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simplifier doesn't detect exp(i x) * exp(- i x) = 1 #188

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light-matters opened this issue Sep 18, 2024 · 0 comments

light-matters commented Sep 18, 2024

Without I, the simplifier does as expected:

(e/simplify (* (e/exp (* -1 (c/complex 'k)))
               (e/exp (* 1 (c/complex 'k)))))  ;=>1

With I, it does something very different:

(e/simplify (* (e/exp (* -1 I (complex 'k)))
               (e/exp (* 1 I (complex 'k)))))
;=> #emmy/complex [(- (* (cos (* -1 k)) (cos k)) (* (sin (* -1 k)) (sin k))) (+ (* (cos (* -1 k)) (sin k)) (* (sin (* -1 k)) (cos k)))]

This is a problem because multiplying by the conjugate is a very common operation.

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