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Display information for equation id:math.254408.7 on revision:254408

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Hash: 2e59f7010fb60e96933d180485aa8523

TeX (original user input):

x=\sqrt{-2\ln(u_1)}\cos(2\pi u_2),\quad  y=\sqrt{-2\ln(u_1)}\sin(2\pi u_2)

TeX (checked):

x={\sqrt {-2\ln(u_{1})}}\cos(2\pi u_{2}),\quad y={\sqrt {-2\ln(u_{1})}}\sin(2\pi u_{2})

LaTeXML (experimental; uses MathML) rendering

MathML (11.264 KB / 1.499 KB) :

x = - 2 ln ( u 1 ) cos ( 2 π u 2 ) , y = - 2 ln ( u 1 ) sin ( 2 π u 2 ) formulae-sequence x 2 subscript u 1 2 π subscript u 2 y 2 subscript u 1 2 π subscript u 2 {\displaystyle x={\sqrt{-2\ln(u_{1})}}\cos(2\pi u_{2}),\quad y={\sqrt{-2\ln(u_% {1})}}\sin(2\pi u_{2})}
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x equals StartRoot minus 2 times ln left-parenthesis u 1 right-parenthesis EndRoot times cosine left-parenthesis 2 times pi times u 2 right-parenthesis comma y equals StartRoot minus 2 times ln left-parenthesis u 1 right-parenthesis EndRoot times sine left-parenthesis 2 times pi times u 2 right-parenthesis

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Translations to Computer Algebra Systems

Translation to Maple

In Maple: x =sqrt(- 2*ln(u[1]))*cos(2*pi*u[2]), y =sqrt(- 2*ln(u[1]))*sin(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


\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: x =Sqrt[- 2*Log[Subscript[u, 1]]]*Cos[2*\[Pi]*Subscript[u, 2]], y =Sqrt[- 2*Log[Subscript[u, 1]]]*Sin[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


\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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