Formule LaTeX avec préambule
authoriinov
jeu., 23 août 2018 23:53:03 +0200
changeset 460 7e0c719c9526
parent 459 9e229fb212ce
child 461 58b2704e601a
Formule LaTeX avec préambule
Data/Topics/maths.xml
RelaxNG/publidoc.rnc
--- a/Data/Topics/maths.xml	dim. août 19 23:56:14 2018 +0200
+++ b/Data/Topics/maths.xml	jeu. août 23 23:53:03 2018 +0200
@@ -132,6 +132,45 @@
           sphère peut se décomposer sur une base d'harmoniques sphériques.
         </p>
       </section>
+
+      <section>
+        <head>
+          <title>Formule avec préambule</title>
+        </head>
+        <section xml:lang="en">
+          <p>
+            Let <math><latex>I_+</latex></math> denote the ideal generated by
+            the <math><latex>S_n</latex></math>-invariant homogeneous
+            polynomials of positive degree in <math>
+            <preambule><newcommand name="C">{\mathbb{C}}</newcommand></preambule>
+            <latex>\C[x_1,\dots, x_n,y_1,\dots, y_n]</latex></math> and set
+          </p>
+          <p>
+            <math display="wide">
+              <preambule><newcommand name="C">{\mathbb{C}}</newcommand></preambule>
+              <latex>R_n :=\C[\mathbf{x},\mathbf{y}] / I_+.</latex>
+            </math>
+          </p>
+          <p>
+            It is known for sometime that the bi-graded Frobenius character of
+            <math><latex>R_n</latex></math> is given by the transformation of
+            the elementary symmetric function <math><latex>e_{n}</latex></math>
+            under Bergeron-Garsia's "nabla" operator, <math><latex>\nabla
+            e_n</latex></math>. In other words, the symmetric function
+            <math><latex>\nabla e_n</latex></math> has an underlying
+            <math><latex>S_{n}</latex></math>-representation.  Roughly stated,
+            <math><latex>\nabla</latex></math> is a
+            <math>
+              <preambule>
+              <newcommand name="mbb">[1]{\mathbb{#1}}</newcommand></preambule>
+              <latex>\mbb{Q}</latex></math>-linear operator defined on the ring
+              of symmetric functions <math><latex>\Lambda</latex></math> in
+              such a way that the modified Macdonald symmetric functions are
+              the eigenfunctions of <math><latex>\nabla</latex></math> with
+              prescribed eigenvalues.
+          </p>
+        </section>
+      </section>
     </section>
  </topic>
 </publidoc>
--- a/RelaxNG/publidoc.rnc	dim. août 19 23:56:14 2018 +0200
+++ b/RelaxNG/publidoc.rnc	jeu. août 23 23:53:03 2018 +0200
@@ -982,7 +982,7 @@
 
 math.content =
    mixed { sup* & sub* & var* & warning* }
- | latex
+ | (preambule?, latex)
 
 # ~~~~~~ latex
 latex = element latex { latex.attributes, latex.content }
@@ -993,6 +993,21 @@
 
 latex.content = text
 
+# ~~~~~~ preambule
+preambule = element preambule { preambule.content }
+
+preambule.content =
+    newcommand+
+
+# ~~~~~~ newcommand
+newcommand = element newcommand { newcommand.attributes, newcommand.content }
+
+newcommand.attributes =
+    newcommand.name.attribute
+newcommand.name.attribute = attribute name { xsd:NMTOKEN }
+
+newcommand.content = text
+
 # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ quote ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 
 quote = element quote { quote.content }