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[Maxima-commits] Maxima, A Computer Algebra System branch, master, updated. 7d852ded553f999a2bf7a3ecfe69d75b0d1686cf
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From: Dieter K. <cra...@us...> - 2011-06-13 18:20:25
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- Log -----------------------------------------------------------------
commit 7d852ded553f999a2bf7a3ecfe69d75b0d1686cf
Author: crategus <cra...@us...>
Date: Mon Jun 13 20:18:07 2011 +0200
Moving documentation to different files and adding documentation:
Moving to Database.texi:
askexp
askinteger
asksign
posfun
unknown
Moving to Polynomials.texi:
radsubstflag
Moving to Series.texi:
intosum
simpsum
sumcontract
sumexpand
Moving to Rules.texi:
maxapplydepth
maxapplyheight
Adding from Polynomials.texi:
combine
New documentation:
evenfun
oddfun
nary
diff --git a/doc/info/Simplification.texi b/doc/info/Simplification.texi
index 5bda996..c8413ad 100644
--- a/doc/info/Simplification.texi
+++ b/doc/info/Simplification.texi
@@ -9,7 +9,7 @@
@c -----------------------------------------------------------------------------
@anchor{additive}
-@defvr {Keyword} additive
+@defvr {Declaration} additive
If @code{declare(f,additive)} has been executed, then:
@@ -43,68 +43,15 @@ of two arguments necessary to convert it to that form.
@closecatbox
@end defvr
-@c After studying src/compar.lisp, it appears that askexp would
-@c work as advertised, except that it doesn't appear to be possible
-@c to open a break prompt with ^A or any other character.
-@c What should we do about askexp ???
-
-@c -----------------------------------------------------------------------------
-@anchor{askexp}
-@defvr {System variable} askexp
-
-When @code{asksign} is called,
-@code{askexp} is the expression @code{asksign} is testing.
-
-At one time, it was possible for a user to inspect @code{askexp}
-by entering a Maxima break with control-A.
-
-@opencatbox
-@category{Declarations and inferences}
-@closecatbox
-@end defvr
-
-@c THERE IS PROBABLY MORE TO THE STORY THAN WHAT IS INDICATED HERE ...
-
-@c -----------------------------------------------------------------------------
-@anchor{askinteger}
-@deffn {Function} askinteger (@var{expr}, integer)
-@deffnx {Function} askinteger (@var{expr})
-@deffnx {Function} askinteger (@var{expr}, even)
-@deffnx {Function} askinteger (@var{expr}, odd)
-
-@code{askinteger (@var{expr}, integer)} attempts to determine from the
-@code{assume} database whether @var{expr} is an integer.
-@code{askinteger} prompts the user if it cannot tell otherwise,
-@c UMM, askinteger AND asksign DO NOT APPEAR TO HAVE ANY EFFECT ON THE assume
-@c DATABASE !!!
-and attempt to install the information in the database if possible.
-@code{askinteger (@var{expr})} is equivalent to
-@code{askinteger (@var{expr}, integer)}.
-
-@code{askinteger (@var{expr}, even)} and @code{askinteger (@var{expr}, odd)}
-likewise attempt to determine if @var{expr} is an even integer or odd integer,
-respectively.
-
-@opencatbox
-@category{Declarations and inferences}
-@closecatbox
-@end deffn
-
-@c THERE IS PROBABLY MORE TO THE STORY THAN WHAT IS INDICATED HERE ...
-
@c -----------------------------------------------------------------------------
-@anchor{asksign}
-@deffn {Function} asksign (@var{expr})
+@deffn {Function} combine (@var{expr})
-First attempts to determine whether the specified
-expression is positive, negative, or zero. If it cannot, it asks the
-user the necessary questions to complete its deduction. The user's
-answer is recorded in the data base for the duration of the current
-computation. The return value of @code{asksign} is one of @code{pos},
-@code{neg}, or @code{zero}.
+Simplifies the sum @var{expr} by combining terms with the same
+denominator into a single term.
+@c NEED EXAMPLE HERE
@opencatbox
-@category{Declarations and inferences}
+@category{Expressions}
@closecatbox
@end deffn
@@ -112,8 +59,8 @@ computation. The return value of @code{asksign} is one of @code{pos},
@anchor{commutative}
@defvr {Declaration} commutative
-If @code{declare(h,commutative)} is done, this tells the simplifier that
-@code{h} is a commutative function. E.g. @code{h(x,z,y)} will simplify to
+If @code{declare(h, commutative)} is done, this tells the simplifier that
+@code{h} is a commutative function. E.g. @code{h(x, z, y)} will simplify to
@code{h(x, y, z)}. This is the same as @code{symmetric}.
@opencatbox
@@ -180,7 +127,6 @@ Examples:
@closecatbox
@end deffn
-
@c -----------------------------------------------------------------------------
@anchor{distribute_over}
@defvr {Option variable} distribute_over
@@ -280,6 +226,33 @@ When @code{domain} is set to @code{complex}, @code{sqrt (x^2)} will remain
@end defvr
@c -----------------------------------------------------------------------------
+@anchor{evenfun}
+@anchor{oddfun}
+@defvr {Declaration} evenfun
+@defvrx {Declaration} oddfun
+
+@code{declare(f, evenfun} or @code{declare(f, oddfun} tells Maxima to recognize
+the function @code{f} as an odd or even function.
+
+Examples:
+
+@example
+(%i1) o (- x) + o (x);
+(%o1) o(x) + o(- x)
+(%i2) declare (o, oddfun);
+(%o2) done
+(%i3) o (- x) + o (x);
+(%o3) 0
+(%i4) e (- x) - e (x);
+(%o4) e(- x) - e(x)
+(%i5) declare (e, evenfun);
+(%o5) done
+(%i6) e (- x) - e (x);
+(%o6) 0
+@end example
+@end defvr
+
+@c -----------------------------------------------------------------------------
@anchor{expand}
@deffn {Function} expand (@var{expr})
@deffnx {Function} expand (@var{expr}, @var{p}, @var{n})
@@ -410,7 +383,7 @@ Expands expression @code{expr} with respect to the
variables @var{x_1}, @dots{}, @var{x_n}.
All products involving the variables appear explicitly. The form returned
will be free of products of sums of expressions that are not free of
-the variables. @var{x_1}, @dots{}, @var{x_n}
+the variables. @var{x_1}, @dots{}, @var{x_n}
may be variables, operators, or expressions.
By default, denominators are not expanded, but this can be controlled by
@@ -519,28 +492,6 @@ less than n.
@c NEEDS CLARIFICATION, EXAMPLES
@c -----------------------------------------------------------------------------
-@anchor{intosum}
-@deffn {Function} intosum (@var{expr})
-
-Moves multiplicative factors outside a summation to inside.
-If the index is used in the
-outside expression, then the function tries to find a reasonable
-index, the same as it does for @code{sumcontract}. This is essentially the
-reverse idea of the @code{outative} property of summations, but note that it
-does not remove this property, it only bypasses it.
-
-@c WHAT ARE THESE CASES ??
-In some cases, a @code{scanmap (multthru, @var{expr})} may be necessary before
-the @code{intosum}.
-
-@opencatbox
-@category{Expressions}
-@closecatbox
-@end deffn
-
-@c NEEDS CLARIFICATION, EXAMPLES
-
-@c -----------------------------------------------------------------------------
@anchor{lassociative}
@defvr {Declaration} lassociative
@@ -579,36 +530,6 @@ See also @code{opproperties}.
