Donuts

A wrapper library for Rings.

This library provides polynomial arithmetic operations based on the Rings library by Stanislav Poslavsky. The main difference from Rings is that this library allows operations between different polynomial rings; for example, addition of two polynomials in Z[x, y] and Z[y, z], respectively, gives a polynomial in Z[x, y, z].

Currently, the following wrapper classes are available:

Donuts	Rings
`Polynomial`	`MultivariatePolynomial<BigInteger>`
`RationalFunction`	`Rational<MultivariatePolynomial<BigInteger>>`

All instances of the above classes of Donuts are immutable objects.

A Python binding is available.

Requirements

Java 8 or later

Example

$ git clone https://github.com/tueda/donuts.git
$ cd donuts
$ ./gradlew shadowJar && jshell --class-path build/libs/donuts-*-all.jar # jshell is available in JDK9+

jshell> import com.github.tueda.donuts.*

jshell> var a = new Polynomial("1 + x + y") // in Z[x, y]
a ==> 1+y+x

jshell> var b = new Polynomial("1 + y + z") // in Z[y, z]
b ==> 1+z+y

jshell> var g = a.add(b) // in Z[x, y, z]
g ==> 2+z+2*y+x

jshell> var ag = a.multiply(g)
ag ==> 2+z+4*y+3*x+y*z+x*z+2*y^2+3*x*y+x^2

jshell> var bg = b.multiply(g)
bg ==> 2+3*z+4*y+x+z^2+3*y*z+x*z+2*y^2+x*y

jshell> ag.gcd(bg) // must be equal to g
$7 ==> 2+z+2*y+x

jshell> ag.divide(bg) // same as new RationalFunction(ag, bg)
$8 ==> (1+y+x)/(1+z+y)

jshell> new Polynomial("-2*x^4*y^3 + 2*x^3*y^4 + 2*x^2*y^5 - 2*x*y^6").factors()
$9 ==> Polynomial[8] { -2, y, y, y, x, -y+x, -y+x, y+x }

Development

./gradlew spotlessApply      # code formatter
./gradlew check              # build and test
./gradlew jacocoTestReport   # code coverage
./gradlew javadoc            # build documents
./gradlew dependencyUpdates  # check dependency updates

# Git hooks
pre-commit install

# for releasing a new version
git-chglog --next-tag v1.0.0  # show the changelog, which must be added to CHANGELOG.md manually
./gradlew release             # release a new version

Acknowledgements

This software was developed as part of the project supported by JSPS KAKENHI Grant Number 19K03831.

License

MIT