This file documents Calc, the GNU Emacs calculator.
@end ifinfo
@ifnotinfo
-This file documents Calc, the GNU Emacs calculator, included with GNU Emacs 23.1.
+This file documents Calc, the GNU Emacs calculator, included with GNU Emacs 23.3.
@end ifnotinfo
Copyright @copyright{} 1990, 1991, 2001, 2002, 2003, 2004,
-2005, 2006, 2007, 2008, 2009 Free Software Foundation, Inc.
+2005, 2006, 2007, 2008, 2009, 2010, 2011 Free Software Foundation, Inc.
@quotation
Permission is granted to copy, distribute and/or modify this document
@end quotation
@end copying
-@dircategory Emacs
+@dircategory Emacs misc features
@direntry
-* Calc: (calc). Advanced desk calculator and mathematical tool.
+* Calc: (calc). Advanced desk calculator and mathematical tool.
@end direntry
@titlepage
@page
@vskip 0pt plus 1filll
-Copyright @copyright{} 1990, 1991, 2001, 2002, 2003, 2004,
- 2005, 2006, 2007, 2008, 2009 Free Software Foundation, Inc.
@insertcopying
@end titlepage
longer Info tutorial.)
@end ifinfo
+@insertcopying
+
@menu
* Getting Started:: General description and overview.
@ifinfo
regularly.
This manual is divided into three major parts:@: the ``Getting
-Started'' chapter you are reading now, the Calc tutorial (chapter 2),
-and the Calc reference manual (the remaining chapters and appendices).
+Started'' chapter you are reading now, the Calc tutorial, and the Calc
+reference manual.
@c [when-split]
@c This manual has been printed in two volumes, the @dfn{Tutorial} and the
@c @dfn{Reference}. Both volumes include a copy of the ``Getting Started''
@end group
@end smallexample
-(Note that by default division had lower precedence than multiplication
-in Calc, so that @samp{1 / ln(x) x} is equivalent to @samp{1 / (ln(x) x)}.)
+(Note that by default, Calc gives division lower precedence than multiplication,
+so that @samp{1 / ln(x) x} is equivalent to @samp{1 / (ln(x) x)}.)
To make this look nicer, you might want to press @kbd{d =} to center
the formula, and even @kbd{d B} to use Big display mode.
non-RPN calculators work. In Algebraic mode, you enter formulas
in traditional @expr{2+3} notation.
-@strong{Warning:} Note that @samp{/} has lower precedence than
-@samp{*}, so that @samp{a/b*c} is interpreted as @samp{a/(b*c)}. See
-below for details.
+@strong{Notice:} Calc gives @samp{/} lower precedence than @samp{*}, so
+that @samp{a/b*c} is interpreted as @samp{a/(b*c)}; this is not
+standard across all computer languages. See below for details.
You don't really need any special ``mode'' to enter algebraic formulas.
You can enter a formula at any time by pressing the apostrophe (@kbd{'})
@smallexample
@group
-1: 1 / cos(x) - sin(x) tan(x)
+1: 2 / cos(x)^2 - 2 tan(x)^2
.
- ' 1/cos(x) - sin(x) tan(x) @key{RET} s 1
+ ' 2/cos(x)^2 - 2tan(x)^2 @key{RET} s 1
@end group
@end smallexample
@noindent
If we were simplifying this by hand, we'd probably replace the
@samp{tan} with a @samp{sin/cos} first, then combine over a common
-denominator. There is no Calc command to do the former; the @kbd{a n}
-algebra command will do the latter but we'll do both with rewrite
+denominator. The @kbd{I a s} command will do the former and the @kbd{a n}
+algebra command will do the latter, but we'll do both with rewrite
rules just for practice.
Rewrite rules are written with the @samp{:=} symbol.
@smallexample
@group
-1: 1 / cos(x) - sin(x)^2 / cos(x)
+1: 2 / cos(x)^2 - 2 sin(x)^2 / cos(x)^2
.
a r tan(a) := sin(a)/cos(a) @key{RET}
@smallexample
@group
-1: (1 - sin(x)^2) / cos(x)
+1: (2 - 2 sin(x)^2) / cos(x)^2
.
a r a/x + b/x := (a+b)/x @key{RET}
Second, meta-variable names are independent from variables in the
target formula. Notice that the meta-variable @samp{x} here matches
-the subformula @samp{cos(x)}; Calc never confuses the two meanings of
+the subformula @samp{cos(x)^2}; Calc never confuses the two meanings of
@samp{x}.
And third, rewrite patterns know a little bit about the algebraic
properties of formulas. The pattern called for a sum of two quotients;
Calc was able to match a difference of two quotients by matching
-@samp{a = 1}, @samp{b = -sin(x)^2}, and @samp{x = cos(x)}.
+@samp{a = 2}, @samp{b = -2 sin(x)^2}, and @samp{x = cos(x)^2}.