@c NEEDS EXAMPLES
@c -----------------------------------------------------------------------------
-@anchor{maxapplydepth}
-@defvr {Option variable} maxapplydepth
-Default value: 10000
-
-@code{maxapplydepth} is the maximum depth to which @code{apply1}
-and @code{apply2} will delve.
-
-@opencatbox
-@category{Function application}
-@closecatbox
-@end defvr
-
-@c NEEDS EXAMPLES
-
-@c -----------------------------------------------------------------------------
-@anchor{maxapplyheight}
-@defvr {Option variable} maxapplyheight
-Default value: 10000
-
-@code{maxapplyheight} is the maximum height to which @code{applyb1}
-will reach before giving up.
-
-@opencatbox
-@category{Function application}
-@closecatbox
-@end defvr
-
-@c NEEDS EXAMPLES
-
-@c -----------------------------------------------------------------------------
@anchor{maxnegex}
@defvr {Option variable} maxnegex
Default value: 1000
@@ -642,7 +563,7 @@ expanded with the @code{expand} command (see also @code{maxnegex}).
@anchor{multiplicative}
@defvr {Declaration} multiplicative
-@code{declare (f, multiplicative)} tells the Maxima simplifier that @code{f}
+@code{declare(f, multiplicative)} tells the Maxima simplifier that @code{f}
is multiplicative.
@enumerate
@@ -720,6 +641,31 @@ noncommutative) over sums. Since quotients are represented as products
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
+@anchor{declaration_nary}
+@defvr {Declaration} nary
+
+@code{declare(f, nary)} tells Maxima to recognize the function @code{f} as an
+n-ary function.
+
+The @code{nary} declaration is not the same as calling the
+@mxref{operator_nary, nary} function. The sole effect of
+@code{declare(f, nary)} is to instruct the Maxima simplifier to flatten nested
+expressions, for example, to simplify @code{foo(x, foo(y, z))} to
+@code{foo(x, y, z)}. See also @mrefdot{declare}
+
+Example:
+
+@example
+(%i1) H (H (a, b), H (c, H (d, e)));
+(%o1) H(H(a, b), H(c, H(d, e)))
+(%i2) declare (H, nary);
+(%o2) done
+(%i3) H (H (a, b), H (c, H (d, e)));
+(%o3) H(a, b, c, d, e)
+@end example
+@end defvr
+
@c NEEDS CLARIFICATION, EXAMPLES
@c -----------------------------------------------------------------------------
@@ -760,7 +706,7 @@ by the Maxima simplifier:
@anchor{outative}
@defvr {Declaration} outative
-@code{declare (f, outative)} tells the Maxima simplifier that constant factors
+@code{declare(f, outative)} tells the Maxima simplifier that constant factors
in the argument of @code{f} can be pulled out.
@enumerate
@@ -783,20 +729,6 @@ simplify to @code{a * f(g(x), x)} for @code{a} free of @code{x}.
@closecatbox
@end defvr
-@c NEEDS EXAMPLES
-
-@c -----------------------------------------------------------------------------
-@anchor{posfun}
-@defvr {Declaration} posfun
-
-@code{declare (f, posfun)} declares @code{f} to be a positive function.
-@code{is (f(x) > 0)} yields @code{true}.
-
-@opencatbox
-@category{Declarations and inferences} @category{Operators}
-@closecatbox
-@end defvr
-
@c -----------------------------------------------------------------------------
@anchor{radcan}
@deffn {Function} radcan (@var{expr})
@@ -889,19 +821,6 @@ Note that @code{domain} only matters when @code{radexpand} is @code{true}.
@closecatbox
@end defvr
-@c -----------------------------------------------------------------------------
-@anchor{radsubstflag}
-@defvr {Option variable} radsubstflag
-Default value: @code{false}
-
-@code{radsubstflag}, if @code{true}, permits @code{ratsubst} to make
-substitutions such as @code{u} for @code{sqrt (x)} in @code{x}.
-
-@opencatbox
-@category{Simplification flags and variables}
-@closecatbox
-@end defvr
-
@c NEEDS CLARIFICATION, EXAMPLES
@c -----------------------------------------------------------------------------
@@ -997,86 +916,6 @@ assignment has occurred during the evaluation phase of the expression.
@c NEEDS CLARIFICATION, EXAMPLES
@c -----------------------------------------------------------------------------
-@anchor{simpsum}
-@defvr {Option variable} simpsum
-Default value: @code{false}
-
-When @code{simpsum} is @code{true}, the result of a @code{sum} is simplified.
-This simplification may sometimes be able to produce a closed form. If
-@code{simpsum} is @code{false} or if the quoted form @code{'sum} is used, the
-value is a sum noun form which is a representation of the sigma notation used
-in mathematics.
-
-@opencatbox
-@category{Sums and products} @category{Simplification flags and variables}
-@closecatbox
-@end defvr
-
-@c NEEDS CLARIFICATION, EXAMPLES
-
-@c -----------------------------------------------------------------------------
-@anchor{sumcontract}
-@deffn {Function} sumcontract (@var{expr})
-
-Combines all sums of an addition that have
-upper and lower bounds that differ by constants. The result is an
-expression containing one summation for each set of such summations
-added to all appropriate extra terms that had to be extracted to form
-this sum. @code{sumcontract} combines all compatible sums and uses one of
-the indices from one of the sums if it can, and then try to form a
-reasonable index if it cannot use any supplied.
-
-@c WHEN IS intosum NECESSARY BEFORE sumcontract ??
-It may be necessary to do an @code{intosum (@var{expr})} before the
-@code{sumcontract}.
-
-@opencatbox
-@category{Sums and products}
-@closecatbox
-@end deffn
-
-@c -----------------------------------------------------------------------------
-@anchor{sumexpand}
-@defvr {Option variable} sumexpand
-Default value: @code{false}
-
-When @code{sumexpand} is @code{true}, products of sums and
-exponentiated sums simplify to nested sums.
-
-See also @code{cauchysum}.
-
-Examples:
-
-@example
-(%i1) sumexpand: true$
-(%i2) sum (f (i), i, 0, m) * sum (g (j), j, 0, n);
-@group
- m n
- ==== ====
- \ \
-(%o2) > > f(i1) g(i2)
- / /
- ==== ====
- i1 = 0 i2 = 0
-@end group
-(%i3) sum (f (i), i, 0, m)^2;
- m m
- ==== ====
- \ \
-(%o3) > > f(i3) f(i4)
- / /
- ==== ====
- i3 = 0 i4 = 0
-@end example
-
-@opencatbox
-@category{Sums and products} @category{Simplification flags and variables}
-@closecatbox
-@end defvr
-
-@c NEEDS CLARIFICATION, EXAMPLES
-
-@c -----------------------------------------------------------------------------
@anchor{symmetric}
@defvr {Declaration} symmetric
@@ -1092,18 +931,6 @@ simplifies to @code{h (x, y, z)}.
@end defvr
@c -----------------------------------------------------------------------------
-@anchor{unknown}
-@deffn {Function} unknown (@var{expr})
-
-Returns @code{true} if and only if @var{expr} contains an operator or function
-not recognized by the Maxima simplifier.
