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Fungrim entry: 59a5d6

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

z \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
Csgncsgn(z)\operatorname{csgn}(z) Real-valued sign function for complex numbers
Signsgn(z)\operatorname{sgn}(z) Sign function
ImIm(z)\operatorname{Im}(z) Imaginary part
ReRe(z)\operatorname{Re}(z) 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.

2019-12-30 15:00:46.909060 UTC