mjo-eja.tex: new file for Euclidean Jordan algebras.

diff --git a/GNUmakefile b/GNUmakefile
index 26bb59f2cb9e3aaa2d74be2fbeb3539cf572ae08..799b6dbd61d2e1c14bf5078d53fdd0943144192b 100644 (file)
--- a/GNUmakefile
+++ b/GNUmakefile
@@ -27,9 +27,9 @@ PN = examples
 #
 MJOTEX  = mjo-algebra.tex mjo-algorithm.tex mjo-arrow.tex mjo-calculus.tex
 MJOTEX += mjo-common.tex mjo-complex.tex mjo-cone.tex mjo-convex.tex
-MJOTEX += mjo-font.tex mjo-linear_algebra.tex mjo-listing.tex mjo-misc.tex
-MJOTEX += mjo-proof_by_cases.tex mjo-theorem.tex mjo-theorem-star.tex
-MJOTEX += mjo-topology.tex mjo.bst
+MJOTEX += mjo-eja.tex mjo-font.tex mjo-linear_algebra.tex mjo-listing.tex
+MJOTEX += mjo-misc.tex mjo-proof_by_cases.tex mjo-theorem.tex
+MJOTEX += mjo-theorem-star.tex mjo-topology.tex mjo.bst
 
 # Compile a list of raw source code listings (*.listing) and their
 # associated output files (*.py) that will be tested by check-sage.

diff --git a/examples.tex b/examples.tex
index b6c4ae1ef56117d0ef0f7f81d9a8d8eaddf35250..cdf2359d4fe22b68738d76ccca052d8b8d719b89 100644 (file)
--- a/examples.tex
+++ b/examples.tex
@@ -116,6 +116,11 @@
     proper face, then we write $F \properfaceof K$.
   \end{section}
 
+  \begin{section}{Euclidean Jordan algebras}
+    The Jordan product of $x$ and $y$ in some Euclidean Jordan algebra
+    is $\jp{x}{y}$.
+  \end{section}
+
   \begin{section}{Font}
     We can write things like Carathéodory and Güler and $\mathbb{R}$.
   \end{section}

diff --git a/mjo-eja.tex b/mjo-eja.tex
new file mode 100644 (file)
index 0000000..0408bea
--- /dev/null
+++ b/mjo-eja.tex
@@ -0,0 +1,20 @@
+%
+% Euclidean Jordan algebras.
+%
+
+% The jordan product of its two arguments.
+%
+% The choice of \circ here (as opposed to, say, \bullet) was a tough
+% one. On the one hand, the \circ operator already means function
+% composition, and function composition does appear in the context of
+% (Euclidean) Jordan algebras. On the other hand, the meaning would
+% be unambiguous to a mathematician. Perhaps more importantly -- the
+% \circ is much easier to write on the board if one intends to teach
+% this material. Finally, the \circ is used by Koecher, Alizadeh,
+% Baes, Gowda, et cetera and seems to be more popular. Full
+% disclosure: the \bullet is used by McCrimmon.
+%
+% It is for this reason that we have segregated the Jordan product
+% into its own LaTeX file; we probably wouldn't want to use \circ as
+% a (bilinear) algebra multiplication in any other context.
+\newcommand*{\jp}[2]{{#1} \circ {#2}}

diff --git a/mjotex.sty b/mjotex.sty
index 39792d58c88f03ec6fa24cb92660f9b0a9fa4a08..43fdfd70617df94c6b2ae6a4199e236b96a1d284 100644 (file)
--- a/mjotex.sty
+++ b/mjotex.sty
@@ -6,6 +6,7 @@
 \input{mjo-complex}
 \input{mjo-cone}
 \input{mjo-convex}
+\input{mjo-eja}
 \input{mjo-font}
 \input{mjo-linear_algebra}
 \input{mjo-listing}