docs, int operations

src/fr.gleam

@@ -3,6 +3,7 @@ import gleam/list
 import gleam/order
 import internal/utils
 
+/// A number type represented as a fraction of two integers
 pub type Fr {
   Fr(n: Int, d: Int)
 }
@@ -25,7 +26,8 @@ pub fn int(n) {
   Fr(n, 1)
 }
 
-pub fn to_string(a: Fr) {
+/// Stringifies the number as a fraction
+pub fn to_frac_string(a: Fr) {
   let a = a |> norm
   let n = a.n |> int.to_string
   let d = a.d |> int.to_string
@@ -36,11 +38,19 @@ pub fn to_string(a: Fr) {
   }
 }
 
+/// Normalizes the fraction to the simplest possible form
 pub fn norm(a: Fr) {
+  // protect from zero division
+  let a = case a.d {
+    0 -> zero
+    _ -> a
+  }
+  // only allow minus sign in the numerator
   let a = case a.d > 0 {
     True -> a
     False -> Fr(-a.n, -a.d)
   }
+  // reduce the fraction if possible
   case utils.gcd(a.n, a.d) {
     1 -> a
     gcd -> Fr(a.n / gcd, a.d / gcd)
@@ -60,14 +70,26 @@ pub fn add(a: Fr, b: Fr) {
   Fr(cd / a.d * a.n + cd / b.d * b.n, cd) |> norm
 }
 
+pub fn add_int(a: Fr, b: Int) {
+  a |> add(int(b))
+}
+
 pub fn sub(a: Fr, b: Fr) {
   b |> neg |> add(a)
 }
 
+pub fn sub_int(a: Fr, b: Int) {
+  a |> sub(int(b))
+}
+
 pub fn mul(a: Fr, b: Fr) {
   Fr(a.n * b.n, a.d * b.d) |> norm
 }
 
+pub fn mul_int(a: Fr, b: Int) {
+  a |> mul(int(b))
+}
+
 pub fn div(a: Fr, b: Fr) {
   case b.n {
     0 -> int(0)
@@ -75,6 +97,10 @@ pub fn div(a: Fr, b: Fr) {
   }
 }
 
+pub fn div_int(a: Fr, b: Int) {
+  a |> div(int(b))
+}
+
 pub fn sum(l: List(Fr)) {
   list.fold(l, zero, add)
 }

src/gleamath.gleam

@@ -1,9 +1,9 @@
 //     fr  fr
-import fr.{Fr}
+import fr
 import gleam/io
 
 pub fn main() {
   fr.pi
-  |> fr.to_string
+  |> fr.to_frac_string
   |> io.println
 }