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[Maxima-commits] Maxima, A Computer Algebra System branch, master, updated. 99e568da2ac8ba6a6b04f568e049d04b372bb344
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From: Dieter K. <cra...@us...> - 2011-06-15 21:12:41
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- Log -----------------------------------------------------------------
commit 99e568da2ac8ba6a6b04f568e049d04b372bb344
Author: crategus <cra...@us...>
Date: Wed Jun 15 23:06:18 2011 +0200
Moving documentation to other files.
to Itensor.texi:
dispcon
show
to Program.texi:
error_size
error_syms
to Matrices.texi:
rmxchar
to Function.texi:
savedef
to Polynomials.texi:
showratvars
to Runtime.texi:
system
diff --git a/doc/info/Input.texi b/doc/info/Input.texi
index 2175e04..44a3898 100644
--- a/doc/info/Input.texi
+++ b/doc/info/Input.texi
@@ -78,27 +78,6 @@ depends on the system like Windows or Linux and on the installation.
@c -----------------------------------------------------------------------------
@c -----------------------------------------------------------------------------
-@anchor{file_output_append}
-@defvr {Option variable} file_output_append
-Default value: @code{false}
-
-@code{file_output_append} governs whether file output functions append or
-truncate their output file. When @code{file_output_append} is @code{true}, such
-functions append to their output file. Otherwise, the output file is truncated.
-
-@code{save}, @code{stringout}, and @code{with_stdout} respect
-@code{file_output_append}. Other functions which write output files do not
-respect @code{file_output_append}. In particular, plotting and translation
-functions always truncate their output file, and @code{tex} and
-@code{appendfile} always append.
-@c WHAT ABOUT WRITEFILE ??
-
-@opencatbox
-@category{File output} @category{Global flags}
-@closecatbox
-@end defvr
-
-@c -----------------------------------------------------------------------------
@anchor{appendfile}
@deffn {Function} appendfile (@var{filename})
@@ -211,100 +190,24 @@ Closes the transcript file opened by @code{writefile} or @code{appendfile}.
@closecatbox
@end deffn
-@c HMM, THIS NEXT ITEM IS DEFINED IN A SHARE FILE (itensor.lisp);
-@c DOES ITS DESCRIPTION WANT TO BE ELSEWHERE ???
-
@c -----------------------------------------------------------------------------
-@anchor{dispcon}
-@deffn {Function} dispcon (@var{tensor_1}, @var{tensor_2}, @dots{})
-@deffnx {Function} dispcon (all)
-
-Displays the contraction properties of its arguments as were given to
-@code{defcon}. @code{dispcon (all)} displays all the contraction properties
-which were defined.
-
-@opencatbox
-@category{Display functions}
-@closecatbox
-@end deffn
-
-@c -----------------------------------------------------------------------------
-@anchor{error_size}
-@defvr {Option variable} error_size
-Default value: 10
-
-@code{error_size} modifies error messages according to the size of expressions
-which appear in them. If the size of an expression (as determined by the Lisp
-function @code{ERROR-SIZE}) is greater than @code{error_size}, the expression is
-replaced in the message by a symbol, and the symbol is assigned the expression.
-The symbols are taken from the list @code{error_syms}.
-
-Otherwise, the expression is smaller than @code{error_size}, and the expression
-is displayed in the message.
-
-See also @code{error} and @code{error_syms}.
-
-Example:
-@c OUTPUT GENERATED BY THE FOLLOWING
-@c U: (C^D^E + B + A)/(cos(X-1) + 1)$
-@c error_size: 20$
-@c error ("Example expression is", U);
-@c errexp1;
-@c error_size: 30$
-@c error ("Example expression is", U);
-
-The size of @code{U}, as determined by @code{ERROR-SIZE}, is 24.
-
-@example
-(%i1) U: (C^D^E + B + A)/(cos(X-1) + 1)$
-
-(%i2) error_size: 20$
-
-(%i3) error ("Example expression is", U);
-
-Example expression is errexp1
- -- an error. Quitting. To debug this try debugmode(true);
-(%i4) errexp1;
- E
- D
- C + B + A
-(%o4) --------------
- cos(X - 1) + 1
-(%i5) error_size: 30$
-
-(%i6) error ("Example expression is", U);
-
- E
- D
- C + B + A
-Example expression is --------------
- cos(X - 1) + 1
- -- an error. Quitting. To debug this try debugmode(true);
-@end example
-
-@opencatbox
-@category{Debugging} @category{Display flags and variables}
-@closecatbox
-@end defvr
-
-@c -----------------------------------------------------------------------------
-@anchor{error_syms}
-@defvr {Option variable} error_syms
-Default value: @code{[errexp1, errexp2, errexp3]}
-
-In error messages, expressions larger than @code{error_size} are replaced by
-symbols, and the symbols are set to the expressions. The symbols are taken from
-the list @code{error_syms}. The first too-large expression is replaced by
-@code{error_syms[1]}, the second by @code{error_syms[2]}, and so on.
+@anchor{file_output_append}
+@defvr {Option variable} file_output_append
+Default value: @code{false}
-If there are more too-large expressions than there are elements of
-@code{error_syms}, symbols are constructed automatically, with the @var{n}-th
-symbol equivalent to @code{concat ('errexp, @var{n})}.
+@code{file_output_append} governs whether file output functions append or
+truncate their output file. When @code{file_output_append} is @code{true}, such
+functions append to their output file. Otherwise, the output file is truncated.
-See also @code{error} and @code{error_size}.
+@code{save}, @code{stringout}, and @code{with_stdout} respect
+@code{file_output_append}. Other functions which write output files do not
+respect @code{file_output_append}. In particular, plotting and translation
+functions always truncate their output file, and @code{tex} and
+@code{appendfile} always append.
+@c WHAT ABOUT WRITEFILE ??
@opencatbox
-@category{Debugging} @category{Display flags and variables}
+@category{File output} @category{Global flags}
@closecatbox
@end defvr
@@ -739,20 +642,6 @@ Examples:
@end example
@end deffn
-@c -----------------------------------------------------------------------------
-@anchor{rmxchar}
-@defvr {Option variable} rmxchar
-Default value: @code{]}
-
-@code{rmxchar} is the character drawn on the right-hand side of a matrix.
-
-See also @code{lmxchar}.
-
-@opencatbox
-@category{Display flags and variables}
-@closecatbox
-@end defvr
-
@c NEEDS EXAMPLES
@c -----------------------------------------------------------------------------
@@ -815,56 +704,6 @@ been assigned new values by the user; see @code{myoptions}.
@closecatbox
@end deffn
-@c NEEDS MORE WORK !!!
-
-@c -----------------------------------------------------------------------------
-@anchor{savedef}
-@defvr {Option variable} savedef
-Default value: @code{true}
-
-When @code{savedef} is @code{true}, the Maxima version of a user function is
-preserved when the function is translated. This permits the definition to be
-displayed by @code{dispfun} and allows the function to be edited.
-
-When @code{savedef} is @code{false}, the names of translated functions are
-removed from the @code{functions} list.
