@@ -470,58 +470,8 @@ \section{cfunctions}
470470\noindent This statement declares commuting\index {commuting}
471471functions\index {functions!commuting}. The name of a
472472function can be followed by some information that specifies additional
473- properties of the preceding function. These can be (name indicates the
474- name of the function to be declared): \vspace {4mm}
475-
476- \leftvitem {4.1cm}{name{\hash }r}
477- \rightvitem {12cm}{The function is considered to be a real\index {real} function (default).}
478-
479- \leftvitem {4.1cm}{name{\hash }c}
480- \rightvitem {12cm}{The function is considered to be a complex\index {complex} function. This means
481- that internally two spaces are reserved. One for the variable name and one
482- for its complex conjugate name{\hash }.}
483-
484- \leftvitem {4.1cm}{name{\hash }i}
485- \rightvitem {12cm}{The function is considered to be imaginary\index {imaginary}.}
486-
487- \leftvitem {4.1cm}{name(s[ymmetric])}
488- \rightvitem {12cm}{The function is totally symmetric\index {symmetric}. This means that during
489- normalization {\FORM } will order the arguments according to its internal
490- notion of order by trying permutations. The result will depend on the order
491- of declaration of variables.}
492-
493- \leftvitem {4.1cm}{name(a[ntisymmetric])}
494- \rightvitem {12cm}{The function is totally antisymmetric\index {antisymmetric}. This means that
495- during normalization {\FORM } will order the arguments according to its
496- internal notion of order and if the resulting permutation of arguments is
497- odd the coefficient of the term will change sign. The order will depend on
498- the order of declaration of variables.}
499-
500- \leftvitem {4.1cm}{name(c[yclesymmetric])}
501- \rightvitem {12cm}{The function is cycle\index {cycle symmetric} symmetric in
502- all its arguments. This means that during normalization {\FORM } will order
503- the arguments according to its internal notion of order by trying cyclic
504- permutations. The result will depend on the order of declaration of
505- variables.}
506-
507- \leftvitem {4.1cm}{name(r[cyclesymmetric)
508-
509- name(r[cyclic])
510-
511- name(r[eversecyclic])}
512- \rightvitem {12cm}{The function is reverse\index {reverse cycle symmetric}
513- cycle symmetric in all its arguments. This means that during normalization
514- {\FORM } will order the arguments according to its internal notion of order
515- by trying cyclic permutations and/or a complete reverse order of all
516- arguments. The result will depend on the order of declaration of
517- variables.}
518-
519- \noindent The complexity properties and the symmetric properties can be
520- combined. In that case the complexity properties should come first as in
521- \begin {verbatim }
522- CFunction f1#i(antisymmetric);
523- \end {verbatim }
524- \vspace {10mm}
473+ properties of the preceding function, which are the same as
474+ those for functions (see \ref {substafunctions }). \vspace {10mm}
525475
526476% --#] cfunctions :
527477% --#[ chainin :
@@ -2073,12 +2023,14 @@ \section{functions}
20732023\noindent \begin {tabular }{ll}
20742024Type & Declaration statement\\
20752025Syntax & f[unctions] {\tt <}list of functions to be declared{\tt >}; \\
2076- See also & cfunctions (\ref {substacfunctions }),
2026+ See also & cfunctions (\ref {substacfunctions }),
2027+ nfunctions (\ref {substanfunctions }),
20772028 tensors (\ref {substatensors }),
2029+ ctensors (\ref {substactensors }),
20782030 ntensors (\ref {substantensors }), \\ &
20792031 table (\ref {substatable }),
2080- ntable (\ref {substantable }),
2081- ctable (\ref {substactable })
2032+ ctable (\ref {substactable }),
2033+ ntable (\ref {substantable })
20822034\end {tabular } \vspace {4mm}
20832035
20842036\noindent Used to declare one or more functions\index {functions}. The functions declared
@@ -2132,13 +2084,13 @@ \section{functions}
21322084complete reverse order of all arguments. The result will depend on the
21332085order of declaration of variables.}
21342086
2135- \leftvitem {4.1cm}{name< number
2087+ \leftvitem {4.1cm}{name$ < $ number
21362088
2137- name<= number
2089+ name$ <= $ number
21382090
2139- name> number
2091+ name$ > $ number
21402092
2141- name>= number}
2093+ name$ >= $ number}
21422094\rightvitem {12cm}{The function has a restriction on the number of
21432095arguments. If the number of arguments of an occurrence of the function is
21442096not fulfilling the condition during normalization {\FORM } will set the term
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