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https://github.com/propensive/baroque

Make coding with complex numbers more real
https://github.com/propensive/baroque

complex-numbers scala

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Make coding with complex numbers more real

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# Baroque



__Make coding with complex numbers more real__



_Baroque_ provides a single generic type, `Complex`, comprising of real and

imaginary values of the same numeric type. This could be a `Double`, `Int` or a

`Quantity` with units (as provided by

[Quantitative](https://github.com/propensive/quantitative/)), or any other type

which defines [Symbolism](https://github.com/propensive/symbolism) typeclass

instances.



## Features



- provides a generic representation of complex numbers

- extends any numerical type to the complex

- provides many standard complex numerical operations on values

- allows conversion between cartesian and polar forms



## Availability Plan



Baroque has not yet been published. The medium-term plan is to build Baroque

with [Fury](https://github.com/propensive/fury) and to publish it as a source build on

[Vent](https://github.com/propensive/vent). This will enable ordinary users to write and build

software which depends on Baroque.



Subsequently, Baroque will also be made available as a binary in the Maven

Central repository. This will enable users of other build tools to use it.



For the overeager, curious and impatient, see [building](#building).



## Getting Started



All terms and types are defined in the `baroque` package, which can be imported

with:

```scala

import baroque.*

```



### Constructing complex numbers



There are several ways to construct complex numbers. The factory method of

specifying real and imaginary part is the most straightforward, for example,

```scala

val complex = Complex(3.2, -1.25)

```

represents the complex number 3.2 - 1.25i.



This is an instance of `Complex[Double]`, since the real and imaginary parts of

the number are both `Double`s. With Quantitative, we could similarly create a

complex quantity, for example,

```scala

val complex2 = Complex(3.2*Metre, -1.25*Metre)

```

which would be a `Complex[Quantity[Metres[1]]]`.



But it is also possible construct a complex number by adding the real part to

the imaginary part, where the imaginary part is created by multiplying a real

number by _i_, the imaginary unit value, which is called `I` in Baroque:

```scala

val complex3 = 0.8 + 1.8*I

```



I further possibility is to specify the complex number in polar form, using the

`Complex.polar` constructor. This takes two parameter, _magnitude_ and

_argument_. The magnitude should have the same type a the real and imaginary

parts of the number, and the argument must be a `Double`, in radians. For

example,

```scala

val complex4 = Complex.polar(12*Kilo(Gram), 0.3845)

```



### Operations with Complex Numbers



Standard arithmetic operations between `Complex` instances, using the `+`, `-`,

`*` and `/` operators work intuitively. Additionally, the prefix `~` operator

can be used to find the complex conjugate of a number.



The methods `modulus` and `argument` on `Complex` values provide, predictably,

the modulus and argument. And `sqrt` will yield one of the two square roots of

a `Complex` number; the other will be its negation.



These operations are defined, in general, so long as the necessary operations

(such as addition, multiplication and square root) are defined on the

underlying type of the real and imaginary parts.



## Status



Baroque is classified as __embryotic__. For reference, Scala One projects are

categorized into one of the following five stability levels:



- _embryonic_: for experimental or demonstrative purposes only, without any guarantees of longevity

- _fledgling_: of proven utility, seeking contributions, but liable to significant redesigns

- _maturescent_: major design decisions broady settled, seeking probatory adoption and refinement

- _dependable_: production-ready, subject to controlled ongoing maintenance and enhancement; tagged as version `1.0.0` or later

- _adamantine_: proven, reliable and production-ready, with no further breaking changes ever anticipated



Projects at any stability level, even _embryonic_ projects, can still be used,

as long as caution is taken to avoid a mismatch between the project's stability

level and the required stability and maintainability of your own project.



Baroque is designed to be _small_. Its entire source code currently consists

of 139 lines of code.



## Building



Baroque will ultimately be built by Fury, when it is published. In the

meantime, two possibilities are offered, however they are acknowledged to be

fragile, inadequately tested, and unsuitable for anything more than

experimentation. They are provided only for the necessity of providing _some_

answer to the question, "how can I try Baroque?".



1. *Copy the sources into your own project*

   

   Read the `fury` file in the repository root to understand Baroque's build

   structure, dependencies and source location; the file format should be short

   and quite intuitive. Copy the sources into a source directory in your own

   project, then repeat (recursively) for each of the dependencies.



   The sources are compiled against the latest nightly release of Scala 3.

   There should be no problem to compile the project together with all of its

   dependencies in a single compilation.



2. *Build with [Wrath](https://github.com/propensive/wrath/)*



   Wrath is a bootstrapping script for building Baroque and other projects in

   the absence of a fully-featured build tool. It is designed to read the `fury`

   file in the project directory, and produce a collection of JAR files which can

   be added to a classpath, by compiling the project and all of its dependencies,

   including the Scala compiler itself.

   

   Download the latest version of

   [`wrath`](https://github.com/propensive/wrath/releases/latest), make it

   executable, and add it to your path, for example by copying it to

   `/usr/local/bin/`.



   Clone this repository inside an empty directory, so that the build can

   safely make clones of repositories it depends on as _peers_ of `baroque`.

   Run `wrath -F` in the repository root. This will download and compile the

   latest version of Scala, as well as all of Baroque's dependencies.



   If the build was successful, the compiled JAR files can be found in the

   `.wrath/dist` directory.



## Contributing



Contributors to Baroque are welcome and encouraged. New contributors may like

to look for issues marked

[beginner](https://github.com/propensive/baroque/labels/beginner).



We suggest that all contributors read the [Contributing

Guide](/contributing.md) to make the process of contributing to Baroque

easier.



Please __do not__ contact project maintainers privately with questions unless

there is a good reason to keep them private. While it can be tempting to

repsond to such questions, private answers cannot be shared with a wider

audience, and it can result in duplication of effort.



## Author



Baroque was designed and developed by Jon Pretty, and commercial support and

training on all aspects of Scala 3 is available from [Propensive

OÜ](https://propensive.com/).



## Name



Baroque music, architecture and design is characterized by its ornate _complexity_ which alludes to _complex numbers_.



In general, Scala One project names are always chosen with some rationale,

however it is usually frivolous. Each name is chosen for more for its

_uniqueness_ and _intrigue_ than its concision or catchiness, and there is no

bias towards names with positive or "nice" meanings—since many of the libraries

perform some quite unpleasant tasks.



Names should be English words, though many are obscure or archaic, and it

should be noted how willingly English adopts foreign words. Names are generally

of Greek or Latin origin, and have often arrived in English via a romance

language.



## Logo



The logo shows an [alto clef](https://en.wikipedia.org/wiki/Clef), used

predominantly in music for viola (which features in Baroque music), and also

resembles a capital B, the first letter of "Baroque".



## License



Baroque is copyright © 2024 Jon Pretty & Propensive OÜ, and

is made available under the [Apache 2.0 License](/license.md).