Multiple-precision Complex

mpc Type

class gmpy2.mpc(c=0, /, precision=0)

class gmpy2.mpc(c=0, /, precision, context)

class gmpy2.mpc(real, /, imag=0, precision=0)

class gmpy2.mpc(real, /, imag, precision, context)

class gmpy2.mpc(s, /, precision=0, base=10)

class gmpy2.mpc(s, /, precision, base, context)

Return a complex floating-point number constructed from a numeric value c or from a pair of two non-complex numbers real and imag or from a string s made of digits in the given base.

A string can be possibly with real-part and/or imaginary-part (that have ‘j’ as a suffix), separated by ‘+’ and parsed the same as the mpfr constructor does (but the base must be up to 36).

The precision can be specified by either a single number that is used for both the real and imaginary components, or as a pair of different precisions for the real and imaginary components. For every component, the meaning of its precision value is the same as in the mpfr type constructor.

__format__(fmt, /)

Return a Python string by formatting self using the format string ‘fmt’.

All of mpfr’s format types and options are supported, with the exception of ‘%’ format type, ‘=’ alignment and zero padding.

conjugate()

Returns the conjugate of self.

digits(base=10, prec=0, /)

Returns up to ‘prec’ digits in the given base. If ‘prec’ is 0, as many digits that are available given self’s precision are returned. ‘base’ must be between 2 and 62. The result consists of 2 three-element tuples that contain the mantissa, exponent, and number of bits of precision of the real and imaginary components.

is_finite()

Return True if self is an actual number (i.e. non NaN or Infinity). If self is an mpc, return True if both self.real and self.imag are finite.

is_infinite()

Return True if self is +Infinity or -Infinity. If self is an mpc, return True if either self.real or self.imag is infinite. Otherwise return False.

is_nan()

Return True if self is NaN (Not-A-Number) else False.

is_zero()

Return True if self is equal to 0. If self is an mpc, return True if both self.real and self.imag are equal to 0.

imag

imaginary component

precision

precision in bits

rc

return code

real

real component

mpc Functions

gmpy2.acos(x, /)

Return inverse cosine of x; result in radians.

gmpy2.acosh(x, /)

Return inverse hyperbolic cosine of x.

gmpy2.asin(x, /)

Return inverse sine of x; result in radians.

gmpy2.asinh(x, /)

Return inverse hyperbolic sine of x.

gmpy2.atan(x, /)

Return inverse tangent of x; result in radians.

gmpy2.atanh(x, /)

Return inverse hyperbolic tangent of x.

gmpy2.cos(x, /)

Return cosine of x; x in radians.

gmpy2.cosh(x, /)

Return hyperbolic cosine of x.

gmpy2.div_2exp(x, n, /)

Return x divided by 2**n.

gmpy2.exp(x, /)

Return the exponential of x.

gmpy2.is_nan(x, /)

Return True if x is NaN (Not-A-Number) else False.

gmpy2.is_zero(x, /)

Return True if x is equal to 0. If x is an mpc, return True if both x.real and x.imag are equal to 0.

gmpy2.log(x, /)

Return the natural logarithm of x.

gmpy2.log10(x, /)

Return the base-10 logarithm of x.

gmpy2.mpc_random(random_state, /)

Return uniformly distributed number in the unit square [0,1]x[0,1].

gmpy2.mul_2exp(x, n, /)

Return x multiplied by 2**n.

gmpy2.norm(x, /)

Return the norm of a complex x. The norm(x) is defined as x.real**2 + x.imag**2. abs(x) is the square root of norm(x).

gmpy2.phase(x, /)

Return the phase angle, also known as argument, of a complex x.

gmpy2.polar(x, /)

Return the polar coordinate form of a complex x that is in rectangular form.

gmpy2.proj(x, /)

Returns the projection of a complex x on to the Riemann sphere.

gmpy2.rect(r, phi, /)

Return the rectangular coordinate form of a complex number that is given in polar form.

gmpy2.root_of_unity(n, k, /)

Return the n-th root of mpc(1) raised to the k-th power..

gmpy2.sin(x, /)

Return sine of x; x in radians.

gmpy2.sin_cos(x, /)

Return a tuple containing the sine and cosine of x; x in radians.

gmpy2.sinh(x, /)

Return hyperbolic sine of x.

gmpy2.sqrt(x, /)

Return the square root of x.

gmpy2.tan(x, /)

Return tangent of x; x in radians.

gmpy2.tanh(x, /)

Return hyperbolic tangent of x.