fold conj, real, imag on the symbolic imaginary unit#924
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Add three `@match` arms in `Base.real`, `Base.conj`, `Base.imag` for
`BasicSymbolic` that match `Sym(:im; type = Number)` structurally and
fold to `0`, `-im`, and `1` respectively.
`Symbolics.IM` is defined as a `Sym{VartypeT}(:im; type = Number)` and
used as a stand-in for `1im` to keep expressions inside `BasicSymbolic{<:Real}`
algebra (where multiplying by a Julia `Complex` literal would otherwise
materialise an opaque `complex(re, im)` `Term`). Until now those three
operations on `IM` produced opaque `conj(im)` / `real(im)` / `imag(im)`
wrappers that `simplify` could not reduce, so downstream code that
algebraically conjugates `IM`-bearing expressions (e.g. SQA's
`qadjoint` / `inner_adjoint`) had to special-case `IM` themselves.
Matching is structural (name + symtype) rather than by identity, so no
new dependency on Symbolics is introduced. A same-named sym with a
non-`Number` symtype is left alone (test case).
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Benchmark Results (Julia v1)Time benchmarks
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Thanks for your attention to these edge cases. I think the better way to phrase this is to move the |
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Three new
@matcharms inBase.real,Base.conj,Base.imagforBasicSymbolicthat matchSym(:im; type = Number)structurally and fold to0,-im,1.Symbolics.IMisSym{VartypeT}(:im; type = Number), used as a stand-in for1imso expressions stay insideBasicSymbolic{<:Real}algebra. Without these arms,conj(IM)/real(IM)/imag(IM)were opaque wrappers thatsimplifycould not reduce, and downstream code (e.g. SQA'sqadjoint/inner_adjoint) had to special-caseIMthemselves to avoidconj(im)leftovers.Matching is purely structural (name + symtype), so SymbolicUtils picks up no Symbolics-side dependency. A same-named sym with a non-
Numbersymtype is unaffected; the test covers that case.