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项目作者： fed

项目描述 ：
MathML and LaTeX examples 👨‍🏫
高级语言：
项目地址: git://github.com/fed/mathml-latex-examples.git
创建时间： 2019-06-26T02:51:43Z
项目社区：https://github.com/fed/mathml-latex-examples
开源协议：
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MathML and LaTeX Examples

Example 1

Example 1

Latex:

  1. x^2+y^2=z^2

MathML:

  1. <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><msup><mi>z</mi><mn>2</mn></msup></math>

Example 2

Example 2

Latex:

  1. z=\sqrt{x^2+y^2}-\frac{x+y}{(x-y)(x+y)}

MathML:

  1. <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi><mo>=</mo><msqrt><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msup><mi>y</mi><mn>2</mn></msup></msqrt><mo>-</mo><mfrac><mrow><mi>x</mi><mo>+</mo><mi>y</mi></mrow><mrow><mo>(</mo><mi>x</mi><mo>-</mo><mi>y</mi><mo>)</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>y</mi><mo>)</mo></mrow></mfrac></math>

Example 3

Example 3

Latex:

  1. \frac1x+\sqrt[x]{3+y}-x\geqslant\mathrm\pi

MathML:

  1. <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mi>x</mi></mfrac><mo>+</mo><mroot><mrow><mn>3</mn><mo>+</mo><mi>y</mi></mrow><mi>x</mi></mroot><mo>-</mo><mi>x</mi><mo>⩾</mo><mi mathvariant="normal">π</mi></math>

Example 4

Example 4

Latex:

  1. x+y-xy=\frac1{\left|x+xy-y\right|}

MathML:

  1. <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mi>y</mi><mo>-</mo><mi>x</mi><mi>y</mi><mo>=</mo><mfrac><mn>1</mn><mfenced open="|" close="|"><mrow><mi>x</mi><mo>+</mo><mi>x</mi><mi>y</mi><mo>-</mo><mi>y</mi></mrow></mfenced></mfrac></math>

Example 5

Example 5

  1. \begin{pmatrix}x-3&1&\frac x2\\3.5&x&4\\5x&6&x+4\end{pmatrix}

MathML:

  1. <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mi>x</mi><mo>-</mo><mn>3</mn></mtd><mtd><mn>1</mn></mtd><mtd><mfrac><mi>x</mi><mn>2</mn></mfrac></mtd></mtr><mtr><mtd><mn>3</mn><mo>.</mo><mn>5</mn></mtd><mtd><mi>x</mi></mtd><mtd><mn>4</mn></mtd></mtr><mtr><mtd><mn>5</mn><mi>x</mi></mtd><mtd><mn>6</mn></mtd><mtd><mi>x</mi><mo>+</mo><mn>4</mn></mtd></mtr></mtable></mfenced></math>

Example 6

Example 6

  1. \overset{10}{\underset{i=0}{\sum i}}\geqslant10

MathML:

  1. <math xmlns="http://www.w3.org/1998/Math/MathML"><munderover><mrow><mo>∑</mo><mi>i</mi></mrow><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>10</mn></munderover><mo>⩾</mo><mn>10</mn></math>

Example 7

Example 7

  1. \left|f(x)-L\right|<\varepsilon\Rightarrow0<\left|x-a\right|<\delta

MathML:

  1. <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="|" close="|"><mrow><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>-</mo><mpadded lspace="-1px"><mi>L</mi></mpadded></mrow></mfenced><mo><</mo><mi>ε</mi><mo>⇒</mo><mn>0</mn><mo><</mo><mfenced open="|" close="|"><mrow><mi>x</mi><mo>-</mo><mi>a</mi></mrow></mfenced><mo><</mo><mi>δ</mi></math>

Example 8

Example 8

Latex:

  1. \pi\approx\sqrt{\frac{40}3-\sqrt{12}}\approx3.141533

MathML:

  1. <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>π</mi><mo>≈</mo><msqrt><mfrac><mn>40</mn><mn>3</mn></mfrac><mo>-</mo><msqrt><mn>12</mn></msqrt></msqrt><mo>≈</mo><mn>3</mn><mo>.</mo><mn>141533</mn></math>

Example 9

Example 9

Latex:

  1. \mathrm e^{\mathrm\pi}-\mathrm\pi=19.999099979...\approx20

MathML:

  1. <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi mathvariant="normal">e</mi><mi mathvariant="normal">π</mi></msup><mo>-</mo><mi mathvariant="normal">π</mi><mo>=</mo><mn>19</mn><mo>.</mo><mn>999099979</mn><mo>.</mo><mo>.</mo><mo>.</mo><mo>≈</mo><mn>20</mn></math>

Example 10

Example 10

Latex:

  1. \mathrm\pi\approx\sqrt{7+\sqrt{6+\sqrt5}}

MathML:

  1. <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">π</mi><mo>≈</mo><msqrt><mn>7</mn><mo>+</mo><msqrt><mn>6</mn><mo>+</mo><msqrt><mn>5</mn></msqrt></msqrt></msqrt></math>

Example 11

Example 11

Latex:

