Clarification on symmetries of metric of clifford object.

The metric of a clifford object may be non-symmetric. Even if
a metric is defined by a symmetric tensor, clifford object may
not be aware of the symmetry and it needs to be explicitly declared.

Signed-off-by: Vladimir V. Kisil <kisilv@maths.leeds.ac.uk>

diff --git a/doc/tutorial/ginac.texi b/doc/tutorial/ginac.texi
index aa01956aa3157df50e02ef38ca1daf8bceff1bc3..eb972664e38e07c0511aa21129ab6cc1ee164ee8 100644 (file)
--- a/doc/tutorial/ginac.texi
+++ b/doc/tutorial/ginac.texi
@@ -3330,6 +3330,15 @@ Note that the call @code{clifford_unit(mu, minkmetric())} creates
 something very close to @code{dirac_gamma(mu)}, although
 @code{dirac_gamma} have more efficient simplification mechanism. 
 @cindex @code{get_metric()}
 something very close to @code{dirac_gamma(mu)}, although
 @code{dirac_gamma} have more efficient simplification mechanism. 
 @cindex @code{get_metric()}

+Also, the object created by @code{clifford_unit(mu, minkmetric())} is
+not aware about the symmetry of its metric, see the start of the pevious
+paragraph. A more accurate analog of 'dirac_gamma(mu)' should be
+specifies as follows:
+
+@example
+    clifford_unit(mu, indexed(minkmetric(),sy_symm(),varidx(symbol("i"),4),varidx(symbol("j"),4)));
+@end example
+

 The method @code{clifford::get_metric()} returns a metric defining this
 Clifford number.
 
 The method @code{clifford::get_metric()} returns a metric defining this
 Clifford number.