(Vector/Matrix Functions): Add index entries for both "v" and "V" key
bindings. Mention that `calc-matrix-brackets' only affects matrices with more than one row.
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2 changed files with 91 additions and 7 deletions
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@ -1,3 +1,9 @@
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2009-07-30 Jay Belanger <jay.p.belanger@gmail.com>
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* calc.texi (Vector/Matrix Functions): Add index entries for both
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"v" and "V" key bindings. Mention that `calc-matrix-brackets' only
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affects matrices with more than one row.
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2009-07-29 Jay Belanger <jay.p.belanger@gmail.com>
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* calc.texi (Stack Manipulation Commands): Add documentation for
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@ -16553,6 +16553,7 @@ or matrix argument, these functions operate element-wise.
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@mindex v p
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@end ignore
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@kindex v p (complex)
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@kindex V p (complex)
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@pindex calc-pack
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The @kbd{v p} (@code{calc-pack}) command can pack the top two numbers on
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the stack into a composite object such as a complex number. With
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@ -16564,6 +16565,7 @@ with an argument of @mathit{-2}, it produces a polar complex number.
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@mindex v u
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@end ignore
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@kindex v u (complex)
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@kindex V u (complex)
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@pindex calc-unpack
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The @kbd{v u} (@code{calc-unpack}) command takes the complex number
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(or other composite object) on the top of the stack and unpacks it
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@ -19365,6 +19367,7 @@ described in this chapter because they are most often used to build
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vectors.
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@kindex v p
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@kindex V p
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@pindex calc-pack
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The @kbd{v p} (@code{calc-pack}) [@code{pack}] command collects several
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elements from the stack into a matrix, complex number, HMS form, error
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@ -19497,6 +19500,7 @@ number of data items does not match the number of items required
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by the mode.
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@kindex v u
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@kindex V u
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@pindex calc-unpack
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The @kbd{v u} (@code{calc-unpack}) command takes the vector, complex
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number, HMS form, or other composite object on the top of the stack and
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@ -19614,6 +19618,7 @@ two stack arguments in the opposite order. Thus @kbd{I |} is equivalent
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to @kbd{@key{TAB} |}, but possibly more convenient and also a bit faster.
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@kindex v d
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@kindex V d
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@pindex calc-diag
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@tindex diag
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The @kbd{v d} (@code{calc-diag}) [@code{diag}] function builds a diagonal
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@ -19632,6 +19637,7 @@ matrix first and then add a constant value to that matrix. (Another
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alternative would be to use @kbd{v b} and @kbd{v a}; see below.)
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@kindex v i
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@kindex V i
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@pindex calc-ident
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@tindex idn
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The @kbd{v i} (@code{calc-ident}) [@code{idn}] function builds an identity
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@ -19652,6 +19658,7 @@ identity matrices are immediately expanded to the current default
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dimensions.
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@kindex v x
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@kindex V x
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@pindex calc-index
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@tindex index
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The @kbd{v x} (@code{calc-index}) [@code{index}] function builds a vector
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@ -19676,6 +19683,7 @@ sequence to be generated. For example, @samp{index(-3, a, b)} produces
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is one for positive @var{n} or two for negative @var{n}.
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@kindex v b
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@kindex V b
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@pindex calc-build-vector
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@tindex cvec
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The @kbd{v b} (@code{calc-build-vector}) [@code{cvec}] function builds a
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@ -19686,7 +19694,9 @@ can also be used to build an @var{n}-by-@var{m} matrix of copies of @var{x}.
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to build a matrix of copies of that row.)
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@kindex v h
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@kindex V h
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@kindex I v h
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@kindex I V h
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@pindex calc-head
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@pindex calc-tail
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@tindex head
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@ -19697,6 +19707,7 @@ function returns the vector with its first element removed. In both
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cases, the argument must be a non-empty vector.
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@kindex v k
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@kindex V k
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@pindex calc-cons
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@tindex cons
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The @kbd{v k} (@code{calc-cons}) [@code{cons}] function takes a value @var{h}
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@ -19706,15 +19717,18 @@ if @var{h} is itself a vector, @kbd{|} will concatenate the two vectors
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whereas @code{cons} will insert @var{h} at the front of the vector @var{t}.
