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Fungrim entry: 31fef8

Image: X-ray of sin ⁣(z)\sin\!\left(z\right) on z[5,5]+[5,5]iz \in \left[-5, 5\right] + \left[-5, 5\right] i
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An X-ray plot illustrates the geometry of a complex analytic function f ⁣(z)f\!\left(z\right). Thick black curves show where Im ⁣(f ⁣(z))=0\operatorname{Im}\!\left(f\!\left(z\right)\right) = 0 (the function is pure real). Thick red curves show where Re ⁣(f ⁣(z))=0\operatorname{Re}\!\left(f\!\left(z\right)\right) = 0 (the function is pure imaginary). Points where black and red curves intersect are zeros or poles. Magnitude level curves f ⁣(z)=C\left|f\!\left(z\right)\right| = C are rendered as thin gray curves, with brighter shades corresponding to larger CC. Blue lines show branch cuts. The value of the function is continuous with the branch cut on the side indicated with a solid line, and discontinuous on the side indicated with a dashed line. Yellow is used to highlight important regions.
Definitions:
Fungrim symbol Notation Short description
Sinsin ⁣(z)\sin\!\left(z\right) Sine
ClosedInterval[a,b]\left[a, b\right] Closed interval
ConstIii Imaginary unit
ImIm ⁣(z)\operatorname{Im}\!\left(z\right) Imaginary part
ReRe ⁣(z)\operatorname{Re}\!\left(z\right) Real part
Absz\left|z\right| Absolute value
Source code for this entry:
Entry(ID("31fef8"),
    Image(Description("X-ray of", Sin(z), "on", Element(z, Add(ClosedInterval(-5, 5), Mul(ClosedInterval(-5, 5), ConstI)))), ImageSource("xray_sin")),
    Description("An X-ray plot illustrates the geometry of a complex analytic function", f(z), ".", "Thick black curves show where", Equal(Im(f(z)), 0), "(the function is pure real).", "Thick red curves show where", Equal(Re(f(z)), 0), "(the function is pure imaginary).", "Points where black and red curves intersect are zeros or poles.", "Magnitude level curves", Equal(Abs(f(z)), C), "are rendered as thin gray curves, with brighter shades corresponding to larger", C, ".", "Blue lines show branch cuts.", "The value of the function is continuous with the branch cut on the side indicated with a solid line, and discontinuous on the side indicated with a dashed line.", "Yellow is used to highlight important regions."))

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

2019-08-25 15:30:03.056001 UTC