-
-@opencatbox
-@category{Translation flags and variables}
-@closecatbox
-@end defvr
-
-@c THIS FUNCTION IS IN THE SHARE PACKAGE itensor.lisp
-@c MOVE THIS DESCRIPTION TO Itensor.texi
-
-@c -----------------------------------------------------------------------------
-@anchor{show}
-@deffn {Function} show (@var{expr})
-
-Displays @code{expr} with the indexed objects in it shown
-having covariant indices as subscripts, contravariant indices as
-superscripts. The derivative indices are displayed as subscripts,
-separated from the covariant indices by a comma.
-
-@opencatbox
-@category{Package itensor} @category{Display functions}
-@closecatbox
-@end deffn
-
-@c -----------------------------------------------------------------------------
-@anchor{showratvars}
-@deffn {Function} showratvars (@var{expr})
-
-Returns a list of the canonical rational expression (CRE) variables in
-expression @code{expr}.
-
-See also @code{ratvars}.
-
-@opencatbox
-@category{Rational expressions} @category{Display functions}
-@closecatbox
-@end deffn
-
@c -----------------------------------------------------------------------------
@anchor{stringout}
@deffn {Function} stringout (@var{filename}, @var{expr_1}, @var{expr_2}, @var{expr_3}, @dots{})
@@ -1316,34 +1155,6 @@ g\left(x\right)+f\left(x\right)
@closecatbox
@end deffn
-@c NEEDS CLARIFICATION
-
-@c -----------------------------------------------------------------------------
-@anchor{system}
-@deffn {Function} system (@var{command})
-
-Executes @var{command} as a separate process. The command is passed to the
-default shell for execution. @code{system} is not supported by all operating
-systems, but generally exists in Unix and Unix-like environments.
-
-Supposing @code{_hist.out} is a list of frequencies which you wish to plot as a
-bar graph using @code{xgraph}.
-
-@example
-(%i1) (with_stdout("_hist.out",
- for i:1 thru length(hist) do (
- print(i,hist[i]))),
- system("xgraph -bar -brw .7 -nl < _hist.out"));
-@end example
-
-In order to make the plot be done in the background (returning control to
-Maxima) and remove the temporary file after it is done do:
-
-@example
-system("(xgraph -bar -brw .7 -nl < _hist.out; rm -f _hist.out)&")
-@end example
-@end deffn
-
@c -----------------------------------------------------------------------------
@anchor{with_stdout}
@deffn {Function} with_stdout (@var{f}, @var{expr_1}, @var{expr_2}, @var{expr_3}, @dots{})
commit 2ed798c1658ddf2738adeb9740a84decbb081ea8
Author: crategus <cra...@us...>
Date: Wed Jun 15 23:03:47 2011 +0200
Adding the documentation for rmxchar from Input.texi.
diff --git a/doc/info/Matrices.texi b/doc/info/Matrices.texi
index 8ebd3fd..962eb48 100644
--- a/doc/info/Matrices.texi
+++ b/doc/info/Matrices.texi
@@ -1804,6 +1804,20 @@ The return value is a matrix.
@end deffn
@c -----------------------------------------------------------------------------
+@anchor{rmxchar}
+@defvr {Option variable} rmxchar
+Default value: @code{]}
+
+@code{rmxchar} is the character drawn on the right-hand side of a matrix.
+
+See also @code{lmxchar}.
+
+@opencatbox
+@category{Display flags and variables}
+@closecatbox
+@end defvr
+
+@c -----------------------------------------------------------------------------
@anchor{scalarmatrixp}
@defvr {Option variable} scalarmatrixp
Default value: @code{true}
commit 72be3f0e16fb6a14e7e5f089bddc1775d4966ef4
Author: crategus <cra...@us...>
Date: Wed Jun 15 23:03:15 2011 +0200
Adding the documentation for savedef from Input.texi.
diff --git a/doc/info/Function.texi b/doc/info/Function.texi
index 918690f..69d8d5c 100644
--- a/doc/info/Function.texi
+++ b/doc/info/Function.texi
@@ -2018,6 +2018,25 @@ which there is no function definition.
@closecatbox
@end deffn
+@c NEEDS MORE WORK !!!
+
+@c -----------------------------------------------------------------------------
+@anchor{savedef}
+@defvr {Option variable} savedef
+Default value: @code{true}
+
+When @code{savedef} is @code{true}, the Maxima version of a user function is
+preserved when the function is translated. This permits the definition to be
+displayed by @code{dispfun} and allows the function to be edited.
+
+When @code{savedef} is @code{false}, the names of translated functions are
+removed from the @code{functions} list.
+
+@opencatbox
+@category{Translation flags and variables}
+@closecatbox
+@end defvr
+
@c IS THERE ANY REASON TO SET transcompile: false ??
@c MAYBE THIS VARIABLE COULD BE PERMANENTLY SET TO true AND STRUCK FROM THE DOCUMENTATION.
commit 7350d88ce6e7dd80aeb6d3b0788f587576e676f5
Author: crategus <cra...@us...>
Date: Wed Jun 15 23:02:28 2011 +0200
Adding the documentation for system from Input.texi.
diff --git a/doc/info/Runtime.texi b/doc/info/Runtime.texi
index 9b38d3a..0cea831 100644
--- a/doc/info/Runtime.texi
+++ b/doc/info/Runtime.texi
@@ -241,6 +241,34 @@ information.
@closecatbox
@end deffn
+@c NEEDS CLARIFICATION
+
+@c -----------------------------------------------------------------------------
+@anchor{system}
+@deffn {Function} system (@var{command})
+
+Executes @var{command} as a separate process. The command is passed to the
+default shell for execution. @code{system} is not supported by all operating
+systems, but generally exists in Unix and Unix-like environments.
+
+Supposing @code{_hist.out} is a list of frequencies which you wish to plot as a
+bar graph using @code{xgraph}.
+
+@example
+(%i1) (with_stdout("_hist.out",
+ for i:1 thru length(hist) do (
+ print(i,hist[i]))),
+ system("xgraph -bar -brw .7 -nl < _hist.out"));
+@end example
+
+In order to make the plot be done in the background (returning control to
+Maxima) and remove the temporary file after it is done do:
+
+@example
+system("(xgraph -bar -brw .7 -nl < _hist.out; rm -f _hist.out)&")
+@end example
+@end deffn
+
@c -----------------------------------------------------------------------------
@anchor{time}
@deffn {Function} time (%o1, %o2, %o3, @dots{})
commit 811489720f57d33a0db65f3a340984f3e7c9e16e
Author: crategus <cra...@us...>
Date: Wed Jun 15 23:01:58 2011 +0200
Adding the documentation for showratvars from Input.texi.
diff --git a/doc/info/Polynomials.texi b/doc/info/Polynomials.texi
index 6df9d43..162dd3d 100644
--- a/doc/info/Polynomials.texi
+++ b/doc/info/Polynomials.texi
@@ -2160,6 +2160,20 @@ containing some of the same factors.