@c [fix-ref Algebraic Properties of Rewrite Rules]
We could just as easily have written @samp{a/x - b/x := (a-b)/x} for
One more rewrite will complete the job. We want to use the identity
@samp{sin(x)^2 + cos(x)^2 = 1}, but of course we must first rearrange
the identity in a way that matches our formula. The obvious rule
-would be @samp{@w{1 - sin(x)^2} := cos(x)^2}, but a little thought shows
+would be @samp{@w{2 - 2 sin(x)^2} := 2 cos(x)^2}, but a little thought shows
that the rule @samp{sin(x)^2 := 1 - cos(x)^2} will also work. The
latter rule has a more general pattern so it will work in many other
situations, too.
@smallexample
@group
-1: (1 + cos(x)^2 - 1) / cos(x) 1: cos(x)
- . .
+1: (2 + 2 cos(x)^2 - 2) / cos(x)^2 1: 2
+ . .
a r sin(x)^2 := 1 - cos(x)^2 @key{RET} a s
@end group
' a/x + b/x := (a+b)/x @key{RET} s t merge @key{RET}
' sin(x)^2 := 1 - cos(x)^2 @key{RET} s t sinsqr @key{RET}
-1: 1 / cos(x) - sin(x) tan(x) 1: cos(x)
+1: 2 / cos(x)^2 - 2 tan(x)^2 1: 2
. .
r 1 a r tsc @key{RET} a r merge @key{RET} a r sinsqr @key{RET} a s
@samp{exp(inf) = inf}. It's tempting to say that the exponential
of infinity must be ``bigger'' than ``regular'' infinity, but as
-far as Calc is concerned all infinities are as just as big.
+far as Calc is concerned all infinities are the same size.
In other words, as @expr{x} goes to infinity, @expr{e^x} also goes
to infinity, but the fact the @expr{e^x} grows much faster than
@expr{x} is not relevant here.
@noindent
@cindex Help commands
@kindex ?
+@kindex a ?
+@kindex b ?
+@kindex c ?
+@kindex d ?
+@kindex f ?
+@kindex g ?
+@kindex j ?
+@kindex k ?
+@kindex m ?
+@kindex r ?
+@kindex s ?
+@kindex t ?
+@kindex u ?
+@kindex v ?
+@kindex V ?
+@kindex z ?
+@kindex Z ?
@pindex calc-help
The @kbd{?} key (@code{calc-help}) displays a series of brief help messages.
Some keys (such as @kbd{b} and @kbd{d}) are prefix keys, like Emacs'
queried whether or not to restore the variable to its original value.
The @kbd{U} key may be pressed any number of times to undo successively
farther back in time; with a numeric prefix argument it undoes a
-specified number of operations. The undo history is cleared only by the
-@kbd{q} (@code{calc-quit}) command. (Recall that @kbd{C-x * c} is
-synonymous with @code{calc-quit} while inside the Calculator; this
-also clears the undo history.)
+specified number of operations. When the Calculator is quit, as with
+the @kbd{q} (@code{calc-quit}) command, the undo history will be
+truncated to the length of the customizable variable
+@code{calc-undo-length} (@pxref{Customizing Calc}), which by default
+is @expr{100}. (Recall that @kbd{C-x * c} is synonymous with
+@code{calc-quit} while inside the Calculator; this also truncates the
+undo history.)
Currently the mode-setting commands (like @code{calc-precision}) are not
undoable. You can undo past a point where you changed a mode, but you
@cindex Julian day counting
Another day counting system in common use is, confusingly, also called
-``Julian.'' The Julian day number is the numbers of days since
-12:00 noon (GMT) on Jan 1, 4713 BC, which in Calc's scheme (in GMT)
+``Julian.'' The Julian day number is the numbers of days since
+12:00 noon (GMT) on Jan 1, 4713 BC, which in Calc's scheme (in GMT)
is @mathit{-1721423.5} (recall that Calc starts at midnight instead
of noon). Thus to convert a Calc date code obtained by unpacking a
date form into a Julian day number, simply add 1721423.5 after
compensating for the time zone difference. The built-in @kbd{t J}
command performs this conversion for you.
-The Julian day number is based on the Julian cycle, which was invented
+The Julian day number is based on the Julian cycle, which was invented
in 1583 by Joseph Justus Scaliger. Scaliger named it the Julian cycle
-since it is involves the Julian calendar, but some have suggested that
+since it involves the Julian calendar, but some have suggested that
Scaliger named it in honor of his father, Julius Caesar Scaliger. The
-Julian cycle is based it on three other cycles: the indiction cycle,
-the Metonic cycle, and the solar cycle. The indiction cycle is a 15
-year cycle originally used by the Romans for tax purposes but later
-used to date medieval documents. The Metonic cycle is a 19 year
-cycle; 19 years is close to being a common multiple of a solar year
-and a lunar month, and so every 19 years the phases of the moon will
-occur on the same days of the year. The solar cycle is a 28 year
-cycle; the Julian calendar repeats itself every 28 years. The
-smallest time period which contains multiples of all three cycles is
-the least common multiple of 15 years, 19 years and 28 years, which
-(since they're pairwise relatively prime) is
+Julian cycle is based on three other cycles: the indiction cycle, the
+Metonic cycle, and the solar cycle. The indiction cycle is a 15 year
+cycle originally used by the Romans for tax purposes but later used to
+date medieval documents. The Metonic cycle is a 19 year cycle; 19
+years is close to being a common multiple of a solar year and a lunar
+month, and so every 19 years the phases of the moon will occur on the
+same days of the year. The solar cycle is a 28 year cycle; the Julian
+calendar repeats itself every 28 years. The smallest time period
+which contains multiples of all three cycles is the least common
+multiple of 15 years, 19 years and 28 years, which (since they're
+pairwise relatively prime) is
@texline @math{15\times 19\times 28 = 7980} years.
