Vladimirs patch for removing the "anti-commuting" branches from Clifford

[ginac.git] / doc / tutorial / ginac.texi

diff --git a/doc/tutorial/ginac.texi b/doc/tutorial/ginac.texi
index d0b12a76817146ae518f6ff5f325241bc4f0066d..4195678e8e0f5d266cad5cc179d95d7bda6b50d9 100644 (file)
--- a/doc/tutorial/ginac.texi
+++ b/doc/tutorial/ginac.texi
@@ -3299,13 +3299,11 @@ and contain symbolic entries. Such generators are created by the
 function 
 
 @example
-    ex clifford_unit(const ex & mu, const ex & metr, unsigned char rl = 0, 
-                                bool anticommuting = false);    
+    ex clifford_unit(const ex & mu, const ex & metr, unsigned char rl = 0);    
 @end example
 
-where @code{mu} should be a @code{varidx} class object indexing the
-generators, an index @code{mu} with a numeric value may be of type
-@code{idx} as well.
+where @code{mu} should be a @code{idx} (or descendant) class object
+indexing the generators.
 Parameter @code{metr} defines the metric @math{M(i, j)} and can be
 represented by a square @code{matrix}, @code{tensormetric} or @code{indexed} class
 object. In fact, any expression either with two free indices or without
@@ -3313,20 +3311,7 @@ indices at all is admitted as @code{metr}. In the later case an @code{indexed}
 object with two newly created indices with @code{metr} as its
 @code{op(0)} will be used.
 Optional parameter @code{rl} allows to distinguish different
-Clifford algebras, which will commute with each other. The last
-optional parameter @code{anticommuting} defines if the anticommuting
-assumption (i.e.
-@tex
-$e_i e_j + e_j e_i = 0$)
-@end tex
-@ifnottex
-e~i e~j + e~j e~i = 0)
-@end ifnottex
-will be used for contraction of Clifford units. If the @code{metric} is
-supplied by a @code{matrix} object, then the value of
-@code{anticommuting} is calculated automatically and the supplied one
-will be ignored. One can overcome this by giving @code{metric} through
-matrix wrapped into an @code{indexed} object.
+Clifford algebras, which will commute with each other. 
 
 Note that the call @code{clifford_unit(mu, minkmetric())} creates
 something very close to @code{dirac_gamma(mu)}, although
@@ -3334,9 +3319,6 @@ something very close to @code{dirac_gamma(mu)}, although
 @cindex @code{clifford::get_metric()}
 The method @code{clifford::get_metric()} returns a metric defining this
 Clifford number.
-@cindex @code{clifford::is_anticommuting()}
-The method @code{clifford::is_anticommuting()} returns the
-@code{anticommuting} property of a unit.
 
 If the matrix @math{M(i, j)} is in fact symmetric you may prefer to create
 the Clifford algebra units with a call like that
@@ -3355,14 +3337,14 @@ ways. For example
 @example
 @{
     ... 
-    varidx nu(symbol("nu"), 4);
+    idx i(symbol("i"), 4);
     realsymbol s("s");
     ex M = diag_matrix(lst(1, -1, 0, s));
-    ex e = clifford_unit(nu, M);
-    ex e0 = e.subs(nu == 0);
-    ex e1 = e.subs(nu == 1);
-    ex e2 = e.subs(nu == 2);
-    ex e3 = e.subs(nu == 3);
+    ex e = clifford_unit(i, M);
+    ex e0 = e.subs(i == 0);
+    ex e1 = e.subs(i == 1);
+    ex e2 = e.subs(i == 2);
+    ex e3 = e.subs(i == 3);
     ...
 @}
 @end example
@@ -3381,7 +3363,7 @@ A similar effect can be achieved from the function
 
 @example
     ex lst_to_clifford(const ex & v, const ex & mu,  const ex & metr,
-                       unsigned char rl = 0, bool anticommuting = false);
+                       unsigned char rl = 0);
     ex lst_to_clifford(const ex & v, const ex & e);
 @end example
 
@@ -3403,19 +3385,19 @@ $v^0 e_0 + v^1 e_1 + ... + v^n e_n$
 with @samp{e.k}
 directly supplied in the second form of the procedure. In the first form
 the Clifford unit @samp{e.k} is generated by the call of
-@code{clifford_unit(mu, metr, rl, anticommuting)}. The previous code may be rewritten
+@code{clifford_unit(mu, metr, rl)}. The previous code may be rewritten
 with the help of @code{lst_to_clifford()} as follows
 
 @example
 @{
     ...
-    varidx nu(symbol("nu"), 4);
+    idx i(symbol("i"), 4);
     realsymbol s("s");
     ex M = diag_matrix(lst(1, -1, 0, s));
-    ex e0 = lst_to_clifford(lst(1, 0, 0, 0), nu, M);
-    ex e1 = lst_to_clifford(lst(0, 1, 0, 0), nu, M);
-    ex e2 = lst_to_clifford(lst(0, 0, 1, 0), nu, M);
-    ex e3 = lst_to_clifford(lst(0, 0, 0, 1), nu, M);
+    ex e0 = lst_to_clifford(lst(1, 0, 0, 0), i, M);
+    ex e1 = lst_to_clifford(lst(0, 1, 0, 0), i, M);
+    ex e2 = lst_to_clifford(lst(0, 0, 1, 0), i, M);
+    ex e3 = lst_to_clifford(lst(0, 0, 0, 1), i, M);
   ...
 @}
 @end example
@@ -3546,9 +3528,9 @@ The next provided function is
 @example
     ex clifford_moebius_map(const ex & a, const ex & b, const ex & c,
                             const ex & d, const ex & v, const ex & G,
-                            unsigned char rl = 0, bool anticommuting = false);
+                            unsigned char rl = 0);
     ex clifford_moebius_map(const ex & M, const ex & v, const ex & G,
-                            unsigned char rl = 0, bool anticommuting = false);
+                            unsigned char rl = 0);
 @end example 
 
 It takes a list or vector @code{v} and makes the Moebius (conformal or
@@ -3556,10 +3538,9 @@ linear-fractional) transformation @samp{v -> (av+b)/(cv+d)} defined by
 the matrix @samp{M = [[a, b], [c, d]]}. The parameter @code{G} defines
 the metric of the surrounding (pseudo-)Euclidean space. This can be an
 indexed object, tensormetric, matrix or a Clifford unit, in the later
-case the optional parameters @code{rl} and @code{anticommuting} are
-ignored even if supplied.  Depending from the type of @code{v} the
-returned value of this function is either a vector or a list holding vector's
-components.
+case the optional parameter @code{rl} is ignored even if supplied.
+Depending from the type of @code{v} the returned value of this function
+is either a vector or a list holding vector's components.
 
 @cindex @code{clifford_max_label()}
 Finally the function