Remove totative ratio from factors API

This value can easily be calculated as φ(r)/r.  There is no need to have
this now that I have a function φ(r) (renamed to its mathematical name,
Totient).

I removed totative ratio instead of totient because, while it is more
important, totient is an integer while totative ratio is a float.  This
means that the totative ratio can be calculated exactly from the
totient, but not the other way round.

3 files changed, 23 insertions, 22 deletions

diff --git a/factor_info.go b/factor_info.go
index f908b9b..c243048 100644
--- a/factor_info.go
+++ b/factor_info.go
@@ -22,7 +22,7 @@ type FactorInfo struct {
 	Score float64
 	// The number of digits that are totatives (numbers that share no
 	// factors with the radix - they are the worst kind of digits)
-	TotativeCount uint
+	Totient uint
 	// The fraction of digits that are totatives (numbers that share no
 	// factors with the radix - they are the worst kind of digits)
 	TotativeRatio float64
@@ -77,10 +77,13 @@ func GetFactorInfo(radix uint, fullMap bool) *FactorInfo {
 		digitMap = []factors.DigitType{}
 	}
 
+	totativeCount := factors.Totient(radix)
+	totativeRatio := float64(totativeCount) / float64(radix)
+
 	return &FactorInfo{radix, factors.PrimeFactorize(radix),
-		r_factors, factors.Score(radix), factors.TotativeCount(radix),
-		factors.TotativeRatio(radix), factors.BasicRank(radix),
-		r_type_ptr, mtc_ptr, math.Log(float64(radix)), digitMap}
+		r_factors, factors.Score(radix), totativeCount, totativeRatio,
+		factors.BasicRank(radix), r_type_ptr, mtc_ptr,
+		math.Log(float64(radix)), digitMap}
 }
 
 func (fi *FactorInfo) WriteTo(w io.Writer) {
@@ -88,7 +91,7 @@ func (fi *FactorInfo) WriteTo(w io.Writer) {
 	fmt.Fprintf(w, "Factors: %v (Score: %.4f)\n", fi.Factors, fi.Score)
 	fmt.Fprintln(w, "2345 Rank:", fi.BasicRank)
 	fmt.Fprintf(w, "Totative Digit Count: %d (%.3f%%)\n",
-		fi.TotativeCount, fi.TotativeRatio * 100.0)
+		fi.Totient, fi.TotativeRatio * 100.0)
 	if fi.Type != nil {
 		writeTypeMessage(w, *fi.Type)
 	}
@@ -105,7 +108,7 @@ func (fi *FactorInfo) WriteTo(w io.Writer) {
 }
 
 func (fi *FactorInfo) WriteToCompact(w io.Writer) {
-	fmt.Fprintf(w, "%d = %s | σ(n)/n: %.2f | τ(n)/n: %.3f\n",
+	fmt.Fprintf(w, "%d = %s | σ(n)/n: %.2f | φ(n)/n: %.3f\n",
 		fi.Radix, fi.PrimeFactorization, fi.Score, fi.TotativeRatio)
 	if fi.Type != nil {
 		fmt.Fprintf(w, "%s | ", typeAbbrev(*fi.Type))
diff --git a/factors/factors_test.go b/factors/factors_test.go
index af91e70..745fd2c 100644
--- a/factors/factors_test.go
+++ b/factors/factors_test.go
@@ -67,17 +67,25 @@ var totativeRatioCases = map[uint]float64{
 	30: 4.0 / 15.0, 60: 4.0 / 15.0, 120: 4.0 / 15.0,
 }
 
+func totativeRatio(n uint) float64 {
+	if n == 0 {
+		panic("0 has no totative ratio!")
+	}
+
+	return float64(Totient(n)) / float64(n)
+}
+
 func TestTotativeRatio(t *testing.T) {
-	tableTest(t, TotativeRatio, totativeRatioCases, stdEquals, "TotativeRatio")
+	tableTest(t, totativeRatio, totativeRatioCases, stdEquals, "TotativeRatio")
 }
 
-var totativeCountCases = map[uint]uint{
-	1: 1, 2: 1, 3: 2, 4: 2, 6: 2, 7: 6, 8: 4, 12: 4,
+var totientCases = map[uint]uint{
+	0: 0, 1: 1, 2: 1, 3: 2, 4: 2, 6: 2, 7: 6, 8: 4, 12: 4,
 	14: 6, 15: 8, 30: 8, 60: 16, 120: 32,
 }
 
 func TestTotativeCount(t *testing.T) {
-	tableTest(t, TotativeCount, totativeCountCases, stdEquals, "TotativeCount")
+	tableTest(t, Totient, totientCases, stdEquals, "Totient")
 }
 
 var factorScoreCases = map[uint]float64{
diff --git a/factors/totative.go b/factors/totative.go
index 7a4bebe..680cc26 100644
--- a/factors/totative.go
+++ b/factors/totative.go
@@ -1,18 +1,8 @@
 package factors
 
-// TotativeRatio calculates the fraction of numbers that
+// Totient calculates the number of numbers less than n that
 // are totatives of n (share no factors with n)
-func TotativeRatio(n uint) float64 {
-	if n == 0 {
-		panic("0 has no totative ratio!")
-	}
-
-	return float64(TotativeCount(n)) / float64(n)
-}
-
-// TotativeCount calculates the number of numbers less than n that
-// are totatives of n (share no factors with n)
-func TotativeCount(n uint) uint {
+func Totient(n uint) uint {
 	if n == 0 {
 		return 0
 	}