@closecatbox
@end defvr
+@c -----------------------------------------------------------------------------
+@anchor{showratvars}
+@deffn {Function} showratvars (@var{expr})
+
+Returns a list of the canonical rational expression (CRE) variables in
+expression @code{expr}.
+
+See also @code{ratvars}.
+
+@opencatbox
+@category{Rational expressions} @category{Display functions}
+@closecatbox
+@end deffn
+
@c I CAN'T TELL WHAT THIS IS SUPPOSED TO BE ABOUT
@c -----------------------------------------------------------------------------
commit ddd3eb21cb0752d8d32b1d377980bb0ff9f656eb
Author: crategus <cra...@us...>
Date: Wed Jun 15 23:01:09 2011 +0200
Adding the documentation for error_size and error_syms from
the file Input.texi.
diff --git a/doc/info/Program.texi b/doc/info/Program.texi
index 0b97537..e3b7cc2 100644
--- a/doc/info/Program.texi
+++ b/doc/info/Program.texi
@@ -347,6 +347,86 @@ This is effectively reprinting the most recent error message.
@end deffn
@c -----------------------------------------------------------------------------
+@anchor{error_size}
+@defvr {Option variable} error_size
+Default value: 10
+
+@code{error_size} modifies error messages according to the size of expressions
+which appear in them. If the size of an expression (as determined by the Lisp
+function @code{ERROR-SIZE}) is greater than @code{error_size}, the expression is
+replaced in the message by a symbol, and the symbol is assigned the expression.
+The symbols are taken from the list @code{error_syms}.
+
+Otherwise, the expression is smaller than @code{error_size}, and the expression
+is displayed in the message.
+
+See also @code{error} and @code{error_syms}.
+
+Example:
+@c OUTPUT GENERATED BY THE FOLLOWING
+@c U: (C^D^E + B + A)/(cos(X-1) + 1)$
+@c error_size: 20$
+@c error ("Example expression is", U);
+@c errexp1;
+@c error_size: 30$
+@c error ("Example expression is", U);
+
+The size of @code{U}, as determined by @code{ERROR-SIZE}, is 24.
+
+@example
+(%i1) U: (C^D^E + B + A)/(cos(X-1) + 1)$
+
+(%i2) error_size: 20$
+
+(%i3) error ("Example expression is", U);
+
+Example expression is errexp1
+ -- an error. Quitting. To debug this try debugmode(true);
+(%i4) errexp1;
+ E
+ D
+ C + B + A
+(%o4) --------------
+ cos(X - 1) + 1
+(%i5) error_size: 30$
+
+(%i6) error ("Example expression is", U);
+
+ E
+ D
+ C + B + A
+Example expression is --------------
+ cos(X - 1) + 1
+ -- an error. Quitting. To debug this try debugmode(true);
+@end example
+
+@opencatbox
+@category{Debugging} @category{Display flags and variables}
+@closecatbox
+@end defvr
+
+@c -----------------------------------------------------------------------------
+@anchor{error_syms}
+@defvr {Option variable} error_syms
+Default value: @code{[errexp1, errexp2, errexp3]}
+
+In error messages, expressions larger than @code{error_size} are replaced by
+symbols, and the symbols are set to the expressions. The symbols are taken from
+the list @code{error_syms}. The first too-large expression is replaced by
+@code{error_syms[1]}, the second by @code{error_syms[2]}, and so on.
+
+If there are more too-large expressions than there are elements of
+@code{error_syms}, symbols are constructed automatically, with the @var{n}-th
+symbol equivalent to @code{concat ('errexp, @var{n})}.
+
+See also @code{error} and @code{error_size}.
+
+@opencatbox
+@category{Debugging} @category{Display flags and variables}
+@closecatbox
+@end defvr
+
+@c -----------------------------------------------------------------------------
@anchor{errormsg}
@deffn {Function} errormsg ()
commit ba8cf80903cdf0cbb343a5ed6273f0e50a5fb2ed
Author: crategus <cra...@us...>
Date: Wed Jun 15 23:00:16 2011 +0200
Adding the documentation for Syntax from Expressions.texi to the
section Introduction to operators.
diff --git a/doc/info/Operators.texi b/doc/info/Operators.texi
index fd60e5f..052b7a3 100644
--- a/doc/info/Operators.texi
+++ b/doc/info/Operators.texi
@@ -13,6 +13,172 @@
@section Introduction to operators
@c -----------------------------------------------------------------------------
+It is possible to define new operators with specified precedence, to undefine
+existing operators, or to redefine the precedence of existing operators. An
+operator may be unary prefix or unary postfix, binary infix, n-ary infix,
+matchfix, or nofix. "Matchfix" means a pair of symbols which enclose their
+argument or arguments, and "nofix" means an operator which takes no arguments.
+As examples of the different types of operators, there are the following.
+
+@table @asis
+@item unary prefix
+negation @code{- a}
+@item unary postfix
+factorial @code{a!}
+@item binary infix
+exponentiation @code{a^b}
+@item n-ary infix
+addition @code{a + b}
+@item matchfix
+list construction @code{[a, b]}
+@end table
+
+(There are no built-in nofix operators; for an example of such an operator,
+see @code{nofix}.)
+
+The mechanism to define a new operator is straightforward. It is only necessary
+to declare a function as an operator; the operator function might or might not
+be defined.
+
+An example of user-defined operators is the following. Note that the explicit
+function call @code{"dd" (a)} is equivalent to @code{dd a}, likewise
+@code{"<-" (a, b)} is equivalent to @code{a <- b}. Note also that the functions
+@code{"dd"} and @code{"<-"} are undefined in this example.
+
+@c ===beg===
+@c prefix ("dd");
+@c dd a;
+@c "dd" (a);
+@c infix ("<-");
+@c a <- dd b;
+@c "<-" (a, "dd" (b));
+@c ===end===
+@example
+(%i1) prefix ("dd");
+(%o1) dd
+(%i2) dd a;
+(%o2) dd a
+(%i3) "dd" (a);
+(%o3) dd a
+(%i4) infix ("<-");
+(%o4) <-
+(%i5) a <- dd b;
+(%o5) a <- dd b
+(%i6) "<-" (a, "dd" (b));
+(%o6) a <- dd b
+@end example
+
+The Maxima functions which define new operators are summarized in this table,
+stating the default left and right binding powers (lbp and rbp, respectively).
+@c REWORK FOLLOWING COMMENT.
+@c IT'S NOT CLEAR ENOUGH, GIVEN THAT IT'S FAIRLY IMPORTANT
+(Binding power determines operator precedence. However, since left and right
+binding powers can differ, binding power is somewhat more complicated than
+precedence.) Some of the operation definition functions take additional
+arguments; see the function descriptions for details.
+
+@c MAKE ANCHORS FOR ALL 6 FUNCTIONS AND CHANGE @code TO @ref ACCORDINGLY
+@table @code
+@item prefix
+rbp=180
+@item postfix
+lbp=180
+@item infix
+lbp=180, rbp=180
+@item nary
+lbp=180, rbp=180
+@item matchfix
+(binding power not applicable)
+@item nofix
+(binding power not applicable)
+@end table
+
+For comparison, here are some built-in operators and their left and right
+binding powers.
