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9894 | 9894 |
|
9895 | 9895 | \indexlibrary{generalized_noncommutative_sum@\tcode{\placeholder{GENERALIZED_NONCOMMUTATIVE_SUM}}}% |
9896 | 9896 | \pnum |
9897 | | -Define \tcode{\placeholdernc{GENERALIZED_NONCOMMUTATIVE_SUM}(op, a1, ..., aN)} |
| 9897 | +Define \tcode{\placeholdernc{GENERALIZED_NONCOMMUTATIVE_SUM}(op, a1, $\dotsc$, aN)} |
9898 | 9898 | as follows: |
9899 | 9899 | \begin{itemize} |
9900 | 9900 | \item |
9901 | 9901 | \tcode{a1} when \tcode{N} is \tcode{1}, otherwise |
9902 | 9902 |
|
9903 | 9903 | \item |
9904 | | -\tcode{op(\placeholdernc{GENERALIZED_NONCOMMUTATIVE_SUM}(op, a1, ..., aK),} \\ |
9905 | | -\tcode{\phantom{op(}\placeholdernc{GENERALIZED_NONCOMMUTATIVE_SUM}(op, aM, ..., aN))} |
| 9904 | +\tcode{op(\placeholdernc{GENERALIZED_NONCOMMUTATIVE_SUM}(op, a1, $\dotsc$, aK),} \\ |
| 9905 | +\tcode{\phantom{op(}\placeholdernc{GENERALIZED_NONCOMMUTATIVE_SUM}(op, aM, $\dotsc$, aN))} |
9906 | 9906 | for any \tcode{K} where $1 < \mathtt{K}+1 = \mathtt{M} \leq \mathtt{N}$. |
9907 | 9907 | \end{itemize} |
9908 | 9908 |
|
9909 | 9909 | \indexlibrary{generalized_sum@\tcode{\placeholder{GENERALIZED_SUM}}}% |
9910 | 9910 | \pnum |
9911 | | -Define \tcode{\placeholdernc{GENERALIZED_SUM}(op, a1, ..., aN)} as |
9912 | | -\tcode{\placeholdernc{GENERALIZED_NONCOMMUTATIVE_SUM}(op, b1, ..., bN)}, |
9913 | | -where |
9914 | | -\tcode{b1, ..., bN} may be any permutation of \tcode{a1, ..., aN}. |
| 9911 | +Define \tcode{\placeholdernc{GENERALIZED_SUM}(op, a1, $\dotsc$, aN)} as |
| 9912 | +\tcode{\placeholdernc{GENERALIZED_NONCOMMUTATIVE_SUM}(op, b1, $\dotsc$, bN)}, |
| 9913 | +\linebreak{}where |
| 9914 | +\tcode{b1, $\dotsc$, bN} may be any permutation of \tcode{a1, $\dotsc$, aN}. |
9915 | 9915 |
|
9916 | 9916 | \rSec2[accumulate]{Accumulate} |
9917 | 9917 |
|
|
10059 | 10059 |
|
10060 | 10060 | \pnum |
10061 | 10061 | \returns |
10062 | | -\tcode{\placeholdernc{GENERALIZED_SUM}(binary_op, init, *i, ...)} |
| 10062 | +\tcode{\placeholdernc{GENERALIZED_SUM}(binary_op, init, *i, $\dotsc$)} |
10063 | 10063 | for every \tcode{i} in \range{first}{last}. |
10064 | 10064 |
|
10065 | 10065 | \pnum |
|
10201 | 10201 | \pnum |
10202 | 10202 | \returns |
10203 | 10203 | \begin{codeblock} |
10204 | | -@\placeholdernc{GENERALIZED_SUM}@(binary_op1, init, binary_op2(*i, *(first2 + (i - first1))), ...) |
| 10204 | +@\placeholdernc{GENERALIZED_SUM}@(binary_op1, init, binary_op2(*i, *(first2 + (i - first1))), @$\dotsc$@) |
10205 | 10205 | \end{codeblock} |
10206 | 10206 | for every iterator \tcode{i} in \range{first1}{last1}. |
10207 | 10207 |
|
|
10250 | 10250 | \pnum |
10251 | 10251 | \returns |
10252 | 10252 | \begin{codeblock} |
10253 | | -@\placeholdernc{GENERALIZED_SUM}@(binary_op, init, unary_op(*i), ...) |
| 10253 | +@\placeholdernc{GENERALIZED_SUM}@(binary_op, init, unary_op(*i), @$\dotsc$@) |
