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Fungrim entry: 59a5d6

csgn ⁣(z)={sgn ⁣(Im ⁣(z)),Re ⁣(z)=0sgn ⁣(Re ⁣(z)),otherwise\operatorname{csgn}\!\left(z\right) = \begin{cases} \operatorname{sgn}\!\left(\operatorname{Im}\!\left(z\right)\right), & \operatorname{Re}\!\left(z\right) = 0\\\operatorname{sgn}\!\left(\operatorname{Re}\!\left(z\right)\right), & \text{otherwise}\\ \end{cases}
Assumptions:zCz \in \mathbb{C}
TeX:
\operatorname{csgn}\!\left(z\right) = \begin{cases} \operatorname{sgn}\!\left(\operatorname{Im}\!\left(z\right)\right), & \operatorname{Re}\!\left(z\right) = 0\\\operatorname{sgn}\!\left(\operatorname{Re}\!\left(z\right)\right), & \text{otherwise}\\ \end{cases}

z \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
Csgncsgn ⁣(z)\operatorname{csgn}\!\left(z\right) Real-valued sign function for complex numbers
Signsgn ⁣(z)\operatorname{sgn}\!\left(z\right) Sign function
ImIm ⁣(z)\operatorname{Im}\!\left(z\right) Imaginary part
ReRe ⁣(z)\operatorname{Re}\!\left(z\right) Real part
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("59a5d6"),
    Formula(Equal(Csgn(z), Cases(Tuple(Sign(Im(z)), Equal(Re(z), 0)), Tuple(Sign(Re(z)), Otherwise)))),
    Variables(z),
    Assumptions(Element(z, CC)))

Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-09-15 14:14:26.267625 UTC