Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
ZigangPan/
Routh
The true Routh Hurwitz test and more
Contributed by: Zigang Pan
This paclet is on the correct version of Routh Hurwitz test for stability of a polynomial, or more precisely the number of roots in the open right half, open left half, and pure imaginary of the complex plane, as in Agashe (1985). It contains other related tests on matrices and polynomials, etc.
Installation Instructions
To install this paclet in your Wolfram Language environment,
evaluate this code:
PacletInstall["ZigangPan/RouthHurwitz"]
To load the code after installation, evaluate this code:
Needs["ZigangPan`RouthHurwitz`"]
Paclet Guide
Examples
Initialization for Examples
| In[1]:= | ![Needs["ZigangPan`RouthHurwitz`"];](https://www.wolframcloud.com/obj/resourcesystem/images/ef8/ef806b06-675e-4bce-948f-18903763b1f1/5a7e8da8d257a797.png){kind=small} |
Basic Examples (1)
For RouthHurwitzTest:
| In[2]:= | ![p = (1 + I) x1^6 + (2 - I) x1^5 + (1 - I) x1^4 + (1 + I) x1^3 + (2 + 2 I) x1^2 + (2 + 3 I) x1 + 1; {np, nn, n0} = InterpretationBox[FrameBox[TagBox[TooltipBox[PaneBox[GridBox[List[List[GraphicsBox[List[Thickness[0.0025`], List[FaceForm[List[RGBColor[0.9607843137254902`, 0.5058823529411764`, 0.19607843137254902`], Opacity[1.`]]], FilledCurveBox[List[List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3]]], List[List[List[205.`, 22.863691329956055`], List[205.`, 212.31669425964355`], List[246.01799774169922`, 235.99870109558105`], List[369.0710144042969`, 307.0436840057373`], 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Function[Annotation[Slot[1], Style[Defer[PacletSymbol["ZigangPan/RouthHurwitz", "ZigangPan`RouthHurwitz`RouthHurwitzTest"]], Rule[ShowStringCharacters, True]], "Tooltip"]]], Rule[Background, RGBColor[0.968`, 0.976`, 0.984`]], Rule[BaselinePosition, Baseline], Rule[DefaultBaseStyle, List[]], Rule[FrameMargins, List[List[0, 0], List[1, 1]]], Rule[FrameStyle, RGBColor[0.831`, 0.847`, 0.85`]], Rule[RoundingRadius, 4]], PacletSymbol["ZigangPan/RouthHurwitz", "ZigangPan`RouthHurwitz`RouthHurwitzTest"], Rule[Selectable, False], Rule[SelectWithContents, True], Rule[BoxID, "PacletSymbolBox"]][p, x1]](https://www.wolframcloud.com/obj/resourcesystem/images/ef8/ef806b06-675e-4bce-948f-18903763b1f1/43c0bf0ee8109313.png) |
| Out[2]= |  |