UNPKG

mathoid-texvcjs

Version:

A TeX/LaTeX validator for MediaWiki.

github.com/wikimedia/texvcjs

wikimedia/texvcjs

25 lines • 4.66 kB
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
{ "0270c7af664da7afddcac31d7ac3ad0f": "\\begin{alignat}2\n \\cos(2x) &= (\\cos{x})^2 +((\\cos{x})^2-1) &&= 2(\\cos{x})^2-1\\\\\n \\sin(2x) &= 2(\\sin{x})(\\cos{x})\\\\\n \\cos(3x) &= (\\cos{x})^3 +3\\cos{x}((\\cos{x})^2-1) &&= 4(\\cos{x})^3-3\\cos{x}\\\\\n \\sin(3x) &= 3(\\cos{x})^2(\\sin{x})-(\\sin{x})^3 &&= 3\\sin{x}-4(\\sin{x})^3.\\\\\n\\end{alignat}", "0448c022977e58b500445d3c92a6579a": "ρ\\colon P \\to N", "0e7c8b2fe70a6310bb546f3506e8c2ae": "a>b\"=\"\\&lt;<", "15212ec94e20fb0a97994cdee3b47dd8": "\\begin{alignat}2\n x &= 0.333333\\ldots\\\\\n 10x &= 3.333333\\ldots&\\quad&\\text{(multiplying each side of the above line by 10)}\\\\\n 9x &= 3 &&\\text{(subtracting the 1st line from the 2nd)}\\\\\n x &= 3/9 = 1/3 &&\\text{(reducing to lowest terms)}\\\\\n\\end{alignat}", "17a71941f66112018c433832caa51851": "U(0)=−1", "267b6df35d46a8a5ef4b910298d1bb16": "\\ln N! ≈ N \\ln N - N", "34cd4915dc9878e6a836e546a1725c86": "P_{\\text{new link to class $[k]$}} \\propto k f(k)", "6007c325e853ca12cfb61f00f9d36109": "|\\pm\\rangle=\\frac{1}{\\sqrt{2}}\\left(\\begin{array}[l]{c}\n 1\\\\\n \\pm i\n \\end{array}\\right).", "629979cd7de132f3d6884d3c48064c76": "CCAI=D-140.7 \\\n (\\log (V+0.85))-80.6-483.5 \\log \\left (\\frac{t+273}{323} \\right )", "665cf2ffe7708e3cae870b92deddfb6d": "\\left<|v|\\right>", "6a844321d746ca110ed895f82c622684": "\\begin{alignat}2\n e_1 &= p_1,\\\\\n e_2 &= \\textstyle\\frac12p_1^2 - \\frac12p_2 &&= \\textstyle\\frac12 ( p_1^2 - p_2 ),\\\\\n e_3 &= \\textstyle\\frac16p_1^3 - \\frac12p_1 p_2 + \\frac13p_3 &&= \\textstyle\\frac{1}{6} ( p_1^3 - 3 p_1 p_2 + 2 p_3 ),\\\\\n e_4 &= \\textstyle\\frac1{24}p_1^4 - \\frac14p_1^2 p_2 + \\frac18p_2^2 + \\frac13p_1 p_3 - \\frac14p_4 \n &&= \\textstyle\\frac1{24} ( p_1^4 - 6 p_1^2 p_2 + 3 p_2^2 + 8 p_1 p_3 - 6 p_4 ),\\\\\n\\end{alignat}", "6e2ea999c31f52054218db930bd4803d": "\n\\begin{align}\n[K_c] & = \\frac{\\prod_{j=1}^p [ {\\rm mol \\; dm^{{-3}} ]^{{y_j}}{\\prod_{i=1}^r [ {\\rm mol \\; dm^{{-3}} ]^{x_i} } \\\\\n & = \\frac{[ {\\rm mol \\; dm^{{-3}} ]^{y_1} [ {\\rm mol \\; dm^{{-3}} ]^{y_2} \\cdots [ {\\rm mol \\; dm^{{-3}} ]^{{y_p}}{[ {\\rm mol \\; dm^{{-3}} ]^{x_1} [ {\\rm mol \\; dm^{{-3}} ]^{x_2} \\cdots [ {\\rm mol \\; dm^{{-3}} ]^{x_r} } \\\\\n & = \\frac{[ {\\rm mol \\; dm^{{-3}} ]^{\\sum_{j=1}^p y_j}}{[ {\\rm mol \\; dm^{{-3}} ]^{\\sum_{i=1}^r x_i} } \\\\\n & = [ {\\rm mol \\; dm^{{-3}} ]^{\\sum_{j=1}^p y_j - \\sum_{i=1}^r x_i}\n\\end{align}\n", "740162aa0b844cc286c4a59c0c81fdfe": "\n\\begin{array}{|l|l|}\n\\hline\n\\alpha_i & \\beta_{ij} \\\\[8pt]\n\\hline\n\\alpha_1 = 0 & \\beta_{21} = \\frac{1}{2} \\\\[8pt]\n\\alpha_2 = \\frac{1}{2} & \\beta_{32} = \\frac{1}{2} \\\\[8pt]\n\\alpha_3 = \\frac{1}{2} & \\beta_{43} = 1 \\\\[8pt]\n\\alpha_4 = 1 & \\\\[8pt]\n\\hline\n\\end{array}\n", "866f63344780c4751fe344d954023fc9": " p_\\pi(\\boldsymbol\\eta|\\boldsymbol\\chi,\\nu) &= f(\\boldsymbol\\chi,\\nu) g(\\boldsymbol\\eta)^\\nu \\exp(\\boldsymbol\\eta^{\\rm T} \\boldsymbol\\chi) \\propto g(\\boldsymbol\\eta)^\\nu \\exp(\\boldsymbol\\eta^{\\rm T} \\boldsymbol\\chi)", "960cf2f7a6a5b4a03beba84473829eb3": "\\begin{alignat}2\n h_1 &= p_1,\\\\\n h_2 &= \\textstyle\\frac12p_1^2 + \\frac12p_2 &&= \\textstyle\\frac12 ( p_1^2 + p_2 ),\\\\\n h_3 &= \\textstyle\\frac16p_1^3 + \\frac12p_1 p_2 + \\frac13p_3 &&= \\textstyle\\frac{1}{6} ( p_1^3 + 3 p_1 p_2 + 2 p_3 ),\\\\\n h_4 &= \\textstyle\\frac1{24}p_1^4 + \\frac14p_1^2 p_2 + \\frac18p_2^2 + \\frac13p_1 p_3 + \\frac14p_4 \n &&= \\textstyle\\frac1{24} ( p_1^4 + 6 p_1^2 p_2 + 3 p_2^2 + 8 p_1 p_3 + 6 p_4 ),\\\\\n\\end{alignat}", "9cd7310f8613eeebb28046da004bc237": "\\left[\\begin{array}{l,l} s&t\\\\u&v \\end{array}\\right ]", "bf76a4641adb9a399d70feec04d37660": "A_iR_j \\subseteq A_{i+j} ⊇ R_iA_j", "c159c37865e286fab2b505de11ad4ce9": "P_{\\text{new link to $i$}} \\propto k_i ", "d3152d83fd1079191e4cbd3995470ddf": " { P_{rad} } = { R_0 \\left<|v|\\right>^2 } ", "e0199f5a37a0ab1813cfd0628f826f80": "\nS = \\left[ N\\ln V\\right] + \\left[\\frac 32 N\\ln\\left(2\\pi e m T\\right)\\right] + \\left[ -3N\\ln h\\right] + \\left[-\\ln N! \\right]\n ≈ N \\ln \\left[\\frac{V}{N} \\left(\\frac{2\\pi m T}{h^2}\\right)^{\\frac 32}\\right] + \\frac 52 N\n", "e3cc368e634d90cee0694fa0834b39b2": "\\left[\\begin{array}{l,l} s&t\\\\u&v \\end{array}\\right ] \\left[\\begin{array}{l} a\\\\b \\end{array}\\right ]\n= \\left[\\begin{array}{c} \\gcd(a,b)\\\\0 \\end{array}\\right ]. ", "e9f6be4c2ba14f4866fe4263bf5c6a0f": "\\mathcal{G} × \\mathcal{H}", "f338c7dea84103c7be9626def39d1c7f": "Z^{X × Y}" }