+
+@example
+Operator lbp rbp
+
+ : 180 20
+ :: 180 20
+ := 180 20
+ ::= 180 20
+ ! 160
+ !! 160
+ ^ 140 139
+ . 130 129
+ * 120
+ / 120 120
+ + 100 100
+ - 100 134
+ = 80 80
+ # 80 80
+ > 80 80
+ >= 80 80
+ < 80 80
+ <= 80 80
+ not 70
+ and 65
+ or 60
+ , 10
+ $ -1
+ ; -1
+@end example
+
+@mref{remove} and @mref{kill} remove operator properties from an atom.
+@code{remove ("@var{a}", op)} removes only the operator properties of @var{a}.
+@code{kill ("@var{a}")} removes all properties of @var{a}, including the
+operator properties. Note that the name of the operator must be enclosed in
+quotation marks.
+
+@c MAYBE COPY THIS EXAMPLE TO remove AND/OR kill
+@c ===beg===
+@c infix ("##");
+@c "##" (a, b) := a^b;
+@c 5 ## 3;
+@c remove ("##", op);
+@c 5 ## 3;
+@c "##" (5, 3);
+@c infix ("##");
+@c 5 ## 3;
+@c kill ("##");
+@c 5 ## 3;
+@c "##" (5, 3);
+@c ===end===
+@example
+(%i1) infix ("##");
+(%o1) ##
+(%i2) "##" (a, b) := a^b;
+ b
+(%o2) a ## b := a
+(%i3) 5 ## 3;
+(%o3) 125
+(%i4) remove ("##", op);
+(%o4) done
+(%i5) 5 ## 3;
+Incorrect syntax: # is not a prefix operator
+5 ##
+ ^
+(%i5) "##" (5, 3);
+(%o5) 125
+(%i6) infix ("##");
+(%o6) ##
+(%i7) 5 ## 3;
+(%o7) 125
+(%i8) kill ("##");
+(%o8) done
+(%i9) 5 ## 3;
+Incorrect syntax: # is not a prefix operator
+5 ##
+ ^
+(%i9) "##" (5, 3);
+(%o9) ##(5, 3)
+@end example
+
+@opencatbox
+@category{Operators} @category{Syntax}
+@closecatbox
+
@c -----------------------------------------------------------------------------
@node Arithmetic operators, Relational operators, Introduction to operators, Operators
@section Arithmetic operators
@@ -1201,7 +1367,7 @@ to its right in an expression. Thus greater @var{lbp} makes @var{op}
right-associative, while greater @var{rbp} makes @var{op} left-associative.
If @var{lbp} is equal to @var{rbp}, @var{op} is left-associative.
-See also @ref{Syntax}.
+See also @ref{Introduction to operators}.
Examples:
@@ -1432,7 +1598,7 @@ to be an @code{nary} operator. Functions may be declared to be @code{nary}. If
@code{declare(j,nary);} is done, this tells the simplifier to simplify, e.g.
@code{j(j(a,b),j(c,d))} to @code{j(a, b, c, d)}.
-See also @ref{Syntax}.
+See also @ref{Introduction to operators}.
@opencatbox
@category{Operators} @category{Syntax}
@@ -1451,7 +1617,7 @@ corresponding function to be evaluated. For example, when one types
@code{nofix} operator. The function @code{nofix("x")} is a syntax extension
function which declares @code{x} to be a @code{nofix} operator.
-See also @ref{Syntax}.
+See also @ref{Introduction to operators}.
@opencatbox
@category{Operators} @category{Syntax}
@@ -1469,7 +1635,7 @@ occurrence of the operator in the input string, e.g. 3!. The
@code{postfix("x")} function is a syntax extension function to declare @code{x}
to be a @code{postfix} operator.
-See also @ref{Syntax}.
+See also @ref{Introduction to operators}.
@opencatbox
@category{Operators} @category{Syntax}
@@ -1486,7 +1652,7 @@ which argument immediately follows an occurrence of the operator.
@code{prefix("x")} is a syntax extension function to declare @code{x} to be a
@code{prefix} operator.
-See also @ref{Syntax}.
+See also @ref{Introduction to operators}.
@opencatbox
@category{Operators} @category{Syntax}
commit 4215aa5aba4a52a86428184119156e9ff7629113
Author: crategus <cra...@us...>
Date: Wed Jun 15 22:59:16 2011 +0200
Moving the section Syntax to the file Operators.texi.
diff --git a/doc/info/Expressions.texi b/doc/info/Expressions.texi
index efd05a1..ee7b96d 100644
--- a/doc/info/Expressions.texi
+++ b/doc/info/Expressions.texi
@@ -3,7 +3,6 @@
* Nouns and Verbs::
* Identifiers::
* Inequality::
-* Syntax::
* Functions and Variables for Expressions::
@end menu
@@ -212,7 +211,7 @@ Examples:
@closecatbox
@c -----------------------------------------------------------------------------
-@node Inequality, Syntax, Identifiers, Expressions
+@node Inequality, Functions and Variables for Expressions, Identifiers, Expressions
@section Inequality
@c -----------------------------------------------------------------------------
@@ -221,178 +220,7 @@ Maxima has the inequality operators @code{<}, @code{<=}, @code{>=}, @code{>},
expressions.
@c -----------------------------------------------------------------------------
-@node Syntax, Functions and Variables for Expressions, Inequality, Expressions
-@section Syntax
-@c -----------------------------------------------------------------------------
-
-It is possible to define new operators with specified precedence, to undefine
-existing operators, or to redefine the precedence of existing operators. An
-operator may be unary prefix or unary postfix, binary infix, n-ary infix,
-matchfix, or nofix. "Matchfix" means a pair of symbols which enclose their
-argument or arguments, and "nofix" means an operator which takes no arguments.
-As examples of the different types of operators, there are the following.
-
-@table @asis
-@item unary prefix
-negation @code{- a}
-@item unary postfix
-factorial @code{a!}
-@item binary infix
-exponentiation @code{a^b}
-@item n-ary infix
-addition @code{a + b}
-@item matchfix
-list construction @code{[a, b]}
-@end table
-
-(There are no built-in nofix operators; for an example of such an operator,
-see @code{nofix}.)
-
-The mechanism to define a new operator is straightforward. It is only necessary
-to declare a function as an operator; the operator function might or might not
-be defined.
-
-An example of user-defined operators is the following. Note that the explicit
-function call @code{"dd" (a)} is equivalent to @code{dd a}, likewise
-@code{"<-" (a, b)} is equivalent to @code{a <- b}. Note also that the functions
-@code{"dd"} and @code{"<-"} are undefined in this example.
