Template:Intmath/testcases

Template:Purge

Note: the Template:Tlx code is tweaked and/or optimized for use inside the Template:Tlx and Template:Tlx templates.

In IE, except for int, all the integrals seem to render in the beautiful font 'Lucida Sans Unicode', but in Firefox we get this ugly font (it is passable for text style, but would be really ugly in display style)! In which [ugly] font do the integral symbols, other than int, render? Also, in which font does int render? — Tentacles^{Talk or ✉ mailto:Tentacles} 17:50, 22 March 2016 (UTC)

No Template:Tl

Compare vertical alignment and obliqueness of [rotated] int with other [italic] integral symbols:

Template:Intmath/sandbox Template:Intmath/sandbox Template:Intmath/sandbox

{{intmath/sandbox|int}}&#x200A;<!-- 1 hair space -->{{intmath/sandbox|oiint}}&#x200A;<!-- 1 hair space -->{{intmath/sandbox|int}}

Gamma function (non-italic int as default)

Sandbox: Γ(z) = Template:Intmath/sandbox e^−t t ^z − 1dt    (With the Template:Tl template, the limits have a much better alignment with the integral symbol.)

Current: Γ(z) = Template:Intmath e^−t t ^z − 1dt

Γ(''z'') = {{intmath||0|∞}} ''e''<sup>−''t''</sup>&#x200A;<!-- hair space -->''t''&#x200A;<!-- hair space --><sup>''z''&#x200A;<!-- hair space -->−&#x200A;<!-- hair space -->1</sup>''dt''

Gamma function

Sandbox: Γ(z) = Template:Intmath/sandbox e^−t t ^{z − 1}dt    (With the Template:Tl template, the limits have a much better alignment with the integral symbol.)

Current: Γ(z) = Template:Intmath e^−t t ^z − 1dt

Γ(''z'') = {{intmath|int|0|∞}} ''e''<sup>−''t''</sup>&#x200A;<!-- hair space -->''t''&#x200A;<!-- hair space --><sup>''z''&#x200A;<!-- hair space -->−&#x200A;<!-- hair space -->1</sup>''dt''

Line integral

Sandbox: Template:Intmath/sandbox F(x) ∙ dx = −Template:Intmath/sandbox F(x) ∙ dx

Current: Template:Intmath F(x) ∙ dx = −Template:Intmath F(x) ∙ dx

{{intmath|varointclockwise|''C''}} ''F''('''x''') ∙ ''d'''''x''' = −{{intmath|ointctrclockwise|''C''}} ''F''('''x''') ∙ ''d'''''x'''

Maxwell's equations

Sandbox:

Gauss's law Template:Intmath/sandbox E ∙ dS = Template:SfracTemplate:Intmath/sandbox ρ dV

Gauss's law for magnetism Template:Intmath/sandbox B ∙ dS = 0

Maxwell–Faraday equation Template:Intmath/sandbox E ∙ dℓ = −Template:Intmath/sandbox Template:Sfrac ∙ dS

Ampère's circuital law Template:Intmath/sandbox B ∙ dℓ = Template:Intmath/sandbox Template:Big μ₀J + Template:SfracTemplate:SfracTemplate:Big ∙ dS

Current:

Gauss's law Template:Intmath E ∙ dS = Template:SfracTemplate:Intmath ρ dV

Gauss's law for magnetism Template:Intmath B ∙ dS = 0

Maxwell–Faraday equation Template:Intmath E ∙ dℓ = −Template:Intmath Template:Sfrac ∙ dS

Ampère's circuital law Template:Intmath B ∙ dℓ = Template:Intmath Template:Big μ₀J + Template:SfracTemplate:SfracTemplate:Big ∙ dS

{{intmath|oiint|∂Ω}} '''E''' ∙ ''d'''''S''' = {{sfrac|1|''ε''<sub>0</sub>}}{{intmath|iiint|Ω}} ''ρ'' ''dV''

{{intmath|oiint|∂Ω}} '''B''' ∙ ''d'''''S''' = 0

{{intmath|oint|∂Σ}} '''E''' ∙ ''d''<nowiki />'''''ℓ<!-- ℓ -->''''' = −{{intmath|iint|Σ}} {{sfrac|∂'''B'''|∂''t''}} ∙ ''d'''''S'''

