multiples of the unity element, even though it's customary to omit it.
E.g. instead of @code{dirac_gamma(mu)*(dirac_slash(q,4)+m)} you have to
write @code{dirac_gamma(mu)*(dirac_slash(q,4)+m*dirac_ONE())}. Otherwise,
-GiNaC may produce incorrect results.
+GiNaC will complain and/or produce incorrect results.
@cindex @code{dirac_gamma5()}
-There's a special element @samp{gamma5} that commutes with all other
-gammas and in 4 dimensions equals @samp{gamma~0 gamma~1 gamma~2 gamma~3},
-provided by
+There is a special element @samp{gamma5} that commutes with all other
+gammas, has a unit square, and in 4 dimensions equals
+@samp{gamma~0 gamma~1 gamma~2 gamma~3}, provided by
@example
ex dirac_gamma5(unsigned char rl = 0);
@end example
-@cindex @code{dirac_gamma6()}
-@cindex @code{dirac_gamma7()}
-The two additional functions
+@cindex @code{dirac_gammaL()}
+@cindex @code{dirac_gammaR()}
+The chiral projectors @samp{(1+/-gamma5)/2} are also available as proper
+objects, constructed by
@example
-ex dirac_gamma6(unsigned char rl = 0);
-ex dirac_gamma7(unsigned char rl = 0);
+ex dirac_gammaL(unsigned char rl = 0);
+ex dirac_gammaR(unsigned char rl = 0);
@end example
-return @code{dirac_ONE(rl) + dirac_gamma5(rl)} and @code{dirac_ONE(rl) - dirac_gamma5(rl)},
-respectively.
+They observe the relations @samp{gammaL^2 = gammaL}, @samp{gammaR^2 = gammaR},
+and @samp{gammaL gammaR = gammaR gammaL = 0}.
@cindex @code{dirac_slash()}
Finally, the function
Such slashed expressions are printed with a trailing backslash, e.g. @samp{e\}.
In products of dirac gammas, superfluous unity elements are automatically
-removed, squares are replaced by their values and @samp{gamma5} is
-anticommuted to the front. The @code{simplify_indexed()} function performs
-contractions in gamma strings, for example
+removed, squares are replaced by their values, and @samp{gamma5}, @samp{gammaL}
+and @samp{gammaR} are moved to the front.
+
+The @code{simplify_indexed()} function performs contractions in gamma strings,
+for example
@example
@{