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@kindex H v h
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@kindex H V h
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@tindex rhead
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@ignore
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@mindex @idots
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@end ignore
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@kindex H I v h
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@kindex H I V h
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@ignore
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@mindex @null
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@end ignore
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@kindex H v k
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@kindex H V k
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@ignore
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@mindex @null
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@end ignore
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@ -19736,6 +19750,7 @@ Also, @samp{head([a, b, c, d]) = a}, @samp{tail([a, b, c, d]) = [b, c, d]},
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@noindent
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@kindex v r
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@kindex V r
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@pindex calc-mrow
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@tindex mrow
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The @kbd{v r} (@code{calc-mrow}) [@code{mrow}] command extracts one row of
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@ -19786,6 +19801,7 @@ of a square matrix in the form of a vector. In algebraic form this
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function is called @code{getdiag}.
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@kindex v c
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@kindex V c
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@pindex calc-mcol
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@tindex mcol
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@tindex mrcol
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@ -19803,6 +19819,7 @@ use subscript notation: @samp{m_i_j} gives row @expr{i}, column @expr{j}
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of matrix @expr{m}.
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@kindex v s
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@kindex V s
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@pindex calc-subvector
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@tindex subvec
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The @kbd{v s} (@code{calc-subvector}) [@code{subvec}] command extracts
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@ -19823,6 +19840,7 @@ end of the vector are used. The infinity symbol, @code{inf}, also
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has this effect when used as the ending index.
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@kindex I v s
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@kindex I V s
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@tindex rsubvec
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With the Inverse flag, @kbd{I v s} [@code{rsubvec}] removes a subvector
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from a vector. The arguments are interpreted the same as for the
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@ -19838,6 +19856,7 @@ vectors one element at a time.
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@noindent
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@kindex v l
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@kindex V l
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@pindex calc-vlength
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@tindex vlen
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The @kbd{v l} (@code{calc-vlength}) [@code{vlen}] command computes the
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@ -19846,6 +19865,7 @@ Note that matrices are just vectors of vectors for the purposes of this
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command.
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@kindex H v l
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@kindex H V l
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@tindex mdims
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With the Hyperbolic flag, @kbd{H v l} [@code{mdims}] computes a vector
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of the dimensions of a vector, matrix, or higher-order object. For
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@ -19856,6 +19876,7 @@ its argument is a
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matrix.
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@kindex v f
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@kindex V f
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@pindex calc-vector-find
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@tindex find
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The @kbd{v f} (@code{calc-vector-find}) [@code{find}] command searches
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@ -19866,6 +19887,7 @@ Otherwise, the result is zero. The numeric prefix argument, if given,
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allows you to select any starting index for the search.
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@kindex v a
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@kindex V a
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@pindex calc-arrange-vector
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@tindex arrange
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@cindex Arranging a matrix
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@ -19896,7 +19918,9 @@ matrix), and @kbd{v a 0} produces the flattened list
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@samp{[1, 2, @w{3, 4}]}.
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@cindex Sorting data
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@kindex v S
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@kindex V S
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@kindex I v S
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@kindex I V S
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@pindex calc-sort
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@tindex sort
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@ -19919,7 +19943,9 @@ The @kbd{I V S} [@code{rsort}] command sorts a vector into decreasing order.
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@cindex Inverse of permutation
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@cindex Index tables
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@cindex Rank tables
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@kindex v G
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@kindex V G
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@kindex I v G
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@kindex I V G
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@pindex calc-grade
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@tindex grade
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@ -19951,6 +19977,7 @@ by phone numbers. Because the sort is stable, any two rows with equal
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phone numbers will remain sorted by name even after the second sort.
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@cindex Histograms
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@kindex v H
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@kindex V H
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@pindex calc-histogram
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@ignore
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@ -19968,6 +19995,7 @@ range are ignored. (You can tell if elements have been ignored by noting
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that the counts in the result vector don't add up to the length of the
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input vector.)
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@kindex H v H
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@kindex H V H
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With the Hyperbolic flag, @kbd{H V H} pulls two vectors from the stack.
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The second-to-top vector is the list of numbers as before. The top
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@ -19977,6 +20005,7 @@ the first weight is 10, then 10 will be added to bin 4 of the result
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vector. Without the hyperbolic flag, every element has a weight of one.
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@kindex v t
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@kindex V t
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@pindex calc-transpose
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@tindex trn
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The @kbd{v t} (@code{calc-transpose}) [@code{trn}] command computes
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@ -19985,6 +20014,7 @@ is a plain vector, it is treated as a row vector and transposed into
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a one-column matrix.
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@kindex v v
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@kindex V v
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@pindex calc-reverse-vector
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@tindex rev
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The @kbd{v v} (@code{calc-reverse-vector}) [@code{rev}] command reverses
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@ -19994,6 +20024,7 @@ principle can be used to apply other vector commands to the columns of
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a matrix.)
