1 files changed, 87 insertions, 0 deletions
diff --git a/std/Math/Rational.bruijn b/std/Math/Rational.bruijn
new file mode 100644
index 0000000..4c2f046
--- /dev/null
+++ b/std/Math/Rational.bruijn
@@ -0,0 +1,87 @@
+# ideas by u/DaVinci103
+# MIT License, Copyright (c) 2024 Marvin Borner
+
+# (p : q) ⇔ (1 / (q + 1))
+
+:import std/Combinator .
+:import std/Logic .
+:import std/Pair .
+:import std/Math N
+
+# returns true if two rational numbers are equal
+eq? &[[&[[N.eq? (N.mul 3 N.++0) (N.mul N.++2 1)]]]] ⧗ Rational → Rational → Boolean
+
+…=?… eq?
+
+:test (((+1) : (+3)) =? ((+2) : (+7))) (true)
+:test ((+0.5) =? (+0.5)) (true)
+:test ((+42.0) =? (+42.0)) (true)
+:test ((+0.4) =? (+0.5)) (false)
+
+# finds smallest equivalent representation of a rational number
+compress &[[[(N.div 2 0) : N.--(N.div N.++1 0)] (N.gcd 1 N.++0)]] ⧗ Rational → Rational
+
+%‣ compress
+
+:test (%((+4) : (+1)) =? (+2.0)) (true)
+:test (%((+4) : (+7)) =? (+0.5)) (true)
+
+# adds two rational numbers
+add &[[&[[p : q]]]] ⧗ Rational → Rational → Rational
+	p N.add (N.mul 3 N.++0) (N.mul 1 N.++2)
+	q N.add (N.mul 2 0) (N.add 2 0)
+
+…+… add
+
+:test ((+0.5) + (+0.5) =? (+1.0)) (true)
+:test ((+1.8) + (+1.2) =? (+3.0)) (true)
+:test ((-1.8) + (+1.2) =? (-0.6)) (true)
+
+# subtracts two rational numbers
+sub &[[&[[p : q]]]] ⧗ Rational → Rational → Rational
+	p N.sub (N.mul 3 N.++0) (N.mul 1 N.++2)
+	q N.add (N.mul 2 0) (N.add 2 0)
+
+…-… sub
+
+:test ((+0.5) - (+0.5) =? (+0.0)) (true)
+:test ((+3.0) - (+1.8) =? (+1.2)) (true)
+:test ((+1.8) - (-1.2) =? (+3.0)) (true)
+
+# negates a rational number
+negate &[[N.-1 : 0]] ⧗ Rational → Rational
+
+-‣ negate
+
+:test (-(+0.0) =? (+0.0)) (true)
+:test (-(+4.2) =? (-4.2)) (true)
+:test (-(-4.2) =? (+4.2)) (true)
+
+# multiplies two rational numbers
+mul &[[&[[p : q]]]] ⧗ Rational → Rational → Rational
+	p N.mul 3 1
+	q N.add (N.mul 2 0) (N.add 2 0)
+
+…⋅… mul
+
+:test ((+5.0) ⋅ (+5.0) =? (+25.0)) (true)
+:test ((+1.8) ⋅ (+1.2) =? (+2.16)) (true)
+
+# finds the multiplicative inverse of a rational number
+invert &[[N.compare-case eq gt lt 1 (+0)]] ⧗ Rational → Rational
+	eq Ω
+	gt N.++0 : N.--1
+	lt N.-(N.++0) : N.--(N.-1)
+
+~‣ invert
+
+:test (~(+0.5) =? (+2.0)) (true)
+:test (~(-0.5) =? (-2.0)) (true)
+
+# divides two rational numbers
+div [[1 ⋅ ~0]] ⧗ Rational → Rational → Rational
+
+…/… div
+
+:test ((+8.0) / (+4.0) =? (+2.0)) (true)
+:test ((+18.0) / (+12.0) =? (+1.5)) (true)