add implicitly chain for angle conversion factors

.travis.yml

@@ -13,6 +13,7 @@ install:
 - rvm use 2.2.3 --install --fuzzy
 - gem update --system
 - gem install sass
+- gem install ruby_dep -v 1.3.1
 - gem install jekyll -v 3.2.1
 before_script:
 - if [ $TRAVIS_PULL_REQUEST = 'false' ]; then git checkout -qf $TRAVIS_BRANCH; fi

src/main/scala/libra/nonsi/package.scala

@@ -32,16 +32,6 @@ package object nonsi {
   implicit def gradian: Show[Gradian] = Show[Gradian]("gon")
   implicit def turn: Show[Turn] = Show[Turn]("tr")
 
-  implicit def degreeArcminuteConversion[A](
-      implicit c: ConvertableTo[A]
-  ): ConversionFactor[A, Angle, Degree, Arcminute] =
-    new ConversionFactor(c.fromInt(60))
-
-  implicit def degreeArcsecondConversion[A](
-      implicit c: ConvertableTo[A]
-  ): ConversionFactor[A, Angle, Degree, Arcsecond] =
-    new ConversionFactor(c.fromInt(3600))
-
   implicit def arcminuteArcsecondConversion[A](
       implicit c: ConvertableTo[A]
   ): ConversionFactor[A, Angle, Arcminute, Arcsecond] =
@@ -52,72 +42,21 @@ package object nonsi {
   ): ConversionFactor[A, Angle, Radian, Degree] =
     new ConversionFactor(c.fromDouble(180.0 / pi))
 
-  implicit def radianArcminuteConversion[A](
-      implicit c: ConvertableTo[A],
-      multiplicative: MultiplicativeSemigroup[A]
-  ): ConversionFactor[A, Angle, Radian, Arcminute] =
-    degreeArcminuteConversion.compose(radianDegreeConversion)
-
-  implicit def radianArcsecondConversion[A](
-      implicit c: ConvertableTo[A],
-      multiplicative: MultiplicativeSemigroup[A]
-  ): ConversionFactor[A, Angle, Radian, Arcsecond] =
-    degreeArcsecondConversion.compose(radianDegreeConversion)
+  implicit def degreeArcminuteConversion[A](
+      implicit c: ConvertableTo[A]
+  ): ConversionFactor[A, Angle, Degree, Arcminute] =
+    new ConversionFactor(c.fromInt(60))
 
   implicit def gradianRadianConversion[A](
       implicit c: ConvertableTo[A]
   ): ConversionFactor[A, Angle, Gradian, Radian] =
     new ConversionFactor(c.fromDouble(pi / 200.0))
 
-  implicit def gradianDegreeConversion[A](
-      implicit c: ConvertableTo[A],
-      multiplicative: MultiplicativeSemigroup[A]
-  ): ConversionFactor[A, Angle, Gradian, Degree] =
-    radianDegreeConversion.compose(gradianRadianConversion)
-
-  implicit def gradianArcminuteConversion[A](
-      implicit c: ConvertableTo[A],
-      multiplicative: MultiplicativeSemigroup[A]
-  ): ConversionFactor[A, Angle, Gradian, Arcminute] =
-    radianArcminuteConversion.compose(gradianRadianConversion)
-
-  implicit def gradianArcsecondConversion[A](
-      implicit c: ConvertableTo[A],
-      multiplicative: MultiplicativeSemigroup[A]
-  ): ConversionFactor[A, Angle, Gradian, Arcsecond] =
-    radianArcsecondConversion.compose(gradianRadianConversion)
-
   implicit def turnGradianConversion[A](
       implicit c: ConvertableTo[A]
   ): ConversionFactor[A, Angle, Turn, Gradian] =
     new ConversionFactor(c.fromInt(400))
 
-  implicit def turnRadianConversion[A](
-      implicit c: ConvertableTo[A],
-      multiplicative: MultiplicativeSemigroup[A]
-  ): ConversionFactor[A, Angle, Turn, Radian] =
-    gradianRadianConversion.compose(turnGradianConversion)
-
-  implicit def turnDegreeConversion[A](
-      implicit c: ConvertableTo[A],
-      multiplicative: MultiplicativeSemigroup[A]
-  ): ConversionFactor[A, Angle, Turn, Degree] =
-    gradianDegreeConversion.compose(turnGradianConversion)
-
-  implicit def turnArcminuteConversion[A](
-      implicit c: ConvertableTo[A],
-      multiplicative: MultiplicativeSemigroup[A]
-  ): ConversionFactor[A, Angle, Turn, Arcminute] =
-    gradianArcminuteConversion.compose(turnGradianConversion)
-
-  implicit def turnArcsecondConversion[A](
-      implicit c: ConvertableTo[A],
-      multiplicative: MultiplicativeSemigroup[A]
-  ): ConversionFactor[A, Angle, Turn, Arcsecond] =
-    gradianArcsecondConversion.compose(turnGradianConversion)
-
-
-
   type AngularVelocityQuantity[A, L <: UnitOfMeasure[Angle], T <: UnitOfMeasure[Time]] =
     Quantity[A, Term[Angle, L, Fraction[1, 1]] :: Term[Time, T, Fraction[-1, 1]] :: HNil]
 

src/main/scala/libra/ops/base.scala

@@ -1,10 +1,10 @@
 package libra
 package ops
 
-import libra.UnitOfMeasure
+import libra.nonsi.Angle
+import shapeless.Lazy
 import spire.algebra._
 import spire.implicits._
-import spire.math.ConvertableFrom
 
 object base {
 
@@ -32,6 +32,16 @@ object base {
       new ConversionFactor(otherConversionFactor.value * value)
   }
 
+  object ConversionFactor {
+    implicit def inductiveAngelConversionFactor[A, From <: UnitOfMeasure[Angle], To <: UnitOfMeasure[Angle], Next <: UnitOfMeasure[Angle]](
+      implicit multiplicativeSemigroup: MultiplicativeSemigroup[A],
+      fromConversion: ConversionFactor[A, Angle, From, Next],
+      toConversion: Lazy[ConversionFactor[A, Angle, Next, To]]
+    ):ConversionFactor[A, Angle, From, To] =
+      new ConversionFactor(fromConversion.value * toConversion.value.value)
+
+  }
+
   /** Derived typeclass for the conversion factor from F to T
     *
     * Two conversions (from and to) are derived from a single conversion factor