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# c42f/SimpleSymbolic.jl

Forked from andyferris/SimpleSymbolic.jl
Last active July 26, 2016 03:05
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Simply symbolic manipulations and some matrix math for Euler angle rotations
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 module SimpleSymbolic immutable S{Ex} x::Ex end macro S(ex) Expr(:call, :S, Expr(:quote, ex)) end Base.show(io::IO, s::S) = print(io, s.x) import Base: +, *, -, / -(a::S) = S(:(-\$(a.x))) +(a::S, b::S) = S(:(\$(a.x) + \$(b.x))) +(a::S, b::Number) = b == 0 ? a : a + S(b) +(a::Number, b::S) = a == 0 ? b : S(a) + b -(a::S, b::S) = S(:(\$(a.x) - \$(b.x))) -(a::S, b::Number) = b == 0 ? -a : a - S(b) -(a::Number, b::S) = a == 0 ? b : S(a) - b *(a::S, b::S) = S(:(\$(a.x) * \$(b.x))) *(a::S, b::Number) = b == 0 ? 0 : b == 1 ? a : a * S(b) *(a::Number, b::S) = a == 0 ? 0 : a == 1 ? b : S(a) * b /(a::S, b::S) = S(:(\$(a.x) / \$(b.x))) /(a::S, b::Number) = b == 1 ? a : a / S(b) /(a::Number, b::S) = a == 0 ? 0 : S(a) / b # Hmm, assumes b != 0 export S, @S end # module #------------------------------------------------------------------------------- using SimpleSymbolic s1 = @S sin(θ₁) c1 = @S cos(θ₁) s2 = @S sin(θ₂) c2 = @S cos(θ₂) s3 = @S sin(θ₃) c3 = @S cos(θ₃) mx1 = [1 0 0; 0 c1 -s1; 0 s1 c1] my1 = [c1 0 s1; 0 1 0; -s1 0 c1] mz1 = [c1 -s1 0; s1 c1 0; 0 0 1] mx2 = [1 0 0; 0 c2 -s2; 0 s2 c2] my2 = [c2 0 s2; 0 1 0; -s2 0 c2] mz2 = [c2 -s2 0; s2 c2 0; 0 0 1] mx3 = [1 0 0; 0 c3 -s3; 0 s3 c3] my3 = [c3 0 s3; 0 1 0; -s3 0 c3] mz3 = [c3 -s3 0; s3 c3 0; 0 0 1] v = [@S(v[1]), @S(v[2]), @S(v[3])] myx = my1 * mx2 mxy = mx1 * my2 mxz = mx1 * mz2 mzx = mz1 * mx2 mzy = mz1 * my2 myz = my1 * mz2 myxy = my1 * mx2 * my3 myxz = my1 * mx2 * mz3 mxyx = mx1 * my2 * mx3 mxyz = mx1 * my2 * mz3 mxzx = mx1 * mz2 * mx3 mxzy = mx1 * mz2 * my3 mzxz = mz1 * mx2 * mz3 mzxy = mz1 * mx2 * my3 mzyz = mz1 * my2 * mz3 mzyx = mz1 * my2 * mx3 myzy = my1 * mz2 * my3 myzx = my1 * mz2 * mx3

### c42f commented Jul 26, 2016

@awbsmith for your amusement, here's a way to construct symbolic representations of Euler rotations directly in Julia. Just a refactor of what @andyferris has been hacking on.

### c42f commented Jul 26, 2016

Oops, just fixed a rather horrible copy & paste bug