@infoline 15*19*28 = 7980 years.
This is the length of a Julian cycle. Working backwards, the previous
With a negative argument @mathit{-@var{n}}, @key{TAB} rotates the stack
to move the object in level @var{n} to the deepest place in the
stack, and the object in level @mathit{@var{n}+1} to the top. @kbd{M-@key{TAB}}
-rotates the deepest stack element to be in level @mathit{n}, also
+rotates the deepest stack element to be in level @var{n}, also
putting the top stack element in level @mathit{@var{n}+1}.
@xref{Selecting Subformulas}, for a way to apply these commands to
any portion of a vector or formula on the stack.
+@kindex C-xC-t
+@pindex calc-transpose-lines
+@cindex Moving stack entries
+The command @kbd{C-x C-t} (@code{calc-transpose-lines}) will transpose
+the stack object determined by the point with the stack object at the
+next higher level. For example, with @samp{10 20 30 40 50} on the
+stack and the point on the line containing @samp{30}, @kbd{C-x C-t}
+creates @samp{10 20 40 30 50}. More generally, @kbd{C-x C-t} acts on
+the stack objects determined by the current point (and mark) similar
+to how the text-mode command @code{transpose-lines} acts on
+lines. With argument @var{n}, @kbd{C-x C-t} will move the stack object
+at the level above the current point and move it past N other objects;
+for example, with @samp{10 20 30 40 50} on the stack and the point on
+the line containing @samp{30}, @kbd{C-u 2 C-x C-t} creates
+@samp{10 40 20 30 50}. With an argument of 0, @kbd{C-x C-t} will switch
+the stack objects at the levels determined by the point and the mark.
+
@node Editing Stack Entries, Trail Commands, Stack Manipulation, Stack and Trail
@section Editing Stack Entries
@cindex Saving mode settings
@cindex Permanent mode settings
@cindex Calc init file, mode settings
-You can save all of the current mode settings in your Calc init file
+You can save all of the current mode settings in your Calc init file
(the file given by the variable @code{calc-settings-file}, typically
-@file{~/.calc.el}) with the @kbd{m m} (@code{calc-save-modes}) command.
-This will cause Emacs to reestablish these modes each time it starts up.
-The modes saved in the file include everything controlled by the @kbd{m}
-and @kbd{d} prefix keys, the current precision and binary word size,
-whether or not the trail is displayed, the current height of the Calc
-window, and more. The current interface (used when you type @kbd{C-x * *})
-is also saved. If there were already saved mode settings in the
-file, they are replaced. Otherwise, the new mode information is
-appended to the end of the file.
+@file{~/.emacs.d/calc.el}) with the @kbd{m m} (@code{calc-save-modes})
+command. This will cause Emacs to reestablish these modes each time
+it starts up. The modes saved in the file include everything
+controlled by the @kbd{m} and @kbd{d} prefix keys, the current
+precision and binary word size, whether or not the trail is displayed,
+the current height of the Calc window, and more. The current
+interface (used when you type @kbd{C-x * *}) is also saved. If there
+were already saved mode settings in the file, they are replaced.
+Otherwise, the new mode information is appended to the end of the
+file.
@kindex m R
@pindex calc-mode-record-mode
in the current radix. (Larger integers will still be displayed in their
entirety.)
+@cindex Two's complements
+With the binary, octal and hexadecimal display modes, Calc can
+display @expr{w}-bit integers using two's complement notation. This
+option is selected with the key sequences @kbd{C-u d 2}, @kbd{C-u d 8}
+and @kbd{C-u d 6}, respectively, and a negative word size might be
+appropriate (@pxref{Binary Functions}). In two's complement
+notation, the integers in the (nearly) symmetric interval from
+@texline @math{-2^{w-1}}
+@infoline @expr{-2^(w-1)}
+to
+@texline @math{2^{w-1}-1}
+@infoline @expr{2^(w-1)-1}
+are represented by the integers from @expr{0} to @expr{2^w-1}:
+the integers from @expr{0} to
+@texline @math{2^{w-1}-1}
+@infoline @expr{2^(w-1)-1}
+are represented by themselves and the integers from
+@texline @math{-2^{w-1}}
+@infoline @expr{-2^(w-1)}
+to @expr{-1} are represented by the integers from
+@texline @math{2^{w-1}}
+@infoline @expr{2^(w-1)}
+to @expr{2^w-1} (the integer @expr{k} is represented by @expr{k+2^w}).
+Calc will display a two's complement integer by the radix (either
+@expr{2}, @expr{8} or @expr{16}), two @kbd{#} symbols, and then its
+representation (including any leading zeros necessary to include all
+@expr{w} bits). In a two's complement display mode, numbers that
+are not displayed in two's complement notation (i.e., that aren't
+integers from
+@texline @math{-2^{w-1}}
+@infoline @expr{-2^(w-1)}
+to
+@c (
+@texline @math{2^{w-1}-1})
+@infoline @expr{2^(w-1)-1})
+will be represented using Calc's usual notation (in the appropriate
+radix).