10254 | 10254 | \end{codeblock} |
10255 | 10255 | for every iterator \tcode{i} in \range{first}{last}. |
10256 | 10256 |
|
|
10403 | 10403 | assigns through \tcode{result + K} the value of: |
10404 | 10404 | \begin{codeblock} |
10405 | 10405 | @\placeholdernc{GENERALIZED_NONCOMMUTATIVE_SUM}@( |
10406 | | - binary_op, init, *(first + 0), *(first + 1), ..., *(first + K - 1)) |
| 10406 | + binary_op, init, *(first + 0), *(first + 1), @$\dotsc$@, *(first + K - 1)) |
10407 | 10407 | \end{codeblock} |
10408 | 10408 |
|
10409 | 10409 | \pnum |
@@ -10527,10 +10527,10 @@ |
10527 | 10527 | \begin{itemize} |
10528 | 10528 | \item |
10529 | 10529 | \tcode{\placeholdernc{GENERALIZED_NONCOMMUTATIVE_SUM}(\\\phantom{\tcode{\ \ \ \ }}binary_op, |
10530 | | - init, *(first + 0), *(first + 1), ..., *(first + K))}\\if \tcode{init} is provided, or |
| 10530 | + init, *(first + 0), *(first + 1), $\dotsc$, *(first + K))}\\if \tcode{init} is provided, or |
10531 | 10531 | \item |
10532 | 10532 | \tcode{\placeholdernc{GENERALIZED_NONCOMMUTATIVE_SUM}(\\\phantom{\tcode{\ \ \ \ }}binary_op, |
10533 | | - *(first + 0), *(first + 1), ..., *(first + K))}\\otherwise. |
| 10533 | + *(first + 0), *(first + 1), $\dotsc$, *(first + K))}\\otherwise. |
10534 | 10534 | \end{itemize} |
10535 | 10535 |
|
10536 | 10536 | \pnum |
|
10604 | 10604 | \begin{codeblock} |
10605 | 10605 | @\placeholdernc{GENERALIZED_NONCOMMUTATIVE_SUM}@( |
10606 | 10606 | binary_op, init, |
10607 | | - unary_op(*(first + 0)), unary_op(*(first + 1)), ..., unary_op(*(first + K - 1))) |
| 10607 | + unary_op(*(first + 0)), unary_op(*(first + 1)), @$\dotsc$@, unary_op(*(first + K - 1))) |
10608 | 10608 | \end{codeblock} |
10609 | 10609 |
|
10610 | 10610 | \pnum |
@@ -10704,10 +10704,10 @@ |
10704 | 10704 | assigns through \tcode{result + K} the value of |
10705 | 10705 | \begin{itemize} |
10706 | 10706 | \item |
10707 | | - \tcode{\placeholdernc{GENERALIZED_NONCOMMUTATIVE_SUM}(\\\phantom{\tcode{\ \ \ \ }}binary_op, init,\\\phantom{\tcode{\ \ \ \ }}unary_op(*(first + 0)), unary_op(*(first + 1)), ..., unary_op(*(first + K)))}\\ |
| 10707 | + \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)))}\\ |
10708 | 10708 | if \tcode{init} is provided, or |
10709 | 10709 | \item |
10710 | | - \tcode{\placeholdernc{GENERALIZED_NONCOMMUTATIVE_SUM}(\\\phantom{\tcode{\ \ \ \ }}binary_op,\\\phantom{\tcode{\ \ \ \ }}unary_op(*(first + 0)), unary_op(*(first + 1)), ..., unary_op(*(first + K)))}\\ |
| 10710 | + \tcode{\placeholdernc{GENERALIZED_NONCOMMUTATIVE_SUM}(\\\phantom{\tcode{\ \ \ \ }}binary_op,\\\phantom{\tcode{\ \ \ \ }}unary_op(*(first + 0)), unary_op(*(first + 1)), $\dotsc$, unary_op(*(first + K)))}\\ |
10711 | 10711 | otherwise. |
10712 | 10712 | \end{itemize} |
10713 | 10713 |
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