typelevel/spire

Powerful new number types and numeric abstractions for Scala.

jeremyrsmith

@jeremyrsmith

AFAIK Field is needed for multiplicative inverse, and subsumes the other requirements. Also identity is required by inverse, don't you think? :smile:

Soren

@srnb_gitlab

I think if I was formally trained in what Wikipedia calls "Ring Theory" I would know :sweat_smile:

jeremyrsmith

@jeremyrsmith

Haha, right there with ya :joy:

I guess maybe "implied" is a better word than "required"

Soren

@srnb_gitlab

Is there a typeclass that witnesses some type T can hold an imaginary value?

If not, I can make one, but

Something like

trait Complicate[T] {

  def i: T

}

object Complicate {

  implicit def complicateComplex[T](implicit t: CRing[T]): Complicate[Complex[T]] = new Complicate[Complex[T]] {
    override def i: Complex[T] = Complex.i
  }

}

Soren

@srnb_gitlab

I'm using it like so:

  def y[T](implicit c: Complicate[T], g: AdditiveGroup[T]): Matrix[2, 2, T] =
    Matrix(Vec(
      Vec(g.zero :: g.negate(c.i) :: HNil) ::
      Vec(c.i :: g.zero :: HNil) ::
      HNil
    ))

so I can just Pauli.y[T] and not something like Pauli.y[Complex[T]]

Soren

@srnb_gitlab

Sorry, Matrix[2, 2, T] instead of Matrix[2, 2, Complex[T]]

Denis Rosset

@denisrosset

@srnb_gitlab there is something slightly more general than a field, a division ring

https://github.com/typelevel/spire/blob/master/core/src/main/scala/spire/algebra/DivisionRing.scala

A field is a division ring, with the condition on top that multiplication is commutative

For example, the quaternions form a division ring, but not a field

For your second question

For your Complicate trait, I can think of two possible structures

One of them, given a type T representing either a subfield of the reals, or an approximation of the reals, returns the corresponding complex type, and provides the imaginary unit

Denis Rosset

@denisrosset

The other one describes a complex structure on top of a real vector space: https://en.wikipedia.org/wiki/Linear_complex_structure

(it's basically a morphism that describes the multiplication by the imaginary unit)

Paul Snively

@paul-snively

@srnb_gitlab: Is Complex not what you want?

Soren

@srnb_gitlab

@paul-snively I want a typeclass. Complex has an instance of that typeclass

@denisrosset Thank you, I'll check division ring out and adjust my code accordingly

Paul Snively

@paul-snively

@srnb_gitlab: Ah, I see what you mean.

Denis Rosset

@denisrosset

@srnb_gitlab Careful if you widen your type to accept noncommutative typeclasses

If you don't test your code with things that actually are noncommutative, bad things happen

I cleaned up some stuff in Spire due to that

You can use Quaternion for tests though

Soren

@srnb_gitlab

@denisrosset Well, I don't know what operations "require" commutative multiplication, persay

I should probably email my past LinAlg prof, I know that he's a software dev (but I'm not sure if he does fp or theory or anything related to that)

Piotr Paradziński

@lemastero

Hello, looks like spire for scalajs is released for 0.6 but there is no artifacts for scalajs 1.0 and 1.1. Any chance to publish for latest scalajs?

Oliver Winks

@PaperPlaneSoftware

Hi guys

is there any support for vectors in Spire?

I'm making a multi-agent simulation and need something to do basic 3d maths stuff

Denis Rosset

@denisrosset

Not really; but you can define your own Vector3D[A] class, and make instances of VectorSpace[Vector3D[A], A] available where A is a field

Then you get the property tests of VectorSpace for free

@lemastero I'm waiting to get publish rights in the typelevel repo

Oliver Winks

@PaperPlaneSoftware

@denisrosset thanks :thumbsup:

@denisrosset I saw some discussion of a cross product implementation and came across Zainab's PR (looked promising) any idea what happened to that work?

Soren

@srnb_gitlab

Is there a good way to send Reals over the wire?

Soren

@srnb_gitlab

Spire Matrices are mutable?

Luka Jacobowitz

@LukaJCB

there’s circe-spire, but I think it might be missing instances for Real

Valeriy Avanesov

@akopich

Hi. Does spire define a type for positive integers? Looks like Naturals include zero.
Feels like it would be extremely useful in combination with non-empty collections.

Paul Snively

@paul-snively

Hi everyone! I'm looking at Erik Osheim's wonderful https://www.youtube.com/watch?v=O78hnJuzQwA and wondering whether that elist library is out there somewhere I should be aware of?

I'm asking here because I figure Erik is likely to see it, sooner or later, but if anyone knows a better way to contact him, I'd appreciate knowing about it.

Carlos Quiroz

@cquiroz

Hello, I’m thinking to use UInt but I noted there is no ConvertableFrom nor ConvertableTo Uint unlike, e.g. Natural

Is there a reason for that?

Denis Rosset

@denisrosset

@akopich Why not use BigInt with https://github.com/fthomas/refined ? Natural is kind of a weird type

@cquiroz The whole ConvertableFrom, ConvertableTo business is not necessarily very principled. That said, using UInt with those typeclasses is likely to lead to boxing if the JIT is not clever enough.

Carlos Quiroz

@cquiroz

Thanks @denisrosset I have an entity that only takes positive numbers, I’ll take a look at refined

Valeriy Avanesov

@akopich

@denisrosset that would be an option, but I want to have at least some basic arithmetics on that type. E.g. positive plus positive should be also positive. Refined types don't give that.

Denis Rosset

@denisrosset

Why not a wrapper that only defines the + operation? Also, are you planning to have collections whose size is bigger than 2^63? You could use a wrapper around a Long then

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