+
@node Grouping Digits, Float Formats, Radix Modes, Display Modes
@subsection Grouping Digits
@mindex v p
@end ignore
@kindex v p (complex)
+@kindex V p (complex)
@pindex calc-pack
The @kbd{v p} (@code{calc-pack}) command can pack the top two numbers on
the stack into a composite object such as a complex number. With
@mindex v u
@end ignore
@kindex v u (complex)
+@kindex V u (complex)
@pindex calc-unpack
The @kbd{v u} (@code{calc-unpack}) command takes the complex number
(or other composite object) on the top of the stack and unpacks it
particular, negative arguments are converted to positive integers modulo
@expr{2^w} by all binary functions.
-If the word size is negative, binary operations produce 2's complement
+If the word size is negative, binary operations produce twos-complement
integers from
@texline @math{-2^{-w-1}}
@infoline @expr{-(2^(-w-1))}
vectors.
@kindex v p
+@kindex V p
@pindex calc-pack
The @kbd{v p} (@code{calc-pack}) [@code{pack}] command collects several
elements from the stack into a matrix, complex number, HMS form, error
by the mode.
@kindex v u
+@kindex V u
@pindex calc-unpack
The @kbd{v u} (@code{calc-unpack}) command takes the vector, complex
number, HMS form, or other composite object on the top of the stack and
to @kbd{@key{TAB} |}, but possibly more convenient and also a bit faster.
@kindex v d
+@kindex V d
@pindex calc-diag
@tindex diag
The @kbd{v d} (@code{calc-diag}) [@code{diag}] function builds a diagonal
alternative would be to use @kbd{v b} and @kbd{v a}; see below.)
@kindex v i
+@kindex V i
@pindex calc-ident
@tindex idn
The @kbd{v i} (@code{calc-ident}) [@code{idn}] function builds an identity
dimensions.
@kindex v x
+@kindex V x
@pindex calc-index
@tindex index
The @kbd{v x} (@code{calc-index}) [@code{index}] function builds a vector
is one for positive @var{n} or two for negative @var{n}.
@kindex v b
+@kindex V b
@pindex calc-build-vector
@tindex cvec
The @kbd{v b} (@code{calc-build-vector}) [@code{cvec}] function builds a
to build a matrix of copies of that row.)
@kindex v h
+@kindex V h
@kindex I v h
+@kindex I V h
@pindex calc-head
@pindex calc-tail
@tindex head
cases, the argument must be a non-empty vector.
@kindex v k
+@kindex V k
@pindex calc-cons
@tindex cons
The @kbd{v k} (@code{calc-cons}) [@code{cons}] function takes a value @var{h}
whereas @code{cons} will insert @var{h} at the front of the vector @var{t}.
@kindex H v h
+@kindex H V h
@tindex rhead
@ignore
@mindex @idots
@end ignore
@kindex H I v h
+@kindex H I V h
@ignore
@mindex @null
@end ignore
@kindex H v k
+@kindex H V k
@ignore
@mindex @null
@end ignore
@noindent
@kindex v r
+@kindex V r
@pindex calc-mrow
@tindex mrow
The @kbd{v r} (@code{calc-mrow}) [@code{mrow}] command extracts one row of
function is called @code{getdiag}.
@kindex v c
+@kindex V c
@pindex calc-mcol
@tindex mcol
@tindex mrcol
of matrix @expr{m}.
@kindex v s
+@kindex V s
@pindex calc-subvector
@tindex subvec
The @kbd{v s} (@code{calc-subvector}) [@code{subvec}] command extracts
has this effect when used as the ending index.
@kindex I v s
+@kindex I V s
@tindex rsubvec
With the Inverse flag, @kbd{I v s} [@code{rsubvec}] removes a subvector
from a vector. The arguments are interpreted the same as for the
@noindent
@kindex v l
+@kindex V l
@pindex calc-vlength
@tindex vlen
The @kbd{v l} (@code{calc-vlength}) [@code{vlen}] command computes the
command.
@kindex H v l
+@kindex H V l
@tindex mdims
With the Hyperbolic flag, @kbd{H v l} [@code{mdims}] computes a vector
of the dimensions of a vector, matrix, or higher-order object. For
matrix.
@kindex v f
+@kindex V f
@pindex calc-vector-find
@tindex find
The @kbd{v f} (@code{calc-vector-find}) [@code{find}] command searches
allows you to select any starting index for the search.
@kindex v a
+@kindex V a
@pindex calc-arrange-vector
@tindex arrange
@cindex Arranging a matrix
@samp{[1, 2, @w{3, 4}]}.
@cindex Sorting data
+@kindex v S
@kindex V S
+@kindex I v S
@kindex I V S
@pindex calc-sort
@tindex sort
@cindex Inverse of permutation
@cindex Index tables
@cindex Rank tables
+@kindex v G
@kindex V G
+@kindex I v G
@kindex I V G
@pindex calc-grade
@tindex grade
phone numbers will remain sorted by name even after the second sort.
