Geometric algebra: Difference between revisions

=={{header|Julia}}==

<lang julia>using LinearAlgebra, GeometryTypes

import Base.*

CliffordVector = Point{32, Float64}

e(n) = (v = zeros(32); v[(1 << n) + 1] = 1.0; CliffordVector(v))

randommultivector() = CliffordVector(rand(32))

randomvector() = sum(i -> rand() * e(i), 0:4)

bitcount(n) = (count = 0; while n != 0 n &= n - 1; count += 1 end; count)

function reorderingsign(i, j)

ssum, i = 0, i >> 1

while i != 0

ssum += bitcount(i & j)

i >>= 1

end

return iseven(ssum) ? 1.0 : -1.0

end

function Base.:*(v1::CliffordVector, v2::CliffordVector)

result = zeros(32)

for (i, x1) in enumerate(v1)

if x1 != 0.0

for (j, x2) in enumerate(v2)

if x2 != 0.0

s = reorderingsign(i - 1, j - 1) * x1 * x2

k = (i - 1) ⊻ (j - 1)

result[k + 1] += s

end

end

end

end

return CliffordVector(result)

end

function testcliffordvector()

for i in 0:4, j in 0:4

if i < j

if dot(e(i), e(j))[1] != 0.0

println("Unexpected nonzero scalar product")

return

end

elseif i == j

if dot(e(i), e(j))[1] == 0.0

println("Unexpected zero scalar product")

end

end

end

a = randommultivector()

b = randommultivector()

c = randommultivector()

x = randomvector()

# (ab)c ≈ a(bc)

@show (a * b) * c ≈ a * (b * c)

# a(b+c) ≈ ab + ac

@show a * (b + c) ≈ a * b + a * c

# (a+b)c ≈ ac + bc

@show (a + b) * c ≈ a * c + b * c

# x^2 is real

isreal(x) = x[1] isa Real && all(y -> y == 0, x[2:end])

@show isreal(x * x)

end

testcliffordvector()

</lang>{{out}}

<pre>

(a * b) * c ≈ a * (b * c) = true

a * (b + c) ≈ a * b + a * c = true

(a + b) * c ≈ a * c + b * c = true

isreal(x * x) = true

</pre>