From: Christian Bauer Date: Fri, 23 Jul 2004 18:29:57 +0000 (+0000) Subject: fixed typos X-Git-Tag: release_1-3-0~48 X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=commitdiff_plain;h=bc6dacb50cc13691efc466d2cc1900048158ec8d fixed typos --- diff --git a/doc/tutorial/ginac.texi b/doc/tutorial/ginac.texi index 380395fb..71912097 100644 --- a/doc/tutorial/ginac.texi +++ b/doc/tutorial/ginac.texi @@ -2811,7 +2811,7 @@ operator (often denoted @samp{&*}) for representing inert products of arbitrary objects. Rather, non-commutativity in GiNaC is a property of the classes of objects involved, and non-commutative products are formed with the usual @samp{*} operator, as are ordinary products. GiNaC is capable of -figuring out by itself which objects commute and will group the factors +figuring out by itself which objects commutate and will group the factors by their class. Consider this example: @example @@ -2827,7 +2827,7 @@ by their class. Consider this example: As can be seen, GiNaC pulls out the overall commutative factor @samp{-16} and groups the non-commutative factors (the gammas and the su(3) generators) together while preserving the order of factors within each class (because -Clifford objects commute with color objects). The resulting expression is a +Clifford objects commutate with color objects). The resulting expression is a @emph{commutative} product with two factors that are themselves non-commutative products (@samp{gamma~mu*gamma~nu} and @samp{T.a*T.b}). For clarification, parentheses are placed around the non-commutative products in the output. @@ -2845,7 +2845,7 @@ than in other computer algebra systems; they can, for example, automatically canonicalize themselves according to rules specified in the implementation of the non-commutative classes. The drawback is that to work with other than the built-in algebras you have to implement new classes yourself. Symbols -always commute and it's not possible to construct non-commutative products +always commutate and it's not possible to construct non-commutative products using symbols to represent the algebra elements or generators. User-defined functions can, however, be specified as being non-commutative. @@ -2864,16 +2864,16 @@ the header file @file{flags.h}), corresponding to three categories of expressions in GiNaC: @itemize -@item @code{return_types::commutative}: Commutes with everything. Most GiNaC +@item @code{return_types::commutative}: Commutates with everything. Most GiNaC classes are of this kind. @item @code{return_types::noncommutative}: Non-commutative, belonging to a certain class of non-commutative objects which can be determined with the - @code{return_type_tinfo()} method. Expressions of this category commute + @code{return_type_tinfo()} method. Expressions of this category commutate with everything except @code{noncommutative} expressions of the same class. @item @code{return_types::noncommutative_composite}: Non-commutative, composed of non-commutative objects of different classes. Expressions of this - category don't commute with any other @code{noncommutative} or + category don't commutate with any other @code{noncommutative} or @code{noncommutative_composite} expressions. @end itemize @@ -2924,7 +2924,7 @@ ex dirac_gamma(const ex & mu, unsigned char rl = 0); which takes two arguments: the index and a @dfn{representation label} in the range 0 to 255 which is used to distinguish elements of different Clifford algebras (this is also called a @dfn{spin line index}). Gammas with different -labels commute with each other. The dimension of the index can be 4 or (in +labels commutate with each other. The dimension of the index can be 4 or (in the framework of dimensional regularization) any symbolic value. Spinor indices on Dirac gammas are not supported in GiNaC. @@ -2942,7 +2942,7 @@ write @code{dirac_gamma(mu)*(dirac_slash(q,4)+m*dirac_ONE())}. Otherwise, GiNaC will complain and/or produce incorrect results. @cindex @code{dirac_gamma5()} -There is a special element @samp{gamma5} that commutes with all other +There is a special element @samp{gamma5} that commutates with all other gammas, has a unit square, and in 4 dimensions equals @samp{gamma~0 gamma~1 gamma~2 gamma~3}, provided by @@ -3098,7 +3098,7 @@ ex color_T(const ex & a, unsigned char rl = 0); which takes two arguments: the index and a @dfn{representation label} in the range 0 to 255 which is used to distinguish elements of different color -algebras. Objects with different labels commute with each other. The +algebras. Objects with different labels commutate with each other. The dimension of the index must be exactly 8 and it should be of class @code{idx}, not @code{varidx}. @@ -3430,7 +3430,7 @@ table: @end cartouche To determine whether an expression is commutative or non-commutative and if -so, with which other expressions it would commute, you use the methods +so, with which other expressions it would commutate, you use the methods @code{return_type()} and @code{return_type_tinfo()}. @xref{Non-commutative objects}, for an explanation of these. diff --git a/ginac/clifford.h b/ginac/clifford.h index f6a9820b..667d7bef 100644 --- a/ginac/clifford.h +++ b/ginac/clifford.h @@ -35,7 +35,7 @@ namespace GiNaC { * algebra (the Dirac gamma matrices). These objects only carry Lorentz * indices. Spinor indices are hidden. A representation label (an unsigned * 8-bit integer) is used to distinguish elements from different Clifford - * algebras (objects with different labels commute). */ + * algebras (objects with different labels commutate). */ class clifford : public indexed { GINAC_DECLARE_REGISTERED_CLASS(clifford, indexed) @@ -124,7 +124,7 @@ protected: }; -/** This class represents the Dirac gamma5 object which anticommutes with +/** This class represents the Dirac gamma5 object which anticommutates with * all other gammas. */ class diracgamma5 : public tensor { diff --git a/ginac/color.h b/ginac/color.h index 6e73ad21..2086909e 100644 --- a/ginac/color.h +++ b/ginac/color.h @@ -33,7 +33,7 @@ namespace GiNaC { * of SU(3), as used for calculations in quantum chromodynamics. A * representation label (an unsigned 8-bit integer) is used to distinguish * elements from different Lie algebras (objects with different labels - * commute). These objects implement an abstract representation of the + * commutate). These objects implement an abstract representation of the * group, not a specific matrix representation. The indices used for color * objects should not have a variance. */ class color : public indexed