@cindex Histograms
+@kindex v H
@kindex V H
@pindex calc-histogram
@ignore
that the counts in the result vector don't add up to the length of the
input vector.)
+@kindex H v H
@kindex H V H
With the Hyperbolic flag, @kbd{H V H} pulls two vectors from the stack.
The second-to-top vector is the list of numbers as before. The top
vector. Without the hyperbolic flag, every element has a weight of one.
@kindex v t
+@kindex V t
@pindex calc-transpose
@tindex trn
The @kbd{v t} (@code{calc-transpose}) [@code{trn}] command computes
a one-column matrix.
@kindex v v
+@kindex V v
@pindex calc-reverse-vector
@tindex rev
The @kbd{v v} (@code{calc-reverse-vector}) [@code{rev}] command reverses
a matrix.)
@kindex v m
+@kindex V m
@pindex calc-mask-vector
@tindex vmask
The @kbd{v m} (@code{calc-mask-vector}) [@code{vmask}] command uses
@xref{Logical Operations}.
@kindex v e
+@kindex V e
@pindex calc-expand-vector
@tindex vexp
The @kbd{v e} (@code{calc-expand-vector}) [@code{vexp}] command
produces @samp{[a, 0, b, 0, 7]}.
@kindex H v e
+@kindex H V e
With the Hyperbolic flag, @kbd{H v e} takes a filler value from the
top of the stack; the mask and target vectors come from the third and
second elements of the stack. This filler is used where the mask is
@code{re}, @code{im}, @code{polar}, @code{rect}, @code{clean},
@code{float}, @code{frac}. @xref{Function Index}.
+@kindex v J
@kindex V J
@pindex calc-conj-transpose
@tindex ctrn
from that point to the origin.
@kindex v n
+@kindex V n
@pindex calc-rnorm
@tindex rnorm
The @kbd{v n} (@code{calc-rnorm}) [@code{rnorm}] command computes the
a matrix, this is the maximum of the row-absolute-value-sums, i.e., of
the sums of the absolute values of the elements along the various rows.
+@kindex v N
@kindex V N
@pindex calc-cnorm
@tindex cnorm
not provided. However, the 2-norm (or Frobenius norm) is provided for
vectors by the @kbd{A} (@code{calc-abs}) command.
+@kindex v C
@kindex V C
@pindex calc-cross
@tindex cross
@samp{/} operator also does a matrix inversion when dividing one
by a matrix.
+@kindex v D
@kindex V D
@pindex calc-mdet
@tindex det
The @kbd{V D} (@code{calc-mdet}) [@code{det}] command computes the
determinant of a square matrix.
+@kindex v L
@kindex V L
@pindex calc-mlud
@tindex lud
algorithm, the second is lower-triangular with ones on the diagonal,
and the third is upper-triangular.
+@kindex v T
@kindex V T
@pindex calc-mtrace
@tindex tr
trace of a square matrix. This is defined as the sum of the diagonal
elements of the matrix.
+@kindex v K
@kindex V K
@pindex calc-kron
@tindex kron
a certain value is a member of a given set. To test if the set @expr{A}
is a subset of the set @expr{B}, use @samp{vdiff(A, B) = []}.
+@kindex v +
@kindex V +
@pindex calc-remove-duplicates
@tindex rdup
other set-based commands apply @kbd{V +} to their inputs before using
them.
+@kindex v V
@kindex V V
@pindex calc-set-union
@tindex vunion
accomplish the same thing by concatenating the sets with @kbd{|},
then using @kbd{V +}.)
+@kindex v ^
@kindex V ^
@pindex calc-set-intersect
@tindex vint
@texline intersection@tie{}(@math{A \cap B}).
@infoline intersection.
+@kindex v -
@kindex V -
@pindex calc-set-difference
@tindex vdiff
your problem is small enough to list in a Calc vector (or simple
enough to express in a few intervals).
+@kindex v X
@kindex V X
@pindex calc-set-xor
@tindex vxor
if it is in one, but @emph{not} both, of the sets. Objects that
occur in both sets ``cancel out.''
+@kindex v ~
@kindex V ~
@pindex calc-set-complement
@tindex vcompl
For example, @samp{vcompl([2, (3 .. 4]])} evaluates to
@samp{[[-inf .. 2), (2 .. 3], (4 .. inf]]}.
+@kindex v F
@kindex V F
@pindex calc-set-floor
@tindex vfloor
the complement with respect to the set of integers you could type
@kbd{V ~ V F} to get @samp{[[-inf .. 1], [3 .. 5], [9 .. inf]]}.
+@kindex v E
@kindex V E
@pindex calc-set-enumerate
@tindex venum
the intervals. This only works for finite sets (i.e., sets which
do not involve @samp{-inf} or @samp{inf}).
+@kindex v :
@kindex V :
@pindex calc-set-span
@tindex vspan
limit will be the largest element. For an empty set, @samp{vspan([])}
returns the empty interval @w{@samp{[0 .. 0)}}.
+@kindex v #
@kindex V #
@pindex calc-set-cardinality
@tindex vcard
The commands in this section allow for more general operations on the
elements of vectors.