-
-@opencatbox
-@category{Predicate functions} @category{Simplification functions}
-@closecatbox
-@end deffn
-
-@c -----------------------------------------------------------------------------
@anchor{xthru}
@deffn {Function} xthru (@var{expr})
commit ef4baa37da180ba3506f6e35a1a4a89990882695
Author: crategus <cra...@us...>
Date: Mon Jun 13 20:13:52 2011 +0200
Reformating the file and adding nodes for cross references.
diff --git a/doc/info/Trigonometric.texi b/doc/info/Trigonometric.texi
index 8d1f862..3ef84be 100644
--- a/doc/info/Trigonometric.texi
+++ b/doc/info/Trigonometric.texi
@@ -3,8 +3,10 @@
* Functions and Variables for Trigonometric::
@end menu
+@c -----------------------------------------------------------------------------
@node Introduction to Trigonometric, Functions and Variables for Trigonometric, Trigonometric, Trigonometric
@section Introduction to Trigonometric
+@c -----------------------------------------------------------------------------
Maxima has many trigonometric functions defined. Not all trigonometric
identities are programmed, but it is possible for the user to add many
@@ -26,9 +28,13 @@ for details.
@category{Trigonometric functions}
@closecatbox
+@c -----------------------------------------------------------------------------
@node Functions and Variables for Trigonometric, , Introduction to Trigonometric, Trigonometric
@section Functions and Variables for Trigonometric
+@c -----------------------------------------------------------------------------
+@c -----------------------------------------------------------------------------
+@anchor{%piargs}
@defvr {Option variable} %piargs
Default value: @code{true}
@@ -48,7 +54,8 @@ Maxima knows some identities which can be applied when @math{\pi}, etc.,
@ifnottex
Maxima knows some identities which can be applied when @math{%pi}, etc.,
@end ifnottex
-are multiplied by an integer variable (that is, a symbol declared to be integer).
+are multiplied by an integer variable (that is, a symbol declared to be
+integer).
Examples:
@@ -99,10 +106,12 @@ Examples:
@end example
@iftex
-Some identities are applied when @math{\pi} and @math{\pi/2} are multiplied by an integer variable.
+Some identities are applied when @math{\pi} and @math{\pi/2} are multiplied by
+an integer variable.
@end iftex
@ifnottex
-Some identities are applied when @math{%pi} and @math{%pi/2} are multiplied by an integer variable.
+Some identities are applied when @math{%pi} and @math{%pi/2} are multiplied by
+an integer variable.
@end ifnottex
@c ===beg===
@@ -123,9 +132,10 @@ Some identities are applied when @math{%pi} and @math{%pi/2} are multiplied by a
@opencatbox
@category{Trigonometric functions} @category{Simplification flags and variables}
@closecatbox
-
@end defvr
+@c -----------------------------------------------------------------------------
+@anchor{%iargs}
@defvr {Option variable} %iargs
Default value: @code{true}
@@ -189,10 +199,11 @@ Even when the argument is demonstrably real, the simplification is applied.
@opencatbox
@category{Trigonometric functions} @category{Hyperbolic functions} @category{Simplification flags and variables}
@closecatbox
-
@end defvr
+@c -----------------------------------------------------------------------------
@deffn {Function} acos (@var{x})
+
-- Arc Cosine.
@opencatbox
@@ -200,7 +211,9 @@ Even when the argument is demonstrably real, the simplification is applied.
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@deffn {Function} acosh (@var{x})
+
-- Hyperbolic Arc Cosine.
@opencatbox
@@ -208,7 +221,9 @@ Even when the argument is demonstrably real, the simplification is applied.
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@deffn {Function} acot (@var{x})
+
-- Arc Cotangent.
@opencatbox
@@ -216,7 +231,9 @@ Even when the argument is demonstrably real, the simplification is applied.
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@deffn {Function} acoth (@var{x})
+
-- Hyperbolic Arc Cotangent.
@opencatbox
@@ -224,7 +241,9 @@ Even when the argument is demonstrably real, the simplification is applied.
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@deffn {Function} acsc (@var{x})
+
-- Arc Cosecant.
@opencatbox
@@ -232,7 +251,9 @@ Even when the argument is demonstrably real, the simplification is applied.
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@deffn {Function} acsch (@var{x})
+
-- Hyperbolic Arc Cosecant.
@opencatbox
@@ -240,7 +261,9 @@ Even when the argument is demonstrably real, the simplification is applied.
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@deffn {Function} asec (@var{x})
+
-- Arc Secant.
@opencatbox
@@ -248,7 +271,9 @@ Even when the argument is demonstrably real, the simplification is applied.
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@deffn {Function} asech (@var{x})
+
-- Hyperbolic Arc Secant.
@opencatbox
@@ -256,7 +281,9 @@ Even when the argument is demonstrably real, the simplification is applied.
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@deffn {Function} asin (@var{x})
+
-- Arc Sine.
@opencatbox
@@ -264,7 +291,9 @@ Even when the argument is demonstrably real, the simplification is applied.
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@deffn {Function} asinh (@var{x})
+
-- Hyperbolic Arc Sine.
@opencatbox
@@ -272,7 +301,9 @@ Even when the argument is demonstrably real, the simplification is applied.
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@deffn {Function} atan (@var{x})
+
-- Arc Tangent.
@opencatbox
@@ -280,16 +311,20 @@ Even when the argument is demonstrably real, the simplification is applied.
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@deffn {Function} atan2 (@var{y}, @var{x})
--- yields the value of @code{atan(@var{y}/@var{x})} in the interval @code{-%pi} to
-@code{%pi}.
+
+-- yields the value of @code{atan(@var{y}/@var{x})} in the interval @code{-%pi}
+to @code{%pi}.
@opencatbox
@category{Trigonometric functions}
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@deffn {Function} atanh (@var{x})
+
-- Hyperbolic Arc Tangent.
@opencatbox
@@ -299,7 +334,10 @@ Even when the argument is demonstrably real, the simplification is applied.
@c IS THIS DESCRIPTION ACCURATE ??
@c LET'S BE EXPLICIT ABOUT EXACTLY WHAT ARE THE RULES IMPLEMENTED BY THIS PACKAGE
+
+@c -----------------------------------------------------------------------------
@defvr {Package} atrig1
+
The @code{atrig1} package contains several additional simplification rules
for inverse trigonometric functions. Together with rules
already known to Maxima, the following angles are fully implemented:
@@ -312,7 +350,9 @@ Do @code{load(atrig1);} to use them.
@closecatbox
@end defvr
+@c -----------------------------------------------------------------------------
@deffn {Function} cos (@var{x})
+
-- Cosine.
@opencatbox
@@ -320,7 +360,9 @@ Do @code{load(atrig1);} to use them.
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@deffn {Function} cosh (@var{x})
+
-- Hyperbolic Cosine.
@opencatbox
@@ -328,7 +370,9 @@ Do @code{load(atrig1);} to use them.
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@deffn {Function} cot (@var{x})
+
-- Cotangent.
@opencatbox
@@ -336,7 +380,9 @@ Do @code{load(atrig1);} to use them.
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@deffn {Function} coth (@var{x})
+
-- Hyperbolic Cotangent.
@opencatbox
@@ -344,7 +390,9 @@ Do @code{load(atrig1);} to use them.
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@deffn {Function} csc (@var{x})
+
-- Cosecant.
