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+:import std/Combinator .
+:import std/Logic .
+:import std/Pair .
+
+# negative trit indicating coefficient of (-1)
+t⁻ [[[2]]]
+
+# positive trit indicating coefficient of (+1)
+t⁺ [[[1]]]
+
+# zero trit indicating coefficient of 0
+t⁰ [[[0]]]
+
+# shifts a negative trit into a balanced ternary number
+↑⁻‣ [[[[[2 (4 3 2 1 0)]]]]]
+
+# shifts a positive trit into a balanced ternary number
+↑⁺‣ [[[[[1 (4 3 2 1 0)]]]]]
+
+# shifts a zero trit into a balanced ternary number
+↑⁰‣ [[[[[0 (4 3 2 1 0)]]]]]
+
+# shifts a specified trit into a balanced ternary number
+…↑… [[[[[[5 2 1 0 (4 3 2 1 0)]]]]]]
+
+# negates a balanced ternary number
+-‣ [[[[[4 3 1 2 0]]]]]
+
+# increments a balanced ternary number (can introduce leading 0s)
+++‣ [~(0 z a⁻ a⁺ a⁰)]
+	z (+0) : (+1)
+	a⁻ &[[↑⁻1 : ↑⁰1]]
+	a⁺ &[[↑⁺1 : ↑⁻0]]
+	a⁰ &[[↑⁰1 : ↑⁺1]]
+
+# decrements a balanced ternary number (can introduce leading 0s)
+--‣ [~(0 z a⁻ a⁺ a⁰)]
+	z (+0) : (-1)
+	a⁻ &[[↑⁻1 : ↑⁺0]]
+	a⁺ &[[↑⁺1 : ↑⁰1]]
+	a⁰ &[[↑⁰1 : ↑⁻1]]
+
+# converts the normal balanced ternary representation into abstract form
+→^‣ [0 z a⁻ a⁺ a⁰]
+	z (+0)
+	a⁻ [[[[[2 4]]]]]
+	a⁺ [[[[[1 4]]]]]
+	a⁰ [[[[[0 4]]]]]
+
+# converts the abstracted balanced ternary representation back to normal
+→_‣ y [[0 z a⁻ a⁺ a⁰]]
+	z (+0)
+	a⁻ [↑⁻(2 0)]
+	a⁺ [↑⁺(2 0)]
+	a⁰ [↑⁰(2 0)]
+
+# adds two balanced ternary numbers (can introduce leading 0s)
+…+… [[[c (0 z a⁻ a⁺ a⁰)] 1 →^0]]
+	b⁻ [1 ↑⁺(3 0 t⁻) ↑⁰(3 0 t⁰) ↑⁻(3 0 t⁰)]
+	b⁰ [1 ↑ (3 0 t⁰)]
+	b⁺ [1 ↑⁰(3 0 t⁰) ↑⁻(3 0 t⁺) ↑⁺(3 0 t⁰)]
+	a⁻ [[[1 (b⁻ 1) b⁻' b⁰ b⁻]]]
+		b⁻' [1 ↑⁰(3 0 t⁻) ↑⁻(3 0 t⁰) ↑⁺(3 0 t⁻)]
+	a⁺ [[[1 (b⁺ 1) b⁰ b⁺' b⁺]]]
+		b⁺' [1 ↑⁺(3 0 t⁰) ↑⁰(3 0 t⁺) ↑⁻(3 0 t⁺)]
+	a⁰ [[[1 (b⁰ 1) b⁻ b⁺ b⁰]]]
+	z [[0 --(→_1) ++(→_1) →_1]]
+	c [[1 0 t⁰]]
+
+# subtracts two balanced ternary numbers (can introduce leading 0s)
+…-… [[1 + -0]]
+
+# multiplicates two balanced ternary numbers (can introduce leading 0s)
+…⋅… [[1 z a⁻ a⁺ a⁰]]
+	z (+0)
+	a⁻ [↑⁰0 - 1]
+	a⁺ [↑⁰0 + 1]
+	a⁰ [↑⁰0]
+
+# true if balanced ternary number is zero
+=?‣ [0 true [false] [false] i]
+
+# true if two balanced ternary numbers are equal
+# → ignores leading 0s!
+…=?… [[[0 z a⁻ a⁺ a⁰] 1 →^0]]
+	z [=?(→_0)]
+	a⁻ [[0 false [2 0] [false] [false]]]
+	a⁺ [[0 false [false] [2 0] [false]]]
+	a⁰ [[0 (1 0) [false] [false] [2 0]]]
+
+main [[0]]
+
+# --- tests/examples ---
+
+:test ((-42) + (-1) =? (-43)) (true)
+:test ((+1) + (+2) =? (+3)) (true)
+:test ((-42) - (-1) =? (-41)) (true)
+:test ((+1) - (+2) =? (-1)) (true)
+:test ((-1) ⋅ (+42) =? (-42)) (true)
+:test ((+3) ⋅ (+11) =? (+33)) (true)