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# andyferris/SimpleSymbolic.jl

Created July 25, 2016 13:11
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Simply symbolic manipulations and some matrix math for Euler angle rotations
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 module SimpleSymbolic immutable S x::Any end Base.show(io::IO, s::S) = print(io, s.x) function Base.:+(s1::S, s2::S) if s1.x == 0 return s2 elseif s2.x == 0 return s1 else if isa(s1.x, Number) && isa(s2.x, Number) return S(s1.x + s2.x) else return S(string(s1.x) * " + " * string(s2.x)) end end end function Base.:*(s1::S, s2::S) if s1.x == 1 return s2 elseif s2.x == 1 return s1 elseif s1.x == 0 || s2.x == 0 return S(0) else if isa(s1.x, Number) && isa(s2.x, Number) return S(s1.x*s2.x) else if isa(s1.x, String) && isa(s2.x, String) if s1.x[1] == '-' && s2.x[1] == '-' return S(string(s1.x[2:end]) * "*" * string(s2.x[2:end])) end end return S(string(s1.x) * "*" * string(s2.x)) end end end using StaticArrays mx1 = @SMatrix [S(1) S(0) S(0); S(0) S("cosθ₁") S("-sinθ₁"); S(0) S("sinθ₁") S("cosθ₁")] my1 = @SMatrix [S("cosθ₁") S(0) S("sinθ₁"); S(0) S(1) S(0); S("-sinθ₁") S(0) S("cosθ₁")] mz1 = @SMatrix [S("cosθ₁") S("-sinθ₁") S(0); S("sinθ₁") S("cosθ₁") S(0); S(0) S(0) S(1)] mx2 = @SMatrix [S(1) S(0) S(0); S(0) S("cosθ₂") S("-sinθ₂"); S(0) S("sinθ₂") S("cosθ₂")] my2 = @SMatrix [S("cosθ₂") S(0) S("sinθ₂"); S(0) S(1) S(0); S("-sinθ₂") S(0) S("cosθ₂")] mz2 = @SMatrix [S("cosθ₂") S("-sinθ₂") S(0); S("sinθ₂") S("cosθ₂") S(0); S(0) S(0) S(1)] mx3 = @SMatrix [S(1) S(0) S(0); S(0) S("cosθ₃") S("-sinθ₃"); S(0) S("sinθ₃") S("cosθ₃")] my3 = @SMatrix [S("cosθ₃") S(0) S("sinθ₃"); S(0) S(1) S(0); S("-sinθ₃") S(0) S("cosθ₃")] mz3 = @SMatrix [S("cosθ₃") S("-sinθ₃") S(0); S("sinθ₃") S("cosθ₃") S(0); S(0) S(0) S(1)] v = @SVector [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 export S, mx1, my1, mz1, mx2, my2, mz2, mx3, my3, mz3, v, mxy, myx, mxz, mxz, mzy, myz, myxy, myxz, mxyx, mxyz, mxzx, mxzy, mzxz, mzxy, mzyz, mzyx, myzy, myzx end # module

### c42f commented Jul 26, 2016

Check out my fork - you can do the above very cleanly with a mixture of builtin arithmetic and Expr :-) More type system usage FTW!

As a side effect, when you actually use this to generate code, you automatically get out the Expr you were looking for :-)