@opencatbox
@@ -352,7 +400,9 @@ Do @code{load(atrig1);} to use them.
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@deffn {Function} csch (@var{x})
+
-- Hyperbolic Cosecant.
@opencatbox
@@ -361,6 +411,7 @@ Do @code{load(atrig1);} to use them.
@end deffn
@c -----------------------------------------------------------------------------
+@anchor{halfangles}
@defvr {Option variable} halfangles
Default value: @code{false}
@@ -392,7 +443,7 @@ arguments @var{z}:
@end verbatim
Maxima knows this factor and similar factors for the functions @code{sin},
-@code{cos}, @code{sinh}, and @code{cosh}. For special values of the argument
+@code{cos}, @code{sinh}, and @code{cosh}. For special values of the argument
@math{z} these factors simplify accordingly.
Examples:
@@ -435,7 +486,10 @@ Examples:
@c IS THIS DESCRIPTION ACCURATE ??
@c LET'S BE EXPLICIT ABOUT EXACTLY WHAT ARE THE RULES IMPLEMENTED BY THIS PACKAGE
+
+@c -----------------------------------------------------------------------------
@defvr {Package} ntrig
+
The @code{ntrig} package contains a set of simplification rules that are
used to simplify trigonometric function whose arguments are of the form
@code{@var{f}(@var{n} %pi/10)} where @var{f} is any of the functions
@@ -447,7 +501,9 @@ used to simplify trigonometric function whose arguments are of the form
@closecatbox
@end defvr
+@c -----------------------------------------------------------------------------
@deffn {Function} sec (@var{x})
+
-- Secant.
@opencatbox
@@ -455,7 +511,9 @@ used to simplify trigonometric function whose arguments are of the form
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@deffn {Function} sech (@var{x})
+
-- Hyperbolic Secant.
@opencatbox
@@ -463,7 +521,9 @@ used to simplify trigonometric function whose arguments are of the form
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@deffn {Function} sin (@var{x})
+
-- Sine.
@opencatbox
@@ -471,7 +531,9 @@ used to simplify trigonometric function whose arguments are of the form
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@deffn {Function} sinh (@var{x})
+
-- Hyperbolic Sine.
@opencatbox
@@ -479,7 +541,9 @@ used to simplify trigonometric function whose arguments are of the form
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@deffn {Function} tan (@var{x})
+
-- Tangent.
@opencatbox
@@ -487,7 +551,9 @@ used to simplify trigonometric function whose arguments are of the form
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
@deffn {Function} tanh (@var{x})
+
-- Hyperbolic Tangent.
@opencatbox
@@ -496,7 +562,11 @@ used to simplify trigonometric function whose arguments are of the form
@end deffn
@c NEEDS CLARIFICATION AND EXAMPLES
+
+@c -----------------------------------------------------------------------------
+@anchor{trigexpand}
@deffn {Function} trigexpand (@var{expr})
+
Expands trigonometric and hyperbolic functions of
sums of angles and of multiple angles occurring in @var{expr}. For best
results, @var{expr} should be expanded. To enhance user control of
@@ -546,6 +616,8 @@ Examples:
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
+@anchor{trigexpandplus}
@defvr {Option variable} trigexpandplus
Default value: @code{true}
@@ -558,23 +630,25 @@ Default value: @code{true}
@opencatbox
@category{Trigonometric functions} @category{Simplification flags and variables}
@closecatbox
-
@end defvr
+@c -----------------------------------------------------------------------------
+@anchor{trigexpandtimes}
@defvr {Option variable} trigexpandtimes
Default value: @code{true}
-@code{trigexpandtimes} controls the "product" rule for
-@code{trigexpand}. Thus, when the @code{trigexpand} command is used or the
-@code{trigexpand} switch set to @code{true}, expansion of products (e.g. @code{sin(2*x)})
+@code{trigexpandtimes} controls the "product" rule for @code{trigexpand}.
+Thus, when the @code{trigexpand} command is used or the @code{trigexpand}
+switch set to @code{true}, expansion of products (e.g. @code{sin(2*x)})
will take place only if @code{trigexpandtimes} is @code{true}.
@opencatbox
@category{Trigonometric functions} @category{Simplification flags and variables}
@closecatbox
-
@end defvr
+@c -----------------------------------------------------------------------------
+@anchor{triginverses}
@defvr {Option variable} triginverses
Default value: @code{true}
@@ -596,11 +670,13 @@ simplifications are turned off.
@opencatbox
@category{Trigonometric functions} @category{Simplification flags and variables}
@closecatbox
-
@end defvr
-@deffn {Function} trigreduce (@var{expr}, @var{x})
+@c -----------------------------------------------------------------------------
+@anchor{trigreduce}
+@deffn {Function} trigreduce (@var{expr}, @var{x})
@deffnx {Function} trigreduce (@var{expr})
+
Combines products and powers of trigonometric
and hyperbolic sin's and cos's of @var{x} into those of multiples of @var{x}.
It also tries to eliminate these functions when they occur in
@@ -620,16 +696,16 @@ See also @code{poissimp}.
@end group
@end example
-@c
+@c
@c OBSOLETE
@c The behavior was changed in order to avoid calling expand in the core
@c simplifier (trigi.lisp rev 1.31)
@c See http://www.math.utexas.edu/pipermail/maxima/2008/010919.html.
-@c
+@c
@c The trigonometric simplification routines will use declared
@c information in some simple cases. Declarations about variables are
@c used as follows, e.g.
-@c
+@c
@c ---beg---
@c declare(j, integer, e, even, o, odd)$
@c sin(x + (e + 1/2)*%pi);
@@ -648,20 +724,24 @@ See also @code{poissimp}.
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
+@anchor{trigsign}
@defvr {Option variable} trigsign
Default value: @code{true}
When @code{trigsign} is @code{true}, it permits simplification of negative
-arguments to trigonometric functions. E.g., @code{sin(-x)} will become
+arguments to trigonometric functions. E.g., @code{sin(-x)} will become
@code{-sin(x)} only if @code{trigsign} is @code{true}.
@opencatbox
@category{Trigonometric functions} @category{Simplification flags and variables}
@closecatbox
-
@end defvr
+@c -----------------------------------------------------------------------------
+@anchor{trigsimp}
@deffn {Function} trigsimp (@var{expr})
+
@iftex
Employs the identities
@tex
@@ -676,8 +756,8 @@ etc., to @code{sin}, @code{cos}, @code{sinh}, @code{cosh}.
@end iftex
@ifnottex
Employs the identities @math{sin(x)^2 + cos(x)^2 = 1} and
-@math{cosh(x)^2 - sinh(x)^2 = 1} to simplify expressions containing @code{tan}, @code{sec},
-etc., to @code{sin}, @code{cos}, @code{sinh}, @code{cosh}.
+@math{cosh(x)^2 - sinh(x)^2 = 1} to simplify expressions containing @code{tan},
+@code{sec}, etc., to @code{sin}, @code{cos}, @code{sinh}, @code{cosh}.
@end ifnottex
@code{trigreduce}, @code{ratsimp}, and @code{radcan} may be
@@ -692,13 +772,18 @@ able to further simplify the result.
