distinctentries = truefalse

Specifies that the entries in the input table t are known to be distinct, i.e. numelems(t)=numelems([entries(t)]). This enables more efficient construction of the output table. The default is false.

nolist = truefalse

Specifying 'nolist' or 'nolist'=true causes each entry in the output table s to be a simple collection of indices of t, without wrapping each index in a list. This is useful for tables where every index is a single object. When 'nolist' is used on a table with expression sequence indices or entries, the pairings may be difficult to deduce in the result.

sort = truefalse

Specifying 'sort' or 'sort'=true indicates that each entry of the output table s should be sorted. This is only useful when a non-default combiner function c has been specified which produces ordered containers (for example a list or Array). The default value is false, which means that if the container type is ordered, the order chosen is not specified.

Returns a table which is the result of reversing the table t while combining keys mapping to the same value with combiner function f.

The tablereverse function takes a table t and returns a table s which is a reversal of t, in the sense that the indices of s are the entries of t and the entries of s are a collection of the indices of t.

By default, an entry s[u] in the output table s consists of a set of lists. Each element v in s[u] is a list whose contents correspond to an entry of the input table t pointing at u, so the property t[op(v)]=u holds.

The optional argument c allows the specification of a combiner function c which accepts an expression sequence of inputs representing keys in t which map to the same value and returns some customized value.

The default combiner function is simply the set constructor `{}` which collects all its arguments together in a set.

$T≔\mathrm{table}\left(\left[''apple''=''fruit''\,''orange''=''fruit''\,''zucchini''=''vegetable''\,''milk''=''dairy''\right]\right)$

$T≔table\left(\left[''orange''=''fruit''\,''milk''=''dairy''\,''apple''=''fruit''\,''zucchini''=''vegetable''\right]\right)$

$\mathrm{tablereverse}\left(T\right)$

$table\left(\left[''vegetable''=\left\{\left[''zucchini''\right]\right\}\,''fruit''=\left\{\left[''apple''\right]\,\left[''orange''\right]\right\}\,''dairy''=\left\{\left[''milk''\right]\right\}\right]\right)$

$\mathrm{tablereverse}\left(T\,\mathrm{nolist}\right)$

$table\left(\left[''vegetable''=\left\{''zucchini''\right\}\,''fruit''=\left\{''apple''\,''orange''\right\}\,''dairy''=\left\{''milk''\right\}\right]\right)$

$\mathrm{tablereverse}\left(T\,\mathrm{`[]`}\,\mathrm{nolist}\,\mathrm{sort}\right)$

$table\left(\left[''vegetable''=\left[''zucchini''\right]\,''fruit''=\left[''apple''\,''orange''\right]\,''dairy''=\left[''milk''\right]\right]\right)$

$\mathrm{BloodPhenotypes}≔\mathrm{table}\left(\mathrm{symmetric}\,\left\{\left(\mathrm{`\$`}\left(''A''\,2\right)\right)=''A''\,\left(\mathrm{`\$`}\left(''B''\,2\right)\right)=''B''\,\left(\mathrm{`\$`}\left(''O''\,2\right)\right)=''O''\,\left(''A''\,''B''\right)=''AB''\,\left(''A''\,''O''\right)=''A''\,\left(''B''\,''O''\right)=''B''\right\}\right)$

$\mathrm{BloodPhenotypes}≔table\left(\mathrm{symmetric}\,\left[\left(''A''\,''B''\right)=''AB''\,\left(''B''\,''B''\right)=''B''\,\left(''O''\,''O''\right)=''O''\,\left(''B''\,''O''\right)=''B''\,\left(''A''\,''O''\right)=''A''\,\left(''A''\,''A''\right)=''A''\right]\right)$

$\mathrm{BloodGenotypes}≔\mathrm{tablereverse}\left(\mathrm{BloodPhenotypes}\right)$

$\mathrm{BloodGenotypes}≔table\left(\left[''B''=\left\{\left[''B''\,''B''\right]\,\left[''B''\,''O''\right]\,\left[''O''\,''B''\right]\right\}\,''AB''=\left\{\left[''A''\,''B''\right]\,\left[''B''\,''A''\right]\right\}\,''A''=\left\{\left[''A''\,''A''\right]\,\left[''A''\,''O''\right]\,\left[''O''\,''A''\right]\right\}\,''O''=\left\{\left[''O''\,''O''\right]\right\}\right]\right)$

$\mathrm{BloodGenotypes}\left[''A''\right]$

$\left\{\left[''A''\,''A''\right]\,\left[''A''\,''O''\right]\,\left[''O''\,''A''\right]\right\}$

$\mathrm{BloodGenotypes}\left[''O''\right]$

$\left\{\left[''O''\,''O''\right]\right\}$

$\mathrm{Capitals}≔\mathrm{table}\left(\left\{''Croatia''=''Zagreb''\,''Jordan''=''Amman''\,''Mali''=''Bamako''\,''Uruguay''=''Montevideo''\,''Cambodia''=''Phnom\; Penh''\,''Cape\; Verde''=''Praia''\,''Sierra\; Leone''=''Freetown''\right\}\right)$

$\mathrm{Capitals}≔table\left(\left[''Mali''=''Bamako''\,''Sierra\; Leone''=''Freetown''\,''Jordan''=''Amman''\,''Croatia''=''Zagreb''\,''Cambodia''=''Phnom\; Penh''\,''Uruguay''=''Montevideo''\,''Cape\; Verde''=''Praia''\right]\right)$

$\mathrm{tablereverse}\left(\mathrm{Capitals}\,\mathrm{distinctentries}\,\mathrm{nolist}\right)$

$table\left(\left[''Freetown''=\left\{''Sierra\; Leone''\right\}\,''Bamako''=\left\{''Mali''\right\}\,''Montevideo''=\left\{''Uruguay''\right\}\,''Amman''=\left\{''Jordan''\right\}\,''Zagreb''=\left\{''Croatia''\right\}\,''Phnom\; Penh''=\left\{''Cambodia''\right\}\,''Praia''=\left\{''Cape\; Verde''\right\}\right]\right)$

$\mathrm{tablereverse}\left(\mathrm{Capitals}\,t\mapsto t\,\mathrm{distinctentries}\,\mathrm{nolist}\right)$

$table\left(\left[''Freetown''=''Sierra\; Leone''\,''Bamako''=''Mali''\,''Montevideo''=''Uruguay''\,''Amman''=''Jordan''\,''Zagreb''=''Croatia''\,''Phnom\; Penh''=''Cambodia''\,''Praia''=''Cape\; Verde''\right]\right)$

The tablereverse command was introduced in Maple 2019.

For more information on Maple 2019 changes, see Updates in Maple 2019.

The tablereverse command was updated in Maple 2022.

The nolist option was introduced in Maple 2022.

For more information on Maple 2022 changes, see Updates in Maple 2022.