@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
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
projects / emacs.git / commitdiff