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Notations mathématiques sur le Web

Cette page sert de test pour les différents moteurs de rendu pour les expressions mathématiques. Pour l'instant, ce n'est vraiment pas le top...

Le principe

Pour ne pas devoir se tracasser de la manière dont nous allons afficher les formules, je ne m'occupe que de leur sémantique au moment ce la conception de la page. Au début de la page, un appel est fait à la méthode statique getInstance() de la classe BrolMath, qui me retourne un un objet (par exemple une instance de BrolMathML, ou de BrolMathHTML).
Toutes les méthodes de génération des différents éléments de la formule sont des méthodes abstraites définies dans la classe BrolMath, et implémentées dans une des classes concrètes.

Dans le cas d'une instance de BrolMathHTML, le code généré utilise simplement des balises (X)HTML. Une feuille de style permet de définir comment ces éléments sont affichés, mais certaines balises influencent directement la présentation (comme par exemple la balise sub), alors que le rendu MathML est plus indépendant de l'affichage.

Si l'option allowAlternate est activée, un message apparaît en bas de page, permettant de sélectionner un autre moyen d'affichage. Dans le cas où une option est sélectionnée, un message apparaît en haut de page pour signaler le type de rendu utilisé, et éventuellement d'autres informations en fonction du type d'affichage.

Le mode texte permet l'affichage des formules en pseudo-code, normalement plus facile à lire pour un non-mathématicien.

Exemples

Vous pouvez consulter la page d'explications sur programmation déclarative pour tester les affichages alternatifs.
Ci-dessous, différents exemples et le code généré :

Contents Haut

Symboles HTML (type html)

Une substitution est un ensemble de la forme σ  =   { X1 / t1, ..., Xn / tn }  tel que  

 ∀ i ∈  { 1, ..., n } Xi ∈ V
 ∀ i ∈  { 1, ..., n } ti ∈ T ... ceci est un extrait, et non la définition complète

Soit σ  =   { X1 / t1, ..., Xn / tn }  une substitution, nous avons
dom(σ)  =   { X1, ..., Xn }  et codom(σ)  =  var(t1, ..., tn)

Tests des ensembles :
ℕ, ℤ, ℚ, ℝ, ℂ;
α, Α, β, Β, γ, Γ, δ, Δ, ε, Ε, θ, Θ, ϑ, λ, μ, ξ, Ξ, π, ρ, σ, Σ, ς, φ, Φ, ψ, ω, Ω, ϒ; ...
A ⊂ B, A ⊆ B, A ⊃ B, A ⊇ B

substitution, division, fraction :
X / 1, X ÷ 1, X/1

Code généré

  1. <p class="pf">Une substitution est un ensemble de la forme
  2. <span class="frmla">
  3. <var>&sigma;
  4. </var>&nbsp;&nbsp;=&nbsp;&nbsp;&nbsp;{&nbsp;
  5. <var>X
  6. <sub>1
  7. </sub>
  8. </var>&nbsp;/&nbsp;
  9. <var>t
  10. <sub>1
  11. </sub>
  12. </var>, ...,
  13. <var>X
  14. <sub>
  15. <var>n
  16. </var>
  17. </sub>
  18. </var>&nbsp;/&nbsp;
  19. <var>t
  20. <sub>
  21. <var>n
  22. </var>
  23. </sub>
  24. </var>&nbsp;}&nbsp;
  25. </span> tel que &nbsp;
  26. <br />
  27. <br />
  28. <span class="frmla">&nbsp;&forall;&nbsp;
  29. <var>i
  30. </var>
  31. <span class="frmla">&nbsp;&isin;&nbsp;&nbsp;{&nbsp;1, ...,
  32. <var>n
  33. </var>&nbsp;}&nbsp;
  34. </span>
  35. <var>X
  36. <sub>
  37. <var>i
  38. </var>
  39. </sub>
  40. </var>&nbsp;&isin;&nbsp;
  41. <var>V
  42. </var>
  43. </span>
  44. <br />
  45. <span class="frmla">&nbsp;&forall;&nbsp;
  46. <var>i
  47. </var>
  48. <span class="frmla">&nbsp;&isin;&nbsp;&nbsp;{&nbsp;1, ...,
  49. <var>n
  50. </var>&nbsp;}&nbsp;
  51. </span>
  52. <var>t
  53. <sub>
  54. <var>i
  55. </var>
  56. </sub>
  57. </var>&nbsp;&isin;&nbsp;
  58. <var>T
  59. </var>
  60. </span> ...
  61. <span class="info">ceci est un extrait, et non la d&eacute;finition compl&egrave;te
  62. </span>
  63. <br />
  64. <br />Soit
  65. <span class="frmla">
  66. <var>&sigma;
  67. </var>&nbsp;&nbsp;=&nbsp;&nbsp;&nbsp;{&nbsp;
  68. <var>X
  69. <sub>1
  70. </sub>
  71. </var>&nbsp;/&nbsp;
  72. <var>t
  73. <sub>1
  74. </sub>
  75. </var>, ...,
  76. <var>X
  77. <sub>
  78. <var>n
  79. </var>
  80. </sub>
  81. </var>&nbsp;/&nbsp;
  82. <var>t
  83. <sub>
  84. <var>n
  85. </var>
  86. </sub>
  87. </var>&nbsp;}&nbsp;
  88. </span> une substitution, nous avons
  89. <br />
  90. <span class="frmla">
  91. <span class="fct">dom(
  92. <var>&sigma;
  93. </var>)
  94. </span>&nbsp;&nbsp;=&nbsp;&nbsp;&nbsp;{&nbsp;
  95. <var>X
  96. <sub>1
  97. </sub>
  98. </var>, ...,
  99. <var>X
  100. <sub>
  101. <var>n
  102. </var>
  103. </sub>
  104. </var>&nbsp;}&nbsp;
  105. </span> et
  106. <span class="frmla">
  107. <span class="fct">codom(
  108. <var>&sigma;
  109. </var>)
  110. </span>&nbsp;&nbsp;=&nbsp;&nbsp;
  111. <span class="fct">var(
  112. <var>t
  113. <sub>1
  114. </sub>
  115. </var>, ...,
  116. <var>t
  117. <sub>
  118. <var>n
  119. </var>
  120. </sub>
  121. </var>)
  122. </span>
  123. </span>
  124. </p>
  125. <p class="pn">Tests des ensembles&nbsp;:
  126. <br />
  127. <span class="frmla">&#x02115;, &#x02124;, &#x0211a;, &#x0211d;, &#x02102;;
  128. <br />
  129. <var>&alpha;
  130. </var>,
  131. <var>&Alpha;
  132. </var>,
  133. <var>&beta;
  134. </var>,
  135. <var>&Beta;
  136. </var>,
  137. <var>&gamma;
  138. </var>,
  139. <var>&Gamma;
  140. </var>,
  141. <var>&delta;
  142. </var>,
  143. <var>&Delta;
  144. </var>,
  145. <var>&epsilon;
  146. </var>,
  147. <var>&Epsilon;
  148. </var>,
  149. <var>&theta;
  150. </var>,
  151. <var>&Theta;
  152. </var>,
  153. <var>&thetasym;
  154. </var>,
  155. <var>&lambda;
  156. </var>,
  157. <var>&mu;
  158. </var>,
  159. <var>&xi;
  160. </var>,
  161. <var>&Xi;
  162. </var>,
  163. <var>&pi;
  164. </var>,
  165. <var>&rho;
  166. </var>,
  167. <var>&sigma;
  168. </var>,
  169. <var>&Sigma;
  170. </var>,
  171. <var>&sigmaf;
  172. </var>,
  173. <var>&phi;
  174. </var>,
  175. <var>&Phi;
  176. </var>,
  177. <var>&psi;
  178. </var>,
  179. <var>&omega;
  180. </var>,
  181. <var>&Omega;
  182. </var>,
  183. <var>&upsih;
  184. </var>; ...
  185. <br />
  186. <var>A
  187. </var>&nbsp;&sub;&nbsp;
  188. <var>B
  189. </var>,
  190. <var>A
  191. </var>&nbsp;&sube;&nbsp;
  192. <var>B
  193. </var>,
  194. <var>A
  195. </var>&nbsp;&sup;&nbsp;
  196. <var>B
  197. </var>,
  198. <var>A
  199. </var>&nbsp;&supe;&nbsp;
  200. <var>B
  201. </var>
  202. </span>
  203. </p>
  204. <p class="pn">substitution, division, fraction&nbsp;:
  205. <br />
  206. <span class="frmla">
  207. <var>X
  208. </var>&nbsp;/&nbsp;1,
  209. <var>X
  210. </var>&nbsp;&#x000f7;&nbsp;1,
  211. <var>X
  212. </var>/1
  213. </span>
  214. </p>

Contents Haut

Symboles MathML (type xml)

Une substitution est un ensemble de la forme σ = {X1/t1, ..., Xn/tn} tel que  

i{1, ..., n}XiV
i{1, ..., n}tiT ... ceci est un extrait, et non la définition complète

Soit σ = {X1/t1, ..., Xn/tn} une substitution, nous avons
dom(σ) = {X1, ..., Xn} et codom(σ) = var(t1, ..., tn)

Tests des ensembles :
, , , , ;
α, Α, β, Β, γ, Γ, δ, Δ, ε, Ε, θ, Θ, ϑ, λ, μ, ξ, Ξ, π, ρ, σ, Σ, ς, φ, Φ, ψ, ω, Ω, ϒ; ...
A ⊂ B, A ⊆ B, A ⊃ B, A ⊇ B

substitution, division, fraction :
X/1, X ÷ 1, X1

Code généré

  1. <p class="pf">Une substitution est un ensemble de la forme
  2. <math xmlns="http://www.w3.org/1998/Math/MathML">
  3. <mi>&sigma;
  4. </mi> 
  5. <mo>=
  6. </mo> 
  7. <mrow>
  8. <mo>{
  9. </mo>
  10. <mrow>
  11. <mi>
  12. <msub>X
  13. <mn>1
  14. </mn>
  15. </msub>
  16. </mi>
  17. <mo>/
  18. </mo>
  19. <mi>
  20. <msub>t
  21. <mn>1
  22. </mn>
  23. </msub>
  24. </mi>
  25. </mrow>, ...,
  26. <mrow>
  27. <mi>
  28. <msub>X
  29. <mi>n
  30. </mi>
  31. </msub>
  32. </mi>
  33. <mo>/
  34. </mo>
  35. <mi>
  36. <msub>t
  37. <mi>n
  38. </mi>
  39. </msub>
  40. </mi>
  41. </mrow>
  42. <mo>}
  43. </mo>
  44. </mrow>
  45. </math> tel que  
  46. <br />
  47. <br />
  48. <math xmlns="http://www.w3.org/1998/Math/MathML">
  49. <mrow>&#x02200;
  50. <mi>i
  51. </mi>
  52. <math xmlns="http://www.w3.org/1998/Math/MathML">
  53. <mrow>&isin;
  54. <mrow>
  55. <mo>{
  56. </mo>
  57. <mn>1
  58. </mn>, ...,
  59. <mi>n
  60. </mi>
  61. <mo>}
  62. </mo>
  63. </mrow>
  64. </mrow>
  65. </math>
  66. </mrow>
  67. <mi>
  68. <msub>X
  69. <mi>i
  70. </mi>
  71. </msub>
  72. </mi>
  73. <mrow>&isin;
  74. <mi>V
  75. </mi>
  76. </mrow>
  77. </math>
  78. <br />
  79. <math xmlns="http://www.w3.org/1998/Math/MathML">
  80. <mrow>&#x02200;
  81. <mi>i
  82. </mi>
  83. <math xmlns="http://www.w3.org/1998/Math/MathML">
  84. <mrow>&isin;
  85. <mrow>
  86. <mo>{
  87. </mo>
  88. <mn>1
  89. </mn>, ...,
  90. <mi>n
  91. </mi>
  92. <mo>}
  93. </mo>
  94. </mrow>
  95. </mrow>
  96. </math>
  97. </mrow>
  98. <mi>
  99. <msub>t
  100. <mi>i
  101. </mi>
  102. </msub>
  103. </mi>
  104. <mrow>&isin;
  105. <mi>T
  106. </mi>
  107. </mrow>
  108. </math> ...
  109. <span class="info">ceci est un extrait, et non la définition complète
  110. </span>
  111. <br />
  112. <br />Soit
  113. <math xmlns="http://www.w3.org/1998/Math/MathML">
  114. <mi>&sigma;
  115. </mi> 
  116. <mo>=
  117. </mo> 
  118. <mrow>
  119. <mo>{
  120. </mo>
  121. <mrow>
  122. <mi>
  123. <msub>X
  124. <mn>1
  125. </mn>
  126. </msub>
  127. </mi>
  128. <mo>/
  129. </mo>
  130. <mi>
  131. <msub>t
  132. <mn>1
  133. </mn>
  134. </msub>
  135. </mi>
  136. </mrow>, ...,
  137. <mrow>
  138. <mi>
  139. <msub>X
  140. <mi>n
  141. </mi>
  142. </msub>
  143. </mi>
  144. <mo>/
  145. </mo>
  146. <mi>
  147. <msub>t
  148. <mi>n
  149. </mi>
  150. </msub>
  151. </mi>
  152. </mrow>
  153. <mo>}
  154. </mo>
  155. </mrow>
  156. </math> une substitution, nous avons
  157. <br />
  158. <math xmlns="http://www.w3.org/1998/Math/MathML">
  159. <mrow>dom
  160. <mo>(
  161. </mo>
  162. <mi>&sigma;
  163. </mi>
  164. <mo>)
  165. </mo>
  166. </mrow> 
  167. <mo>=
  168. </mo> 
  169. <mrow>
  170. <mo>{
  171. </mo>
  172. <mi>
  173. <msub>X
  174. <mn>1
  175. </mn>
  176. </msub>
  177. </mi>, ...,
  178. <mi>
  179. <msub>X
  180. <mi>n
  181. </mi>
  182. </msub>
  183. </mi>
  184. <mo>}
  185. </mo>
  186. </mrow>
  187. </math> et
  188. <math xmlns="http://www.w3.org/1998/Math/MathML">
  189. <mrow>codom
  190. <mo>(
  191. </mo>
  192. <mi>&sigma;
  193. </mi>
  194. <mo>)
  195. </mo>
  196. </mrow> 
  197. <mo>=
  198. </mo> 
  199. <mrow>var
  200. <mo>(
  201. </mo>
  202. <mi>
  203. <msub>t
  204. <mn>1
  205. </mn>
  206. </msub>
  207. </mi>, ...,
  208. <mi>
  209. <msub>t
  210. <mi>n
  211. </mi>
  212. </msub>
  213. </mi>
  214. <mo>)
  215. </mo>
  216. </mrow>
  217. </math>
  218. </p>
  219. <p class="pn">Tests des ensembles :
  220. <br />
  221. <math xmlns="http://www.w3.org/1998/Math/MathML">&#x02115;
  222. <mtext>,
  223. </mtext>&#x02124;
  224. <mtext>,
  225. </mtext>&#x0211a;
  226. <mtext>,
  227. </mtext>&#x0211d;
  228. <mtext>,
  229. </mtext>&#x02102;
  230. <mtext>;
  231. <br />
  232. </mtext>
  233. <mi>&alpha;
  234. </mi>
  235. <mtext>,
  236. </mtext>
  237. <mi>&Alpha;
  238. </mi>
  239. <mtext>,
  240. </mtext>
  241. <mi>&beta;
  242. </mi>
  243. <mtext>,
  244. </mtext>
  245. <mi>&Beta;
  246. </mi>
  247. <mtext>,
  248. </mtext>
  249. <mi>&gamma;
  250. </mi>
  251. <mtext>,
  252. </mtext>
  253. <mi>&Gamma;
  254. </mi>
  255. <mtext>,
  256. </mtext>
  257. <mi>&delta;
  258. </mi>
  259. <mtext>,
  260. </mtext>
  261. <mi>&Delta;
  262. </mi>
  263. <mtext>,
  264. </mtext>
  265. <mi>&epsilon;
  266. </mi>
  267. <mtext>,
  268. </mtext>
  269. <mi>&Epsilon;
  270. </mi>
  271. <mtext>,
  272. </mtext>
  273. <mi>&theta;
  274. </mi>
  275. <mtext>,
  276. </mtext>
  277. <mi>&Theta;
  278. </mi>
  279. <mtext>,
  280. </mtext>
  281. <mi>&thetasym;
  282. </mi>
  283. <mtext>,
  284. </mtext>
  285. <mi>&lambda;
  286. </mi>
  287. <mtext>,
  288. </mtext>
  289. <mi>&mu;
  290. </mi>
  291. <mtext>,
  292. </mtext>
  293. <mi>&xi;
  294. </mi>
  295. <mtext>,
  296. </mtext>
  297. <mi>&Xi;
  298. </mi>
  299. <mtext>,
  300. </mtext>
  301. <mi>&pi;
  302. </mi>
  303. <mtext>,
  304. </mtext>
  305. <mi>&rho;
  306. </mi>
  307. <mtext>,
  308. </mtext>
  309. <mi>&sigma;
  310. </mi>
  311. <mtext>,
  312. </mtext>
  313. <mi>&Sigma;
  314. </mi>
  315. <mtext>,
  316. </mtext>
  317. <mi>&sigmaf;
  318. </mi>
  319. <mtext>,
  320. </mtext>
  321. <mi>&phi;
  322. </mi>
  323. <mtext>,
  324. </mtext>
  325. <mi>&Phi;
  326. </mi>
  327. <mtext>,
  328. </mtext>
  329. <mi>&psi;
  330. </mi>
  331. <mtext>,
  332. </mtext>
  333. <mi>&omega;
  334. </mi>
  335. <mtext>,
  336. </mtext>
  337. <mi>&Omega;
  338. </mi>
  339. <mtext>,
  340. </mtext>
  341. <mi>&upsih;
  342. </mi>
  343. <mtext>; ...
  344. <br />
  345. </mtext>
  346. <mi>A
  347. </mi> &sub; 
  348. <mi>B
  349. </mi>
  350. <mtext>,
  351. </mtext>
  352. <mi>A
  353. </mi> &sube; 
  354. <mi>B
  355. </mi>
  356. <mtext>,
  357. </mtext>
  358. <mi>A
  359. </mi> &sup; 
  360. <mi>B
  361. </mi>
  362. <mtext>,
  363. </mtext>
  364. <mi>A
  365. </mi> &supe; 
  366. <mi>B
  367. </mi>
  368. </math>
  369. </p>
  370. <p class="pn">substitution, division, fraction :
  371. <br />
  372. <math xmlns="http://www.w3.org/1998/Math/MathML">
  373. <mi>X
  374. </mi>
  375. <mo>/
  376. </mo>
  377. <mn>1
  378. </mn>
  379. <mtext>,
  380. </mtext>
  381. <mi>X
  382. </mi> &#x000f7; 
  383. <mn>1
  384. </mn>
  385. <mtext>,
  386. </mtext>
  387. <mfrac>
  388. <mi>X
  389. </mi>
  390. <mn>1
  391. </mn>
  392. </mfrac>
  393. </math>
  394. </p>

Contents Haut

Symboles texte (type html)

Une substitution est un ensemble de la forme sigma  =   { X1 est SUBSTITUE par t1, ..., Xn est SUBSTITUE par tn }  tel que  

( POUR TOUT i est INCLU dans  { 1, ..., n } ) Xi est INCLU dans V
( POUR TOUT i est INCLU dans  { 1, ..., n } ) ti est INCLU dans T ... ceci est un extrait, et non la définition complète

Soit sigma  =   { X1 est SUBSTITUE par t1, ..., Xn est SUBSTITUE par tn }  une substitution, nous avons
une FONCTION dom(AVEC sigma COMME ARGUMENTS)  =   { X1, ..., Xn }  et une FONCTION codom(AVEC sigma COMME ARGUMENTS)  =  une FONCTION var(AVEC t1, ..., tn COMME ARGUMENTS)

Tests des ensembles :
Ensemble_des_entiers_naturels, Ensemble_des_entiers_relatifs, Ensemble_des_nombres_rationnels, Ensemble_des_nombres_réels, Ensemble_des_nombres_complexes;
alpha, Alpha, beta, Beta, gamma, Gamma, delta, Delta, epsilon, Epsilon, theta, Theta, thetasym, lambda, mu, xi, Xi, pi, rho, sigma, Sigma, sigmaf, phi, Phi, psi, omega, Omega, upsih; ...
(A est un SOUS-ENSEMBLE de B) , (A est EGAL ou est un SOUS-ENSEMBLE de B) , (A CONTIENT B) , (A est EGAL ou CONTIENT B)

substitution, division, fraction :
X est SUBSTITUE par 1, (X DIVISE PAR 1) , ( FRACTION de X sur 1)

