Indexing Functions (for tables and arrays) - Maple Programming Help

Indexing Functions (for tables and arrays)

 Calling Sequence table(indexfcn, indexfcn...) array(indexfcn, indexfcn...)

Description

 • The indexfcn arguments to table or array are a sequence of named indexing methods used when assigning to or evaluating entries in the table or array. If no indexing methods are specified, then Maple's ordinary indexing is used.
 • All indexing is done through the first indexing method specified for the table or array. The procedure index/method is invoked with two or three parameters. If simply evaluating the table entry, then only two parameters are passed. The first is a list containing the indices to be used and the second is a named table using the remaining indexing methods. In this way, later indexing methods modify the behavior of earlier methods. If the entry is being assigned to, a third argument, a list of the values being assigned, is passed to the indexing function.
 • The following names are known as built-in or library-defined indexing functions:  symmetric, antisymmetric, sparse, diagonal, identity, and exception.
 • If indexfcn is not a built-in indexing function, cat(index,"/",indexfcn) is used as the name of the procedure that defines the indexing function.
 • The example below constructs an indexing function that returns infinity for all unassigned entries in the table (similar to the sparse indexing function which returns zero). The second example demonstrates the chaining of multiple indexing functions to get the desired effect.
 • Note: The command array has been superseded by Array.  Information on indexing functions for Arrays can be found at rtable_indexfcn.

Built-in Indexing Functions

 • Several indexing functions are built into Maple.  For more information, see the corresponding help page.

Examples

Use the built-in symmetric indexing function with a table

 > $t≔\mathrm{table}\left(\mathrm{symmetric}\right):$
 > ${t}_{1,2}≔1$
 ${{t}}_{{1}{,}{2}}{≔}{1}$ (1)
 > ${t}_{1,2}$
 ${1}$ (2)
 > ${t}_{2,1}$
 ${1}$ (3)

Define a custom indexing function infinity and use it.

 > index/infinity := proc(Idx::list,Tbl::table,Entry::list)     if (nargs = 2) then         if assigned(Tbl[op(Idx)]) then Tbl[op(Idx)];         else infinity;         end if;     elif Entry = [infinity] then         infinity;     else         Tbl[op(Idx)] := op(Entry);     end if; end proc:
 > $t≔\mathrm{table}\left(\mathrm{∞}\right):$
 > ${t}_{1,2}≔1:$
 > ${t}_{1,2}$
 ${1}$ (4)
 > ${t}_{1,1}$
 ${\mathrm{\infty }}$ (5)

Use the built-in indexing function symmetric together with the custom one defined earlier.

 > $t≔\mathrm{table}\left(\mathrm{symmetric},\mathrm{∞}\right):$
 > ${t}_{1,2}≔1$
 ${{t}}_{{1}{,}{2}}{≔}{1}$ (6)
 > ${t}_{1,2}$
 ${1}$ (7)
 > ${t}_{2,1}$
 ${1}$ (8)
 > ${t}_{1,1}$
 ${\mathrm{\infty }}$ (9)