  1. \sin\left(\theta\right)=\cos\left(\frac{3\pi}2+\theta\right)=\frac{\tan\left(\theta\right)}{\sqrt{1+\tan^2\left(\theta\right)}}

MathML:

  1. <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sin</mi><mfenced><mi>θ</mi></mfenced><mo>=</mo><mi>cos</mi><mfenced><mrow><mfrac><mrow><mn>3</mn><mi>π</mi></mrow><mn>2</mn></mfrac><mo>+</mo><mi>θ</mi></mrow></mfenced><mo>=</mo><mfrac><mrow><mi>tan</mi><mfenced><mi>θ</mi></mfenced></mrow><msqrt><mn>1</mn><mo>+</mo><msup><mi>tan</mi><mn>2</mn></msup><mfenced><mi>θ</mi></mfenced></msqrt></mfrac></math>

Example 12

Example 12

Latex:

  1. \tan\left(\alpha\right)=\frac{\sin\left(\alpha\right)}{\cos\left(\alpha\right)}=\tan\left(\alpha+\pi\right)

MathML:

  1. <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tan</mi><mfenced><mi>α</mi></mfenced><mo>=</mo><mfrac><mrow><mi>sin</mi><mfenced><mi>α</mi></mfenced></mrow><mrow><mi>cos</mi><mfenced><mi>α</mi></mfenced></mrow></mfrac><mo>=</mo><mi>tan</mi><mfenced><mrow><mi>α</mi><mo>+</mo><mi>π</mi></mrow></mfenced></math>

Example 13

Example 13

Latex:

  1. \sqrt2\in\mathfrak R

MathML:

  1. <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>2</mn></msqrt><mo>∈</mo><mi mathvariant="fraktur">R</mi></math>

Example 14

Example 14

Latex:

  1. {(\alpha+\beta)}^2=\alpha^2+2\alpha\beta+\beta^2

MathML:

  1. <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mrow><mo>(</mo><mi>α</mi><mo>+</mo><mi>β</mi><mo>)</mo></mrow><mn>2</mn></msup><mo>=</mo><msup><mi>α</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mi>α</mi><mi>β</mi><mo>+</mo><msup><mi>β</mi><mn>2</mn></msup></math>

Example 15

Example 15

Latex:

  1. \sqrt a\cdot\sqrt[3]b=\ln\left(ab\right)

MathML:

  1. <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mi>a</mi></msqrt><mo>·</mo><mroot><mi>b</mi><mn>3</mn></mroot><mo>=</mo><mi>ln</mi><mfenced><mrow><mi>a</mi><mi>b</mi></mrow></mfenced></math>

Example 16

Example 16

Latex:

  1. \int_0^1\frac{x^3+3x}2\operatorname dx

MathML:

  1. <math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mo>∫</mo><mn>0</mn><mn>1</mn></msubsup><mfrac><mrow><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>3</mn><mi>x</mi></mrow><mn>2</mn></mfrac><mo>d</mo><mi>x</mi></math>

Example 17

Example 17

Latex:

  1. \lim_{x\rightarrow\infty}\sqrt{\frac x{x^2+2x+1}}

MathML:

  1. <math xmlns="http://www.w3.org/1998/Math/MathML"><munder><mi>lim</mi><mrow><mi>x</mi><mo>→</mo><mo>∞</mo></mrow></munder><msqrt><mfrac><mi>x</mi><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfrac></msqrt></math>

Example 18

Example 18

Latex:

  1. \left|\int_a^bf(t)\operatorname dt\right|\leqslant\int_a^b\left|f(t)\right|\operatorname dt

MathML:

  1. <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="|" close="|"><mrow><msubsup><mo>∫</mo><mi>a</mi><mi>b</mi></msubsup><mi>f</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>d</mo><mi>t</mi></mrow></mfenced><mo>⩽</mo><msubsup><mo>∫</mo><mi>a</mi><mi>b</mi></msubsup><mfenced open="|" close="|"><mrow><mi>f</mi><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mfenced><mo>d</mo><mi>t</mi></math>

Example 19

Example 19

Latex:

  1. \iint_Dxy^2\operatorname dA=\int_0^1\left(\int_0^2xy^2\operatorname dx\right)\operatorname dy

MathML:

  1. <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mo>∬</mo><mi>D</mi></msub><mi>x</mi><msup><mi>y</mi><mn>2</mn></msup><mo>d</mo><mi>A</mi><mo>=</mo><msubsup><mo>∫</mo><mn>0</mn><mn>1</mn></msubsup><mfenced><mrow><msubsup><mo>∫</mo><mn>0</mn><mn>2</mn></msubsup><mi>x</mi><msup><mi>y</mi><mn>2</mn></msup><mo>d</mo><mi>x</mi></mrow></mfenced><mo>d</mo><mi>y</mi></math>

Example 20

Example 20

Latex:

  1. \prod_{x=1}^52x+1

MathML:

  1. <math xmlns="http://www.w3.org/1998/Math/MathML"><munderover><mo>∏</mo><mrow><mi>x</mi><mo>=</mo><mn>1</mn></mrow><mn>5</mn></munderover><mn>2</mn><mi>x</mi><mo>+</mo><mn>1</mn></math>