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Display information for equation id:math.223294.0 on revision:223294

* Page found: Box–Muller transform (eq math.223294.0)

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Hash: ea633b182d50dacff94acf269b6c69f7

TeX (original user input):

Z_0 = R \cos(\Theta) =\sqrt{-2 \ln U_1} \cos(2 \pi U_2)\,

TeX (checked):

Z_{0}=R\cos(\Theta )={\sqrt {-2\ln U_{1}}}\cos(2\pi U_{2})\,

LaTeXML (experimental; uses MathML) rendering

MathML (7.259 KB / 1.222 KB) :

Z 0 = R cos ( Θ ) = - 2 ln U 1 cos ( 2 π U 2 ) subscript Z 0 R normal-Θ 2 subscript U 1 2 π subscript U 2 {\displaystyle Z_{0}=R\cos(\Theta)={\sqrt{-2\ln U_{1}}}\cos(2\pi U_{2})\,}
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SVG (12.711 KB / 4.6 KB) :

upper Z 0 equals upper R times cosine left-parenthesis normal upper Theta right-parenthesis equals StartRoot minus 2 times ln upper U 1 EndRoot times cosine left-parenthesis 2 times pi times upper U 2 right-parenthesis

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Translations to Computer Algebra Systems

Translation to Maple

In Maple: Z[0]= R*cos(Theta)=sqrt(- 2*ln(U)[1])*cos(2*pi*U[2])

Information about the conversion process:

\cos: Cosine; Example: \cos@@{z}

Will be translated to: cos($0)

Relevant links to definitions:

DLMF: http://dlmf.nist.gov/4.14#E2

Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=cos


\ln: Natural logarithm; Example: \ln@@{z}

Will be translated to: ln($0)

Constraints: z != 0

Branch Cuts: (-\infty, 0]

Relevant links to definitions:

DLMF: http://dlmf.nist.gov/4.2#E2

Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=ln


\pi: Could be the ratio of a circle's circumference to its diameter == Archimedes' constant.

But it is also a Greek letter. Be aware, that this program translated the letter as a normal Greek letter and not as a constant!

Use the DLMF-Macro \cpi to translate \pi as a constant.



Translation to Mathematica

In Mathematica: Subscript[Z, 0]= R*Cos[\[CapitalTheta]]=Sqrt[- 2*Subscript[Log[U], 1]]*Cos[2*\[Pi]*Subscript[U, 2]]

Information about the conversion process:

\cos: Cosine; Example: \cos@@{z}

Will be translated to: Cos[$0]

Relevant links to definitions:

DLMF: http://dlmf.nist.gov/4.14#E2

Mathematica: https://reference.wolfram.com/language/ref/Cos.html


\ln: Natural logarithm; Example: \ln@@{z}

Will be translated to: Log[$0]

Constraints: z != 0

Branch Cuts: (-\infty, 0]

Relevant links to definitions:

DLMF: http://dlmf.nist.gov/4.2#E2

Mathematica: https://reference.wolfram.com/language/ref/Log.html


\pi: Could be the ratio of a circle's circumference to its diameter == Archimedes' constant.

But it is also a Greek letter. Be aware, that this program translated the letter as a normal Greek letter and not as a constant!

Use the DLMF-Macro \cpi to translate \pi as a constant.



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