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, each index u appearing in the output table s is mapped to an entry s[u] which is a set of lists. Each list v in the set s[u] will satisfy the property that t[op(v)]=u.

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The tablereverse command was introduced in Maple 2019.

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