{{intmath|oint|∂Σ}} '''B''' ∙ ''d''<nowiki />'''''ℓ<!-- ℓ -->''''' = {{intmath|iint|Σ}} {{big|(}} <!-- hair space -->''μ''<sub>0</sub>'''J''' + {{sfrac|1|''c''<sup>2</sup>}}{{sfrac|∂'''E'''|∂''t''}}{{big|)}} ∙ ''d'''''S'''

Template:Tl

Compare vertical alignment and obliqueness of [rotated] int with other [italic] integral symbols:

Template:Math

{{math| {{intmath/sandbox|int}}&#x200A;<!-- 1 hair space -->{{intmath/sandbox|oiint}}&#x200A;<!-- 1 hair space -->{{intmath/sandbox|int}} }}

Gamma function (non-italic int as default)

Sandbox: Template:Math

Current: Template:Math

{{math|Γ(''z'') {{=}} {{intmath||0|∞}} ''e''<sup>−''t''</sup>&#x200A;<!-- hair space -->''t''&#x200A;<!-- hair space --><sup>''z''&#x200A;<!-- hair space -->−&#x200A;<!-- hair space -->1</sup>''dt''}}

Gamma function

Sandbox: Template:Math

Current: Template:Math

{{math|Γ(''z'') {{=}} {{intmath|int|0|∞}} ''e''<sup>−''t''</sup>&#x200A;<!-- hair space -->''t''&#x200A;<!-- hair space --><sup>''z''&#x200A;<!-- hair space -->−&#x200A;<!-- hair space -->1</sup>''dt''}}

Line integral

Sandbox: Template:Math

Current: Template:Math

{{math|{{intmath|varointclockwise|''C''}} ''F''('''x''') ∙ ''d'''''x''' {{=}} −{{intmath|ointctrclockwise|''C''}} ''F''('''x''') ∙ ''d'''''x'''}}

Maxwell's equations

Sandbox:

Gauss's law Template:Math

Gauss's law for magnetism Template:Math

Maxwell–Faraday equation Template:Math

Ampère's circuital law Template:Math

Current:

Gauss's law Template:Math

Gauss's law for magnetism Template:Math

Maxwell–Faraday equation Template:Math

Ampère's circuital law Template:Math

{{math|{{intmath|oiint|∂Ω}} '''E''' ∙ ''d'''''S''' {{=}} {{sfrac|1|''ε''<sub>0</sub>}}{{intmath|iiint|Ω}} ''ρ'' ''dV''}}

{{math|{{intmath|oiint|∂Ω}} '''B''' ∙ ''d'''''S''' {{=}} 0}}

{{math|{{intmath|oint|∂Σ}} '''E''' ∙ ''d''<nowiki />'''''ℓ<!-- ℓ -->''''' {{=}} −{{intmath|iint|Σ}} {{sfrac|∂'''B'''|∂''t''}} ∙ ''d'''''S'''}}

{{math|{{intmath|oint|∂Σ}} '''B''' ∙ ''d''<nowiki />'''''ℓ<!-- ℓ -->''''' {{=}} {{intmath|iint|Σ}} {{big|(}} <!-- 1 hair space -->''μ''<sub>0</sub>'''J''' + {{sfrac|1|''c''<sup>2</sup>}}{{sfrac|∂'''E'''|∂''t''}}{{big|)}} ∙ ''d'''''S'''}}

Text style inline formulae

Template:Tl

Sandbox: Line spacing is undisturbed.

Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Gauss's Law: Template:Math Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum. Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Template:Math Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum. Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat.

Current: Messes up the line spacing.

Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Gauss's Law: Template:Math Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum. Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Template:Math Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum. Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat.

