--- 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 }