@end deffn
@c NEEDS CLARIFICATION
+
+@c -----------------------------------------------------------------------------
+@anchor{trigrat}
@deffn {Function} trigrat (@var{expr})
-Gives a canonical simplifyed quasilinear form of a
-trigonometrical expression; @var{expr} is a rational fraction of several @code{sin},
-@code{cos} or @code{tan}, the arguments of them are linear forms in some variables (or
-kernels) and @code{%pi/@var{n}} (@var{n} integer) with integer coefficients. The result is a
-simplified fraction with numerator and denominator linear in @code{sin} and @code{cos}.
-Thus @code{trigrat} linearize always when it is possible.
+
+Gives a canonical simplifyed quasilinear form of a trigonometrical expression;
+@var{expr} is a rational fraction of several @code{sin}, @code{cos} or
+@code{tan}, the arguments of them are linear forms in some variables (or
+kernels) and @code{%pi/@var{n}} (@var{n} integer) with integer coefficients.
+The result is a simplified fraction with numerator and denominator linear in
+@code{sin} and @code{cos}. Thus @code{trigrat} linearize always when it is
+possible.
@c ===beg===
@c trigrat(sin(3*a)/sin(a+%pi/3));
@@ -779,3 +864,4 @@ Addison-Wesley), section 1.5.5, Morley theorem.
@category{Trigonometric functions} @category{Simplification functions}
@closecatbox
@end deffn
+
commit d76100f8371031a1ba67143c9730a5945b53fadf
Author: crategus <cra...@us...>
Date: Mon Jun 13 20:13:05 2011 +0200
Adding documentation from the file Simplification.texi:
askexp
askinteger
asksign
posfun
unknown
diff --git a/doc/info/Database.texi b/doc/info/Database.texi
index 1751ea1..d56ef66 100644
--- a/doc/info/Database.texi
+++ b/doc/info/Database.texi
@@ -541,6 +541,20 @@ Example:
@closecatbox
@end deffn
+@c NEEDS EXAMPLES
+
+@c -----------------------------------------------------------------------------
+@anchor{posfun}
+@defvr {Declaration} posfun
+
+@code{declare (f, posfun)} declares @code{f} to be a positive function.
+@code{is (f(x) > 0)} yields @code{true}.
+
+@opencatbox
+@category{Declarations and inferences} @category{Operators}
+@closecatbox
+@end defvr
+
@c NEEDS WORK ESPECIALLY EXAMPLES
@c WHOLE BUSINESS WITH PROPERTIES IS PRETTY CONFUSING, TRY TO CLEAR IT UP
@@ -567,6 +581,71 @@ cannot otherwise be displayed, i.e. for @mrefcomma{atvalue}@w{}
@section Functions and Variables for Facts
@c -----------------------------------------------------------------------------
+@c After studying src/compar.lisp, it appears that askexp would
+@c work as advertised, except that it doesn't appear to be possible
+@c to open a break prompt with ^A or any other character.
+@c What should we do about askexp ???
+
+@c -----------------------------------------------------------------------------
+@anchor{askexp}
+@defvr {System variable} askexp
+
+When @code{asksign} is called,
+@code{askexp} is the expression @code{asksign} is testing.
+
+At one time, it was possible for a user to inspect @code{askexp}
+by entering a Maxima break with control-A.
+
+@opencatbox
+@category{Declarations and inferences}
+@closecatbox
+@end defvr
+
+@c THERE IS PROBABLY MORE TO THE STORY THAN WHAT IS INDICATED HERE ...
+
+@c -----------------------------------------------------------------------------
+@anchor{askinteger}
+@deffn {Function} askinteger (@var{expr}, integer)
+@deffnx {Function} askinteger (@var{expr})
+@deffnx {Function} askinteger (@var{expr}, even)
+@deffnx {Function} askinteger (@var{expr}, odd)
+
+@code{askinteger (@var{expr}, integer)} attempts to determine from the
+@code{assume} database whether @var{expr} is an integer.
+@code{askinteger} prompts the user if it cannot tell otherwise,
+@c UMM, askinteger AND asksign DO NOT APPEAR TO HAVE ANY EFFECT ON THE assume
+@c DATABASE !!!
+and attempt to install the information in the database if possible.
+@code{askinteger (@var{expr})} is equivalent to
+@code{askinteger (@var{expr}, integer)}.
+
+@code{askinteger (@var{expr}, even)} and @code{askinteger (@var{expr}, odd)}
+likewise attempt to determine if @var{expr} is an even integer or odd integer,
+respectively.
+
+@opencatbox
+@category{Declarations and inferences}
+@closecatbox
+@end deffn
+
+@c THERE IS PROBABLY MORE TO THE STORY THAN WHAT IS INDICATED HERE ...
+
+@c -----------------------------------------------------------------------------
+@anchor{asksign}
+@deffn {Function} asksign (@var{expr})
+
+First attempts to determine whether the specified
+expression is positive, negative, or zero. If it cannot, it asks the
+user the necessary questions to complete its deduction. The user's
+answer is recorded in the data base for the duration of the current
+computation. The return value of @code{asksign} is one of @code{pos},
+@code{neg}, or @code{zero}.
+
+@opencatbox
+@category{Declarations and inferences}
+@closecatbox
+@end deffn
+
@c -----------------------------------------------------------------------------
@anchor{is}
@deffn {Function} is (@var{expr})
@@ -1065,6 +1144,18 @@ Examples:
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
+@anchor{unknown}
+@deffn {Function} unknown (@var{expr})
+
+Returns @code{true} if and only if @var{expr} contains an operator or function
+not recognized by the Maxima simplifier.
+
+@opencatbox
+@category{Predicate functions} @category{Simplification functions}
+@closecatbox
+@end deffn
+
@c THIS FUNCTION APPEARS TO BE A HACK; SEE 4'TH ITEM BELOW
@c DUNNO WHETHER WE CAN CLEAR THIS UP
commit e99e2f579add71bf1b5f695aea773891a3210e43
Author: crategus <cra...@us...>
Date: Mon Jun 13 20:11:05 2011 +0200
Adding cross references for the html-documentation.
diff --git a/doc/info/Evaluation.texi b/doc/info/Evaluation.texi
index c9d5713..846d28f 100644
--- a/doc/info/Evaluation.texi
+++ b/doc/info/Evaluation.texi
@@ -34,10 +34,10 @@ means return the noun form of @code{f} applied to @code{[x]}.
The single quote does not prevent simplification.
-When the global flag @code{noundisp} is @code{true}, nouns display with a single
+When the global flag @mref{noundisp} is @code{true}, nouns display with a single
quote. This switch is always @code{true} when displaying function definitions.
-See also the quote-quote operator @code{''} and @code{nouns}.
+See also the quote-quote operator @mxref{quote-quote, ''} and @mrefdot{nouns}
Examples:
@@ -175,9 +175,9 @@ evaluation when evaluation is otherwise suppressed, such as in function
definitions, lambda expressions, and expressions quoted by single quote
@code{'}.
-Quote-quote is recognized by @code{batch} and @code{load}.
+Quote-quote is recognized by @mref{batch} and @mrefdot{load}
-See also the single-quote operator @code{'} and @code{nouns}.
+See also the single-quote operator @mxref{quote, '} and @mrefdot{nouns}
Examples:
@@ -367,52 +367,52 @@ be any or all of the following.
@itemize @bullet
@item
-@code{simp} causes @var{expr} to be simplified regardless of the setting of the
+@mref{simp} causes @var{expr} to be simplified regardless of the setting of the
switch @code{simp} which inhibits simplification if @code{false}.
