Introduction

What is a mathematical experiment?

It's great if you can deduct what lemmas you should prove to form solution of some problem. But quite often it is very difficult to come up with which lemmas you need to prove. For example, it is not that obvious that $1^2 + \dots + n^2 = \frac{n(n+1)(2n+1)}{6}$. But the moment you guessed the formula you can easily prove it via induction.

And how can you come up with formula for the expression? You can try interpolating the polynomial by first three terms. There is straightforward formula for the interpolation, but it's error-prone if you try to calculate it manually. And here computer enters the chat. You can write program that interpolates it for you. That's how you start conducting mathematical experiments.

Thus, mathematical experiment is an experiment where you try computing or iterating something to come up with a hypothesis and prove it later. And it is obviously nice if you can make computer do the hard computations for you.

Then what's the problem with computer mathematical experiments?

The problem is very simple. There is no already written algorithms for very basic manipulations. So you have to write your own implementations of polynomials or of cartesian product of collections.

This library tries to fill the gap.

How is Kone organised?

Kone is made to simplify your mathematical experimentation experience. So it is divided to small modules each of which meets some purpose. There is no module you need by default. Each module describes its tools and concepts to solve some atomic problem. So you can plug in necessary modules one by one to collect your one puzzle.

There are 3 types of Kone modules.

Main modules

Part "Main" consists of modules that meet some common purpose. Like linear algebra, number Theory, polynomials, and so on. They are main modules that you would usually use to compute something.

Misc modules

Part "Misc" consists of modules that solve highly specialised problems. Like olympiad geometry problems solving and so on. They are the modules that you would use for their specific problems.

Util modules

Part "Util" consists of private modules that are used as utilities for main and misc modules. Usually they are short, and you won't be interested in using them. But some of them are large and may have some functionality that would interest you.

Dependencies

All the modules are available on Maven Central. You can see their full artifact paths on corresponding docs pages.

But main rule is that their group is com.lounres and their artifact is their own names prefixed with some prefix. Main modules' prefix is kone., whereas misc and util modules' prefixes are kone.misc. and kone.util. respectively.

For example, here is the full artifact paths of the main module algebraic, the misc module `planimetricsCalculations.

Gradle Kotlin DSL

build.gradle.kts

dependencies {
    implementation("com.lounres:kone.algebraic:0.0.0-dev-1")
}

Gradle Groovy DSL

build.gradle

dependencies {
    implementation 'com.lounres:kone.algebraic:0.0.0-dev-1'
}

Maven

pom.xml

<dependency>
    <groupId>com.lounres</groupId>
    <artifactId>kone.algebraic</artifactId>
    <version>0.0.0-dev-1</version>
</dependency>

Benchmarks and Examples

Each module has specified source sets for benchmarks (one source set per target including meta target) and for examples (jvmExamples source set in src/examples/kotlin).