Display style standalone formulae

Template:Tl

Compare vertical alignment and obliqueness of [rotated] int with other [italic] integral symbols:

Template:Bigmath

{{Bigmath| {{intmath/sandbox|int}}&#x200A;<!-- 1 hair space -->{{intmath/sandbox|oiint}}&#x200A;<!-- 1 hair space -->{{intmath/sandbox|int}} }}

Gamma function

LaTeX:

The Gamma function is defined as

$\mathrm{\Gamma }(z)=\underset{0}{\overset{\mathrm{\infty }}{\int }}{e}^{-t}{t}^{z-1}dt.$

Sandbox:

The Gamma function is defined as

Template:Bigmath

Current:

The Gamma function is defined as

Template:Bigmath

{{Bigmath|Γ(''z'') {{=}} {{intmath|int|0|∞}} ''e''<sup>−''t''</sup>&#x200A;<!-- hair space -->''t''&#x200A;<!-- hair space --><sup>''z''&#x200A;<!-- hair space -->−&#x200A;<!-- hair space -->1</sup>''dt''.}}

Maxwell's equations

LaTeX:

Gauss's law:

Template:Oiint

Gauss's law for magnetism:

Template:Oiint

Maxwell–Faraday equation:

${\oint }_{\partial \mathrm{\Sigma }}𝐄\cdot d\mathit{\ell }=-\underset{\mathrm{\Sigma }}{\iint }\frac{\partial 𝐁}{\partial t}\cdot d𝐒$

Ampère's circuital law:

${\oint }_{\partial \mathrm{\Sigma }}𝐁\cdot d\mathit{\ell }=\underset{\mathrm{\Sigma }}{\iint }({\mu }_0𝐉+\frac{1}{c^2}\frac{\partial 𝐄}{\partial t})\cdot d𝐒$

Sandbox:

Gauss's law:

Template:Bigmath

Gauss's law for magnetism:

Template:Bigmath

Maxwell–Faraday equation:

Template:Bigmath

Ampère's circuital law:

Template:Bigmath

Current:

Gauss's law:

Template:Bigmath

Gauss's law for magnetism:

Template:Bigmath

Maxwell–Faraday equation:

Template:Bigmath

Ampère's circuital law:

Template:Bigmath

Gauss's law: :{{Bigmath|{{intmath|oiint|∂Ω}} '''E''' ∙ ''d'''''S''' {{=}} {{sfrac|1|''ε''<sub>0</sub>}}{{intmath|iiint|Ω}} ''ρ'' ''dV''}}

Gauss's law for magnetism: :{{Bigmath|{{intmath|oiint|∂Ω}} '''B''' ∙ ''d'''''S''' {{=}} 0}}

Maxwell–Faraday equation: :{{Bigmath|{{intmath|oint|∂Σ}} '''E''' ∙ ''d''<nowiki />'''''ℓ<!-- ℓ -->''''' {{=}} −{{intmath|iint|Σ}} {{sfrac|∂'''B'''|∂''t''}} ∙ ''d'''''S'''}}

Ampère's circuital law: :{{Bigmath|{{intmath|oint|∂Σ}} '''B''' ∙ ''d''<nowiki />'''''ℓ<!-- ℓ -->''''' {{=}} {{intmath|iint|Σ}} {{big|(}} <!-- 1 hair space -->''μ''<sub>0</sub>'''J''' + {{sfrac|1|''c''<sup>2</sup>}}{{sfrac|∂'''E'''|∂''t''}}{{big|)}} ∙ ''d'''''S'''}}

\iiiint and \idotsint

LaTeX:

<math>H {{=}} \iiiint_{\rm 4\mbox{-}ball} dH</math> yields

$H=\underset{\mathrm{4}\text{-}\mathrm{b}\mathrm{a}\mathrm{l}\mathrm{l}}{⨌}dH$

<math>H {{=}} \idotsint_{n{\rm \mbox{-}ball}} dH</math> yields

Failed to parse (unknown function "\idotsint"): {\displaystyle H {{=}} \idotsint_{n{\rm \mbox{-}ball}} dH}

<math>H {{=}} \int \cdots \int_{n{\rm \mbox{-}ball}} dH</math> yields

$H=\int \cdots \underset{n\text{-}\mathrm{b}\mathrm{a}\mathrm{l}\mathrm{l}}{\int }dH$

<math>H {{=}} \int \!\cdots\! \int_{n{\rm \mbox{-}ball}} dH</math> yields (the better spaced)

$H=\int \cdots \underset{n\text{-}\mathrm{b}\mathrm{a}\mathrm{l}\mathrm{l}}{\int }dH$

