Why Mathematica does not simplify Sinh[ArcCosh[x]]

Re:Why Mathematica does not simplify Sinh[ArcCosh[x]] by yorwba on Sunday March 15, 2026 @06:21AM (#47385968)

For x = -i, square(x) = -1, sqrt(square(x)) = i. Meanwhile, abs(x) = 1. You're right that it simplifies to abs(x) for real x, but that no longer holds for arbitrary complex values.

[ Parent | on HN ]

Re:Why Mathematica does not simplify Sinh[ArcCosh[x]] by NooneAtAll3 on Sunday March 15, 2026 @09:12AM (#47387069)

for arbitrary complex values sqrt() gives 2 answers with +- signs

so sqrt(square(-i)) = +-i, one of which is x

[ Parent | on HN ]

Re:Why Mathematica does not simplify Sinh[ArcCosh[x]] by Armisael16 on Sunday March 15, 2026 @12:18PM (#47388862)

The sqrt function returns the principle square root, not both. That’s true for all numbers, positive, negative, and complex alike.

[ Parent | on HN ]

Re:Why Mathematica does not simplify Sinh[ArcCosh[x]] by syockit on Sunday March 15, 2026 @09:57AM (#47387432)

I've never seen a CAS that gives two answers for sqrt. Mathematica doesn't, sympy doesn't, and IIRC Maxima also doesn't.

[ Parent | on HN ]