Make Field inherit from DivisionRing

Addresses typelevel/algebra#246 (comment)

algebra-core/src/main/scala/cats/algebra/ring/DivisionRing.scala

@@ -7,7 +7,15 @@ import scala.{specialized => sp}
 trait DivisionRing[@sp(Byte, Short, Int, Long, Float, Double) A] extends Any with Ring[A] with MultiplicativeGroup[A] {
   self =>
 
-  def fromDouble(a: Double): A = Field.defaultFromDouble[A](a)(self, self)
+  /**
+   * This is implemented in terms of basic Ring ops. However, this is
+   * probably significantly less efficient than can be done with a
+   * specific type. So, it is recommended that this method be
+   * overriden.
+   *
+   * This is possible because a Double is a rational number.
+   */
+  def fromDouble(a: Double): A = DivisionRing.defaultFromDouble[A](a)(self, self)
 
 }
 

algebra-core/src/main/scala/cats/algebra/ring/Field.scala

@@ -4,7 +4,11 @@ package ring
 
 import scala.{specialized => sp}
 
-trait Field[@sp(Int, Long, Float, Double) A] extends Any with EuclideanRing[A] with MultiplicativeCommutativeGroup[A] {
+trait Field[@sp(Int, Long, Float, Double) A]
+    extends Any
+    with EuclideanRing[A]
+    with DivisionRing[A]
+    with MultiplicativeCommutativeGroup[A] {
   self =>
 
   // default implementations for GCD
@@ -20,16 +24,6 @@ trait Field[@sp(Int, Long, Float, Double) A] extends Any with EuclideanRing[A] w
   def emod(a: A, b: A): A = zero
   override def equotmod(a: A, b: A): (A, A) = (div(a, b), zero)
 
-  /**
-   * This is implemented in terms of basic Field ops. However, this is
-   * probably significantly less efficient than can be done with a
-   * specific type. So, it is recommended that this method be
-   * overriden.
-   *
-   * This is possible because a Double is a rational number.
-   */
-  def fromDouble(a: Double): A = Field.defaultFromDouble(a)(self, self)
-
 }
 
 trait FieldFunctions[F[T] <: Field[T]] extends EuclideanRingFunctions[F] with MultiplicativeGroupFunctions[F] {

algebra-laws/shared/src/main/scala/cats/algebra/laws/RingLaws.scala

@@ -257,6 +257,29 @@ trait RingLaws[A] extends GroupLaws[A] { self =>
     }
   )
 
+  def divisionRing(implicit A: DivisionRing[A]) = new RingProperties(
+    name = "division ring",
+    al = additiveCommutativeGroup,
+    ml = multiplicativeGroup,
+    parents = Seq(ring),
+    "fromDouble" -> forAll { (n: Double) =>
+      if (Platform.isJvm) {
+        // TODO: BigDecimal(n) is busted in scalajs, so we skip this test.
+        val bd = new java.math.BigDecimal(n)
+        val unscaledValue = new BigInt(bd.unscaledValue)
+        val expected =
+          if (bd.scale > 0) {
+            A.div(A.fromBigInt(unscaledValue), A.fromBigInt(BigInt(10).pow(bd.scale)))
+          } else {
+            A.fromBigInt(unscaledValue * BigInt(10).pow(-bd.scale))
+          }
+        DivisionRing.fromDouble[A](n) ?== expected
+      } else {
+        Prop(true)
+      }
+    }
+  )
+
   // boolean rings
 
   def boolRng(implicit A: BoolRng[A]) = RingProperties.fromParent(
@@ -286,23 +309,7 @@ trait RingLaws[A] extends GroupLaws[A] { self =>
     name = "field",
     al = additiveCommutativeGroup,
     ml = multiplicativeCommutativeGroup,
-    parents = Seq(euclideanRing),
-    "fromDouble" -> forAll { (n: Double) =>
-      if (Platform.isJvm) {
-        // TODO: BigDecimal(n) is busted in scalajs, so we skip this test.
-        val bd = new java.math.BigDecimal(n)
-        val unscaledValue = new BigInt(bd.unscaledValue)
-        val expected =
-          if (bd.scale > 0) {
-            A.div(A.fromBigInt(unscaledValue), A.fromBigInt(BigInt(10).pow(bd.scale)))
-          } else {
-            A.fromBigInt(unscaledValue * BigInt(10).pow(-bd.scale))
-          }
-        Field.fromDouble[A](n) ?== expected
-      } else {
-        Prop(true)
-      }
-    }
+    parents = Seq(euclideanRing, divisionRing)
   )
 
   // Approximate fields such a Float or Double, even through filtered using FPFilter, do not work well with