functions

Module nustd.cmath.functions.

Module-level functions and constants for nustd.cmath.

cmath is a function module - free functions over complex numbers plus a few constants - so this is the function half of the surface: typed wrappers that mirror cmath.sqrt / cmath.phase / cmath.polar 1-1, plus the module constants. Each wrapper builds its interaction atom (lazily imported, like nustd.math) and returns the Form that matches the host return type:

most functions -> complex (the Form for the builtin)
phase -> Float
polar -> Tuple (the (r, phi) pair)
isnan / isinf / isfinite / isclose -> Bool
rect(r, phi) -> complex

Constants are plain values, so they ride on Literal instead of an atom. pi / e / tau / inf / nan are floats; infj / nanj are complex, so they are wrapped in the complex Form.

Name	Call	Meaning
acos	`cmath.acos(x)`	The arc cosine of `x`: mirrors `cmath.acos()`.
asin	`cmath.asin(x)`	The arc sine of `x`: mirrors `cmath.asin()`.
atan	`cmath.atan(x)`	The arc tangent of `x`: mirrors `cmath.atan()`.
cos	`cmath.cos(x)`	The cosine of `x`: mirrors `cmath.cos()`.
cosh	`cmath.cosh(x)`	The hyperbolic cosine of `x`: mirrors `cmath.cosh()`.
exp	`cmath.exp(x)`	`e` raised to `x`: mirrors `cmath.exp()`.
isclose	`cmath.isclose(a, b)`	Whether `a` and `b` are close: mirrors `cmath.isclose()`.
isfinite	`cmath.isfinite(x)`	Whether both components of `x` are finite: mirrors `cmath.isfinite()`.
isinf	`cmath.isinf(x)`	Whether `x` has an infinite component: mirrors `cmath.isinf()`.
isnan	`cmath.isnan(x)`	Whether `x` has a NaN component: mirrors `cmath.isnan()`.
log	`cmath.log(x, base=None)`	The logarithm of `x` (natural, or to `base`): mirrors `cmath.log()`.
log10	`cmath.log10(x)`	The base-10 logarithm of `x`: mirrors `cmath.log10()`.
phase	`cmath.phase(x)`	The phase angle of `x`, in radians: mirrors `cmath.phase()`.
polar	`cmath.polar(x)`	`x` as the polar pair `(r, phi)`: mirrors `cmath.polar()`.
rect	`cmath.rect(r, phi)`	The complex number with modulus `r` and phase `phi`: mirrors `cmath.rect()`.
sin	`cmath.sin(x)`	The sine of `x`: mirrors `cmath.sin()`.
sinh	`cmath.sinh(x)`	The hyperbolic sine of `x`: mirrors `cmath.sinh()`.
sqrt	`cmath.sqrt(x)`	The square root of `x`: mirrors `cmath.sqrt()`.
tan	`cmath.tan(x)`	The tangent of `x`: mirrors `cmath.tan()`.
tanh	`cmath.tanh(x)`	The hyperbolic tangent of `x`: mirrors `cmath.tanh()`.

acos

The arc cosine of x: mirrors cmath.acos().

cmath.acos(x)

Path nustd.cmath.acos. Defined on nustd.cmath.functions, bound as a function. Builds complex.

Arguments

Name	Type	Default	Meaning
`x`	`ComplexArg`

Undocumented: example.

asin

The arc sine of x: mirrors cmath.asin().

cmath.asin(x)

Path nustd.cmath.asin. Defined on nustd.cmath.functions, bound as a function. Builds complex.

Arguments

Name	Type	Default	Meaning
`x`	`ComplexArg`

Undocumented: example.

atan

The arc tangent of x: mirrors cmath.atan().

cmath.atan(x)

Path nustd.cmath.atan. Defined on nustd.cmath.functions, bound as a function. Builds complex.

Arguments

Name	Type	Default	Meaning
`x`	`ComplexArg`

Undocumented: example.

cos

The cosine of x: mirrors cmath.cos().

cmath.cos(x)

Path nustd.cmath.cos. Defined on nustd.cmath.functions, bound as a function. Builds complex.

Arguments

Name	Type	Default	Meaning
`x`	`ComplexArg`

Undocumented: example.

cosh

The hyperbolic cosine of x: mirrors cmath.cosh().

cmath.cosh(x)

Path nustd.cmath.cosh. Defined on nustd.cmath.functions, bound as a function. Builds complex.

Arguments

Name	Type	Default	Meaning
`x`	`ComplexArg`

Undocumented: example.

exp

e raised to x: mirrors cmath.exp().

cmath.exp(x)

Path nustd.cmath.exp. Defined on nustd.cmath.functions, bound as a function. Builds complex.

