refactor: Make generics more strict via templates

This commit also adds a built-in `typeOf` function to every PocomathInstance.
  It also adds a notation (prefix '!') for "eager" templeates that
  instantiate themselves for all types immediately upon definition.

src/complex/add.mjs

@@ -1,10 +1,20 @@
 export * from './Types/Complex.mjs'
 
 export const add = {
+   /* Relying on conversions for both complex + number and complex + bigint
+    * leads to an infinite loop when adding a number and a bigint, since they
+    * both convert to Complex.
+    */
    'Complex,number': ({
       'self(number,number)': addNum,
       'complex(any,any)': cplx
    }) => (z,x) => cplx(addNum(z.re, x), z.im),
+
+   'Complex,bigint': ({
+      'self(bigint,bigint)': addBigInt,
+      'complex(any,any)': cplx
+   }) => (z,x) => cplx(addBigInt(z.re, x), z.im),
+
    'Complex,Complex': ({
       self,
       'complex(any,any)': cplx

src/complex/equal.mjs

@@ -0,0 +1,19 @@
+export * from './Types/Complex.mjs'
+
+export const equal = {
+   'Complex,number': ({
+      'isZero(number)': isZ,
+      'self(number,number)': eqNum
+   }) => (z, x) => eqNum(z.re, x) && isZ(z.im),
+
+   'Complex,bigint': ({
+      'isZero(bigint)': isZ,
+      'self(bigint,bigint)': eqBigInt
+   }) => (z, b) => eqBigInt(z.re, b) && isZ(z.im),
+
+   'Complex,Complex': ({self}) => (w,z) => self(w.re, z.re) && self(w.im, z.im),
+
+   'GaussianInteger,GaussianInteger': ({
+      'self(bigint,bigint)': eq
+   }) => (a,b) => eq(a.re, b.re) && eq(a.im, b.im)
+}

src/complex/native.mjs

@@ -7,6 +7,7 @@ export {absquare} from './absquare.mjs'
 export {add} from './add.mjs'
 export {conjugate} from './conjugate.mjs'
 export {complex} from './complex.mjs'
+export {equal} from './equal.mjs'
 export {gcd} from './gcd.mjs'
 export {invert} from './invert.mjs'
 export {isZero} from './isZero.mjs'

src/complex/sqrt.mjs

@@ -3,7 +3,7 @@ export * from './Types/Complex.mjs'
 export const sqrt = {
    Complex: ({
       config,
-      zero,
+      isZero,
       sign,
       one,
       add,
@@ -16,11 +16,8 @@ export const sqrt = {
    }) => {
       if (config.predictable) {
          return z => {
-            const imZero = zero(z.im)
-            const imSign = sign(z.im)
             const reOne = one(z.re)
-            const reSign = sign(z.re)
-            if (imSign === imZero && reSign === reOne) return complex(self(z.re))
+            if (isZero(z.im) && sign(z.re) === reOne) return complex(self(z.re))
             const reTwo = add(reOne, reOne)
             return complex(
                multiply(sign(z.im), self(divide(add(abs(z),z.re), reTwo))),
@@ -29,11 +26,8 @@ export const sqrt = {
          }
       }
       return z => {
-         const imZero = zero(z.im)
-         const imSign = sign(z.im)
          const reOne = one(z.re)
-         const reSign = sign(z.re)
-         if (imSign === imZero && reSign === reOne) return self(z.re)
+         if (isZero(z.im) && sign(z.re) === reOne) return self(z.re)
          const reTwo = add(reOne, reOne)
          return complex(
             multiply(sign(z.im), self(divide(add(abs(z),z.re), reTwo))),