass:: sympy.functions.elementary.exponential.LambertW :members: log --- .. autoclass:: sympy.functions.elementary.exponential.log :members: .. seealso:: classes :py:class:`sympy.functions.elementary.exponential.exp` Min --- Returns the minimum of two (comparable) expressions. Examples:: >>> from sympy.functions import Min >>> Min(1,2) 1 >>> from sympy.abc import x >>> Min(1, x) Min(1, x) It is named Min and not min to avoid conflicts with the built-in function min. .. autoclass:: sympy.functions.elementary.miscellaneous.Min :members: Max --- Returns the maximum of two (comparable) expressions It is named Max and not max to avoid conflicts with the built-in function max. .. autoclass:: sympy.functions.elementary.miscellaneous.Max :members: Piecewise --------- .. autoclass:: sympy.functions.elementary.piecewise.Piecewise :members: .. autofunction:: sympy.functions.elementary.piecewise.piecewise_fold 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.complexes.re :members: .. seealso:: :py:class:`sympy.functions.elementary.complexes.im` root ---- .. autofunction:: sympy.functions.elementary.miscellaneous.root RoundFunction ------------- .. autoclass:: sympy.functions.elementary.integers.RoundFunction sin --- .. autoclass:: sympy.functions.elementary.trigonometric.sin :members: sinh ---- .. autoclass:: sympy.functions.elementary.hyperbolic.sinh :members: 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.miscellaneous.sqrt :members: sign ---- .. autoclass:: sympy.functions.elementary.complexes.sign :members: tan --- .. autoclass:: sympy.functions.elementary.trigonometric.tan :members: tanh ---- .. autoclass:: sympy.functions.elementary.hyperbolic.tanh :members: