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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, ..., X_n / t_n } tel que

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

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

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

Code HTML (214 lignes)

<p class="pf">Une substitution est un ensemble de la forme 
<span class="frmla">
<var>&sigma;
</var>&nbsp;&nbsp;=&nbsp;&nbsp;&nbsp;{&nbsp;
<var>X
<sub>1
</sub>
</var>&nbsp;/&nbsp;
<var>t
<sub>1
</sub>
</var>, ..., 
<var>X
<sub>
<var>n
</var>
</sub>
</var>&nbsp;/&nbsp;
<var>t
<sub>
<var>n
</var>
</sub>
</var>&nbsp;}&nbsp;
</span> tel que &nbsp;
<br />
<br />
<span class="frmla">&nbsp;&forall;&nbsp;
<var>i
</var>
<span class="frmla">&nbsp;&isin;&nbsp;&nbsp;{&nbsp;1, ..., 
<var>n
</var>&nbsp;}&nbsp;
</span>
<var>X
<sub>
<var>i
</var>
</sub>
</var>&nbsp;&isin;&nbsp;
<var>V
</var>
</span>
<br />
<span class="frmla">&nbsp;&forall;&nbsp;
<var>i
</var>
<span class="frmla">&nbsp;&isin;&nbsp;&nbsp;{&nbsp;1, ..., 
<var>n
</var>&nbsp;}&nbsp;
</span>
<var>t
<sub>
<var>i
</var>
</sub>
</var>&nbsp;&isin;&nbsp;
<var>T
</var>
</span> ... 
<span class="info">ceci est un extrait, et non la d&eacute;finition compl&egrave;te
</span>
<br />
<br />Soit 
<span class="frmla">
<var>&sigma;
</var>&nbsp;&nbsp;=&nbsp;&nbsp;&nbsp;{&nbsp;
<var>X
<sub>1
</sub>
</var>&nbsp;/&nbsp;
<var>t
<sub>1
</sub>
</var>, ..., 
<var>X
<sub>
<var>n
</var>
</sub>
</var>&nbsp;/&nbsp;
<var>t
<sub>
<var>n
</var>
</sub>
</var>&nbsp;}&nbsp;
</span> une substitution, nous avons
<br />
<span class="frmla">
<span class="fct">dom(
<var>&sigma;
</var>)
</span>&nbsp;&nbsp;=&nbsp;&nbsp;&nbsp;{&nbsp;
<var>X
<sub>1
</sub>
</var>, ..., 
<var>X
<sub>
<var>n
</var>
</sub>
</var>&nbsp;}&nbsp;
</span> et 
<span class="frmla">
<span class="fct">codom(
<var>&sigma;
</var>)
</span>&nbsp;&nbsp;=&nbsp;&nbsp;
<span class="fct">var(
<var>t
<sub>1
</sub>
</var>, ..., 
<var>t
<sub>
<var>n
</var>
</sub>
</var>)
</span>
</span>
</p>
<p class="pn">Tests des ensembles&nbsp;: 
<br />
<span class="frmla">&#x02115;, &#x02124;, &#x0211a;, &#x0211d;, &#x02102;;
<br />
<var>&alpha;
</var>, 
<var>&Alpha;
</var>, 
<var>&beta;
</var>, 
<var>&Beta;
</var>, 
<var>&gamma;
</var>, 
<var>&Gamma;
</var>, 
<var>&delta;
</var>, 
<var>&Delta;
</var>, 
<var>&epsilon;
</var>, 
<var>&Epsilon;
</var>, 
<var>&theta;
</var>, 
<var>&Theta;
</var>, 
<var>&thetasym;
</var>, 
<var>&lambda;
</var>, 
<var>&mu;
</var>, 
<var>&xi;
</var>, 
<var>&Xi;
</var>, 
<var>&pi;
</var>, 
<var>&rho;
</var>, 
<var>&sigma;
</var>, 
<var>&Sigma;
</var>, 
<var>&sigmaf;
</var>, 
<var>&phi;
</var>, 
<var>&Phi;
</var>, 
<var>&psi;
</var>, 
<var>&omega;
</var>, 
<var>&Omega;
</var>, 
<var>&upsih;
</var>; ...
<br />
<var>A
</var>&nbsp;&sub;&nbsp;
<var>B
</var>, 
<var>A
</var>&nbsp;&sube;&nbsp;
<var>B
</var>, 
<var>A
</var>&nbsp;&sup;&nbsp;
<var>B
</var>, 
<var>A
</var>&nbsp;&supe;&nbsp;
<var>B
</var>
</span>
</p>
<p class="pn">substitution, division, fraction&nbsp;: 
<br />
<span class="frmla">
<var>X
</var>&nbsp;/&nbsp;1, 
<var>X
</var>&nbsp;&#x000f7;&nbsp;1, 
<var>X
</var>/1
</span>
</p>

Retourner au début du code

Contents Haut

Symboles MathML (type xml)

Une substitution est un ensemble de la forme $σ = {X_{1} / t_{1}, ..., X_{n} / t_{n}}$ tel que

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

Soit $σ = {X_{1} / t_{1}, ..., X_{n} / t_{n}}$ une substitution, nous avons
$dom (σ) = {X_{1}, ..., X_{n}}$ et $codom (σ) = var (t_{1}, ..., t_{n})$

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 :
$X / 1, X ÷ 1, \frac{X}{1}$

Code généré

Code XML (394 lignes)

<p class="pf">Une substitution est un ensemble de la forme 
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>&sigma;
</mi> 
<mo>=
</mo> 
<mrow>
<mo>{
</mo>
<mrow>
<mi>
<msub>X
<mn>1
</mn>
</msub>
</mi>
<mo>/
</mo>
<mi>
<msub>t
<mn>1
</mn>
</msub>
</mi>
</mrow>, ..., 
<mrow>
<mi>
<msub>X
<mi>n
</mi>
</msub>
</mi>
<mo>/
</mo>
<mi>
<msub>t
<mi>n
</mi>
</msub>
</mi>
</mrow>
<mo>}
</mo>
</mrow>
</math> tel que  
<br />
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>&#x02200;
<mi>i
</mi>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>&isin;
<mrow>
<mo>{
</mo>
<mn>1
</mn>, ..., 
<mi>n
</mi>
<mo>}
</mo>
</mrow>
</mrow>
</math>
</mrow>
<mi>
<msub>X
<mi>i
</mi>
</msub>
</mi>
<mrow>&isin;
<mi>V
</mi>
</mrow>
</math>
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>&#x02200;
<mi>i
</mi>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>&isin;
<mrow>
<mo>{
</mo>
<mn>1
</mn>, ..., 
<mi>n
</mi>
<mo>}
</mo>
</mrow>
</mrow>
</math>
</mrow>
<mi>
<msub>t
<mi>i
</mi>
</msub>
</mi>
<mrow>&isin;
<mi>T
</mi>
</mrow>
</math> ... 
<span class="info">ceci est un extrait, et non la définition complète
</span>
<br />
<br />Soit 
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>&sigma;
</mi> 
<mo>=
</mo> 
<mrow>
<mo>{
</mo>
<mrow>
<mi>
<msub>X
<mn>1
</mn>
</msub>
</mi>
<mo>/
</mo>
<mi>
<msub>t
<mn>1
</mn>
</msub>
</mi>
</mrow>, ..., 
<mrow>
<mi>
<msub>X
<mi>n
</mi>
</msub>
</mi>
<mo>/
</mo>
<mi>
<msub>t
<mi>n
</mi>
</msub>
</mi>
</mrow>
<mo>}
</mo>
</mrow>
</math> une substitution, nous avons
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>dom
<mo>(
</mo>
<mi>&sigma;
</mi>
<mo>)
</mo>
</mrow> 
<mo>=
</mo> 
<mrow>
<mo>{
</mo>
<mi>
<msub>X
<mn>1
</mn>
</msub>
</mi>, ..., 
<mi>
<msub>X
<mi>n
</mi>
</msub>
</mi>
<mo>}
</mo>
</mrow>
</math> et 
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>codom
<mo>(
</mo>
<mi>&sigma;
</mi>
<mo>)
</mo>
</mrow> 
<mo>=
</mo> 
<mrow>var
<mo>(
</mo>
<mi>
<msub>t
<mn>1
</mn>
</msub>
</mi>, ..., 
<mi>
<msub>t
<mi>n
</mi>
</msub>
</mi>
<mo>)
</mo>
</mrow>
</math>
</p>
<p class="pn">Tests des ensembles : 
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">&#x02115;
<mtext>, 
</mtext>&#x02124;
<mtext>, 
</mtext>&#x0211a;
<mtext>, 
</mtext>&#x0211d;
<mtext>, 
</mtext>&#x02102;
<mtext>;
<br />
</mtext>
<mi>&alpha;
</mi>
<mtext>, 
</mtext>
<mi>&Alpha;
</mi>
<mtext>, 
</mtext>
<mi>&beta;
</mi>
<mtext>, 
</mtext>
<mi>&Beta;
</mi>
<mtext>, 
</mtext>
<mi>&gamma;
</mi>
<mtext>, 
</mtext>
<mi>&Gamma;
</mi>
<mtext>, 
</mtext>
<mi>&delta;
</mi>
<mtext>, 
</mtext>
<mi>&Delta;
</mi>
<mtext>, 
</mtext>
<mi>&epsilon;
</mi>
<mtext>, 
</mtext>
<mi>&Epsilon;
</mi>
<mtext>, 
</mtext>
<mi>&theta;
</mi>
<mtext>, 
</mtext>
<mi>&Theta;
</mi>
<mtext>, 
</mtext>
<mi>&thetasym;
</mi>
<mtext>, 
</mtext>
<mi>&lambda;
</mi>
<mtext>, 
</mtext>
<mi>&mu;
</mi>
<mtext>, 
</mtext>
<mi>&xi;
</mi>
<mtext>, 
</mtext>
<mi>&Xi;
</mi>
<mtext>, 
</mtext>
<mi>&pi;
</mi>
<mtext>, 
</mtext>
<mi>&rho;
</mi>
<mtext>, 
</mtext>
<mi>&sigma;
</mi>
<mtext>, 
</mtext>
<mi>&Sigma;
</mi>
<mtext>, 
</mtext>
<mi>&sigmaf;
</mi>
<mtext>, 
</mtext>
<mi>&phi;
</mi>
<mtext>, 
</mtext>
<mi>&Phi;
</mi>
<mtext>, 
</mtext>
<mi>&psi;
</mi>
<mtext>, 
</mtext>
<mi>&omega;
</mi>
<mtext>, 
</mtext>
<mi>&Omega;
</mi>
<mtext>, 
</mtext>
<mi>&upsih;
</mi>
<mtext>; ...
<br />
</mtext>
<mi>A
</mi> &sub; 
<mi>B
</mi>
<mtext>, 
</mtext>
<mi>A
</mi> &sube; 
<mi>B
</mi>
<mtext>, 
</mtext>
<mi>A
</mi> &sup; 
<mi>B
</mi>
<mtext>, 
</mtext>
<mi>A
</mi> &supe; 
<mi>B
</mi>
</math>
</p>
<p class="pn">substitution, division, fraction : 
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>X
</mi>
<mo>/
</mo>
<mn>1
</mn>
<mtext>, 
</mtext>
<mi>X
</mi> &#x000f7; 
<mn>1
</mn>
<mtext>, 
</mtext>
<mfrac>
<mi>X
</mi>
<mn>1
</mn>
</mfrac>
</math>
</p>

Retourner au début du code

Contents Haut

Symboles texte (type html)

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

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

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

Code HTML (380 lignes)

<p class="pf">Une substitution est un ensemble de la forme 
<span class="frmla" title="Math en mode texte">
<var title="variable">sigma
</var>&nbsp;&nbsp;=&nbsp;&nbsp;&nbsp;{&nbsp;
<var title="variable">X
<sub>1
</sub>
</var>
<span class="frmlatxt">&nbsp;est SUBSTITUE par&nbsp;
</span>
<var title="variable">t
<sub>1
</sub>
</var>, ..., 
<var title="variable">X
<sub>
<var title="variable">n
</var>
</sub>
</var>
<span class="frmlatxt">&nbsp;est SUBSTITUE par&nbsp;
</span>
<var title="variable">t
<sub>
<var title="variable">n
</var>
</sub>
</var>&nbsp;}&nbsp;
</span> tel que &nbsp;
<br />
<br />
<span class="frmla" title="Math en mode texte">
<span class="frmlatxt"> (
</span>
<span class="frmlatxt">&nbsp;POUR TOUT&nbsp;
</span>
<var title="variable">i
</var>
<span class="frmla" title="Math en mode texte">
<span class="frmlatxt">&nbsp;est INCLU dans&nbsp;
</span>&nbsp;{&nbsp;1, ..., 
<var title="variable">n
</var>&nbsp;}&nbsp;
</span>
<span class="frmlatxt">) 
</span>
<var title="variable">X
<sub>
<var title="variable">i
</var>
</sub>
</var>
<span class="frmlatxt">&nbsp;est INCLU dans&nbsp;
</span>
<var title="variable">V
</var>
</span>
<br />
<span class="frmla" title="Math en mode texte">
<span class="frmlatxt"> (
</span>
<span class="frmlatxt">&nbsp;POUR TOUT&nbsp;
</span>
<var title="variable">i
</var>
<span class="frmla" title="Math en mode texte">
<span class="frmlatxt">&nbsp;est INCLU dans&nbsp;
</span>&nbsp;{&nbsp;1, ..., 
<var title="variable">n
</var>&nbsp;}&nbsp;
</span>
<span class="frmlatxt">) 
</span>
<var title="variable">t
<sub>
<var title="variable">i
</var>
</sub>
</var>
<span class="frmlatxt">&nbsp;est INCLU dans&nbsp;
</span>
<var title="variable">T
</var>
</span> ... 
<span class="info">ceci est un extrait, et non la d&eacute;finition compl&egrave;te
</span>
<br />
<br />Soit 
<span class="frmla" title="Math en mode texte">
<var title="variable">sigma
</var>&nbsp;&nbsp;=&nbsp;&nbsp;&nbsp;{&nbsp;
<var title="variable">X
<sub>1
</sub>
</var>
<span class="frmlatxt">&nbsp;est SUBSTITUE par&nbsp;
</span>
<var title="variable">t
<sub>1
</sub>
</var>, ..., 
<var title="variable">X
<sub>
<var title="variable">n
</var>
</sub>
</var>
<span class="frmlatxt">&nbsp;est SUBSTITUE par&nbsp;
</span>
<var title="variable">t
<sub>
<var title="variable">n
</var>
</sub>
</var>&nbsp;}&nbsp;
</span> une substitution, nous avons
<br />
<span class="frmla" title="Math en mode texte">
<span class="frmlatxt">une FONCTION 
</span>dom(
<span class="frmlatxt">AVEC 
</span>
<var title="variable">sigma
</var>
<span class="frmlatxt"> COMME ARGUMENTS
</span>)&nbsp;&nbsp;=&nbsp;&nbsp;&nbsp;{&nbsp;
<var title="variable">X
<sub>1
</sub>
</var>, ..., 
<var title="variable">X
<sub>
<var title="variable">n
</var>
</sub>
</var>&nbsp;}&nbsp;
</span> et 
<span class="frmla" title="Math en mode texte">
<span class="frmlatxt">une FONCTION 
</span>codom(
<span class="frmlatxt">AVEC 
</span>
<var title="variable">sigma
</var>
<span class="frmlatxt"> COMME ARGUMENTS
</span>)&nbsp;&nbsp;=&nbsp;&nbsp;
<span class="frmlatxt">une FONCTION 
</span>var(
<span class="frmlatxt">AVEC 
</span>
<var title="variable">t
<sub>1
</sub>
</var>, ..., 
<var title="variable">t
<sub>
<var title="variable">n
</var>
</sub>
</var>
<span class="frmlatxt"> COMME ARGUMENTS
</span>)
</span>
</p>
<p class="pn">Tests des ensembles&nbsp;: 
<br />
<span class="frmla" title="Math en mode texte">
<span class="frmlatxt">Ensemble_des_entiers_naturels
</span>
<span class="frmlatxt">, 
</span>
<span class="frmlatxt">Ensemble_des_entiers_relatifs
</span>
<span class="frmlatxt">, 
</span>
<span class="frmlatxt">Ensemble_des_nombres_rationnels
</span>
<span class="frmlatxt">, 
</span>
<span class="frmlatxt">Ensemble_des_nombres_r&eacute;els
</span>
<span class="frmlatxt">, 
</span>
<span class="frmlatxt">Ensemble_des_nombres_complexes
</span>
<span class="frmlatxt">;
<br />
</span>
<var title="variable">alpha
</var>
<span class="frmlatxt">, 
</span>
<var title="variable">Alpha
</var>
<span class="frmlatxt">, 
</span>
<var title="variable">beta
</var>
<span class="frmlatxt">, 
</span>
<var title="variable">Beta
</var>
<span class="frmlatxt">, 
</span>
<var title="variable">gamma
</var>
<span class="frmlatxt">, 
</span>
<var title="variable">Gamma
</var>
<span class="frmlatxt">, 
</span>
<var title="variable">delta
</var>
<span class="frmlatxt">, 
</span>
<var title="variable">Delta
</var>
<span class="frmlatxt">, 
</span>
<var title="variable">epsilon
</var>
<span class="frmlatxt">, 
</span>
<var title="variable">Epsilon
</var>
<span class="frmlatxt">, 
</span>
<var title="variable">theta
</var>
<span class="frmlatxt">, 
</span>
<var title="variable">Theta
</var>
<span class="frmlatxt">, 
</span>
<var title="variable">thetasym
</var>
<span class="frmlatxt">, 
</span>
<var title="variable">lambda
</var>
<span class="frmlatxt">, 
</span>
<var title="variable">mu
</var>
<span class="frmlatxt">, 
</span>
<var title="variable">xi
</var>
<span class="frmlatxt">, 
</span>
<var title="variable">Xi
</var>
<span class="frmlatxt">, 
</span>
<var title="variable">pi
</var>
<span class="frmlatxt">, 
</span>
<var title="variable">rho
</var>
<span class="frmlatxt">, 
</span>
<var title="variable">sigma
</var>
<span class="frmlatxt">, 
</span>
<var title="variable">Sigma
</var>
<span class="frmlatxt">, 
</span>
<var title="variable">sigmaf
</var>
<span class="frmlatxt">, 
</span>
<var title="variable">phi
</var>
<span class="frmlatxt">, 
</span>
<var title="variable">Phi
</var>
<span class="frmlatxt">, 
</span>
<var title="variable">psi
</var>
<span class="frmlatxt">, 
</span>
<var title="variable">omega
</var>
<span class="frmlatxt">, 
</span>
<var title="variable">Omega
</var>
<span class="frmlatxt">, 
</span>
<var title="variable">upsih
</var>
<span class="frmlatxt">; ...
<br />
</span>
<span class="frmlatxt"> (
</span>
<var title="variable">A
</var>
<span class="frmlatxt">&nbsp;est un SOUS-ENSEMBLE de&nbsp;
</span>
<var title="variable">B
</var>
<span class="frmlatxt">) 
</span>
<span class="frmlatxt">, 
</span>
<span class="frmlatxt"> (
</span>
<var title="variable">A
</var>
<span class="frmlatxt">&nbsp;est EGAL ou est un SOUS-ENSEMBLE de&nbsp;
</span>
<var title="variable">B
</var>
<span class="frmlatxt">) 
</span>
<span class="frmlatxt">, 
</span>
<span class="frmlatxt"> (
</span>
<var title="variable">A
</var>
<span class="frmlatxt">&nbsp;CONTIENT&nbsp;
</span>
<var title="variable">B
</var>
<span class="frmlatxt">) 
</span>
<span class="frmlatxt">, 
</span>
<span class="frmlatxt"> (
</span>
<var title="variable">A
</var>
<span class="frmlatxt">&nbsp;est EGAL ou CONTIENT&nbsp;
</span>
<var title="variable">B
</var>
<span class="frmlatxt">) 
</span>
</span>
</p>
<p class="pn">substitution, division, fraction&nbsp;: 
<br />
<span class="frmla" title="Math en mode texte">
<var title="variable">X
</var>
<span class="frmlatxt">&nbsp;est SUBSTITUE par&nbsp;
</span>1
<span class="frmlatxt">, 
</span>
<span class="frmlatxt"> (
</span>
<var title="variable">X
</var>
<span class="frmlatxt"> DIVISE PAR 
</span>1
<span class="frmlatxt">) 
</span>
<span class="frmlatxt">, 
</span>
<span class="frmlatxt"> (
</span>
<span class="frmlatxt"> FRACTION de 
</span>
<var title="variable">X
</var>
<span class="frmlatxt"> sur 
</span>1
<span class="frmlatxt">) 
</span>
</span>
</p>

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Fraction simple avec HTML (type html)

a₀ + 1/x

Code généré

Code HTML (8 lignes)

<span class="frmla">
<var>a
</var>
<sub>0
</sub>&nbsp;+&nbsp;1/
<var>x
</var>
</span>

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Fraction simple avec MathML (type xml)

a_{0} + \frac{1}{x}

Code généré

Code XML (16 lignes)

<math xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mi>a
</mi>
<mn>0
</mn>
</msub>
<mo>+
</mo>
<mfrac>
<mn>1
</mn>
<mi>x
</mi>
</mfrac>
</math>

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Fractions multiples avec HTML (type html)

a₄ + 1/a₃ + 1/a₂ + 1/a₁ + 1/a₀ + 1/x

Code généré

Code HTML (24 lignes)

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

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Fractions multiples avec MathML (type xml)

a_{4} + \frac{1}{a_{3}}

Code généré

Code XML (64 lignes)

<math xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mi>a
</mi>
<mn>4
</mn>
</msub>
<mo>+
</mo>
<mfrac>
<mn>1
</mn>
<msub>
<mi>a
</mi>
<mn>3
</mn>
</msub>
<mo>+
</mo>
<mfrac>
<mn>1
</mn>
<msub>
<mi>a
</mi>
<mn>2
</mn>
</msub>
<mo>+
</mo>
<mfrac>
<mn>1
</mn>
<msub>
<mi>a
</mi>
<mn>1
</mn>
</msub>
<mo>+
</mo>
<mfrac>
<mn>1
</mn>
<msub>
<mi>a
</mi>
<mn>0
</mn>
</msub>
<mo>+
</mo>
<mfrac>
<mn>1
</mn>
<mi>x
</mi>
</mfrac>
</mfrac>
</mfrac>
</mfrac>
</mfrac>
</math>

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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

Code HTML (106 lignes)

<section>
<section>
<h4 id="test8-1-t">
<span id="test8-1" class="brol-scrollfix toc-c">
</span>Test 3-1
</h4>
<span class="frmla">
<table class="noborder">
<tr>
<td>The quick brown fox jumps over
</td>
</tr>
<tr>
<td>the lazy dog
</td>
</tr>
</table>
</span>
</section>
<section>
<h4 id="test8-2-t">
<span id="test8-2" class="brol-scrollfix toc-c">
</span>Test 3-2
</h4>
<span class="frmla">
<table class="noborder">
<tr>
<td>base
</td>
</tr>
<tr>
<td>under
</td>
</tr>
</table>
</span>
</section>
<section>
<h4 id="test8-3-t">
<span id="test8-3" class="brol-scrollfix toc-c">
</span>Test 3-3
</h4>
<span class="frmla">
<table class="noborder">
<tr>
<td>over
</td>
</tr>
<tr>
<td>base
</td>
</tr>
<tr>
<td>under
</td>
</tr>
</table>
</span>
<span class="frmla">
</span>
</section>
<section>
<h4 id="test8-4-t">
<span id="test8-4" class="brol-scrollfix toc-c">
</span>Test 3-4
</h4>
<span class="frmla">
<table class="noborder">
<tr>
<td>over
</td>
</tr>
<tr>
<td>base
</td>
</tr>
<tr>
<td>under
</td>
</tr>
</table>&nbsp;+&nbsp;
<table class="noborder">
<tr>
<td>base
</td>
</tr>
<tr>
<td>under
</td>
</tr>
</table>&nbsp;&and;&nbsp;
<var>a
</var>
<sub>2
</sub>&nbsp;+&nbsp;1/
<var>a
</var>
<sub>1
</sub>&nbsp;+&nbsp;1/
<var>a
</var>
<sub>0
</sub>&nbsp;+&nbsp;1/
<var>x
</var>
</span>

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Superpositions avec MathML (type xml)

Test 3-1

\overset{The quick brown fox jumps over}{the lazy dog}

Test 3-2

\underset{under}{base}

Test 3-3

{base}_{under}^{over}

Test 3-4

{base}_{under}^{over} + \underset{under}{base} ∧ a_{2} + \frac{1}{a_{1}}

Code généré

Code XML (110 lignes)

<section>
<section>
<h4 id="test9-1-t">
<span id="test9-1" class="brol-scrollfix toc-c">
</span>Test 3-1
</h4>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mover>
<mtext>the lazy dog
</mtext>
<mtext>The quick brown fox jumps over
</mtext>
</mover>
</math>
</section>
<section>
<h4 id="test9-2-t">
<span id="test9-2" class="brol-scrollfix toc-c">
</span>Test 3-2
</h4>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<munder>
<mtext>base
</mtext>
<mtext>under
</mtext>
</munder>
</math>
</section>
<section>
<h4 id="test9-3-t">
<span id="test9-3" class="brol-scrollfix toc-c">
</span>Test 3-3
</h4>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<munderover>
<mtext>base
</mtext>
<mtext>under
</mtext>
<mtext>over
</mtext>
</munderover>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
</math>
</section>
<section>
<h4 id="test9-4-t">
<span id="test9-4" class="brol-scrollfix toc-c">
</span>Test 3-4
</h4>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<munderover>
<mtext>base
</mtext>
<mtext>under
</mtext>
<mtext>over
</mtext>
</munderover>
<mo>+
</mo>
<mrow>
<munder>
<mtext>base
</mtext>
<mtext>under
</mtext>
</munder> &#x02227; 
<msub>
<mi>a
</mi>
<mn>2
</mn>
</msub>
<mo>+
</mo>
<mfrac>
<mn>1
</mn>
<msub>
<mi>a
</mi>
<mn>1
</mn>
</msub>
<mo>+
</mo>
<mfrac>
<mn>1
</mn>
<msub>
<mi>a
</mi>
<mn>0
</mn>
</msub>
<mo>+
</mo>
<mfrac>
<mn>1
</mn>
<mi>x
</mi>
</mfrac>
</mfrac>
</mfrac>
</mrow>
</math>

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Exemples MathML

$\sum_{n=0}^{+\infty} rac{x^n}{n!}$

$\frac{a}{\sqrt{2}} + x^{3}$

Code généré

Code XML (47 lignes)

<p>
	<math display="block">
		<semantics>
			<mrow>
				<munderover>
					<mo>∑</mo>
					<mrow>
						<mi>n</mi>
						<mo>=</mo>
						<mn>0</mn>
					</mrow>
					<mrow>
						<mo>+</mo>
						<mn>∞</mn>
					</mrow>
				</munderover>
				<mfrac>
					<msup>
						<mi>x</mi>
						<mi>n</mi>
					</msup>
					<mrow>
						<mi>n</mi>
						<mo>!</mo>
					</mrow>
				</mfrac>
			</mrow>
			<annotation encoding="TeX">\sum_{n=0}^{+\infty} rac{x^n}{n!}
			</annotation>
		</semantics>
	</math>
</p>
<p>
	<math>
		<mfrac>
			<mi>a</mi>
			<msqrt>
				<mn>2</mn>
			</msqrt>
		</mfrac>
		<mo>+</mo>
		<msup>
			<mi>x</mi>
			<mn>3</mn>
		</msup>
	</math>
</p>

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English translation

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Document created the 05/06/2010, last modified the 08/03/2020
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

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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