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@kindex v m
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@kindex V m
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@pindex calc-mask-vector
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@tindex vmask
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The @kbd{v m} (@code{calc-mask-vector}) [@code{vmask}] command uses
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@ -20006,6 +20037,7 @@ to zeros in the mask vector deleted. Thus, for example,
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@xref{Logical Operations}.
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@kindex v e
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@kindex V e
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@pindex calc-expand-vector
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@tindex vexp
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The @kbd{v e} (@code{calc-expand-vector}) [@code{vexp}] command
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@ -20019,6 +20051,7 @@ unreplaced in the result. Thus @samp{vexp([2, 0, 3, 0, 7], [a, b])}
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produces @samp{[a, 0, b, 0, 7]}.
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@kindex H v e
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@kindex H V e
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With the Hyperbolic flag, @kbd{H v e} takes a filler value from the
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top of the stack; the mask and target vectors come from the third and
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second elements of the stack. This filler is used where the mask is
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@ -20051,6 +20084,7 @@ vectors or matrices: @code{change-sign}, @code{conj}, @code{arg},
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@code{re}, @code{im}, @code{polar}, @code{rect}, @code{clean},
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@code{float}, @code{frac}. @xref{Function Index}.
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@kindex v J
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@kindex V J
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@pindex calc-conj-transpose
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@tindex ctrn
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@ -20074,6 +20108,7 @@ a point in two- or three-dimensional space, this is the distance
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from that point to the origin.
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@kindex v n
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@kindex V n
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@pindex calc-rnorm
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@tindex rnorm
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The @kbd{v n} (@code{calc-rnorm}) [@code{rnorm}] command computes the
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@ -20082,6 +20117,7 @@ vector, this is the maximum of the absolute values of the elements. For
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a matrix, this is the maximum of the row-absolute-value-sums, i.e., of
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the sums of the absolute values of the elements along the various rows.
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@kindex v N
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@kindex V N
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@pindex calc-cnorm
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@tindex cnorm
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not provided. However, the 2-norm (or Frobenius norm) is provided for
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vectors by the @kbd{A} (@code{calc-abs}) command.
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@kindex v C
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@kindex V C
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@pindex calc-cross
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@tindex cross
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@ -20121,12 +20158,14 @@ command simply computes @expr{1/x}. This is okay, because the
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@samp{/} operator also does a matrix inversion when dividing one
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by a matrix.
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@kindex v D
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@kindex V D
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@pindex calc-mdet
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@tindex det
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The @kbd{V D} (@code{calc-mdet}) [@code{det}] command computes the
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determinant of a square matrix.
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@kindex v L
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@kindex V L
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@pindex calc-mlud
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@tindex lud
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@ -20137,6 +20176,7 @@ The first is a permutation matrix that arises from pivoting in the
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algorithm, the second is lower-triangular with ones on the diagonal,
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and the third is upper-triangular.
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@kindex v T
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@kindex V T
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@pindex calc-mtrace
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@tindex tr
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@ -20144,6 +20184,7 @@ The @kbd{V T} (@code{calc-mtrace}) [@code{tr}] command computes the
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trace of a square matrix. This is defined as the sum of the diagonal
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elements of the matrix.
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@kindex v K
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@kindex V K
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@pindex calc-kron
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@tindex kron
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@ -20184,6 +20225,7 @@ single interval, the interval itself is returned instead.
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a certain value is a member of a given set. To test if the set @expr{A}
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is a subset of the set @expr{B}, use @samp{vdiff(A, B) = []}.
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@kindex v +
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@kindex V +
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@pindex calc-remove-duplicates
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@tindex rdup
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@ -20196,6 +20238,7 @@ necessary. You rarely need to use @kbd{V +} explicitly, since all the
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other set-based commands apply @kbd{V +} to their inputs before using
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them.
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@kindex v V
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@kindex V V
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@pindex calc-set-union
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@tindex vunion
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@ -20205,6 +20248,7 @@ only if it is in either (or both) of the input sets. (You could
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accomplish the same thing by concatenating the sets with @kbd{|},
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then using @kbd{V +}.)
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@kindex v ^
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@kindex V ^
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@pindex calc-set-intersect
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@tindex vint
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@ -20221,6 +20265,7 @@ and
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@texline intersection@tie{}(@math{A \cap B}).
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@infoline intersection.
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@kindex v -
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@kindex V -
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@pindex calc-set-difference
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@tindex vdiff
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@ -20235,6 +20280,7 @@ Obviously this is only practical if the set of all possible values in
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your problem is small enough to list in a Calc vector (or simple
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enough to express in a few intervals).
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@kindex v X
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@kindex V X
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@pindex calc-set-xor
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@tindex vxor
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@ -20244,6 +20290,7 @@ An object is in the symmetric difference of two sets if and only
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if it is in one, but @emph{not} both, of the sets. Objects that
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occur in both sets ``cancel out.''
