src/boolean/__test__/BooleanT.spec.js

@@ -11,7 +11,7 @@ describe('BooleanT Type', () => {
    })
    it('autoconverts to number type', () => {
       assert.strictEqual(math.abs(false), 0)
-      assert.strictEqual(math.absquare(true), 1)
+      assert.strictEqual(math.normsq(true), 1)
       assert.strictEqual(math.add(true, true), 2)
       assert.strictEqual(math.divide(false, true), 0)
       assert.strictEqual(math.cbrt(true), 1)

src/complex/__test__/arithmetic.spec.js

@@ -9,10 +9,17 @@ const CplxNum = Complex(NumberT)
 const {full} = ReturnTyping
 
 describe('complex arithmetic operations', () => {
-   it('computes absquare of complex numbers', () => {
+   it('computes norm-square of complex numbers', () => {
-      assert.strictEqual(math.absquare(cplx(3, 4)), 25)
+      assert.strictEqual(math.normsq(cplx(3, 4)), 25)
-      assert.strictEqual(math.absquare(cplx(cplx(2, 3), cplx(4,5))), 54)
+      assert.strictEqual(math.normsq(cplx(cplx(2, 3), cplx(4, 5))), 54)
-      assert.strictEqual(math.absquare(cplx(true, true)), 2)
+      assert.strictEqual(math.normsq(cplx(true, true)), 2)
+   })
+   it('computes norm-magnitude of complex numbers', () => {
+      assert.strictEqual(math.norm(cplx(-3, 4)), 5)
+      assert.strictEqual(
+         math.norm(cplx(cplx(2, -3), cplx(-4, 5))), Math.sqrt(54))
+      const boolnorm = math.norm(cplx(true, true))
+      assert(math.equal(boolnorm * boolnorm, 2))
    })
    it('adds complex numbers', () => {
       const z = cplx(3, 4)

src/complex/arithmetic.js

@@ -7,11 +7,11 @@ import {ReturnsAs} from '#generic/helpers.js'
 
 const {conservative, full, free} = ReturnTyping
 
-export const absquare = match(Complex, (math, C, strategy) => {
+export const normsq = match(Complex, (math, C, strategy) => {
-   const compAbsq = math.absquare.resolve(C.Component, full)
+   const compNormsq = math.normsq.resolve(C.Component, full)
-   const R = compAbsq.returns
+   const R = compNormsq.returns
    const add = math.add.resolve([R,R], strategy)
-   return ReturnsAs(add, z => add(compAbsq(z.re), compAbsq(z.im)))
+   return ReturnsAs(add, z => add(compNormsq(z.re), compNormsq(z.im)))
 })
 
 export const add = promoteBinary('add')
@@ -38,12 +38,12 @@ export const divide = [
 
 export const invert = match(Complex, (math, C, strategy) => {
    const conj = math.conj.resolve(C, full)
-   const norm = math.absquare.resolve(C, full)
+   const normsq = math.normsq.resolve(C, full)
-   const div = math.divide.resolve([C.Component, norm.returns], full)
+   const div = math.divide.resolve([C.Component, normsq.returns], full)
    const cplx = maybeComplex(math, strategy, div.returns, div.returns)
    return ReturnsAs(cplx, z => {
       const c = conj(z)
-      const d = norm(z)
+      const d = normsq(z)
       return cplx(div(c.re, d), div(c.im, d))
    })
 })

src/generic/arithmetic.js

@@ -3,11 +3,14 @@ import {ReturnsAs} from './helpers.js'
 import {Returns, ReturnTyping} from '#core/Type.js'
 import {match, Any} from '#core/TypePatterns.js'
 
-export const abs = match(Any, (math, T) => {
+export const norm = match(Any, (math, T) => {
-   const absq = math.absquare.resolve(T)
+   const normsq = math.normsq.resolve(T)
-   const sqrt = math.sqrt.resolve(absq.returns, ReturnTyping.conservative)
+   const sqrt = math.sqrt.resolve(normsq.returns, ReturnTyping.conservative)
-   return ReturnsAs(sqrt, t => sqrt(absq(t)))
+   return ReturnsAs(sqrt, t => sqrt(normsq(t)))
 })
+
+export const abs = norm // coincide for most types (scalars)
+
 export const conj = match(Any, (_math, T) => Returns(T, t => t))
 export const square = match(Any, (math, T, strategy) => {
    const mult = math.multiply.resolve([T, T], strategy)

src/number/__test__/arithmetic.spec.js

@@ -5,7 +5,8 @@ import {ReturnTyping} from '#core/Type.js'
 describe('number arithmetic', () => {
    it('supports basic operations', () => {
       assert.strictEqual(math.abs(-Infinity), Infinity)
-      assert.strictEqual(math.absquare(-2), 4)
+      assert(isNaN(math.norm(NaN)))
+      assert.strictEqual(math.normsq(-2), 4)
       assert.strictEqual(math.add(2, 2), 4)
       assert.strictEqual(math.divide(6, 4), 1.5)
       assert.strictEqual(math.cbrt(-8), -2)

src/number/arithmetic.js

@@ -7,7 +7,8 @@ import {Complex} from '#complex/Complex.js'
 const {conservative, full} = ReturnTyping
 
 export const abs = plain(Math.abs)
-export const absquare = plain(a => a*a)
+export const norm = abs
+export const normsq = plain(a => a*a)
 export const add = plain((a, b) => a + b)
 export const divide = plain((a, b) => a / b)
 export const cbrt = plain(a => {