Fix reduce code

@@ -61,7 +61,11 @@ impl Fractional {
         // the precision but ensures smaller numbers for numerator and
         // denominator.
         if _d > 1 && (_n % _d) * 10000000 < _n {
-            Self(_n / _d, 1)
+            if n == _n {
+                Self(_n / _d, 1)
+            } else {
+                Self(1, _n / _d)
+            }
         } else {
             Self(n / hcf(n, d), d / hcf(n, d))
         }

@@ -21,6 +21,8 @@
 use std::convert::{TryFrom, TryInto, Into};
 use std::num::TryFromIntError;
 use std::f64::consts::PI as FPI;
+use std::fmt::Display;
+use std::ops::{Add,Sub,Neg,Mul,Div};
 
 use fractional::continuous::Continuous;
 use fractional::fractional::{Fractional, from_vector};
@@ -96,7 +98,7 @@ fn pi() {
 }
 
 fn _sin() {
-    for d in [ 0, 45, 90, 135, 180, 225, 270, 315
+    for d in [ 0, 30, 45, 90, 135, 180, 225, 270, 315
              , 9, 17, 31, 73, 89, 123, 213, 312, 876 ].iter() {
         let s       = Fractional::sin(*d as i32);
         let sr :f64 = s.try_into().unwrap();
@@ -107,7 +109,7 @@ fn _sin() {
 }
 
 fn _tan() {
-    for d in [ 0, 45, 90, 135, 180, 225, 270, 315
+    for d in [ 0, 30, 45, 90, 135, 180, 225, 270, 315
              , 9, 17, 31, 73, 89, 123, 213, 312, 876 ].iter() {
         let t       = Fractional::tan(*d as i32);
         let tr :f64 = t.try_into().unwrap();
@@ -118,7 +120,7 @@ fn _tan() {
 }
 
 fn _cos() {
-    for d in [ 0, 45, 90, 135, 180, 225, 270, 315
+    for d in [ 0, 30, 45, 90, 135, 180, 225, 270, 315
              , 9, 17, 31, 73, 89, 123, 213, 312, 876 ].iter() {
         let c       = Fractional::cos(*d as i32);
         let cr :f64 = c.try_into().unwrap();
@@ -128,11 +130,25 @@ fn _cos() {
     }
 }
 
-fn _vector() {
+fn _vector1() {
     let v1 = Vector(1.into(), 2.into(), 3.into());
     let v2 = Vector(2.into(), 2.into(), 3.into());
     let s :Fractional = 3.into();
 
+    _vector(v1, v2, s);
+}
+
+fn _vector2() {
+    let v1 = Vector(1.0, 2.0, 3.0);
+    let v2 = Vector(2.0, 2.0, 3.0);
+    let s = 3.0;
+
+    _vector(v1, v2, s);
+}
+
+fn _vector<T>(v1 :Vector<T>, v2 :Vector<T>, s :T)
+    where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
+           + Mul<Output = T> + Div<Output = T> + Trig + Copy + Display {
     println!("{:>14} : {}", "Vector v1", v1);
     println!("{:>14} : {}", "Vector v2", v2);
     println!("{:>14} : {}", "abs v1", v1.abs());
@@ -153,16 +169,34 @@ fn _vector() {
     println!("{:>14} : {}", "v2 * v1", v2 * v1);
 }
 
-fn _transform() {
-    let v   = Vector(Fractional(1,1), Fractional(1,1), Fractional(1,1));
-    let v1  = Vector(Fractional(1,1), Fractional(2,1), Fractional(3,1));
-    let mt  = translate(v);
+fn _transform1() {
+    let v  = Vector(Fractional(1,1), Fractional(1,1), Fractional(1,1));
+    let v1 = Vector(Fractional(1,1), Fractional(2,1), Fractional(3,1));
+    let v2 = Vector(Fractional(1,1), Fractional(1,1), Fractional(0,1));
+    let v3 = Vector(Fractional(1,1), Fractional(0,1), Fractional(1,1));
+
+    _transform(v, v1, v2, v3);
+}
+
+fn _transform2() {
+    let v  = Vector(1.0, 1.0, 1.0);
+    let v1 = Vector(1.0, 2.0, 3.0);
+    let v2 = Vector(1.0, 1.0, 0.0);
+    let v3 = Vector(1.0, 0.0, 1.0);
+
+    _transform(v, v1, v2, v3);
+}
+
+fn _transform<T>(v :Vector<T>, v1 :Vector<T>, v2 :Vector<T>, v3 :Vector<T>)
+    where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
+           + Mul<Output = T> + Div<Output = T> + Trig
+           + From<i32> + Copy + Display {
+    let mt = translate(v);
 
     println!("{:>14} : {}", "Vector v1", v1);
     println!("{:>14} : {}", "translate v1", mt.apply(&v1));
     println!();
 
-    let v2  = Vector(1.into(), 1.into(), 0.into());
     println!("{:>14} : {}", "Vector v2", v2);
     for d in [ 30, 45, 60, 90, 120, 135, 150, 180
              , 210, 225, 240, 270, 300, 315, 330 ].iter() {
@@ -186,7 +220,6 @@ fn _transform() {
     }
     println!();
 
-    let v3  = Vector(Fractional(1,1), Fractional(0,1), Fractional(1,1));
     println!("{:>14} : {}", "Vector v3", v3);
     for d in [ 30, 45, 60, 90, 120, 135, 150, 180
              , 210, 225, 240, 270, 300, 315, 330 ].iter() {
@@ -217,7 +250,11 @@ fn main() {
     println!();
     _tan();
     println!();
-    _vector();
+    _vector1();
+    println!();
+    _vector2();
+    println!();
+    _transform1();
     println!();
-    _transform();
+    _transform2();
 }