emmy.complex.impl — org.mentat/emmy 0.32.0

This namespace provides the primitive implementation of complex arithmetic for Emmy. The authors are indebted to Robert Eisele's Complex.js implementation from which we have borrowed freely and which is licensed as follows:

• Copyright (c) 2020, Robert Eisele ([e-mail])
• Dual licensed under the MIT or GPL Version 2 licenses.

-I clj/s

abs clj/s

(abs z)

Calculate the magnitude of the complex number. The implementation tactic used here (pre-dividing by the greater of the components) comes from the GNU ISO C++ standard library.

acos clj/s

(acos z)

Calculate the complex arc cosine

acosh clj/s

(acosh z)

Compute the complex arc hyperbolic cosine

acot clj/s

(acot z)

Calculate the complex arc cotangent.

acoth clj/s

(acoth z)

Calculate the complex arc hyperbolic cotangent.

acsc clj/s

(acsc z)

Compute the complex arc cosecant.

acsch clj/s

(acsch z)

Calculate the complex arc hyperbolic cosecant.

add clj/s

(add l r)

Compute the complex sum.

arg clj/s

(arg z)

Calculate the angle of the complex number.

asec clj/s

(asec z)

Calculate the complex arc secant.

asech clj/s

(asech z)

Calculate the complex arc hyperbolic secant.

asin clj/s

(asin z)

Calculate the complex arc sine

asinh clj/s

(asinh z)

Calculate the arc hyperbolic sine.

atan clj/s

(atan z)

Calculate the complex arctangent

atanh clj/s

(atanh z)

Calculate the complex hyperbolic tangent.

ceil clj/s

(ceil z)

(ceil z places)

Ceils the actual complex number

conjugate clj/s

(conjugate z)

Returns the complex conjugate

cos clj/s

(cos z)

cos-1 clj/s

(cos-1 x)

Computes $\cos(x)-1$ using Taylor series if $|x|\le{\pi\over 4}$), otherwise just subtracts one from (Math/cos x). Doing the latter when x is small squanders significant digits.

cosh clj/s

(cosh z)

Calculate the complex hyperbolic cosine

cot clj/s

(cot z)

coth clj/s

(coth z)

Calculate the complex hyperbolic cotangent

csc clj/s

(csc z)

csch clj/s

(csch z)

Compute the complex hyperbolic cosecant.

div clj/s

(div l r)

Compute the complex quotient.

equal? clj/s

(equal? z w)

Returns true if the supplied complex number z is equal to the value w. The rules for [[eq]] are as follows:

• If w is complex, returns true if all coefficients match, false otherwise

• If w is sequential with a count of 2, it's interpreted as complex in the obvious way

Else, if z is a [[real?]] complex number, returns true if the real component of z is emmy.value/= to w, false otherwise.

exp clj/s

(exp z)

Calculate the complex exponential.

exp-1 clj/s

(exp-1 z)

Calculate the complex exponent and subtracts one. This may be more accurate than (- (exp z) 1) if z is small.

floor clj/s

(floor z)

(floor z places)

Floors the actual complex number

I clj/s

imaginary clj/s

(imaginary z)

INFINITY clj/s

inverse clj/s

(inverse z)

Calculate the complex inverse 1/z

LN2 clj/s

log clj/s

(log z)

Calculate complex the natural log.

mul clj/s

(mul l r)

Compute the complex product.

NAN clj/s

nan? clj/s

(nan? z)

Determines whether a complex number is not on the Riemann sphere.

neg clj/s

(neg z)

Gets the negated complex number

ONE clj/s

one-like clj/s

(one-like c)

Constructs an identity-like complex number of the same kind as the example

parse clj/s

(parse s)

Parse a complex number. We expect one or two floating point numbers. If two, they must be separated by a sign (perhaps surrounded by at most one space, the second number followed by I or i. Example: 1.2-3.4i)

pow clj/s

(pow l r)

Calculate the power of two complex numbers. 0 to any power is zero, unless that power has an imaginary component, in which case NaN. Integral powers of the imaginary unit are treated exactly; everything else uses logarithms.

real clj/s

(real z)

sec clj/s

(sec z)

sech clj/s

(sech z)

Calculate the complex hyperbolic secant.

sin clj/s

(sin z)

Calculate the complex sine.

sinh clj/s

(sinh z)

Calculate the complex hyperbolic sine

sqrt clj/s

(sqrt z)

Calculate the complex square root

sub clj/s

(sub l r)

Compute the complex difference.

tan clj/s

(tan z)

tanh clj/s

(tanh z)

Caclulate the complex hyperbolic tangent

ZERO clj/s

zero-like clj/s

(zero-like c)

Constructs an identity-like complex number of the same kind as the example

zero? clj/s

(zero? z)

Determines whether or not a complex number is at the zero pole of the Riemann sphere.