Sandbox:

{{math| H {{=}} {{intmath/sandbox|iiiint|4-ball}} ''dH'' }} yields the HTML text style Template:Math

{{math| H {{=}} {{intmath/sandbox|idotsint|''n''-ball}} ''dH'' }} yields the HTML text style Template:Math

{{bigmath| H {{=}} {{intmath/sandbox|iiiint|4-ball}} ''dH'' }} yields the HTML display style

Template:Bigmath

{{bigmath| H {{=}} {{intmath/sandbox|idotsint|''n''-ball}} ''dH'' }} yields the HTML display style

Template:Bigmath

Quotient of integrals

LaTeX:

<math>\frac{ \int_0^\infty x^{2n} e^{-a x^2}\,dx }{ \int_0^\infty x^{2(n-1)} e^{-a x^2}\,dx } = \frac{2n-1}{2a}</math> yields

$\frac{\underset{0}{\overset{\mathrm{\infty }}{\int }}{x}^{2n}{e}^{-a{x}^2}dx}{\underset{0}{\overset{\mathrm{\infty }}{\int }}{x}^{2(n-1)}{e}^{-a{x}^2}dx}=\frac{2n-1}{2a}$

Sandbox (without the tiny [fourth parameter] option):

:{{bigmath|<!-- 
-->{{sfrac
   | {{intmath/sandbox|int|0|∞}} ''x''<sup>2''n''</sup> ''e''<sup>−''ax''<sup>2</sup></sup> ''dx''<!-- 
-->| {{intmath/sandbox|int|0|∞}} ''x''<sup>2(''n''−1)</sup>  ''e''<sup>−''ax''<sup>2</sup></sup> ''dx''<!-- 
-->}} {{=}} {{sfrac|2''n'' − 1|2''a''}} }}

yields (Template:Tl should have vertical-align: middle;)

Template:Bigmath

Sandbox (with the tiny [fourth parameter] option):

:{{bigmath|<!-- 
-->{{sfrac
   | {{intmath/sandbox|int|0|∞|tiny}} ''x''<sup>2''n''</sup> ''e''<sup>−''ax''<sup>2</sup></sup> ''dx''<!-- 
-->| {{intmath/sandbox|int|0|∞|tiny}} ''x''<sup>2(''n''−1)</sup>  ''e''<sup>−''ax''<sup>2</sup></sup> ''dx''<!-- 
-->}} {{=}} {{sfrac|2''n'' − 1|2''a''}} }}

yields (Template:Tl should have vertical-align: middle;)

Template:Bigmath

Current:

:{{bigmath|<!-- 
-->{{sfrac
   | {{intmath|int|0|∞}} ''x''<sup>2''n''</sup> ''e''<sup>−''ax''<sup>2</sup></sup> ''dx''<!-- 
-->| {{intmath|int|0|∞}} ''x''<sup>2(''n''−1)</sup>  ''e''<sup>−''ax''<sup>2</sup></sup> ''dx''<!-- 
-->}} {{=}} {{sfrac|2''n'' − 1|2''a''}} }}

yields

Template:Bigmath

Sandbox (without the tiny [fourth parameter] option):

:{{bigmath|<!-- 
-->{{sfrac
   | {{intmath/sandbox|oiint|∂Ω}} '''E''' ∙ ''d'''''S'''<!-- 
-->| {{intmath/sandbox|iiint|Ω}} ''ρ'' ''dV''<!-- 
-->}} {{=}} {{sfrac|1|''ε''<sub>0</sub>}} }}

yields (Template:Tl should have vertical-align: middle;)

Template:Bigmath

Sandbox (with the tiny [fourth parameter] option):

:{{bigmath|<!-- 
-->{{sfrac
   | {{intmath/sandbox|oiint|∂Ω||tiny}} '''E''' ∙ ''d'''''S'''<!-- 
-->| {{intmath/sandbox|iiint|Ω||tiny}} ''ρ'' ''dV''<!-- 
-->}} {{=}} {{sfrac|1|''ε''<sub>0</sub>}} }}

yields (Template:Tl should have vertical-align: middle;)

Template:Bigmath