Code généré

  1. <p class="pf">Une substitution est un ensemble de la forme
  2. <span class="frmla" title="Math en mode texte">
  3. <var title="variable">sigma
  4. </var>&nbsp;&nbsp;=&nbsp;&nbsp;&nbsp;{&nbsp;
  5. <var title="variable">X
  6. <sub>1
  7. </sub>
  8. </var>
  9. <span class="frmlatxt">&nbsp;est SUBSTITUE par&nbsp;
  10. </span>
  11. <var title="variable">t
  12. <sub>1
  13. </sub>
  14. </var>, ...,
  15. <var title="variable">X
  16. <sub>
  17. <var title="variable">n
  18. </var>
  19. </sub>
  20. </var>
  21. <span class="frmlatxt">&nbsp;est SUBSTITUE par&nbsp;
  22. </span>
  23. <var title="variable">t
  24. <sub>
  25. <var title="variable">n
  26. </var>
  27. </sub>
  28. </var>&nbsp;}&nbsp;
  29. </span> tel que &nbsp;
  30. <br />
  31. <br />
  32. <span class="frmla" title="Math en mode texte">
  33. <span class="frmlatxt"> (
  34. </span>
  35. <span class="frmlatxt">&nbsp;POUR TOUT&nbsp;
  36. </span>
  37. <var title="variable">i
  38. </var>
  39. <span class="frmla" title="Math en mode texte">
  40. <span class="frmlatxt">&nbsp;est INCLU dans&nbsp;
  41. </span>&nbsp;{&nbsp;1, ...,
  42. <var title="variable">n
  43. </var>&nbsp;}&nbsp;
  44. </span>
  45. <span class="frmlatxt">)
  46. </span>
  47. <var title="variable">X
  48. <sub>
  49. <var title="variable">i
  50. </var>
  51. </sub>
  52. </var>
  53. <span class="frmlatxt">&nbsp;est INCLU dans&nbsp;
  54. </span>
  55. <var title="variable">V
  56. </var>
  57. </span>
  58. <br />
  59. <span class="frmla" title="Math en mode texte">
  60. <span class="frmlatxt"> (
  61. </span>
  62. <span class="frmlatxt">&nbsp;POUR TOUT&nbsp;
  63. </span>
  64. <var title="variable">i
  65. </var>
  66. <span class="frmla" title="Math en mode texte">
  67. <span class="frmlatxt">&nbsp;est INCLU dans&nbsp;
  68. </span>&nbsp;{&nbsp;1, ...,
  69. <var title="variable">n
  70. </var>&nbsp;}&nbsp;
  71. </span>
  72. <span class="frmlatxt">)
  73. </span>
  74. <var title="variable">t
  75. <sub>
  76. <var title="variable">i
  77. </var>
  78. </sub>
  79. </var>
  80. <span class="frmlatxt">&nbsp;est INCLU dans&nbsp;
  81. </span>
  82. <var title="variable">T
  83. </var>
  84. </span> ...
  85. <span class="info">ceci est un extrait, et non la d&eacute;finition compl&egrave;te
  86. </span>
  87. <br />
  88. <br />Soit
  89. <span class="frmla" title="Math en mode texte">
  90. <var title="variable">sigma
  91. </var>&nbsp;&nbsp;=&nbsp;&nbsp;&nbsp;{&nbsp;
  92. <var title="variable">X
  93. <sub>1
  94. </sub>
  95. </var>
  96. <span class="frmlatxt">&nbsp;est SUBSTITUE par&nbsp;
  97. </span>
  98. <var title="variable">t
  99. <sub>1
  100. </sub>
  101. </var>, ...,
  102. <var title="variable">X
  103. <sub>
  104. <var title="variable">n
  105. </var>
  106. </sub>
  107. </var>
  108. <span class="frmlatxt">&nbsp;est SUBSTITUE par&nbsp;
  109. </span>
  110. <var title="variable">t
  111. <sub>
  112. <var title="variable">n
  113. </var>
  114. </sub>
  115. </var>&nbsp;}&nbsp;
  116. </span> une substitution, nous avons
  117. <br />
  118. <span class="frmla" title="Math en mode texte">
  119. <span class="frmlatxt">une FONCTION
  120. </span>dom(
  121. <span class="frmlatxt">AVEC
  122. </span>
  123. <var title="variable">sigma
  124. </var>
  125. <span class="frmlatxt"> COMME ARGUMENTS
  126. </span>)&nbsp;&nbsp;=&nbsp;&nbsp;&nbsp;{&nbsp;
  127. <var title="variable">X
  128. <sub>1
  129. </sub>
  130. </var>, ...,
  131. <var title="variable">X
  132. <sub>
  133. <var title="variable">n
  134. </var>
  135. </sub>
  136. </var>&nbsp;}&nbsp;
  137. </span> et
  138. <span class="frmla" title="Math en mode texte">
  139. <span class="frmlatxt">une FONCTION
  140. </span>codom(
  141. <span class="frmlatxt">AVEC
  142. </span>
  143. <var title="variable">sigma
  144. </var>
  145. <span class="frmlatxt"> COMME ARGUMENTS
  146. </span>)&nbsp;&nbsp;=&nbsp;&nbsp;
  147. <span class="frmlatxt">une FONCTION
  148. </span>var(
  149. <span class="frmlatxt">AVEC
  150. </span>
  151. <var title="variable">t
  152. <sub>1
  153. </sub>
  154. </var>, ...,
  155. <var title="variable">t
  156. <sub>
  157. <var title="variable">n
  158. </var>
  159. </sub>
  160. </var>
  161. <span class="frmlatxt"> COMME ARGUMENTS
  162. </span>)
  163. </span>
  164. </p>
  165. <p class="pn">Tests des ensembles&nbsp;:
  166. <br />
  167. <span class="frmla" title="Math en mode texte">
  168. <span class="frmlatxt">Ensemble_des_entiers_naturels
  169. </span>
  170. <span class="frmlatxt">,
  171. </span>
  172. <span class="frmlatxt">Ensemble_des_entiers_relatifs
  173. </span>
  174. <span class="frmlatxt">,
  175. </span>
  176. <span class="frmlatxt">Ensemble_des_nombres_rationnels
  177. </span>
  178. <span class="frmlatxt">,
  179. </span>
  180. <span class="frmlatxt">Ensemble_des_nombres_r&eacute;els
  181. </span>
  182. <span class="frmlatxt">,
  183. </span>
  184. <span class="frmlatxt">Ensemble_des_nombres_complexes
  185. </span>
  186. <span class="frmlatxt">;
  187. <br />
  188. </span>
  189. <var title="variable">alpha
  190. </var>
  191. <span class="frmlatxt">,
  192. </span>
  193. <var title="variable">Alpha
  194. </var>
  195. <span class="frmlatxt">,
  196. </span>
  197. <var title="variable">beta
  198. </var>
  199. <span class="frmlatxt">,
  200. </span>
  201. <var title="variable">Beta
  202. </var>
  203. <span class="frmlatxt">,
  204. </span>
  205. <var title="variable">gamma
  206. </var>
  207. <span class="frmlatxt">,
  208. </span>
  209. <var title="variable">Gamma
  210. </var>
  211. <span class="frmlatxt">,
  212. </span>
  213. <var title="variable">delta
  214. </var>
  215. <span class="frmlatxt">,
  216. </span>
  217. <var title="variable">Delta
  218. </var>
  219. <span class="frmlatxt">,
  220. </span>
  221. <var title="variable">epsilon
  222. </var>
  223. <span class="frmlatxt">,
  224. </span>
  225. <var title="variable">Epsilon
  226. </var>
  227. <span class="frmlatxt">,
  228. </span>
  229. <var title="variable">theta
  230. </var>
  231. <span class="frmlatxt">,
  232. </span>
  233. <var title="variable">Theta
  234. </var>
  235. <span class="frmlatxt">,
  236. </span>
  237. <var title="variable">thetasym
  238. </var>
  239. <span class="frmlatxt">,
  240. </span>
  241. <var title="variable">lambda
  242. </var>
  243. <span class="frmlatxt">,
  244. </span>
  245. <var title="variable">mu
  246. </var>
  247. <span class="frmlatxt">,
  248. </span>
  249. <var title="variable">xi
  250. </var>
  251. <span class="frmlatxt">,
  252. </span>
  253. <var title="variable">Xi
  254. </var>
  255. <span class="frmlatxt">,
  256. </span>
  257. <var title="variable">pi
  258. </var>
  259. <span class="frmlatxt">,
  260. </span>
  261. <var title="variable">rho
  262. </var>
  263. <span class="frmlatxt">,
  264. </span>
  265. <var title="variable">sigma
  266. </var>
  267. <span class="frmlatxt">,
  268. </span>
  269. <var title="variable">Sigma
  270. </var>
  271. <span class="frmlatxt">,
  272. </span>
  273. <var title="variable">sigmaf
  274. </var>
  275. <span class="frmlatxt">,
  276. </span>
  277. <var title="variable">phi
  278. </var>
  279. <span class="frmlatxt">,
  280. </span>
  281. <var title="variable">Phi
  282. </var>
  283. <span class="frmlatxt">,
  284. </span>
  285. <var title="variable">psi
  286. </var>
  287. <span class="frmlatxt">,
  288. </span>
  289. <var title="variable">omega
  290. </var>
  291. <span class="frmlatxt">,
  292. </span>
  293. <var title="variable">Omega
  294. </var>
  295. <span class="frmlatxt">,
  296. </span>
  297. <var title="variable">upsih
  298. </var>
  299. <span class="frmlatxt">; ...
  300. <br />
  301. </span>
  302. <span class="frmlatxt"> (
  303. </span>
  304. <var title="variable">A
  305. </var>
  306. <span class="frmlatxt">&nbsp;est un SOUS-ENSEMBLE de&nbsp;
  307. </span>
  308. <var title="variable">B
  309. </var>
  310. <span class="frmlatxt">)
  311. </span>
  312. <span class="frmlatxt">,
  313. </span>
  314. <span class="frmlatxt"> (
  315. </span>
  316. <var title="variable">A
  317. </var>
  318. <span class="frmlatxt">&nbsp;est EGAL ou est un SOUS-ENSEMBLE de&nbsp;
  319. </span>
  320. <var title="variable">B
  321. </var>
  322. <span class="frmlatxt">)
  323. </span>
  324. <span class="frmlatxt">,
  325. </span>
  326. <span class="frmlatxt"> (
  327. </span>
  328. <var title="variable">A
  329. </var>
  330. <span class="frmlatxt">&nbsp;CONTIENT&nbsp;
  331. </span>
  332. <var title="variable">B
  333. </var>
  334. <span class="frmlatxt">)
  335. </span>
  336. <span class="frmlatxt">,
  337. </span>
  338. <span class="frmlatxt"> (
  339. </span>
  340. <var title="variable">A
  341. </var>
  342. <span class="frmlatxt">&nbsp;est EGAL ou CONTIENT&nbsp;
  343. </span>
  344. <var title="variable">B
  345. </var>
  346. <span class="frmlatxt">)
  347. </span>
  348. </span>
  349. </p>
  350. <p class="pn">substitution, division, fraction&nbsp;:
  351. <br />
  352. <span class="frmla" title="Math en mode texte">
  353. <var title="variable">X
  354. </var>
  355. <span class="frmlatxt">&nbsp;est SUBSTITUE par&nbsp;
  356. </span>1
  357. <span class="frmlatxt">,
  358. </span>
  359. <span class="frmlatxt"> (
  360. </span>
  361. <var title="variable">X
  362. </var>
  363. <span class="frmlatxt"> DIVISE PAR
  364. </span>1
  365. <span class="frmlatxt">)
  366. </span>
  367. <span class="frmlatxt">,
  368. </span>
  369. <span class="frmlatxt"> (
  370. </span>
  371. <span class="frmlatxt"> FRACTION de
  372. </span>
  373. <var title="variable">X
  374. </var>
  375. <span class="frmlatxt"> sur
  376. </span>1
  377. <span class="frmlatxt">)
  378. </span>
  379. </span>
  380. </p>

