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lprvtkoeppe
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[numeric.ops] Use \dotsc for a non-code ellipsis
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source/algorithms.tex

Lines changed: 16 additions & 16 deletions
Original file line numberDiff line numberDiff line change
@@ -9900,24 +9900,24 @@
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\indexlibrary{generalized_noncommutative_sum@\tcode{\placeholder{GENERALIZED_NONCOMMUTATIVE_SUM}}}%
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\pnum
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Define \tcode{\placeholdernc{GENERALIZED_NONCOMMUTATIVE_SUM}(op, a1, ..., aN)}
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Define \tcode{\placeholdernc{GENERALIZED_NONCOMMUTATIVE_SUM}(op, a1, $\dotsc$, aN)}
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as follows:
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\begin{itemize}
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\item
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\tcode{a1} when \tcode{N} is \tcode{1}, otherwise
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\item
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\tcode{op(\placeholdernc{GENERALIZED_NONCOMMUTATIVE_SUM}(op, a1, ..., aK),} \\
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\tcode{\phantom{op(}\placeholdernc{GENERALIZED_NONCOMMUTATIVE_SUM}(op, aM, ..., aN))}
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\tcode{op(\placeholdernc{GENERALIZED_NONCOMMUTATIVE_SUM}(op, a1, $\dotsc$, aK),} \\
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\tcode{\phantom{op(}\placeholdernc{GENERALIZED_NONCOMMUTATIVE_SUM}(op, aM, $\dotsc$, aN))}
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for any \tcode{K} where $1 < \mathtt{K}+1 = \mathtt{M} \leq \mathtt{N}$.
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\end{itemize}
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\indexlibrary{generalized_sum@\tcode{\placeholder{GENERALIZED_SUM}}}%
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\pnum
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Define \tcode{\placeholdernc{GENERALIZED_SUM}(op, a1, ..., aN)} as
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\tcode{\placeholdernc{GENERALIZED_NONCOMMUTATIVE_SUM}(op, b1, ..., bN)},
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where
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\tcode{b1, ..., bN} may be any permutation of \tcode{a1, ..., aN}.
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Define \tcode{\placeholdernc{GENERALIZED_SUM}(op, a1, $\dotsc$, aN)} as
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\tcode{\placeholdernc{GENERALIZED_NONCOMMUTATIVE_SUM}(op, b1, $\dotsc$, bN)},
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\linebreak{}where
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\tcode{b1, $\dotsc$, bN} may be any permutation of \tcode{a1, $\dotsc$, aN}.
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\rSec2[accumulate]{Accumulate}
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@@ -10065,7 +10065,7 @@
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\pnum
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\returns
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\tcode{\placeholdernc{GENERALIZED_SUM}(binary_op, init, *i, ...)}
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\tcode{\placeholdernc{GENERALIZED_SUM}(binary_op, init, *i, $\dotsc$)}
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for every \tcode{i} in \range{first}{last}.
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\pnum
@@ -10207,7 +10207,7 @@
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\pnum
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\returns
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\begin{codeblock}
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@\placeholdernc{GENERALIZED_SUM}@(binary_op1, init, binary_op2(*i, *(first2 + (i - first1))), ...)
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@\placeholdernc{GENERALIZED_SUM}@(binary_op1, init, binary_op2(*i, *(first2 + (i - first1))), @$\dotsc$@)
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\end{codeblock}
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for every iterator \tcode{i} in \range{first1}{last1}.
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@@ -10256,7 +10256,7 @@
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\pnum
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\returns
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\begin{codeblock}
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@\placeholdernc{GENERALIZED_SUM}@(binary_op, init, unary_op(*i), ...)
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@\placeholdernc{GENERALIZED_SUM}@(binary_op, init, unary_op(*i), @$\dotsc$@)
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\end{codeblock}
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for every iterator \tcode{i} in \range{first}{last}.
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@@ -10409,7 +10409,7 @@
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assigns through \tcode{result + K} the value of:
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\begin{codeblock}
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@\placeholdernc{GENERALIZED_NONCOMMUTATIVE_SUM}@(
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binary_op, init, *(first + 0), *(first + 1), ..., *(first + K - 1))
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binary_op, init, *(first + 0), *(first + 1), @$\dotsc$@, *(first + K - 1))
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\end{codeblock}
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\pnum
@@ -10533,10 +10533,10 @@
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\begin{itemize}
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\item
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\tcode{\placeholdernc{GENERALIZED_NONCOMMUTATIVE_SUM}(\\\phantom{\tcode{\ \ \ \ }}binary_op,
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init, *(first + 0), *(first + 1), ..., *(first + K))}\\if \tcode{init} is provided, or
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init, *(first + 0), *(first + 1), $\dotsc$, *(first + K))}\\if \tcode{init} is provided, or
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\item
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\tcode{\placeholdernc{GENERALIZED_NONCOMMUTATIVE_SUM}(\\\phantom{\tcode{\ \ \ \ }}binary_op,
10539-
*(first + 0), *(first + 1), ..., *(first + K))}\\otherwise.
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*(first + 0), *(first + 1), $\dotsc$, *(first + K))}\\otherwise.
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\end{itemize}
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\pnum
@@ -10610,7 +10610,7 @@
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\begin{codeblock}
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@\placeholdernc{GENERALIZED_NONCOMMUTATIVE_SUM}@(
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binary_op, init,
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unary_op(*(first + 0)), unary_op(*(first + 1)), ..., unary_op(*(first + K - 1)))
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unary_op(*(first + 0)), unary_op(*(first + 1)), @$\dotsc$@, unary_op(*(first + K - 1)))
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\end{codeblock}
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\pnum
@@ -10710,10 +10710,10 @@
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assigns through \tcode{result + K} the value of
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\begin{itemize}
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\item
10713-
\tcode{\placeholdernc{GENERALIZED_NONCOMMUTATIVE_SUM}(\\\phantom{\tcode{\ \ \ \ }}binary_op, init,\\\phantom{\tcode{\ \ \ \ }}unary_op(*(first + 0)), unary_op(*(first + 1)), ..., unary_op(*(first + K)))}\\
10713+
\tcode{\placeholdernc{GENERALIZED_NONCOMMUTATIVE_SUM}(\\\phantom{\tcode{\ \ \ \ }}binary_op, init,\\\phantom{\tcode{\ \ \ \ }}unary_op(*(first + 0)), unary_op(*(first + 1)), $\dotsc$, unary_op(*(first + K)))}\\
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if \tcode{init} is provided, or
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\item
10716-
\tcode{\placeholdernc{GENERALIZED_NONCOMMUTATIVE_SUM}(\\\phantom{\tcode{\ \ \ \ }}binary_op,\\\phantom{\tcode{\ \ \ \ }}unary_op(*(first + 0)), unary_op(*(first + 1)), ..., unary_op(*(first + K)))}\\
10716+
\tcode{\placeholdernc{GENERALIZED_NONCOMMUTATIVE_SUM}(\\\phantom{\tcode{\ \ \ \ }}binary_op,\\\phantom{\tcode{\ \ \ \ }}unary_op(*(first + 0)), unary_op(*(first + 1)), $\dotsc$, unary_op(*(first + K)))}\\
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otherwise.
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\end{itemize}
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