+@kindex v A
@kindex V A
@pindex calc-apply
@tindex apply
@subsection Mapping
@noindent
+@kindex v M
@kindex V M
@pindex calc-map
@tindex map
@subsection Reducing
@noindent
+@kindex v R
@kindex V R
@pindex calc-reduce
@tindex reduce
and so on. In general, reducing @code{f} over the vector @samp{[a, b, c, d]}
produces @samp{f(f(f(a, b), c), d)}.
+@kindex I v R
@kindex I V R
@tindex rreduce
The @kbd{I V R} [@code{rreduce}] command is similar to @kbd{V R} except
or @samp{a - b + c - d}. This ``alternating sum'' occurs frequently
in power series expansions.
+@kindex v U
@kindex V U
@tindex accum
The @kbd{V U} (@code{calc-accumulate}) [@code{accum}] command does an
the vector @samp{[a, b, c, d]} produces the vector
@samp{[a, a + b, a + b + c, a + b + c + d]}.
+@kindex I v U
@kindex I V U
@tindex raccum
The @kbd{I V U} [@code{raccum}] command does a right-to-left accumulation.
@subsection Nesting and Fixed Points
@noindent
+@kindex H v R
@kindex H V R
@tindex nest
The @kbd{H V R} [@code{nest}] command applies a function to a given
negative if Calc knows an inverse for the function @samp{f}; for
example, @samp{nest(sin, a, -2)} returns @samp{arcsin(arcsin(a))}.
+@kindex H v U
@kindex H V U
@tindex anest
The @kbd{H V U} [@code{anest}] command is an accumulating version of
@samp{F} is the inverse of @samp{f}, then the result is of the
form @samp{[a, F(a), F(F(a)), F(F(F(a)))]}.
+@kindex H I v R
@kindex H I V R
@tindex fixp
@cindex Fixed points
applied until it reaches a ``fixed point,'' i.e., until the result
no longer changes.
+@kindex H I v U
@kindex H I V U
@tindex afixp
The @kbd{H I V U} [@code{afixp}] command is an accumulating @code{fixp}.
@node Generalized Products, , Nesting and Fixed Points, Reducing and Mapping
@subsection Generalized Products
+@kindex v O
@kindex V O
@pindex calc-outer-product
@tindex outer
the result matrix is obtained by applying the operator to element @var{r}
of the lefthand vector and element @var{c} of the righthand vector.
+@kindex v I
@kindex V I
@pindex calc-inner-product
@tindex inner
influenced by the @kbd{d O} (@code{calc-flat-language}) mode;
@pxref{Normal Language Modes}.
+@kindex v <
@kindex V <
@pindex calc-matrix-left-justify
+@kindex v =
@kindex V =
@pindex calc-matrix-center-justify
+@kindex v >
@kindex V >
@pindex calc-matrix-right-justify
The commands @kbd{v <} (@code{calc-matrix-left-justify}), @kbd{v >}
(@code{calc-matrix-center-justify}) control whether matrix elements
are justified to the left, right, or center of their columns.
+@kindex v [
@kindex V [
@pindex calc-vector-brackets
+@kindex v @{
@kindex V @{
@pindex calc-vector-braces
+@kindex v (
@kindex V (
@pindex calc-vector-parens
The @kbd{v [} (@code{calc-vector-brackets}) command turns the square
and parentheses may never be used for this purpose.
@kindex V ]
+@kindex v ]
+@kindex V )
+@kindex v )
+@kindex V @}
+@kindex v @}
@pindex calc-matrix-brackets
The @kbd{v ]} (@code{calc-matrix-brackets}) command controls the
-``big'' style display of matrices. It prompts for a string of code
-letters; currently implemented letters are @code{R}, which enables
-brackets on each row of the matrix; @code{O}, which enables outer
-brackets in opposite corners of the matrix; and @code{C}, which
-enables commas or semicolons at the ends of all rows but the last.
-The default format is @samp{RO}. (Before Calc 2.00, the format
-was fixed at @samp{ROC}.) Here are some example matrices:
+``big'' style display of matrices, for matrices which have more than
+one row. It prompts for a string of code letters; currently
+implemented letters are @code{R}, which enables brackets on each row
+of the matrix; @code{O}, which enables outer brackets in opposite
+corners of the matrix; and @code{C}, which enables commas or
+semicolons at the ends of all rows but the last. The default format
+is @samp{RO}. (Before Calc 2.00, the format was fixed at @samp{ROC}.)
+Here are some example matrices:
@example
@group
@samp{OC} are all recognized as matrices during reading, while
the others are useful for display only.
+@kindex v ,
@kindex V ,
@pindex calc-vector-commas
The @kbd{v ,} (@code{calc-vector-commas}) command turns commas on and
ambiguity) by adding the letter @code{P} to the control string you
give to @kbd{v ]} (as described above).
+@kindex v .
@kindex V .
@pindex calc-full-vectors
The @kbd{v .} (@code{calc-full-vectors}) command turns abbreviated
large vectors, this mode will improve the speed of all operations
that involve the trail.