-
-@c ===beg===
-@c prefix ("dd");
-@c dd a;
-@c "dd" (a);
-@c infix ("<-");
-@c a <- dd b;
-@c "<-" (a, "dd" (b));
-@c ===end===
-@example
-(%i1) prefix ("dd");
-(%o1) dd
-(%i2) dd a;
-(%o2) dd a
-(%i3) "dd" (a);
-(%o3) dd a
-(%i4) infix ("<-");
-(%o4) <-
-(%i5) a <- dd b;
-(%o5) a <- dd b
-(%i6) "<-" (a, "dd" (b));
-(%o6) a <- dd b
-@end example
-
-The Maxima functions which define new operators are summarized in this table,
-stating the default left and right binding powers (lbp and rbp, respectively).
-@c REWORK FOLLOWING COMMENT.
-@c IT'S NOT CLEAR ENOUGH, GIVEN THAT IT'S FAIRLY IMPORTANT
-(Binding power determines operator precedence. However, since left and right
-binding powers can differ, binding power is somewhat more complicated than
-precedence.) Some of the operation definition functions take additional
-arguments; see the function descriptions for details.
-
-@c MAKE ANCHORS FOR ALL 6 FUNCTIONS AND CHANGE @code TO @ref ACCORDINGLY
-@table @code
-@item prefix
-rbp=180
-@item postfix
-lbp=180
-@item infix
-lbp=180, rbp=180
-@item nary
-lbp=180, rbp=180
-@item matchfix
-(binding power not applicable)
-@item nofix
-(binding power not applicable)
-@end table
-
-For comparison, here are some built-in operators and their left and right
-binding powers.
-
-@example
-Operator lbp rbp
-
- : 180 20
- :: 180 20
- := 180 20
- ::= 180 20
- ! 160
- !! 160
- ^ 140 139
- . 130 129
- * 120
- / 120 120
- + 100 100
- - 100 134
- = 80 80
- # 80 80
- > 80 80
- >= 80 80
- < 80 80
- <= 80 80
- not 70
- and 65
- or 60
- , 10
- $ -1
- ; -1
-@end example
-
-@mref{remove} and @mref{kill} remove operator properties from an atom.
-@code{remove ("@var{a}", op)} removes only the operator properties of @var{a}.
-@code{kill ("@var{a}")} removes all properties of @var{a}, including the
-operator properties. Note that the name of the operator must be enclosed in
-quotation marks.
-
-@c MAYBE COPY THIS EXAMPLE TO remove AND/OR kill
-@c ===beg===
-@c infix ("##");
-@c "##" (a, b) := a^b;
-@c 5 ## 3;
-@c remove ("##", op);
-@c 5 ## 3;
-@c "##" (5, 3);
-@c infix ("##");
-@c 5 ## 3;
-@c kill ("##");
-@c 5 ## 3;
-@c "##" (5, 3);
-@c ===end===
-@example
-(%i1) infix ("##");
-(%o1) ##
-(%i2) "##" (a, b) := a^b;
- b
-(%o2) a ## b := a
-(%i3) 5 ## 3;
-(%o3) 125
-(%i4) remove ("##", op);
-(%o4) done
-(%i5) 5 ## 3;
-Incorrect syntax: # is not a prefix operator
-5 ##
- ^
-(%i5) "##" (5, 3);
-(%o5) 125
-(%i6) infix ("##");
-(%o6) ##
-(%i7) 5 ## 3;
-(%o7) 125
-(%i8) kill ("##");
-(%o8) done
-(%i9) 5 ## 3;
-Incorrect syntax: # is not a prefix operator
-5 ##
- ^
-(%i9) "##" (5, 3);
-(%o9) ##(5, 3)
-@end example
-
-@opencatbox
-@category{Operators} @category{Syntax}
-@closecatbox
-
-@c -----------------------------------------------------------------------------
-@node Functions and Variables for Expressions, , Syntax, Expressions
+@node Functions and Variables for Expressions, , Inequality, Expressions
@section Functions and Variables for Expressions
@c -----------------------------------------------------------------------------
commit 84466052f69ee1b63964eff124524308413e5e4b
Author: crategus <cra...@us...>
Date: Wed Jun 15 22:58:20 2011 +0200
Cutting out the file Floating.texi.
Cutting out the section Syntax.
diff --git a/doc/info/include-maxima.texi.in b/doc/info/include-maxima.texi.in
index 7554a0c..3f088f0 100644
--- a/doc/info/include-maxima.texi.in
+++ b/doc/info/include-maxima.texi.in
@@ -97,7 +97,6 @@ Maxima infrastructure
* Maximas Database:: Declarations, Contexts, Facts, and Properties.
* Plotting:: 2D and 3D graphical output.
* File Input and Output:: File input and output.
-* Floating Point:: Low level numerical routines.
Support for specific areas of mathematics
@@ -222,7 +221,6 @@ Expressions
* Nouns and Verbs::
* Identifiers::
* Inequality::
-* Syntax::
* Functions and Variables for Expressions::
Operators
@@ -274,10 +272,6 @@ File Input and Output
* Files::
* Functions and Variables for File Input and Output::
-Floating Point
-
-* Functions and Variables for Floating Point::
-
Polynomials
* Introduction to Polynomials::
@@ -699,15 +693,11 @@ zeilberger
@chapter Plotting
@include Plotting.texi
-@node File Input and Output, Floating Point, Plotting, Top
+@node File Input and Output, Polynomials, Plotting, Top
@chapter File Input and Output
@include Input.texi
-@node Floating Point, Polynomials, File Input and Output, Top
-@chapter Floating Point
-@include Floating.texi
-
-@node Polynomials, Special Functions, Floating Point, Top
+@node Polynomials, Special Functions, File Input and Output, Top
@chapter Polynomials
@include Polynomials.texi
commit 07a8146ac68f07212beb02d143426fe407b381f6
Author: crategus <cra...@us...>
Date: Wed Jun 15 22:57:15 2011 +0200
Adding documentation for dispcon and show from Input.texi
diff --git a/doc/info/Itensor.texi b/doc/info/Itensor.texi
index 7c1b2b9..104a26b 100644
--- a/doc/info/Itensor.texi
+++ b/doc/info/Itensor.texi
@@ -8,11 +8,14 @@
* Functions and Variables for itensor::
@end menu
+@c -----------------------------------------------------------------------------
@node Introduction to itensor, Functions and Variables for itensor, itensor, itensor
@section Introduction to itensor
+@c -----------------------------------------------------------------------------
Maxima implements symbolic tensor manipulation of two distinct types:
-component tensor manipulation (@code{ctensor} package) and indicial tensor manipulation (@code{itensor} package).
+component tensor manipulation (@code{ctensor} package) and indicial tensor
+manipulation (@code{itensor} package).
Nota bene: Please see the note on 'new tensor notation' below.
@@ -77,7 +80,9 @@ the Hamiltonian associated with the theory's scalar field.