Contents Haut

Fraction simple avec HTML (type html)

a0 + 1/x

Code généré

  1. <span class="frmla">
  2. <var>a
  3. </var>
  4. <sub>0
  5. </sub>&nbsp;+&nbsp;1/
  6. <var>x
  7. </var>
  8. </span>

Contents Haut

Fraction simple avec MathML (type xml)

a0+1x

Code généré

  1. <math xmlns="http://www.w3.org/1998/Math/MathML">
  2. <msub>
  3. <mi>a
  4. </mi>
  5. <mn>0
  6. </mn>
  7. </msub>
  8. <mo>+
  9. </mo>
  10. <mfrac>
  11. <mn>1
  12. </mn>
  13. <mi>x
  14. </mi>
  15. </mfrac>
  16. </math>

Contents Haut

Fractions multiples avec HTML (type html)

a4 + 1/a3 + 1/a2 + 1/a1 + 1/a0 + 1/x

Code généré

  1. <span class="frmla">
  2. <var>a
  3. </var>
  4. <sub>4
  5. </sub>&nbsp;+&nbsp;1/
  6. <var>a
  7. </var>
  8. <sub>3
  9. </sub>&nbsp;+&nbsp;1/
  10. <var>a
  11. </var>
  12. <sub>2
  13. </sub>&nbsp;+&nbsp;1/
  14. <var>a
  15. </var>
  16. <sub>1
  17. </sub>&nbsp;+&nbsp;1/
  18. <var>a
  19. </var>
  20. <sub>0
  21. </sub>&nbsp;+&nbsp;1/
  22. <var>x
  23. </var>
  24. </span>

Contents Haut

Fractions multiples avec MathML (type xml)

a4+1a3+1a2+1a1+1a0+1x

Code généré

  1. <math xmlns="http://www.w3.org/1998/Math/MathML">
  2. <msub>
  3. <mi>a
  4. </mi>
  5. <mn>4
  6. </mn>
  7. </msub>
  8. <mo>+
  9. </mo>
  10. <mfrac>
  11. <mn>1
  12. </mn>
  13. <msub>
  14. <mi>a
  15. </mi>
  16. <mn>3
  17. </mn>
  18. </msub>
  19. <mo>+
  20. </mo>
  21. <mfrac>
  22. <mn>1
  23. </mn>
  24. <msub>
  25. <mi>a
  26. </mi>
  27. <mn>2
  28. </mn>
  29. </msub>
  30. <mo>+
  31. </mo>
  32. <mfrac>
  33. <mn>1
  34. </mn>
  35. <msub>
  36. <mi>a
  37. </mi>
  38. <mn>1
  39. </mn>
  40. </msub>
  41. <mo>+
  42. </mo>
  43. <mfrac>
  44. <mn>1
  45. </mn>
  46. <msub>
  47. <mi>a
  48. </mi>
  49. <mn>0
  50. </mn>
  51. </msub>
  52. <mo>+
  53. </mo>
  54. <mfrac>
  55. <mn>1
  56. </mn>
  57. <mi>x
  58. </mi>
  59. </mfrac>
  60. </mfrac>
  61. </mfrac>
  62. </mfrac>
  63. </mfrac>
  64. </math>

Contents Haut

Superpositions avec HTML (type html)

Test 3-1

The quick brown fox jumps over
the lazy dog

Test 3-2

base
under

Test 3-3

over
base
under

Test 3-4

over
base
under
 + 
base
under
 ∧ a2 + 1/a1 + 1/a0 + 1/x

Code généré

  1. <section>
  2. <section>
  3. <h4 id="test8-1-t">
  4. <span id="test8-1" class="brol-scrollfix toc-c">
  5. </span>Test 3-1
  6. </h4>
  7. <span class="frmla">
  8. <table class="noborder">
  9. <tr>
  10. <td>The quick brown fox jumps over
  11. </td>
  12. </tr>
  13. <tr>
  14. <td>the lazy dog
  15. </td>
  16. </tr>
  17. </span>
  18. </section>
  19. <section>
  20. <h4 id="test8-2-t">
  21. <span id="test8-2" class="brol-scrollfix toc-c">
  22. </span>Test 3-2
  23. </h4>
  24. <span class="frmla">
  25. <table class="noborder">
  26. <tr>
  27. <td>base
  28. </td>
  29. </tr>
  30. <tr>
  31. <td>under
  32. </td>
  33. </tr>
  34. </span>
  35. </section>
  36. <section>
  37. <h4 id="test8-3-t">
  38. <span id="test8-3" class="brol-scrollfix toc-c">
  39. </span>Test 3-3
  40. </h4>
  41. <span class="frmla">
  42. <table class="noborder">
  43. <tr>
  44. <td>over
  45. </td>
  46. </tr>
  47. <tr>
  48. <td>base
  49. </td>
  50. </tr>
  51. <tr>
  52. <td>under
  53. </td>
  54. </tr>
  55. </span>
  56. <span class="frmla">
  57. </span>
  58. </section>
  59. <section>
  60. <h4 id="test8-4-t">
  61. <span id="test8-4" class="brol-scrollfix toc-c">
  62. </span>Test 3-4
  63. </h4>
  64. <span class="frmla">
  65. <table class="noborder">
  66. <tr>
  67. <td>over
  68. </td>
  69. </tr>
  70. <tr>
  71. <td>base
  72. </td>
  73. </tr>
  74. <tr>
  75. <td>under
  76. </td>
  77. </tr>
  78. </table>&nbsp;+&nbsp;
  79. <table class="noborder">
  80. <tr>
  81. <td>base
  82. </td>
  83. </tr>
  84. <tr>
  85. <td>under
  86. </td>
  87. </tr>
  88. </table>&nbsp;&and;&nbsp;
  89. <var>a
  90. </var>
  91. <sub>2
  92. </sub>&nbsp;+&nbsp;1/
  93. <var>a
  94. </var>
  95. <sub>1
  96. </sub>&nbsp;+&nbsp;1/
  97. <var>a
  98. </var>
  99. <sub>0
  100. </sub>&nbsp;+&nbsp;1/
  101. <var>x
  102. </var>
  103. </span>