+@kindex v /
@kindex V /
@pindex calc-break-vectors
The @kbd{v /} (@code{calc-break-vectors}) command turns multi-line
selected quotient or equation by that formula. It simplifies each
side with @kbd{a s} (@code{calc-simplify}) before re-forming the
quotient or equation. You can suppress this simplification by
-providing any numeric prefix argument. There is also a @kbd{j /}
+providing a prefix argument: @kbd{C-u j *}. There is also a @kbd{j /}
(@code{calc-sel-div-both-sides}) which is similar to @kbd{j *} but
dividing instead of multiplying by the factor you enter.
-As a special feature, if the numerator of the quotient is 1, then
-the denominator is expanded at the top level using the distributive
-law (i.e., using the @kbd{C-u -1 a x} command). Suppose the
-formula on the stack is @samp{1 / (sqrt(a) + 1)}, and you wish
-to eliminate the square root in the denominator by multiplying both
-sides by @samp{sqrt(a) - 1}. Calc's default simplifications would
-change the result @samp{(sqrt(a) - 1) / (sqrt(a) - 1) (sqrt(a) + 1)}
-right back to the original form by cancellation; Calc expands the
-denominator to @samp{sqrt(a) (sqrt(a) - 1) + sqrt(a) - 1} to prevent
-this. (You would now want to use an @kbd{a x} command to expand
-the rest of the way, whereupon the denominator would cancel out to
-the desired form, @samp{a - 1}.) When the numerator is not 1, this
-initial expansion is not necessary because Calc's default
-simplifications will not notice the potential cancellation.
+If the selection is a quotient with numerator 1, then Calc's default
+simplifications would normally cancel the new factors. To prevent
+this, when the @kbd{j *} command is used on a selection whose numerator is
+1 or -1, the denominator is expanded at the top level using the
+distributive law (as if using the @kbd{C-u 1 a x} command). Suppose the
+formula on the stack is @samp{1 / (a + 1)} and you wish to multiplying the
+top and bottom by @samp{a - 1}. Calc's default simplifications would
+normally change the result @samp{(a - 1) /(a + 1) (a - 1)} back
+to the original form by cancellation; when @kbd{j *} is used, Calc
+expands the denominator to @samp{a (a - 1) + a - 1} to prevent this.
+
+If you wish the @kbd{j *} command to completely expand the denominator
+of a quotient you can call it with a zero prefix: @kbd{C-u 0 j *}. For
+example, if the formula on the stack is @samp{1 / (sqrt(a) + 1)}, you may
+wish to eliminate the square root in the denominator by multiplying
+the top and bottom by @samp{sqrt(a) - 1}. If you did this simply by using
+a simple @kbd{j *} command, you would get
+@samp{(sqrt(a)-1)/ (sqrt(a) (sqrt(a) - 1) + sqrt(a) - 1)}. Instead,
+you would probably want to use @kbd{C-u 0 j *}, which would expand the
+bottom and give you the desired result @samp{(sqrt(a)-1)/(a-1)}. More
+generally, if @kbd{j *} is called with an argument of a positive
+integer @var{n}, then the denominator of the expression will be
+expanded @var{n} times (as if with the @kbd{C-u @var{n} a x} command).
If the selection is an inequality, @kbd{j *} and @kbd{j /} will
accept any factor, but will warn unless they can prove the factor
@noindent
@kindex a s
+@kindex I a s
+@kindex H a s
@pindex calc-simplify
@tindex simplify
The @kbd{a s} (@code{calc-simplify}) [@code{simplify}] command applies
simplification occurs automatically. Normally only the ``default
simplifications'' occur.
+There are some simplifications that, while sometimes useful, are never
+done automatically. For example, the @kbd{I} prefix can be given to
+@kbd{a s}; the @kbd{I a s} command will change any trigonometric
+function to the appropriate combination of @samp{sin}s and @samp{cos}s
+before simplifying. This can be useful in simplifying even mildly
+complicated trigonometric expressions. For example, while @kbd{a s}
+can reduce @samp{sin(x) csc(x)} to @samp{1}, it will not simplify
+@samp{sin(x)^2 csc(x)}. The command @kbd{I a s} can be used to
+simplify this latter expression; it will transform @samp{sin(x)^2
+csc(x)} into @samp{sin(x)}. However, @kbd{I a s} will also perform
+some ``simplifications'' which may not be desired; for example, it
+will transform @samp{tan(x)^2} into @samp{sin(x)^2 / cos(x)^2}. The
+Hyperbolic prefix @kbd{H} can be used similarly; the @kbd{H a s} will
+replace any hyperbolic functions in the formula with the appropriate
+combinations of @samp{sinh}s and @samp{cosh}s before simplifying.
+
+
@menu
* Default Simplifications::
* Algebraic Simplifications::
@vindex calc-gnuplot-name
If you have GNUPLOT installed on your system but Calc is unable to
-find it, you may need to set the @code{calc-gnuplot-name} variable
-in your Calc init file or @file{.emacs}. You may also need to set some Lisp
-variables to show Calc how to run GNUPLOT on your system; these
-are described under @kbd{g D} and @kbd{g O} below. If you are
-using the X window system, Calc will configure GNUPLOT for you
-automatically. If you have GNUPLOT 3.0 or later and you are not using X,
-Calc will configure GNUPLOT to display graphs using simple character
-graphics that will work on any terminal.
