|
9900 | 9900 |
|
9901 | 9901 | \indexlibrary{generalized_noncommutative_sum@\tcode{\placeholder{GENERALIZED_NONCOMMUTATIVE_SUM}}}%
|
9902 | 9902 | \pnum
|
9903 |
| -Define \tcode{\placeholdernc{GENERALIZED_NONCOMMUTATIVE_SUM}(op, a1, ..., aN)} |
| 9903 | +Define \tcode{\placeholdernc{GENERALIZED_NONCOMMUTATIVE_SUM}(op, a1, $\dotsc$, aN)} |
9904 | 9904 | as follows:
|
9905 | 9905 | \begin{itemize}
|
9906 | 9906 | \item
|
9907 | 9907 | \tcode{a1} when \tcode{N} is \tcode{1}, otherwise
|
9908 | 9908 |
|
9909 | 9909 | \item
|
9910 |
| -\tcode{op(\placeholdernc{GENERALIZED_NONCOMMUTATIVE_SUM}(op, a1, ..., aK),} \\ |
9911 |
| -\tcode{\phantom{op(}\placeholdernc{GENERALIZED_NONCOMMUTATIVE_SUM}(op, aM, ..., aN))} |
| 9910 | +\tcode{op(\placeholdernc{GENERALIZED_NONCOMMUTATIVE_SUM}(op, a1, $\dotsc$, aK),} \\ |
| 9911 | +\tcode{\phantom{op(}\placeholdernc{GENERALIZED_NONCOMMUTATIVE_SUM}(op, aM, $\dotsc$, aN))} |
9912 | 9912 | for any \tcode{K} where $1 < \mathtt{K}+1 = \mathtt{M} \leq \mathtt{N}$.
|
9913 | 9913 | \end{itemize}
|
9914 | 9914 |
|
9915 | 9915 | \indexlibrary{generalized_sum@\tcode{\placeholder{GENERALIZED_SUM}}}%
|
9916 | 9916 | \pnum
|
9917 |
| -Define \tcode{\placeholdernc{GENERALIZED_SUM}(op, a1, ..., aN)} as |
9918 |
| -\tcode{\placeholdernc{GENERALIZED_NONCOMMUTATIVE_SUM}(op, b1, ..., bN)}, |
9919 |
| -where |
9920 |
| -\tcode{b1, ..., bN} may be any permutation of \tcode{a1, ..., aN}. |
| 9917 | +Define \tcode{\placeholdernc{GENERALIZED_SUM}(op, a1, $\dotsc$, aN)} as |
| 9918 | +\tcode{\placeholdernc{GENERALIZED_NONCOMMUTATIVE_SUM}(op, b1, $\dotsc$, bN)}, |
| 9919 | +\linebreak{}where |
| 9920 | +\tcode{b1, $\dotsc$, bN} may be any permutation of \tcode{a1, $\dotsc$, aN}. |
9921 | 9921 |
|
9922 | 9922 | \rSec2[accumulate]{Accumulate}
|
9923 | 9923 |
|
|
10065 | 10065 |
|
10066 | 10066 | \pnum
|
10067 | 10067 | \returns
|
10068 |
| -\tcode{\placeholdernc{GENERALIZED_SUM}(binary_op, init, *i, ...)} |
| 10068 | +\tcode{\placeholdernc{GENERALIZED_SUM}(binary_op, init, *i, $\dotsc$)} |
10069 | 10069 | for every \tcode{i} in \range{first}{last}.
|
10070 | 10070 |
|
10071 | 10071 | \pnum
|
|
10207 | 10207 | \pnum
|
10208 | 10208 | \returns
|
10209 | 10209 | \begin{codeblock}
|
10210 |
| -@\placeholdernc{GENERALIZED_SUM}@(binary_op1, init, binary_op2(*i, *(first2 + (i - first1))), ...) |
| 10210 | +@\placeholdernc{GENERALIZED_SUM}@(binary_op1, init, binary_op2(*i, *(first2 + (i - first1))), @$\dotsc$@) |
10211 | 10211 | \end{codeblock}
|
10212 | 10212 | for every iterator \tcode{i} in \range{first1}{last1}.
|
10213 | 10213 |
|
|
10256 | 10256 | \pnum
|
10257 | 10257 | \returns
|
10258 | 10258 | \begin{codeblock}
|
10259 |
| -@\placeholdernc{GENERALIZED_SUM}@(binary_op, init, unary_op(*i), ...) |
| 10259 | +@\placeholdernc{GENERALIZED_SUM}@(binary_op, init, unary_op(*i), @$\dotsc$@) |
10260 | 10260 | \end{codeblock}
|
10261 | 10261 | for every iterator \tcode{i} in \range{first}{last}.
|
10262 | 10262 |
|
|
10409 | 10409 | assigns through \tcode{result + K} the value of:
|
10410 | 10410 | \begin{codeblock}
|
10411 | 10411 | @\placeholdernc{GENERALIZED_NONCOMMUTATIVE_SUM}@(
|
10412 |
| - binary_op, init, *(first + 0), *(first + 1), ..., *(first + K - 1)) |
| 10412 | + binary_op, init, *(first + 0), *(first + 1), @$\dotsc$@, *(first + K - 1)) |
10413 | 10413 | \end{codeblock}
|
10414 | 10414 |
|
10415 | 10415 | \pnum
|
@@ -10533,10 +10533,10 @@
|
10533 | 10533 | \begin{itemize}
|
10534 | 10534 | \item
|
10535 | 10535 | \tcode{\placeholdernc{GENERALIZED_NONCOMMUTATIVE_SUM}(\\\phantom{\tcode{\ \ \ \ }}binary_op,
|
10536 |
| - init, *(first + 0), *(first + 1), ..., *(first + K))}\\if \tcode{init} is provided, or |
| 10536 | + init, *(first + 0), *(first + 1), $\dotsc$, *(first + K))}\\if \tcode{init} is provided, or |
10537 | 10537 | \item
|
10538 | 10538 | \tcode{\placeholdernc{GENERALIZED_NONCOMMUTATIVE_SUM}(\\\phantom{\tcode{\ \ \ \ }}binary_op,
|
10539 |
| - *(first + 0), *(first + 1), ..., *(first + K))}\\otherwise. |
| 10539 | + *(first + 0), *(first + 1), $\dotsc$, *(first + K))}\\otherwise. |
10540 | 10540 | \end{itemize}
|
10541 | 10541 |
|
10542 | 10542 | \pnum
|
|
10610 | 10610 | \begin{codeblock}
|
10611 | 10611 | @\placeholdernc{GENERALIZED_NONCOMMUTATIVE_SUM}@(
|
10612 | 10612 | binary_op, init,
|
10613 |
| - unary_op(*(first + 0)), unary_op(*(first + 1)), ..., unary_op(*(first + K - 1))) |
| 10613 | + unary_op(*(first + 0)), unary_op(*(first + 1)), @$\dotsc$@, unary_op(*(first + K - 1))) |
10614 | 10614 | \end{codeblock}
|
10615 | 10615 |
|
10616 | 10616 | \pnum
|
@@ -10710,10 +10710,10 @@
|
10710 | 10710 | assigns through \tcode{result + K} the value of
|
10711 | 10711 | \begin{itemize}
|
10712 | 10712 | \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)))}\\ |
10714 | 10714 | if \tcode{init} is provided, or
|
10715 | 10715 | \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)))}\\ |
10717 | 10717 | otherwise.
|
10718 | 10718 | \end{itemize}
|
10719 | 10719 |
|
|
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