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@kindex v ~
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@kindex V ~
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@pindex calc-set-complement
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@tindex vcompl
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@ -20253,6 +20300,7 @@ Thus @samp{vcompl(x)} is equivalent to @samp{vdiff([-inf .. inf], x)}.
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For example, @samp{vcompl([2, (3 .. 4]])} evaluates to
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@samp{[[-inf .. 2), (2 .. 3], (4 .. inf]]}.
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@kindex v F
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@kindex V F
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@pindex calc-set-floor
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@tindex vfloor
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@ -20265,6 +20313,7 @@ complement of the set @samp{[2, 6, 7, 8]} is messy, but if you wanted
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the complement with respect to the set of integers you could type
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@kbd{V ~ V F} to get @samp{[[-inf .. 1], [3 .. 5], [9 .. inf]]}.
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@kindex v E
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@kindex V E
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@pindex calc-set-enumerate
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@tindex venum
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@ -20274,6 +20323,7 @@ the set are expanded out to lists of all integers encompassed by
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the intervals. This only works for finite sets (i.e., sets which
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do not involve @samp{-inf} or @samp{inf}).
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@kindex v :
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@kindex V :
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@pindex calc-set-span
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@tindex vspan
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@ -20283,6 +20333,7 @@ The lower limit will be the smallest element in the set; the upper
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limit will be the largest element. For an empty set, @samp{vspan([])}
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returns the empty interval @w{@samp{[0 .. 0)}}.
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@kindex v #
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@kindex V #
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@pindex calc-set-cardinality
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@tindex vcard
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@ -20702,6 +20753,7 @@ $$ r_{x\!y} = { \sigma_{x\!y}^2 \over \sigma_x^2 \sigma_y^2 } $$
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The commands in this section allow for more general operations on the
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elements of vectors.
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@kindex v A
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@kindex V A
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@pindex calc-apply
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@tindex apply
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@ -20879,6 +20931,7 @@ about it.)
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@subsection Mapping
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@noindent
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@kindex v M
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@kindex V M
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@pindex calc-map
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@tindex map
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@ -20975,6 +21028,7 @@ variable's stored value using a @kbd{V M}-like operator.
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@subsection Reducing
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@noindent
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@kindex v R
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@kindex V R
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@pindex calc-reduce
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@tindex reduce
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@ -20987,6 +21041,7 @@ the remaining elements. Reducing @code{max} computes the maximum element
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and so on. In general, reducing @code{f} over the vector @samp{[a, b, c, d]}
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produces @samp{f(f(f(a, b), c), d)}.
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||||
|
||||
@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
|
||||
|
@ -20996,6 +21051,7 @@ but @kbd{I V R -} on the same vector produces @samp{a - (b - (c - d))},
|
|||
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
|
||||
|
@ -21005,6 +21061,7 @@ a vector of all the intermediate results. Accumulating @code{+} over
|
|||
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.
|
||||
|
@ -21052,6 +21109,7 @@ rows of the matrix. @xref{Grabbing From Buffers}.
|
|||
@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
|
||||
|
@ -21062,6 +21120,7 @@ is 3, the result is @samp{f(f(f(a)))}. The number @samp{n} may be
|
|||
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
|
||||
|
@ -21070,6 +21129,7 @@ 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
|
||||
|
@ -21078,6 +21138,7 @@ that it takes only an @samp{a} value from the stack; the function is
|
|||
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}.
|
||||
|
@ -21127,6 +21188,7 @@ when 20 steps have been taken, whichever is sooner.
|
|||
@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
|
||||
|
@ -21138,6 +21200,7 @@ and @samp{[x, y, z]} on the stack produces a multiplication table:
|
|||
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
|
||||
|
@ -21170,10 +21233,13 @@ in the same way (@pxref{Display Modes}). Matrix display is also
|
|||
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 >}
|
||||
|
@ -21181,10 +21247,13 @@ 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
|
||||
|
@ -21199,15 +21268,21 @@ display mode, either brackets or braces may be used to enter vectors,
|
|||
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
|
||||
|
@ -21246,6 +21321,7 @@ Note that of the formats shown here, @samp{RO}, @samp{ROC}, and
|
|||
@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
|
||||
|
@ -21261,6 +21337,7 @@ case as @samp{[(a b)]}. You can disable these extra parentheses
|
|||
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
|
||||
|
@ -21282,6 +21359,7 @@ unable to recover those vectors. If you are working with very
|
|||
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
|
||||
|
|
Loading…
Add table
Reference in a new issue