+find it, you may need to set the @code{calc-gnuplot-name} variable in
+your Calc init file or @file{.emacs}. You may also need to set some
+Lisp variables to show Calc how to run GNUPLOT on your system; these
+are described under @kbd{g D} and @kbd{g O} below. If you are using
+the X window system or MS-Windows, Calc will configure GNUPLOT for you
+automatically. If you have GNUPLOT 3.0 or later and you are using a
+Unix or GNU system without X, Calc will configure GNUPLOT to display
+graphs using simple character graphics that will work on any
+Posix-compatible terminal.
@menu
* Basic Graphics::
blank line this command shows you the current default. The special
name @code{default} signifies that Calc should choose @code{x11} if
the X window system is in use (as indicated by the presence of a
-@code{DISPLAY} environment variable), or otherwise @code{dumb} under
-GNUPLOT 3.0 and later, or @code{postscript} under GNUPLOT 2.0.
-This is the initial default value.
+@code{DISPLAY} environment variable), @code{windows} on MS-Windows, or
+otherwise @code{dumb} under GNUPLOT 3.0 and later, or
+@code{postscript} under GNUPLOT 2.0. This is the initial default
+value.
The @code{dumb} device is an interface to ``dumb terminals,'' i.e.,
terminals with no special graphics facilities. It writes a crude
@kindex g O
@pindex calc-graph-output
-The @kbd{g O} (@code{calc-graph-output}) command sets the name of
-the output file used by GNUPLOT. For some devices, notably @code{x11},
-there is no output file and this information is not used. Many other
-``devices'' are really file formats like @code{postscript}; in these
-cases the output in the desired format goes into the file you name
-with @kbd{g O}. Type @kbd{g O stdout @key{RET}} to set GNUPLOT to write
-to its standard output stream, i.e., to @samp{*Gnuplot Trail*}.
-This is the default setting.
+The @kbd{g O} (@code{calc-graph-output}) command sets the name of the
+output file used by GNUPLOT. For some devices, notably @code{x11} and
+@code{windows}, there is no output file and this information is not
+used. Many other ``devices'' are really file formats like
+@code{postscript}; in these cases the output in the desired format
+goes into the file you name with @kbd{g O}. Type @kbd{g O stdout
+@key{RET}} to set GNUPLOT to write to its standard output stream,
+i.e., to @samp{*Gnuplot Trail*}. This is the default setting.
Another special output name is @code{tty}, which means that GNUPLOT
is going to write graphics commands directly to its standard output,
The normal value is @code{default}, which generally means your
window manager will let you place the window interactively.
Entering @samp{800x500+0+0} would create an 800-by-500 pixel
-window in the upper-left corner of the screen.
+window in the upper-left corner of the screen. This command has no
+effect if the current device is @code{windows}.
The buffer called @samp{*Gnuplot Trail*} holds a transcript of the
session with GNUPLOT. This shows the commands Calc has ``typed'' to
GNUPLOT and the responses it has received. Calc tries to notice when an
error message has appeared here and display the buffer for you when
this happens. You can check this buffer yourself if you suspect
-something has gone wrong.
+something has gone wrong@footnote{
+On MS-Windows, due to the peculiarities of how the Windows version of
+GNUPLOT (called @command{wgnuplot}) works, the GNUPLOT responses are
+not communicated back to Calc. Instead, you need to look them up in
+the GNUPLOT command window that is displayed as in normal interactive
+usage of GNUPLOT.
+}.
@kindex g C
@pindex calc-graph-command
This happens automatically when Calc thinks there is something you
will want to see in either of these buffers. If you type @kbd{g v}
or @kbd{g V} when the relevant buffer is already displayed, the
-buffer is hidden again.
+buffer is hidden again. (Note that on MS-Windows, the @samp{*Gnuplot
+Trail*} buffer will usually show nothing of interest, because
+GNUPLOT's responses are not communicated back to Calc.)
One reason to use @kbd{g v} is to add your own commands to the
@samp{*Gnuplot Commands*} buffer. Press @kbd{g v}, then use
@smallexample
(let ((calc-command-flags nil))
(unwind-protect
- (save-excursion
+ (save-current-buffer
(calc-select-buffer)
@emph{body of function}
@emph{renumber stack}
of @code{calc-multiplication-has-precedence} is @code{t}.
@end defvar
+@defvar calc-undo-length
+The variable @code{calc-undo-length} determines the number of undo
+steps that Calc will keep track of when @code{calc-quit} is called.
+If @code{calc-undo-length} is a non-negative integer, then this is the
+number of undo steps that will be preserved; if
+@code{calc-undo-length} has any other value, then all undo steps will
+be preserved. The default value of @code{calc-undo-length} is @expr{100}.
+@end defvar
+
@node Reporting Bugs, Summary, Customizing Calc, Top
@appendix Reporting Bugs
so any efforts can be coordinated.
The latest version of Calc is available from Savannah, in the Emacs
-CVS tree. See @uref{http://savannah.gnu.org/projects/emacs}.
+repository. See @uref{http://savannah.gnu.org/projects/emacs}.
@c [summary]
@node Summary, Key Index, Reporting Bugs, Top
HCoop / bpt / emacs.git / blobdiff