@category{Tensors} @category{Share packages} @category{Package itensor}
@closecatbox
+@c -----------------------------------------------------------------------------
@subsection New tensor notation
+@c -----------------------------------------------------------------------------
Earlier versions of the @code{itensor} package in Maxima used a notation that sometimes
led to incorrect index ordering. Consider the following, for instance:
@@ -130,8 +135,9 @@ notation, there is a considerable chance that "new" tensors will fail to
interoperate with certain functions or features. These bugs will be fixed
as they are encountered... until then, caveat emptor!
-
+@c -----------------------------------------------------------------------------
@subsection Indicial tensor manipulation
+@c -----------------------------------------------------------------------------
The indicial tensor manipulation package may be loaded by
@code{load(itensor)}. Demos are also available: try @code{demo(tensor)}.
@@ -260,15 +266,29 @@ specify the name of the metric, and perform some simple calculations.
(%t22) 0
@end example
-
-
@c end concepts itensor
+@c -----------------------------------------------------------------------------
@node Functions and Variables for itensor, , Introduction to itensor, itensor
-
@section Functions and Variables for itensor
@subsection Managing indexed objects
+@c -----------------------------------------------------------------------------
+@c -----------------------------------------------------------------------------
+@anchor{dispcon}
+@deffn {Function} dispcon (@var{tensor_1}, @var{tensor_2}, @dots{})
+@deffnx {Function} dispcon (all)
+
+Displays the contraction properties of its arguments as were given to
+@code{defcon}. @code{dispcon (all)} displays all the contraction properties
+which were defined.
+
+@opencatbox
+@category{Display functions}
+@closecatbox
+@end deffn
+
+@c -----------------------------------------------------------------------------
@deffn {Function} entertensor (@var{name})
is a function which, by prompting, allows one to create an indexed
@@ -281,6 +301,7 @@ null) is acceptable input (see the example under @code{covdiff}).
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@deffn {Function} changename (@var{old}, @var{new}, @var{expr})
will change the name of all indexed objects called @var{old} to @var{new}
@@ -294,6 +315,7 @@ renamed to @var{new}.
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@deffn {Function} listoftens
Lists all tensors in a tensorial expression, complete with their indices. E.g.,
@@ -316,6 +338,7 @@ Lists all tensors in a tensorial expression, complete with their indices. E.g.,
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@deffn {Function} ishow (@var{expr})
displays @var{expr} with the indexed objects in it shown having their
@@ -329,6 +352,7 @@ throughout this document).
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@deffn {Function} indices (@var{expr})
Returns a list of two elements. The first is a list of the free
@@ -354,12 +378,12 @@ illegal. @code{indices} attempts to deal with these expressions in a
reasonable manner; however, when it is called to operate upon such an
illegal expression, its behavior should be considered undefined.
-
@opencatbox
@category{Package itensor}
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@deffn {Function} rename (@var{expr})
@deffnx {Function} rename (@var{expr}, @var{count})
@@ -427,6 +451,24 @@ ichr2([%3,%5],[%1])*ichr2([%4,%6],[%3])*ichr2([%7,r],[%2]),noeval$
@closecatbox
@end deffn
+@c THIS FUNCTION IS IN THE SHARE PACKAGE itensor.lisp
+@c MOVE THIS DESCRIPTION TO Itensor.texi
+
+@c -----------------------------------------------------------------------------
+@anchor{show}
+@deffn {Function} show (@var{expr})
+
+Displays @code{expr} with the indexed objects in it shown
+having covariant indices as subscripts, contravariant indices as
+superscripts. The derivative indices are displayed as subscripts,
+separated from the covariant indices by a comma.
+
+@opencatbox
+@category{Package itensor} @category{Display functions}
+@closecatbox
+@end deffn
+
+@c -----------------------------------------------------------------------------
@defvr {Option variable} flipflag
Default: @code{false}. If @code{false} then the indices will be
@@ -445,6 +487,7 @@ under @code{rename}).
@closecatbox
@end defvr
+@c -----------------------------------------------------------------------------
@deffn {Function} defcon (@var{tensor_1})
@deffnx {Function} defcon (@var{tensor_1}, @var{tensor_2}, @var{tensor_3})
gives @var{tensor_1} the property that the
@@ -468,6 +511,7 @@ contraction properties with @code{defcon}.
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@deffn {Function} remcon (@var{tensor_1}, ..., @var{tensor_n})
@deffnx {Function} remcon (all)
removes all the contraction properties
@@ -479,6 +523,7 @@ properties from all indexed objects.
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@deffn {Function} contract (@var{expr})
Carries out the tensorial contractions in @var{expr} which may be any
@@ -494,6 +539,7 @@ cancellations are unnecessary.
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@deffn {Function} indexed_tensor (@var{tensor})
Must be executed before assigning components to a @var{tensor} for which
@@ -505,6 +551,7 @@ a built in value already exists as with @code{ichr1}, @code{ichr2},
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@deffn {Function} components (@var{tensor}, @var{expr})
permits one to assign an indicial value to an expression
@@ -625,6 +672,8 @@ Unbinds all values from @var{tensor} which were assigned with the
@end deffn
@c NEED LIST OF ARGUMENTS HERE
+
+@c -----------------------------------------------------------------------------
@deffn {Function} showcomps (@var{tensor})
Shows component assignments of a tensor, as made using the @code{components}
@@ -677,6 +726,7 @@ rank higher than 2.
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@deffn {Function} idummy ()
Increments @code{icounter} and returns as its value an index of the form
@@ -699,6 +749,7 @@ Is the prefix for dummy indices (see the example under @code{indices}).
@closecatbox
@end defvr
+@c -----------------------------------------------------------------------------
@defvr {Option variable} icounter
Default value: @code{1}
@@ -711,6 +762,7 @@ determined by the option @code{idummy} (default: @code{%}).
@closecatbox
@end defvr
+@c -----------------------------------------------------------------------------
@deffn {Function} kdelta (@var{L1}, @var{L2})
is the generalized Kronecker delta function defined in
the @code{itensor} package with @var{L1} the list of covariant indices and @var{L2}
@@ -730,6 +782,7 @@ imply that @code{kdelta([i,j],[])} is a valid tensorial object.
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@deffn {Function} kdels (@var{L1}, @var{L2})
Symmetrized Kronecker delta, used in some calculations. For instance:
@@ -758,6 +811,7 @@ Symmetrized Kronecker delta, used in some calculations. For instance:
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@deffn {Function} levi_civita (@var{L})
is the permutation (or Levi-Civita) tensor which yields 1 if
the list @var{L} consists of an even permutation of integers, -1 if it
@@ -769,6 +823,7 @@ repeated.
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@deffn {Function} lc2kdt (@var{expr})
Simplifies expressions containing the Levi-Civita symbol, converting these
to Kronecker-delta expressions when possible. The main difference between
@@ -852,6 +907,8 @@ To reenable the Lisp debugger set *debugger-hook* to nil.
@end deffn
@c HMM, WHICH CATEGORY DOES THIS FALL INTO -- FUNCTION, VARIABLE, OTHER ??
+
+@c -----------------------------------------------------------------------------
@deffn {Function} lc_l
Simplification rule used for expressions containing the unevaluated Levi-Civita
@@ -884,6 +941,8 @@ For example:
@end deffn
@c HMM, WHICH CATEGORY DOES THIS FALL INTO -- FUNCTION, VARIABLE, OTHER ??
