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Display information for equation id:math.223294.1 on revision:223294

* Page found: Box–Muller transform (eq math.223294.1)

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Hash: 7d8c56fae89c0d543ed0560b785a2073

TeX (original user input):

Z_1 = R \sin(\Theta) = \sqrt{-2 \ln U_1} \sin(2 \pi U_2).\,

TeX (checked):

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

LaTeXML (experimental; uses MathML) rendering

MathML (7.486 KB / 1.231 KB) :

Z 1 = R sin ( Θ ) = - 2 ln U 1 sin ( 2 π U 2 ) . subscript Z 1 R normal-Θ 2 subscript U 1 2 π subscript U 2 {\displaystyle Z_{1}=R\sin(\Theta)={\sqrt{-2\ln U_{1}}}\sin(2\pi U_{2}).\,}
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SVG (12.414 KB / 4.389 KB) :

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

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Translations to Computer Algebra Systems

Translation to Maple

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

Information about the conversion process:

\sin: Sine; Example: \sin@@{z}

Will be translated to: sin($0)

Relevant links to definitions:

DLMF: http://dlmf.nist.gov/4.14#E1

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


\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, 1]= R*Sin[\[CapitalTheta]]=Sqrt[- 2*Subscript[Log[U], 1]]*Sin[2*\[Pi]*Subscript[U, 2]]

Information about the conversion process:

\sin: Sine; Example: \sin@@{z}

Will be translated to: Sin[$0]

Relevant links to definitions:

DLMF: http://dlmf.nist.gov/4.14#E1

Mathematica: https://reference.wolfram.com/language/ref/Sin.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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