feat: Add complex numbers

No negation (and therefore no subtraction) since that needs self-reference.

complex/Complex.mjs

@@ -0,0 +1,14 @@
+import typed from 'typed-function'
+
+/* Use a plain object with keys re and im for a complex */
+typed.addType({
+   name: 'Complex',
+   test: z => z && typeof z === 'object' && 're' in z && 'im' in z
+})
+
+typed.addConversion({
+   from: 'number',
+   to: 'Complex',
+   convert: x => ({re: x, im: 0})
+})
+

complex/add.mjs

@@ -0,0 +1,12 @@
+import './Complex.mjs'
+
+export const add = {
+   '...Complex': [[], addends => {
+      const sum = {re: 0, im: 0}
+      addends.forEach(addend => {
+         sum.re += addend.re
+         sum.im += addend.im
+      })
+      return sum
+   }]
+}

complex/all.mjs

@@ -0,0 +1,2 @@
+export {complex} from './complex.mjs'
+export {add} from './add.mjs'

complex/complex.mjs

@@ -0,0 +1,6 @@
+import './Complex.mjs'
+
+export const complex = {
+   'number, number': [[], (x, y) => ({re: x, im: y})],
+   Complex: [[], z => z]
+}

pocomath.mjs

@@ -1,8 +1,10 @@
 /* Core of pocomath: generates the default instance */
 import PocomathInstance from './PocomathInstance.mjs'
 import * as numbers from './number/all.mjs'
+import * as complex from './complex/all.mjs'
 
 const math = new PocomathInstance('math')
 math.install(numbers)
+math.install(complex)
 
 export default math

test/_pocomath.mjs

@@ -16,4 +16,18 @@ describe('The default full pocomath instance "math"', () => {
       assert.strictEqual(math.negate(-1), 1)
       assert.strictEqual(math.add(10, math.negate(3)), 7)
    })
+
+   it('can be extended', () => {
+      math.install({'add': {
+         '...string': [[], addends => addends.reduce((x,y) => x+y, '')]
+      }})
+      assert.strictEqual(math.add('Kilroy',' is here'), 'Kilroy is here')
+   })
+
+   it('handles complex numbers', () => {
+      const norm13 = {re: 2, im: 3}
+      assert.deepStrictEqual(math.complex(2,3), norm13)
+      assert.deepStrictEqual(math.complex(2), math.complex(2,0))
+      assert.deepStrictEqual(math.add(2, math.complex(0,3)), norm13)
+   })
 })

test/custom.mjs

@@ -0,0 +1,21 @@
+import assert from 'assert'
+import typed from 'typed-function'
+import PocomathInstance from '../PocomathInstance.mjs'
+import * as numbers from '../number/all.mjs'
+import * as complex from '../complex/all.mjs'
+
+const bw = new PocomathInstance('backwards')
+describe('A custom instance', () => {
+   it("works when partially assembled", () => {
+      bw.install(complex)
+      assert.deepStrictEqual(bw.add(2, bw.complex(0, 3)), {re: 2, im: 3})
+   })
+
+   it("can be assembled in any order", () => {
+      bw.install(numbers)
+      typed.addConversion({from: 'string', to: 'number', convert: x => +x})
+      assert.strictEqual(bw.subtract(16, bw.add(3,4,2)), 7)
+      assert.strictEqual(bw.negate('8'), -8)
+      assert.deepStrictEqual(bw.add(bw.complex(1,3), 1), {re: 2, im: 3})
+   })
+})