math::complexnumbers(n)

math::complexnumbers 💖

okay bestie, welcome to the n manual page for math::complexnumbers — the Tcl Math Library's whole entire complex number situation ✨ (that's the manual section, "n", she lives there, it's giving nerd royalty 👑).

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NAME 🎀

math::complexnumbers — Straightforward complex number package

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SYNOPSIS 🌸

package require Tcl 8.5 9

package require math::complexnumbers ?1.0.3?

::math::complexnumbers::+ z1 z2

::math::complexnumbers::- z1 z2

::math::complexnumbers::* z1 z2

::math::complexnumbers::/ z1 z2

::math::complexnumbers::conj z1

::math::complexnumbers::real z1

::math::complexnumbers::imag z1

::math::complexnumbers::mod z1

::math::complexnumbers::arg z1

::math::complexnumbers::complex real imag

::math::complexnumbers::tostring z1

::math::complexnumbers::exp z1

::math::complexnumbers::sin z1

::math::complexnumbers::cos z1

::math::complexnumbers::tan z1

::math::complexnumbers::log z1

::math::complexnumbers::sqrt z1

::math::complexnumbers::pow z1 z2

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DESCRIPTION 🦋

so the mathematical module complexnumbers gives you a straightforward implementation of complex numbers, written in pure Tcl. no cap, fully pure. ✨

the philosophy here — and bestie this is the vibe check that matters — is that you already know you're dealing with complex numbers in an abstract way, and you want the highest performance possible given that we're working inside an interpreted language. periodt. 💅

which means: the procedures in this package assume your arguments are valid (representations of) "complex numbers". translate: a list of two numbers defining the real and imaginary part of a complex number. though honestly that's a mere detail — just rely on the complex command to construct a valid number and go live your life 🫶

most procedures do the basic arithmetic operations or elementary functions, and several others convert to and from different representations:

set z [complex 0 1]
puts "z = [tostring $z]"
puts "z**2 = [* $z $z]

would result in:

z = i
z**2 = -1

not me leaving that quote exactly as the original has it 😭 the manual said it, I said it, we don't editorialize facts around here 🙈

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AVAILABLE PROCEDURES 👑

the package implements all or most basic operations and elementary functions. obsessed honestly.

the arithmetic operations ✨

::math::complexnumbers::+ z1 z2

Add the two arguments and return the resulting complex number 🔥

• complex z1 (in) — First argument in the summation
• complex z2 (in) — Second argument in the summation

::math::complexnumbers::- z1 z2

Subtract the second argument from the first and return the resulting complex number. If there is only one argument, the opposite of z1 is returned (i.e. -z1) 💫

• complex z1 (in) — First argument in the subtraction
• complex z2 (in) — Second argument in the subtraction (optional)

::math::complexnumbers::* z1 z2

Multiply the two arguments and return the resulting complex number ✖️

• complex z1 (in) — First argument in the multiplication
• complex z2 (in) — Second argument in the multiplication

::math::complexnumbers::/ z1 z2

Divide the first argument by the second and return the resulting complex number ➗

• complex z1 (in) — First argument (numerator) in the division
• complex z2 (in) — Second argument (denominator) in the division

::math::complexnumbers::conj z1

Return the conjugate of the given complex number 🪞

• complex z1 (in) — Complex number in question

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Conversion/inquiry procedures 🔍

::math::complexnumbers::real z1

Return the real part of the given complex number 💜

• complex z1 (in) — Complex number in question

::math::complexnumbers::imag z1

Return the imaginary part of the given complex number 🌈

• complex z1 (in) — Complex number in question

::math::complexnumbers::mod z1

Return the modulus of the given complex number 📏

• complex z1 (in) — Complex number in question

::math::complexnumbers::arg z1

Return the argument ("angle" in radians) of the given complex number 📐

• complex z1 (in) — Complex number in question

::math::complexnumbers::complex real imag

Construct the complex number "real + imag*i" and return it 🛠️

• float real (in) — The real part of the new complex number
• float imag (in) — The imaginary part of the new complex number

::math::complexnumbers::tostring z1

Convert the complex number to the form "real + imag*i" and return the string ✍️

• float complex (in) — The complex number to be converted

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Elementary functions 🌸

::math::complexnumbers::exp z1

Calculate the exponential for the given complex argument and return the result ⭐

• complex z1 (in) — The complex argument for the function

::math::complexnumbers::sin z1

Calculate the sine function for the given complex argument and return the result 🎀

• complex z1 (in) — The complex argument for the function

::math::complexnumbers::cos z1

Calculate the cosine function for the given complex argument and return the result 🧚

• complex z1 (in) — The complex argument for the function

::math::complexnumbers::tan z1

Calculate the tangent function for the given complex argument and return the result 💅

• complex z1 (in) — The complex argument for the function

::math::complexnumbers::log z1

Calculate the (principle value of the) logarithm for the given complex argument and return the result 🍓

• complex z1 (in) — The complex argument for the function

::math::complexnumbers::sqrt z1

Calculate the (principle value of the) square root for the given complex argument and return the result 🌱

• complex z1 (in) — The complex argument for the function

::math::complexnumbers::pow z1 z2

Calculate "z1 to the power of z2" and return the result 💥

• complex z1 (in) — The complex number to be raised to a power
• complex z2 (in) — The complex power to be used

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BUGS, IDEAS, FEEDBACK 😭

ngl, this document, and the package it describes, will undoubtedly contain bugs and other problems. it's giving "we know, we know". please report such in the category math :: complexnumbers of the Tcllib Trackers at [http://core.tcl.tk/tcllib/reportlist]. also please report any ideas for enhancements you may have for either the package and/or the documentation 🫶

when proposing code changes, please provide unified diffs, i.e the output of diff -u. bestie, don't make them guess 🙈

note further that attachments are strongly preferred over inlined patches. attachments can be made by going to the Edit form of the ticket immediately after its creation, and then using the left-most button in the secondary navigation bar. iconic little workflow, honestly 👑

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KEYWORDS ✨

complex numbers, math

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CATEGORY 🌈

Mathematics

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COPYRIGHT 💖

Copyright (c) 2004 Arjen Markus <arjenmarkus@users.sourceforge.net>

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and that's the whole page, bestie 🥹 source and version: tcllib, version 1.0.3, and it's filed under math::complexnumbers(n) — go forth and be imaginary 💜🦋✨