@item
-@code{noeval} supresses the evaluation phase of @code{ev} (see step (4) below).
+@mref{noeval} suppresses the evaluation phase of @code{ev} (see step (4) below).
This is useful in conjunction with the other switches and in causing
@var{expr} to be resimplified without being reevaluated.
@item
-@code{nouns} causes the evaluation of noun forms (typically unevaluated
+@mref{nouns} causes the evaluation of noun forms (typically unevaluated
functions such as @code{'integrate} or @code{'diff}) in @var{expr}.
@item
-@code{expand} causes expansion.
+@mref{expand} causes expansion.
@item
@code{expand (@var{m}, @var{n})} causes expansion, setting the values of
-@code{maxposex} and @code{maxnegex} to @var{m} and @var{n} respectively.
+@mref{maxposex} and @mref{maxnegex} to @var{m} and @var{n} respectively.
@item
-@code{detout} causes any matrix inverses computed in @var{expr} to have their
+@mref{detout} causes any matrix inverses computed in @var{expr} to have their
determinant kept outside of the inverse rather than dividing through
each element.
@item
-@code{diff} causes all differentiations indicated in @var{expr} to be performed.
+@mref{diff} causes all differentiations indicated in @var{expr} to be performed.
@item
@code{derivlist (@var{x}, @var{y}, @var{z}, ...)} causes only differentiations
-with respect to the indicated variables.
+with respect to the indicated variables. See also @mrefdot{derivlist}
@item
@code{risch} causes integrals in @var{expr} to be evaluated using the Risch
-algorithm. See @code{risch}. The standard integration routine is invoked when
-using the special symbol @code{nouns}.
+algorithm. See @mrefdot{risch} The standard integration routine is invoked
+when using the special symbol @mrefdot{nouns}
@item
-@code{float} causes non-integral rational numbers to be converted to floating
+@mref{float} causes non-integral rational numbers to be converted to floating
point.
@item
-@code{numer} causes some mathematical functions (including exponentiation)
+@mref{numer} causes some mathematical functions (including exponentiation)
with numerical arguments to be evaluated in floating point. It causes
variables in @var{expr} which have been given numervals to be replaced by
-their values. It also sets the @code{float} switch on.
+their values. It also sets the @mref{float} switch on.
@item
-@code{pred} causes predicates (expressions which evaluate to @code{true} or
+@mref{pred} causes predicates (expressions which evaluate to @code{true} or
@code{false}) to be evaluated.
@item
-@code{eval} causes an extra post-evaluation of @var{expr} to occur.
+@mref{eval} causes an extra post-evaluation of @var{expr} to occur.
(See step (5) below.)
@code{eval} may occur multiple times. For each instance of @code{eval}, the
expression is evaluated again.
@item
-@code{A} where @code{A} is an atom declared to be an evaluation flag (see
-@code{evflag}) causes @code{A} to be bound to @code{true} during the evaluation
+@code{A} where @code{A} is an atom declared to be an evaluation flag
+@mref{evflag} causes @code{A} to be bound to @code{true} during the evaluation
of @var{expr}.
@item
@code{V: expression} (or alternately @code{V=expression}) causes @code{V} to be
@@ -423,9 +423,9 @@ its value during the evaluation of @var{expr}. If more than one argument to
a non-atomic expression then a substitution rather than a binding is performed.
@item
@code{F} where @code{F}, a function name, has been declared to be an evaluation
-function (see @code{evfun}) causes @code{F} to be applied to @var{expr}.
+function @mref{evfun} causes @code{F} to be applied to @var{expr}.
@item
-Any other function names (e.g., @code{sum}) cause evaluation of occurrences
+Any other function names, e.g. @mrefcomma{sum} cause evaluation of occurrences
of those names in @var{expr} as though they were verbs.
@item
In addition a function occurring in @var{expr} (say @code{F(x)}) may be defined
@@ -439,7 +439,7 @@ If the result is a list then the members of the list are treated as if they were
additional arguments given to @code{ev}. This permits a list of equations to be
given (e.g. @code{[X=1, Y=A**2]}) or a list of names of equations (e.g.,
@code{[%t1, %t2]} where @code{%t1} and @code{%t2} are equations) such as that
-returned by @code{solve}.
+returned by @mrefdot{solve}
@end itemize
The arguments of @code{ev} may be given in any order with the exception of
@@ -447,9 +447,9 @@ substitution equations which are handled in sequence, left to right, and
evaluation functions which are composed, e.g., @code{ev (@var{expr}, ratsimp,
realpart)} is handled as @code{realpart (ratsimp (@var{expr}))}.
-The @code{simp}, @code{numer}, and @code{float} switches may also be set locally
-in a block, or globally in Maxima so that they will remain in effect until being
-reset.
+The @mrefcomma{simp} @mrefcomma{numer} and @mref{float} switches may also be set
+locally in a block, or globally in Maxima so that they will remain in effect
+until being reset.
If @var{expr} is a canonical rational expression (CRE), then the expression
returned by @code{ev} is also a CRE, provided the @code{numer} and @code{float}
@@ -470,12 +470,12 @@ If any substitutions are indicated by the arguments, they are carried out now.
@item
The resulting expression is then re-evaluated (unless one of the arguments was
-@code{noeval}) and simplified according to the arguments. Note that any
+@mref{noeval}) and simplified according to the arguments. Note that any
function calls in @var{expr} will be carried out after the variables in it are
evaluated and that @code{ev(F(x))} thus may behave like @code{F(ev(x))}.
@item
-For each instance of @code{eval} in the arguments, steps (3) and (4) are
+For each instance of @mref{eval} in the arguments, steps (3) and (4) are
repeated.
@end enumerate
@@ -548,7 +548,7 @@ Solution
@defvr {Special symbol} eval
As an argument in a call to @code{ev (@var{expr})}, @code{eval} causes an extra
-evaluation of @var{expr}. See @code{ev}.
+evaluation of @var{expr}. See @mrefdot{ev}
Example:
@@ -774,7 +774,7 @@ Examples:
@anchor{infeval}
@defvr {Option variable} infeval
-Enables "infinite evaluation" mode. @code{ev} repeatedly evaluates an
+Enables "infinite evaluation" mode. @mref{ev} repeatedly evaluates an
expression until it stops changing. To prevent a variable, say @code{X}, from
being evaluated away in this mode, simply include @code{X='X} as an argument to
@code{ev}. Of course expressions such as @code{ev (X, X=X+1, infeval)} will
@@ -792,7 +792,7 @@ generate an infinite loop.
@anchor{noeval}
@defvr {Special symbol} noeval
-@code{noeval} suppresses the evaluation phase of @code{ev}. This is useful in
+@code{noeval} suppresses the evaluation phase of @mrefdot{ev} This is useful in
conjunction with other switches and in causing expressions
to be resimplified without being reevaluated.
@@ -807,10 +807,10 @@ to be resimplified without being reevaluated.
@anchor{nouns}
@defvr {Special symbol} nouns
-@code{nouns} is an @code{evflag}. When used as an option to the @code{ev}
+@code{nouns} is an @mrefdot{evflag} When used as an option to the @mref{ev}@w{}
command, @code{nouns} converts all "noun" forms occurring in the expression
-being @code{ev}'d to "verbs", i.e., evaluates them. See also @code{noun},
-@code{nounify}, @code{verb}, and @code{verbify}.