+
+@c -----------------------------------------------------------------------------
@deffn {Function} lc_u
Simplification rule used for expressions containing the unevaluated Levi-Civita
@@ -896,6 +955,7 @@ For details, see @code{lc_l}.
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@deffn {Function} canten (@var{expr})
Simplifies @var{expr} by renaming (see @code{rename})
and permuting dummy indices. @code{rename} is restricted to sums of tensor
@@ -913,6 +973,7 @@ set to @code{true}.
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@deffn {Function} concan (@var{expr})
Similar to @code{canten} but also performs index contraction.
@@ -921,8 +982,11 @@ Similar to @code{canten} but also performs index contraction.
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@subsection Tensor symmetries
+@c -----------------------------------------------------------------------------
+@c -----------------------------------------------------------------------------
@defvr {Option variable} allsym
Default: @code{false}. if @code{true} then all indexed objects
@@ -936,6 +1000,7 @@ unless @code{iframe_flag} is set to @code{true}.
@closecatbox
@end defvr
+@c -----------------------------------------------------------------------------
@deffn {Function} decsym (@var{tensor}, @var{m}, @var{n}, [@var{cov_1}, @var{cov_2}, ...], [@var{contr_1}, @var{contr_2}, ...])
Declares symmetry properties for @var{tensor} of @var{m} covariant and
@@ -990,12 +1055,12 @@ illustrates.
@end example
-
@opencatbox
@category{Package itensor}
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@deffn {Function} remsym (@var{tensor}, @var{m}, @var{n})
Removes all symmetry properties from @var{tensor} which has @var{m}
covariant indices and @var{n} contravariant indices.
@@ -1005,6 +1070,7 @@ covariant indices and @var{n} contravariant indices.
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@deffn {Function} canform (@var{expr})
@deffnx {Function} canform (@var{expr}, @var{rename})
Simplifies @var{expr} by renaming dummy
@@ -1026,8 +1092,11 @@ The optional second parameter @var{rename}, if set to @code{false}, suppresses r
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@subsection Indicial tensor calculus
+@c -----------------------------------------------------------------------------
+@c -----------------------------------------------------------------------------
@deffn {Function} diff (@var{expr}, @var{v_1}, [@var{n_1}, [@var{v_2}, @var{n_2}] ...])
is the usual Maxima differentiation function which has been expanded
@@ -1055,6 +1124,7 @@ the Einstein tensor and field equations from the action principle.
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@deffn {Function} idiff (@var{expr}, @var{v_1}, [@var{n_1}, [@var{v_2}, @var{n_2}] ...])
Indicial differentiation. Unlike @code{diff}, which differentiates
with respect to an independent variable, @code{idiff)} can be used
@@ -1074,6 +1144,7 @@ is chosen appropriately.
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@deffn {Function} liediff (@var{v}, @var{ten})
Computes the Lie-derivative of the tensorial expression @var{ten} with
@@ -1101,6 +1172,7 @@ field. For example:
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@deffn {Function} rediff (@var{ten})
Evaluates all occurrences of the @code{idiff} command in the tensorial
@@ -1111,6 +1183,7 @@ expression @var{ten}.
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@deffn {Function} undiff (@var{expr})
Returns an expression equivalent to @var{expr} but with all derivatives
@@ -1126,6 +1199,7 @@ in @var{expr} and then carry out the differentiation by saying
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@deffn {Function} evundiff (@var{expr})
Equivalent to the execution of @code{undiff}, followed by @code{ev} and
@@ -1192,6 +1266,7 @@ so @code{evundiff} is no longer necessary for expressions like this:
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@deffn {Function} flush (@var{expr}, @var{tensor_1}, @var{tensor_2}, ...)
Set to zero, in
@var{expr}, all occurrences of the @var{tensor_i} that have no derivative indices.
@@ -1201,6 +1276,7 @@ Set to zero, in
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@deffn {Function} flushd (@var{expr}, @var{tensor_1}, @var{tensor_2}, ...)
Set to zero, in
@var{expr}, all occurrences of the @var{tensor_i} that have derivative indices.
@@ -1210,6 +1286,7 @@ Set to zero, in
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@deffn {Function} flushnd (@var{expr}, @var{tensor}, @var{n})
Set to zero, in @var{expr}, all
occurrences of the differentiated object @var{tensor} that have @var{n} or more
@@ -1233,6 +1310,7 @@ derivative indices as the following example demonstrates.
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@deffn {Function} coord (@var{tensor_1}, @var{tensor_2}, ...)
Gives @var{tensor_i} the coordinate differentiation property that the
@@ -1246,6 +1324,7 @@ been done then @code{idiff(x([],[i]),j)} gives @code{kdelta([i],[j])}.
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@deffn {Function} remcoord (@var{tensor_1}, @var{tensor_2}, ...)
@deffnx {Function} remcoord (all)
@@ -1258,6 +1337,7 @@ removes this property from all indexed objects.
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@deffn {Function} makebox (@var{expr})
Display @var{expr} in the same manner as @code{show}; however,
any tensor d'Alembertian occurring in @var{expr} will be indicated using the
@@ -1269,6 +1349,7 @@ symbol @code{[]}. For example, @code{[]p([m],[n])} represents
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@deffn {Function} conmetderiv (@var{expr}, @var{tensor})
Simplifies expressions containing ordinary derivatives of
@@ -1296,6 +1377,7 @@ symbols as seen from the following:
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@deffn {Function} simpmetderiv (@var{expr})
@deffnx {Function} simpmetderiv (@var{expr}[, @var{stop}])
@@ -1388,6 +1470,7 @@ and @code{conmetderiv} together to simplify contractions of the Weyl tensor.
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@deffn {Function} flush1deriv (@var{expr}, @var{tensor})
Set to zero, in @code{expr}, all occurrences of @code{tensor} that have
@@ -1398,8 +1481,11 @@ exactly one derivative index.
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@subsection Tensors in curved spaces
+@c -----------------------------------------------------------------------------
+@c -----------------------------------------------------------------------------
@deffn {Function} imetric (@var{g})
@deffnx {System variable} imetric
@@ -1414,6 +1500,7 @@ the @code{imetric(@var{g})} command.
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@deffn {Function} idim (@var{n})
Sets the dimensions of the metric. Also initializes the antisymmetry
properties of the Levi-Civita symbols for the given dimension.
@@ -1423,6 +1510,7 @@ properties of the Levi-Civita symbols for the given dimension.
