@schrepfler I guess the easiest way is to provide your own implicit conversion:
import cats.Monoid
import cats.implicits._
import spire.math._
import spire.implicits._
import algebra.ring.AdditiveMonoid
implicit def additiveToMonoid[A: AdditiveMonoid]: Monoid[A] =
AdditiveMonoid[A].additive
val x = List(Rational(4) / 5, Rational(2) / 3).combineAll
println(x)
My
Rational is just spire.math.Rational
I actually think
AdditiveMonoid should just be Monoid 😝
I don’t really understand why if you have two possible instances, instead of choosing one, you just don’t choose either and get nothing :smile:
And then if you want to use the multiplicative monoid instance just use something like this:
case class Multiplicative[A](a: A) extends AnyVal // or opaque type
implicit def multiplicativeMonoidSemiring[A: Semiring]: Monoid[Multiplicative[A]] = …
and actually, if something should be a default monoid, it should be the multiplicative one due to the representation of groups as matrices (that's the standard use in algebra, see "Group ring")
Indeed, it is painful to not be able to use the wonderful
cats derivations to combine Map (for example, when a Map represents a polynomial)
But then, an additive monoid -> monoid conversion is the way to go
A Semiring can be non commutative?
I thought it was always commutative in its addition :o
Oh I realized I had an error in my code above, what I meant was this:
trait Semiring[A] extends CommutativeMonoid[A] {
def times[A](x: A, y: A): A
def plus[A](x: A, y: A): A = combine(x, y)
def zero[A] = empty[A]
}
trait Rig[A] extends Semiring[A] {
def one[A]: A
}
Spire does not extend the
cats instances yet, and we haven't taken a position on whether our instances/laws/... should be inherited through the chain cats-kernel/algebra/spire
You're very welcome to add an optional
Monoid[Rational] in spire.optional; however, I'm not clear about the default instances in spire, and reluctant to pile more stuff on top of it
(we are currently at ~ 50% code coverage, which is a shame)
Me too! Love that we actually have a better type tower than Haskell in some places (TruncatedDivision notably!)
:p
Should I open the issue in Typelevel/algebra? Technically
Semiring is defined there
Another underlying theme is whether we should share default instances as well.
Where are the notes for 0.15 and 0.16? Latest I see here is 0.14.1 https://github.com/non/spire/blob/master/CHANGES.md
Also, I assume they're not compatible? My tests freak out with cNoSuchMethodError...
The biggest pain with Spire now is that some parts are production ready (and simply need more test coverage), while others are shaky.
@LukaJCB That would be cool!