+being @code{ev}'d to "verbs", i.e., evaluates them. See also
+@mrefcomma{noun} @mrefcomma{nounify} @code{verb}, and @mrefdot{verbify}
@opencatbox
@category{Evaluation flags} @category{Nouns and verbs}
@@ -823,7 +823,7 @@ being @code{ev}'d to "verbs", i.e., evaluates them. See also @code{noun},
As an argument in a call to @code{ev (@var{expr})}, @code{pred} causes
predicates (expressions which evaluate to @code{true} or @code{false}) to be
-evaluated. See @code{ev}.
+evaluated. See @mrefdot{ev}
Example:
commit 1b651d7f3124c5fab0359c92a2f1bc315a7255fb
Author: crategus <cra...@us...>
Date: Mon Jun 13 20:10:23 2011 +0200
Reformating and adding nodes for cross references of the files:
Logarithms.texi
Matrices.texi
diff --git a/doc/info/Logarithms.texi b/doc/info/Logarithms.texi
index eac302e..04a3676 100644
--- a/doc/info/Logarithms.texi
+++ b/doc/info/Logarithms.texi
@@ -1,27 +1,32 @@
-
@menu
* Functions and Variables for Logarithms::
@end menu
+@c -----------------------------------------------------------------------------
@node Functions and Variables for Logarithms, , Logarithms, Logarithms
@section Functions and Variables for Logarithms
+@c -----------------------------------------------------------------------------
+@c -----------------------------------------------------------------------------
+@anchor{%e_to_numlog}
@defvr {Option variable} %e_to_numlog
Default value: @code{false}
-When @code{true}, @code{r} some rational number, and
-@code{x} some expression, @code{%e^(r*log(x))} will be simplified into @code{x^r} . It
-should be noted that the @code{radcan} command also does this transformation,
-and more complicated transformations of this ilk as well.
-The @code{logcontract} command "contracts" expressions containing @code{log}.
+When @code{true}, @code{r} some rational number, and @code{x} some expression,
+@code{%e^(r*log(x))} will be simplified into @code{x^r} . It should be noted
+that the @code{radcan} command also does this transformation, and more
+complicated transformations of this ilk as well. The @code{logcontract}
+command "contracts" expressions containing @code{log}.
@opencatbox
@category{Exponential and logarithm functions} @category{Simplification flags and variables}
@closecatbox
-
@end defvr
+@c -----------------------------------------------------------------------------
+@anchor{li}
@deffn {Function} li [@var{s}] (@var{z})
+
Represents the polylogarithm function of order @var{s} and argument @var{z},
defined by the infinite series
@@ -40,12 +45,12 @@ $${\rm Li}_s \left(z\right) = \sum_{k=1}^\infty {z^k \over k^s}$$
@end example
@end ifnottex
-@code{li [1]} is @code{- log (1 - z)}.
-@code{li [2]} and @code{li [3]} are the dilogarithm and trilogarithm functions, respectively.
+@code{li [1]} is @code{- log (1 - z)}. @code{li [2]} and @code{li [3]} are the
+dilogarithm and trilogarithm functions, respectively.
-When the order is 1, the polylogarithm simplifies to @code{- log (1 - z)},
-which in turn simplifies to a numerical value
-if @var{z} is a real or complex floating point number or the @code{numer} evaluation flag is present.
+When the order is 1, the polylogarithm simplifies to @code{- log (1 - z)}, which
+in turn simplifies to a numerical value if @var{z} is a real or complex floating
+point number or the @code{numer} evaluation flag is present.
When the order is 2 or 3,
the polylogarithm simplifies to a numerical value
@@ -107,7 +112,9 @@ Examples:
@end deffn
@c -----------------------------------------------------------------------------
+@anchor{log}
@deffn {Function} log (@var{x})
+
Represents the natural (base @math{e}) logarithm of @var{x}.
Maxima does not have a built-in function for the base 10 logarithm or other
@@ -151,24 +158,28 @@ command "contracts" expressions containing @code{log}.
@closecatbox
@end deffn
+@c -----------------------------------------------------------------------------
+@anchor{logabs}
@defvr {Option variable} logabs
Default value: @code{false}
-When doing indefinite integration where
-logs are generated, e.g. @code{integrate(1/x,x)}, the answer is given in
-terms of @code{log(abs(...))} if @code{logabs} is @code{true}, but in terms of @code{log(...)} if
-@code{logabs} is @code{false}. For definite integration, the @code{logabs:true} setting is
-used, because here "evaluation" of the indefinite integral at the
+When doing indefinite integration where logs are generated, e.g.
+@code{integrate(1/x,x)}, the answer is given in terms of @code{log(abs(...))}
+if @code{logabs} is @code{true}, but in terms of @code{log(...)} if
+@code{logabs} is @code{false}. For definite integration, the @code{logabs:true}
+setting is used, because here "evaluation" of the indefinite integral at the
endpoints is often needed.
@opencatbox
@category{Exponential and logarithm functions} @category{Integral calculus} @category{Global flags}
@closecatbox
-
@end defvr
@c NEEDS EXAMPLES
-@defvr {Option variable} logarc
+
+@c -----------------------------------------------------------------------------
+@anchor{logarc}
+@defvr {Option variable} logarc
@defvrx {Function} logarc (@var{expr})
When the global variable @code{logarc} is @code{true},
@@ -183,9 +194,10 @@ without setting the global variable @code{logarc}.
@opencatbox
@category{Exponential and logarithm functions} @category{Simplification flags and variables} @category{Simplification functions}
@closecatbox
-
@end defvr
+@c -----------------------------------------------------------------------------
+@anchor{logconcoeffp}
@defvr {Option variable} logconcoeffp
Default value: @code{false}
@@ -199,10 +211,12 @@ logconfun(m):=featurep(m,integer) or ratnump(m)$} . Then
@opencatbox
@category{Exponential and logarithm functions} @category{Simplification flags and variables}
@closecatbox
-
@end defvr
+@c -----------------------------------------------------------------------------
+@anchor{logcontract}
@deffn {Function} logcontract (@var{expr})
+
Recursively scans the expression @var{expr}, transforming
subexpressions of the form @code{a1*log(b1) + a2*log(b2) + c} into
@code{log(ratsimp(b1^a1 * b2^a2)) + c}
@@ -234,13 +248,14 @@ logconfun(m):=featurep(m,integer) or ratnump(m)$} . Then
@end deffn
@c -----------------------------------------------------------------------------
+@anchor{logexpand}
@defvr {Option variable} logexpand
Default value: @code{false}
If @code{true} causes @code{log(a^b)} to become @code{b*log(a)}. If it is set
to @code{all}, @code{log(a*b)} will also simplify to @code{log(a)+log(b)}. If
it is set to @code{super}, then @code{log(a/b)} will also simplify to
-@code{log(a)-log(b)} for rational numbers @code{a/b}, @code{a#1}.
+@code{log(a)-log(b)} for rational numbers @code{a/b}, @code{a#1}.
(@code{log(1/b)}, for integer @code{b}, always simplifies.) If it is set to
@code{false}, that is the default value, all of these simplifications will be
turned off.
@@ -250,6 +265,8 @@ turned off.
