70 lines
2.7 KiB
JavaScript
70 lines
2.7 KiB
JavaScript
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import {Complex} from './Complex.js'
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import {promoteBinary, promoteUnary} from './helpers.js'
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import {ResolutionError} from '#core/helpers.js'
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import {match} from '#core/TypePatterns.js'
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import {ReturnsAs} from '#generic/helpers.js'
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export const absquare = match(Complex, (math, C) => {
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const compAbsq = math.absquare.resolve([C.Component])
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const R = compAbsq.returns
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const add = math.add.resolve([R,R])
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return ReturnsAs(add, z => add(compAbsq(z.re), compAbsq(z.im)))
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})
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export const add = promoteBinary('add')
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export const conj = match(Complex, (math, C) => {
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const neg = math.negate.resolve(C.Component)
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const compConj = math.conj.resolve(C.Component)
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const cplx = math.complex.resolve([compConj.returns, neg.returns])
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return ReturnsAs(cplx, z => cplx(compConj(z.re), neg(z.im)))
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})
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export const divide = [
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match([Complex, T => !T.complex], (math, [C, R]) => {
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const div = math.divide.resolve([C.Component, R])
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const cplx = math.complex.resolve([div.returns, div.returns])
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return ReturnsAs(cplx, (z, r) => cplx(div(z.re, r), div(z.im, r)))
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}),
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match([Complex, Complex], (math, [W, Z]) => {
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const inv = math.invert.resolve(Z)
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const mult = math.multiply.resolve([W, inv.returns])
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return ReturnsAs(mult, (w, z) => mult(w, inv(z)))
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})
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]
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export const invert = match(Complex, (math, C) => {
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const conj = math.conj.resolve(C)
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const norm = math.absquare.resolve(C)
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const div = math.divide.resolve([C.Component, norm.returns])
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const cplx = math.complex.resolve([div.returns, div.returns])
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return ReturnsAs(cplx, z => {
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const c = conj(z)
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const d = norm(z)
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return cplx(div(c.re, d), div(c.im, d))
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})
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})
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// We want this to work for complex numbers, quaternions, octonions, etc
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// See https://math.ucr.edu/home/baez/octonions/node5.html
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export const multiply = match([Complex, Complex], (math, [W, Z]) => {
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const conj = math.conj.resolve(W.Component)
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if (conj.returns !== W.Component) {
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throw new ResolutionError(
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`conjugation on ${W.Component} returns other type (${conj.returns})`)
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}
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const mWZ = math.multiply.resolve([W.Component, Z.Component])
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const mZW = math.multiply.resolve([Z.Component, W.Component])
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const sub = math.subtract.resolve([mWZ.returns, mZW.returns])
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const add = math.add.resolve([mWZ.returns, mZW.returns])
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const cplx = math.complex.resolve([sub.returns, add.returns])
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return ReturnsAs(cplx, (w, z) => {
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const real = sub(mWZ( w.re, z.re), mZW(z.im, conj(w.im)))
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const imag = add(mWZ(conj(w.re), z.im), mZW(z.re, w.im))
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return cplx(real, imag)
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})
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})
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export const negate = promoteUnary('negate')
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export const subtract = promoteBinary('subtract')
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