feat: Implement subtypes

This should eventually be moved into typed-function itself, but for
  now it can be implemented on top of the existing typed-function.

  Uses subtypes to define (and error-check) gcd and lcm, which are only
  defined for integer arguments.

  Resolves #36.

src/complex/Types/Complex.mjs

@@ -12,9 +12,19 @@ const Complex = new PocomathInstance('Complex')
 Complex.installType('Complex', {
    test: isComplex,
    from: {
-      number: x => ({re: x, im: 0}),
+      number: x => ({re: x, im: 0})
+   }
+})
+Complex.installType('GaussianInteger', {
+   test: z => typeof z.re == 'bigint' && typeof z.im == 'bigint',
+   refines: 'Complex',
+   from: {
       bigint: x => ({re: x, im: 0n})
    }
 })
 
+Complex.promoteUnary = {
+   Complex: ({self,complex}) => z => complex(self(z.re), self(z.im))
+}
+
 export {Complex}

src/complex/abs.mjs

@@ -1,5 +1,5 @@
 export * from './Types/Complex.mjs'
 
-export const abs = {Complex: ({sqrt, add, multiply}) => z => {
-    return sqrt(add(multiply(z.re, z.re), multiply(z.im, z.im)))
-}}
+export const abs = {
+    Complex: ({sqrt, 'absquare(Complex)': absq}) => z => sqrt(absq(z))
+}

src/complex/absquare.mjs

@@ -0,0 +1,5 @@
+export * from './Types/Complex.mjs'
+
+export const absquare = {
+   Complex: ({add, square}) => z => add(square(z.re), square(z.im))
+}

src/complex/conjugate.mjs

@@ -0,0 +1,6 @@
+export * from './Types/Complex.mjs'
+
+export const conjugate = {
+   Complex: ({negate, complex}) => z => complex(z.re, negate(z.im))
+}
+

src/complex/gcd.mjs

@@ -0,0 +1,17 @@
+import PocomathInstance from '../core/PocomathInstance.mjs'
+import * as Complex from './Types/Complex.mjs'
+import gcdType from '../generic/gcdType.mjs'
+
+const imps = {
+   gcdComplexRaw: gcdType('Complex'),
+   gcd: { // Only return gcds with positive real part
+      'Complex, Complex': ({gcdComplexRaw, sign, one, negate}) => (z,m) => {
+         const raw = gcdComplexRaw(z, m)
+         if (sign(raw.re) === one(raw.re)) return raw
+         return negate(raw)
+      }
+   }
+}
+
+export const gcd = PocomathInstance.merge(Complex, imps)
+

src/complex/isZero.mjs

@@ -0,0 +1,5 @@
+export * from './Types/Complex.mjs'
+
+export const isZero = {
+   Complex: ({self}) => z => self(z.re) && self(z.im)
+}

src/complex/multiply.mjs

@@ -0,0 +1,14 @@
+export * from './Types/Complex.mjs'
+
+export const multiply = {
+   'Complex,Complex': ({
+      'complex(any,any)': cplx,
+      add,
+      subtract,
+      self
+   }) => (w,z) => {
+      return cplx(
+         subtract(self(w.re, z.re), self(w.im, z.im)),
+         add(self(w.re, z.im), self(w.im, z.re)))
+   }
+}

src/complex/native.mjs

@@ -1,8 +1,18 @@
+import gcdType from '../generic/gcdType.mjs'
+
 export * from './Types/Complex.mjs'
 
 export {abs} from './abs.mjs'
+export {absquare} from './absquare.mjs'
 export {add} from './add.mjs'
+export {conjugate} from './conjugate.mjs'
 export {complex} from './complex.mjs'
+export {gcd} from './gcd.mjs'
+export {isZero} from './isZero.mjs'
+export {multiply} from './multiply.mjs'
 export {negate} from './negate.mjs'
+export {quotient} from './quotient.mjs'
+export {roundquotient} from './roundquotient.mjs'
 export {sqrt} from './sqrt.mjs'
+export {zero} from './zero.mjs'
 

src/complex/negate.mjs

@@ -1,5 +1,5 @@
-export * from './Types/Complex.mjs'
+import {Complex} from './Types/Complex.mjs'
 
-export const negate = {
-   Complex: ({self}) => z => ({re: self(z.re), im: self(z.im)})
-}
+const negate = Complex.promoteUnary
+
+export {Complex, negate}

src/complex/quotient.mjs

@@ -0,0 +1,5 @@
+export * from './roundquotient.mjs'
+
+export const quotient = {
+   'Complex,Complex': ({roundquotient}) => (w,z) => roundquotient(w,z)
+}

src/complex/roundquotient.mjs

@@ -0,0 +1,17 @@
+export * from './Types/Complex.mjs'
+
+export const roundquotient = {
+   'Complex,Complex': ({
+      'isZero(Complex)': isZ,
+      conjugate,
+      'multiply(Complex,Complex)': mult,
+      absquare,
+      self,
+      complex
+   }) => (n,d) => {
+      if (isZ(d)) return d
+      const cnum = mult(n, conjugate(d))
+      const dreal = absquare(d)
+      return complex(self(cnum.re, dreal), self(cnum.im, dreal))
+   }
+}

src/complex/zero.mjs

@@ -0,0 +1,5 @@
+import {Complex} from './Types/Complex.mjs'
+
+const zero = Complex.promoteUnary
+
+export {Complex, zero}