Geometric algebra: Difference between revisions
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<pre>prompt$ jsish -u geometricAlgebra.jsi
[PASS] geometricAlgebra.jsi</pre>
=={{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>
=={{header|Kotlin}}==
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