From 880efac15bba02e7c3f61a0fe4eead3e0040b5ba Mon Sep 17 00:00:00 2001
From: Glen Whitney <glen@studioinfinity.org>
Date: Tue, 2 Aug 2022 10:32:06 -0700
Subject: [PATCH] feat(gcd,lcm): Allow arbitrarily many arguments

  And add an 'associate' predicate for two complex numbers to check the results
---
 src/complex/associate.mjs  | 17 +++++++++++++++++
 src/complex/native.mjs     |  1 +
 src/generic/arithmetic.mjs |  1 +
 src/generic/lcm.mjs        |  3 +++
 test/_pocomath.mjs         |  9 +++++++++
 5 files changed, 31 insertions(+)
 create mode 100644 src/complex/associate.mjs

diff --git a/src/complex/associate.mjs b/src/complex/associate.mjs
new file mode 100644
index 0000000..c6fab9e
--- /dev/null
+++ b/src/complex/associate.mjs
@@ -0,0 +1,17 @@
+export * from './Types/Complex.mjs'
+
+/* Returns true if w is z multiplied by a complex unit */
+export const associate = {
+    'Complex,Complex': ({
+        'multiply(Complex,Complex)': times,
+        'equal(Complex,Complex)': eq,
+        zero,
+        one,
+        complex,
+        'negate(Complex)': neg
+    }) => (w,z) => {
+        if (eq(w,z) || eq(w,neg(z))) return true
+        const ti = times(z, complex(zero(z.re), one(z.im)))
+        return eq(w,ti) || eq(w,neg(ti))
+    }
+}
diff --git a/src/complex/native.mjs b/src/complex/native.mjs
index bea1db8..4f63c8f 100644
--- a/src/complex/native.mjs
+++ b/src/complex/native.mjs
@@ -3,6 +3,7 @@ export * from './Types/Complex.mjs'
 export {abs} from './abs.mjs'
 export {absquare} from './absquare.mjs'
 export {add} from './add.mjs'
+export {associate} from './associate.mjs'
 export {conjugate} from './conjugate.mjs'
 export {complex} from './complex.mjs'
 export {equal} from './equal.mjs'
diff --git a/src/generic/arithmetic.mjs b/src/generic/arithmetic.mjs
index f6abd23..04948df 100644
--- a/src/generic/arithmetic.mjs
+++ b/src/generic/arithmetic.mjs
@@ -3,6 +3,7 @@ import {reducingOperation} from './reducingOperation.mjs'
 export * from './Types/generic.mjs'
 
 export const add = reducingOperation
+export const gcd = reducingOperation
 export {lcm} from './lcm.mjs'
 export {mean} from './mean.mjs'
 export {mod} from './mod.mjs'
diff --git a/src/generic/lcm.mjs b/src/generic/lcm.mjs
index adc3dfb..04e78b5 100644
--- a/src/generic/lcm.mjs
+++ b/src/generic/lcm.mjs
@@ -1,3 +1,5 @@
+import {reducingOperation} from './reducingOperation.mjs'
+
 export const lcm = {
    'T,T': ({
       'multiply(T,T)': multT,
@@ -5,3 +7,4 @@ export const lcm = {
       'gcd(T,T)': gcdT
    }) => (a,b) => multT(quotT(a, gcdT(a,b)), b)
 }
+Object.assign(lcm, reducingOperation)
diff --git a/test/_pocomath.mjs b/test/_pocomath.mjs
index 18643b0..1d7d1e9 100644
--- a/test/_pocomath.mjs
+++ b/test/_pocomath.mjs
@@ -103,4 +103,13 @@ describe('The default full pocomath instance "math"', () => {
       assert.strictEqual(math.choose(21n, 2n), 210n)
    })
 
+   it('calculates multi-way gcds and lcms', () => {
+      assert.strictEqual(math.gcd(30,105,42), 3)
+      assert.ok(
+         math.associate(
+            math.lcm(
+               math.complex(2n,1n), math.complex(1n,1n), math.complex(0n,1n)),
+            math.complex(1n,3n)))
+   })
+
 })