Arguments

Name	Type	Default	Meaning
`x`	`ComplexArg`

Undocumented: example.

isclose

Whether a and b are close: mirrors cmath.isclose().

cmath.isclose(a, b)

Path nustd.cmath.isclose. Defined on nustd.cmath.functions, bound as a function. Builds Bool.

Arguments

Name	Type	Default	Meaning
`a`	`ComplexArg`
`b`	`ComplexArg`

Undocumented: example.

isfinite

Whether both components of x are finite: mirrors cmath.isfinite().

cmath.isfinite(x)

Path nustd.cmath.isfinite. Defined on nustd.cmath.functions, bound as a function. Builds Bool.

Arguments

Name	Type	Default	Meaning
`x`	`ComplexArg`

Undocumented: example.

isinf

Whether x has an infinite component: mirrors cmath.isinf().

cmath.isinf(x)

Path nustd.cmath.isinf. Defined on nustd.cmath.functions, bound as a function. Builds Bool.

Arguments

Name	Type	Default	Meaning
`x`	`ComplexArg`

Undocumented: example.

isnan

Whether x has a NaN component: mirrors cmath.isnan().

cmath.isnan(x)

Path nustd.cmath.isnan. Defined on nustd.cmath.functions, bound as a function. Builds Bool.

Arguments

Name	Type	Default	Meaning
`x`	`ComplexArg`

Undocumented: example.

log

The logarithm of x (natural, or to base): mirrors cmath.log().

cmath.log(x, base=None)

Path nustd.cmath.log. Defined on nustd.cmath.functions, bound as a function. Builds complex.

Arguments

Name	Type	Default	Meaning
`x`	`ComplexArg`
`base`	`ComplexArg \| None`	`None`

Undocumented: example.

log10

The base-10 logarithm of x: mirrors cmath.log10().

cmath.log10(x)

Path nustd.cmath.log10. Defined on nustd.cmath.functions, bound as a function. Builds complex.

Arguments

Name	Type	Default	Meaning
`x`	`ComplexArg`

Undocumented: example.

phase

The phase angle of x, in radians: mirrors cmath.phase().

cmath.phase(x)

Path nustd.cmath.phase. Defined on nustd.cmath.functions, bound as a function. Builds Float.

Arguments

Name	Type	Default	Meaning
`x`	`ComplexArg`

Undocumented: example.

polar

x as the polar pair (r, phi): mirrors cmath.polar().

cmath.polar(x)

Path nustd.cmath.polar. Defined on nustd.cmath.functions, bound as a function. Builds Tuple.

Arguments

Name	Type	Default	Meaning
`x`	`ComplexArg`

Undocumented: example.

rect

The complex number with modulus r and phase phi: mirrors cmath.rect().

cmath.rect(r, phi)

Path nustd.cmath.rect. Defined on nustd.cmath.functions, bound as a function. Builds complex.

Arguments

Name	Type	Default	Meaning
`r`	`FloatArg`
`phi`	`FloatArg`

Undocumented: example.

sin

The sine of x: mirrors cmath.sin().

cmath.sin(x)

Path nustd.cmath.sin. Defined on nustd.cmath.functions, bound as a function. Builds complex.

Arguments

Name	Type	Default	Meaning
`x`	`ComplexArg`

Undocumented: example.

sinh

The hyperbolic sine of x: mirrors cmath.sinh().

cmath.sinh(x)

Path nustd.cmath.sinh. Defined on nustd.cmath.functions, bound as a function. Builds complex.

Arguments

Name	Type	Default	Meaning
`x`	`ComplexArg`

Undocumented: example.

sqrt

The square root of x: mirrors cmath.sqrt().

cmath.sqrt(x)

Path nustd.cmath.sqrt. Defined on nustd.cmath.functions, bound as a function. Builds complex.

Arguments

Name	Type	Default	Meaning
`x`	`ComplexArg`

Undocumented: example.

tan

The tangent of x: mirrors cmath.tan().

cmath.tan(x)

Path nustd.cmath.tan. Defined on nustd.cmath.functions, bound as a function. Builds complex.

Arguments

Name	Type	Default	Meaning
`x`	`ComplexArg`

Undocumented: example.

tanh

The hyperbolic tangent of x: mirrors cmath.tanh().

cmath.tanh(x)

Path nustd.cmath.tanh. Defined on nustd.cmath.functions, bound as a function. Builds complex.

Arguments

Name	Type	Default	Meaning
`x`	`ComplexArg`

Undocumented: example.

functions

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