@closecatbox
@end defvr
+@c -----------------------------------------------------------------------------
+@anchor{lognegint}
@defvr {Option variable} lognegint
Default value: @code{false}
@@ -259,23 +276,25 @@ If @code{true} implements the rule
@opencatbox
@category{Exponential and logarithm functions} @category{Simplification flags and variables}
@closecatbox
-
@end defvr
+@c -----------------------------------------------------------------------------
+@anchor{lognumer}
@defvr {Option variable} lognumer
Default value: @code{false}
-If @code{true} then negative floating point
-arguments to @code{log} will always be converted to their absolute value
-before the @code{log} is taken. If @code{numer} is also @code{true}, then negative integer
-arguments to @code{log} will also be converted to their absolute value.
+If @code{true} then negative floating point arguments to @code{log} will always
+be converted to their absolute value before the @code{log} is taken. If
+@code{numer} is also @code{true}, then negative integer arguments to @code{log}
+will also be converted to their absolute value.
@opencatbox
@category{Exponential and logarithm functions} @category{Simplification flags and variables} @category{Numerical evaluation}
@closecatbox
-
@end defvr
+@c -----------------------------------------------------------------------------
+@anchor{logsimp}
@defvr {Option variable} logsimp
Default value: @code{true}
@@ -285,10 +304,12 @@ power containing @code{log}'s is done.
@opencatbox
@category{Exponential and logarithm functions} @category{Simplification flags and variables}
@closecatbox
-
@end defvr
+@c -----------------------------------------------------------------------------
+@anchor{plog}
@deffn {Function} plog (@var{x})
+
Represents the principal branch of the complex-valued natural
logarithm with @code{-%pi} < @code{carg(@var{x})} <= @code{+%pi} .
diff --git a/doc/info/Matrices.texi b/doc/info/Matrices.texi
index 924e2ce..8ebd3fd 100644
--- a/doc/info/Matrices.texi
+++ b/doc/info/Matrices.texi
@@ -3,8 +3,10 @@
* Functions and Variables for Matrices and Linear Algebra::
@end menu
+@c -----------------------------------------------------------------------------
@node Introduction to Matrices and Linear Algebra, Functions and Variables for Matrices and Linear Algebra, Matrices and Linear Algebra, Matrices and Linear Algebra
@section Introduction to Matrices and Linear Algebra
+@c -----------------------------------------------------------------------------
@menu
* Dot::
@@ -12,15 +14,20 @@
* eigen::
@end menu
+@c -----------------------------------------------------------------------------
@node Dot, Vectors, Introduction to Matrices and Linear Algebra, Introduction to Matrices and Linear Algebra
@subsection Dot
-The operator @code{.} represents noncommutative multiplication and scalar product.
-When the operands are 1-column or 1-row matrices @code{a} and @code{b},
-the expression @code{a.b} is equivalent to @code{sum (a[i]*b[i], i, 1, length(a))}.
-If @code{a} and @code{b} are not complex, this is the scalar product,
-also called the inner product or dot product, of @code{a} and @code{b}.
-The scalar product is defined as @code{conjugate(a).b} when @code{a} and @code{b} are complex;
-@code{innerproduct} in the @code{eigen} package provides the complex scalar product.
+@c -----------------------------------------------------------------------------
+
+The operator @code{.} represents noncommutative multiplication and scalar
+product. When the operands are 1-column or 1-row matrices @code{a} and
+@code{b}, the expression @code{a.b} is equivalent to
+@code{sum (a[i]*b[i], i, 1, length(a))}. If @code{a} and @code{b} are not
+complex, this is the scalar product, also called the inner product or dot
+product, of @code{a} and @code{b}. The scalar product is defined as
+@code{conjugate(a).b} when @code{a} and @code{b} are complex;
+@code{innerproduct} in the @code{eigen} package provides the complex scalar
+product.
When the operands are more general matrices,
the product is the matrix product @code{a} and @code{b}.
@@ -28,21 +35,24 @@ The number of rows of @code{b} must equal the number of columns of @code{a},
and the result has number of rows equal to the number of rows of @code{a}
and number of columns equal to the number of columns of @code{b}.
-To distinguish @code{.} as an arithmetic operator from
-the decimal point in a floating point number,
-it may be necessary to leave spaces on either side.
-For example, @code{5.e3} is @code{5000.0} but @code{5 . e3} is @code{5} times @code{e3}.
+To distinguish @code{.} as an arithmetic operator from the decimal point in a
+floating point number, it may be necessary to leave spaces on either side.
+For example, @code{5.e3} is @code{5000.0} but @code{5 . e3} is @code{5}
+times @code{e3}.
There are several flags which govern the simplification of
expressions involving @code{.}, namely
-@code{dot}, @code{dot0nscsimp}, @code{dot0simp}, @code{dot1simp}, @code{dotassoc},
-@code{dotconstrules}, @code{dotdistrib}, @code{dotexptsimp}, @code{dotident},
-and @code{dotscrules}.
+@code{dot}, @code{dot0nscsimp}, @code{dot0simp}, @code{dot1simp},
+@code{dotassoc}, @code{dotconstrules}, @code{dotdistrib}, @code{dotexptsimp},
+@code{dotident}, and @code{dotscrules}.
+@c -----------------------------------------------------------------------------
@node Vectors, eigen, Dot, Introduction to Matrices and Linear Algebra
@subsection Vectors
-@code{vect} is a package of functions for vector analysis.
-@code{load ("vect")} loads this package, and @code{demo ("vect")} displays a demonstration.
+@c -----------------------------------------------------------------------------
+
+@code{vect} is a package of functions for vector analysis. @code{load ("vect")}
+loads this package, and @code{demo ("vect")} displays a demonstration.
@c find maxima -name \*orth\* YIELDS NOTHING; ARE THESE FUNCTIONS IN ANOTHER FILE NOW ??
@c and SHARE;VECT ORTH contains definitions of various orthogonal curvilinear coordinate systems.
@@ -69,9 +79,10 @@ commutative operator. To get a commutative dot operator @code{.}, the command
@category{Vectors} @category{Share packages} @category{Package vect}
@closecatbox
-
+@c -----------------------------------------------------------------------------
@node eigen, , Vectors, Introduction to Matrices and Linear Algebra
@subsection eigen
+@c -----------------------------------------------------------------------------
The package @code{eigen} contains several functions devoted to the
symbolic computation of eigenvalues and eigenvectors.
@@ -84,22 +95,25 @@ of this package.
@code{batch ("eigen")} executes the same demonstration,
but without the user prompt between successive computations.
-The functions in the @code{eigen} package are
-@flushleft
+The functions in the @code{eigen} package are:@*
@code{innerproduct}, @code{unitvector}, @code{columnvector}, @code{gramschmidt}, @code{eigenvalues},
@code{eigenvectors}, @code{uniteigenvectors}, and @code{similaritytransform}.
-@end flushleft
@opencatbox
@category{Vectors} @category{Matrices} @category{Share packages} @category{Package eigen}
@closecatbox
-
@c end concepts Matrices and Linear Algebra
+
+@c -----------------------------------------------------------------------------
@node Functions and Variables for Matrices and Linear Algebra, , Introduction to Matrices and Linear Algebra, Matrices and Linear Algebra
@section Functions and Variables for Matrices and Linear Algebra
+@c -----------------------------------------------------------------------------
+
+@c -----------------------------------------------------------------------------
+@anchor{addcol}
+@deffn {Function} add...
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