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@deffn {Function} ichr1 ([@var{i}, @var{j}, @var{k}])
Yields the Christoffel symbol of the first kind via the
definition
@@ -1439,6 +1527,7 @@ variable @code{imetric} must be assigned a name as in the example under @code{ch
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@deffn {Function} ichr2 ([@var{i}, @var{j}], [@var{k}])
Yields the Christoffel symbol of the second kind
defined by the relation
@@ -1453,6 +1542,7 @@ defined by the relation
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@deffn {Function} icurvature ([@var{i}, @var{j}, @var{k}], [@var{h}])
Yields the Riemann
curvature tensor in terms of the Christoffel symbols of the second
@@ -1471,6 +1561,7 @@ kind (@code{ichr2}). The following notation is used:
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@deffn {Function} covdiff (@var{expr}, @var{v_1}, @var{v_2}, ...)
Yields the covariant derivative of @var{expr} with
respect to the variables @var{v_i} in terms of the Christoffel symbols of the
@@ -1525,6 +1616,7 @@ Enter a list of the derivative indices: [];
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@deffn {Function} lorentz_gauge (@var{expr})
Imposes the Lorentz condition by substituting 0 for all
indexed objects in @var{expr} that have a derivative index identical to a
@@ -1535,6 +1627,7 @@ contravariant index.
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@deffn {Function} igeodesic_coords (@var{expr}, @var{name})
Causes undifferentiated Christoffel symbols and
@@ -1581,7 +1674,9 @@ curvature tensor using the @code{igeodesic_coords} function.
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@subsection Moving frames
+@c -----------------------------------------------------------------------------
Maxima now has the ability to perform calculations using moving frames.
These can be orthonormal frames (tetrads, vielbeins) or an arbitrary frame.
@@ -1658,7 +1753,7 @@ the @code{iframe_bracket_form} flag is set to @code{false}:
@end example
-
+@c -----------------------------------------------------------------------------
@deffn {Function} iframes ()
Since in this version of Maxima, contraction identities for @code{ifr} and
@@ -1670,6 +1765,7 @@ function does nothing.
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@defvr {Variable} ifb
The frame bracket. The contribution of the frame metric to the connection
@@ -1713,7 +1809,7 @@ ifb = (ifr ifr - ifr ifr ) ifri
@closecatbox
@end defvr
-
+@c -----------------------------------------------------------------------------
@defvr {Variable} icc1
Connection coefficients of the first kind. In @code{itensor}, defined as
@@ -1738,6 +1834,7 @@ Lastly, of @code{inonmet_flag} is @code{false},
@closecatbox
@end defvr
+@c -----------------------------------------------------------------------------
@defvr {Variable} icc2
Connection coefficients of the second kind. In @code{itensor}, defined as
@@ -1763,6 +1860,7 @@ Lastly, of @code{inonmet_flag} is @code{false},
@closecatbox
@end defvr
+@c -----------------------------------------------------------------------------
@defvr {Variable} ifc1
Frame coefficient of the first kind (also known as Ricci-rotation
@@ -1785,6 +1883,7 @@ ifc1 = --------------------------------
@closecatbox
@end defvr
+@c -----------------------------------------------------------------------------
@defvr {Variable} ifc2
Frame coefficient of the second kind. This tensor represents the contribution
@@ -1805,6 +1904,7 @@ ifc2 = ifg ifc1
@closecatbox
@end defvr
+@c -----------------------------------------------------------------------------
@defvr {Variable} ifr
The frame field. Contracts with the inverse frame field (@code{ifri}) to
@@ -1815,6 +1915,7 @@ form the frame metric (@code{ifg}).
@closecatbox
@end defvr
+@c -----------------------------------------------------------------------------
@defvr {Variable} ifri
The inverse frame field. Specifies the frame base (dual basis vectors). Along
@@ -1826,6 +1927,7 @@ frames.
@closecatbox
@end defvr
+@c -----------------------------------------------------------------------------
@defvr {Variable} ifg
The frame metric. Defaults to @code{kdelta}, but can be changed using
@@ -1836,6 +1938,7 @@ The frame metric. Defaults to @code{kdelta}, but can be changed using
@closecatbox
@end defvr
+@c -----------------------------------------------------------------------------
@defvr {Variable} ifgi
The inverse frame metric. Contracts with the frame metric (@code{ifg})
@@ -1846,6 +1949,7 @@ to @code{kdelta}.
@closecatbox
@end defvr
+@c -----------------------------------------------------------------------------
@defvr {Option variable} iframe_bracket_form
Default value: @code{true}
@@ -1856,13 +1960,16 @@ Specifies how the frame bracket (@code{ifb}) is computed.
@closecatbox
@end defvr
+@c -----------------------------------------------------------------------------
@subsection Torsion and nonmetricity
+@c -----------------------------------------------------------------------------
Maxima can now take into account torsion and nonmetricity. When the flag
@code{itorsion_flag} is set to @code{true}, the contribution of torsion
is added to the connection coefficients. Similarly, when the flag
@code{inonmet_flag} is true, nonmetricity components are included.
+@c -----------------------------------------------------------------------------
@defvr {Variable} inm
The nonmetricity vector. Conformal nonmetricity is defined through the
@@ -1882,7 +1989,7 @@ g =- g inm
@closecatbox
@end defvr
-
+@c -----------------------------------------------------------------------------
@defvr {Variable} inmc1
Covariant permutation of the nonmetricity vector components. Defined as
@@ -1903,6 +2010,7 @@ inmc1 = ------------------------------
@closecatbox
@end defvr
+@c -----------------------------------------------------------------------------
@defvr {Variable} inmc2
Contravariant permutation of the nonmetricity vector components. Used
@@ -1926,6 +2034,7 @@ inmc2 = -------------------------------------------
@closecatbox
@end defvr
+@c -----------------------------------------------------------------------------
@defvr {Variable} ikt1
Covariant permutation of the torsion tensor (also known as contorsion).
@@ -1948,6 +2057,7 @@ ikt1 = ----------------------------------
@closecatbox
@end defvr
+@c -----------------------------------------------------------------------------
@defvr {Variable} ikt2
Contravariant permutation of the torsion tensor (also known as contorsion).
@@ -1968,6 +2078,7 @@ ikt2 = g ikt1
@closecatbox
@end defvr
+@c -----------------------------------------------------------------------------
@defvr {Variable} itr
The torsion tensor. For a metric with torsion, repeated covariant
@@ -2031,7 +2142,9 @@ by the following example:
@closecatbox
@end defvr
+@c -----------------------------------------------------------------------------
@subsection Exterior algebra
+@c -----------------------------------------------------------------------------
The @code{itensor} package can perform operations on totally antisymmetric
covariant tensor fields. A totally antisymmetric tensor field of rank
@@ -2128,6 +2241,7 @@ The behavior of the wedge product operator is controlled by the
@closecatbox
@end defvr
+@c -----------------------------------------------------------------------------
@defvr {Operator} |
@ifinfo
@fnindex Contraction with a vector
@@ -2167,6 +2281,7 @@ the results will be incorrect.
@closecatbox
@end defvr
+@c -----------------------------------------------------------------------------
@deffn {Function} extdiff (@var{expr}, @var{i})
Computes the exterior derivative of @var{expr} with respect to the index
@@ -2206,6 +2321,7 @@ For instance:
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@deffn {Function} hodge (@var{expr})
Compute the Hodge-dual of @...
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