Contents Haut

Superpositions avec MathML (type xml)

Test 3-1

the lazy dogThe quick brown fox jumps over

Test 3-2

baseunder

Test 3-3

baseunderover

Test 3-4

baseunderover+baseunder ∧ a2+1a1+1a0+1x

Code généré

  1. <section>
  2. <section>
  3. <h4 id="test9-1-t">
  4. <span id="test9-1" class="brol-scrollfix toc-c">
  5. </span>Test 3-1
  6. </h4>
  7. <math xmlns="http://www.w3.org/1998/Math/MathML">
  8. <mover>
  9. <mtext>the lazy dog
  10. </mtext>
  11. <mtext>The quick brown fox jumps over
  12. </mtext>
  13. </mover>
  14. </math>
  15. </section>
  16. <section>
  17. <h4 id="test9-2-t">
  18. <span id="test9-2" class="brol-scrollfix toc-c">
  19. </span>Test 3-2
  20. </h4>
  21. <math xmlns="http://www.w3.org/1998/Math/MathML">
  22. <munder>
  23. <mtext>base
  24. </mtext>
  25. <mtext>under
  26. </mtext>
  27. </munder>
  28. </math>
  29. </section>
  30. <section>
  31. <h4 id="test9-3-t">
  32. <span id="test9-3" class="brol-scrollfix toc-c">
  33. </span>Test 3-3
  34. </h4>
  35. <math xmlns="http://www.w3.org/1998/Math/MathML">
  36. <munderover>
  37. <mtext>base
  38. </mtext>
  39. <mtext>under
  40. </mtext>
  41. <mtext>over
  42. </mtext>
  43. </munderover>
  44. </math>
  45. <math xmlns="http://www.w3.org/1998/Math/MathML">
  46. </math>
  47. </section>
  48. <section>
  49. <h4 id="test9-4-t">
  50. <span id="test9-4" class="brol-scrollfix toc-c">
  51. </span>Test 3-4
  52. </h4>
  53. <math xmlns="http://www.w3.org/1998/Math/MathML">
  54. <munderover>
  55. <mtext>base
  56. </mtext>
  57. <mtext>under
  58. </mtext>
  59. <mtext>over
  60. </mtext>
  61. </munderover>
  62. <mo>+
  63. </mo>
  64. <mrow>
  65. <munder>
  66. <mtext>base
  67. </mtext>
  68. <mtext>under
  69. </mtext>
  70. </munder> &#x02227; 
  71. <msub>
  72. <mi>a
  73. </mi>
  74. <mn>2
  75. </mn>
  76. </msub>
  77. <mo>+
  78. </mo>
  79. <mfrac>
  80. <mn>1
  81. </mn>
  82. <msub>
  83. <mi>a
  84. </mi>
  85. <mn>1
  86. </mn>
  87. </msub>
  88. <mo>+
  89. </mo>
  90. <mfrac>
  91. <mn>1
  92. </mn>
  93. <msub>
  94. <mi>a
  95. </mi>
  96. <mn>0
  97. </mn>
  98. </msub>
  99. <mo>+
  100. </mo>
  101. <mfrac>
  102. <mn>1
  103. </mn>
  104. <mi>x
  105. </mi>
  106. </mfrac>
  107. </mfrac>
  108. </mfrac>
  109. </mrow>
  110. </math>

Exemples MathML

n=0+xnn!\sum_{n=0}^{+\infty} \frac{x^n}{n!}

a2+x3

Code généré

  1. <p>
  2. <math display="block">
  3. <semantics>
  4. <mrow>
  5. <munderover>
  6. <mo>
  7. </mo>
  8. <mrow>
  9. <mi>n
  10. </mi>
  11. <mo>=
  12. </mo>
  13. <mn>0
  14. </mn>
  15. </mrow>
  16. <mrow>
  17. <mo>+
  18. </mo>
  19. <mn>
  20. </mn>
  21. </mrow>
  22. </munderover>
  23. <mfrac>
  24. <msup>
  25. <mi>x
  26. </mi>
  27. <mi>n
  28. </mi>
  29. </msup>
  30. <mrow>
  31. <mi>n
  32. </mi>
  33. <mo>!
  34. </mo>
  35. </mrow>
  36. </mfrac>
  37. </mrow>
  38. <annotation encoding="TeX">\sum_{n=0}^{+\infty} \frac{x^n}{n!}
  39. </annotation>
  40. </semantics>
  41. </math>
  42. </p>
  43. <p>
  44. <math>
  45. <mfrac>
  46. <mi>a
  47. </mi>
  48. <msqrt>
  49. <mn>2
  50. </mn>
  51. </msqrt>
  52. </mfrac>
  53. <mo>+
  54. </mo>
  55. <msup>
  56. <mi>x
  57. </mi>
  58. <mn>3
  59. </mn>
  60. </msup>
  61. </math>
  62. </p>

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English translation

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Document created the 05/06/2010, last modified the 31/10/2018
Source of the printed document:https://www.gaudry.be/en/math-rendering.html

The infobrol is a personal site whose content is my sole responsibility. The text is available under CreativeCommons license (BY-NC-SA). More info on the terms of use and the author.

References

  1. View the nbsp;document Language of the document:fr Table des caractères Unicode : unicode.org, U2200 (15/06/10)

These references and links indicate documents consulted during the writing of this page, or which may provide additional information, but the authors of these sources can not be held responsible for the content of this page.
The author This site is solely responsible for the way in which the various concepts, and the freedoms that are taken with the reference works, are presented here. Remember that you must cross multiple source information to reduce the risk of errors.

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