Documentation

misc::maprec

Map a function to subexpressions of an expression

Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

Syntax

misc::maprec(ex, selector = funci, …, <PreMap | PostMap>, <NoOperators>, <Unsimplified>)

Description

misc::maprec(ex, selector=funci) maps the function funci to all subexpressions of the expression ex that satisfy a given criterion (defined by selector) and replaces each selected subexpression s by funci(s).

Several different functions may be mapped to subexpressions satisfying different selection criteria.

misc::maprec(ex, selector1 = funci1, …, selectorn = funcin) does two steps: it tests whether ex meets a selection criterion defined by some selector selector_k (and, if yes, replaces ex by funci_k(ex)); and it applies itself recursively to all operands of ex. The order of these steps is determined by the options PreMap and PostMap.

Selectors are applied from left to right; if the expression meets some selection criterion, no further selectors are tried.

selector can have two forms. It can be a set {t1, …, tn}. Here a subexpression s of ex is selected if type(s1) is one of the types t1, …, tn. If it is not a set, a subexpression s of ex is selected if p(s) returns TRUE. As every MuPAD® object may be applied as a function to s, p may be of any type in the latter case.

In order not to select a subexpression, the selector need not return FALSE; it suffices that it does not return TRUE.

If neither the option PreMap nor the option PostMap is given, then PreMap is used.

Use a misc::breakmap command inside funci in order to stop the recursive mapping. See the help page of misc::breakmap for an example.

    Note:   Only subexpressions of domain type DOM_ARRAY, DOM_EXPR, DOM_LIST, DOM_SET, and DOM_TABLE are mapped recursively, as well as domain elements of a domain T for which a slot T::enableMaprec exists and equals TRUE; a slot T::map working properly must then exist, too. To subexpressions of other types, selector is applied, but misc::maprec is not mapped to their operands. (This is to avoid unwanted substitutions.) If you want to recurse on them, either add an enableMaprec-slot, or use a selector that selects such subexpressions, and make funci initiate another recursive mapping.

misc::maprec is overloadable. If the domain of a subexpression has a method "maprec", then this method is called with the subexpression and the other arguments of the call.

    Note:   The subexpression is replaced by the result, but misc::maprec is not mapped to its operands; such recursive mapping must be done by the domain method if desired.

    Note:   The operators of expressions (op(expression, 0)) are also mapped recursively like all the other operands. Use NoOperators to switch this off.

Examples

Example 1

In the following example every integer of the given expression a+3+4 is substituted by the value 10. Since 10(n) returns 10 for every integer n, it suffices to write 10 instead of n -> 10 here.

misc::maprec(hold(a+3+4), {DOM_INT} = 10)

In the example above, we used hold to suppress the evaluation of the expression because otherwise a+3+4 is evaluated to a+7 and we get the result:

misc::maprec(a+3+4, {DOM_INT} = 10)

The simplification of the resulting 10 + 10 to 20 can be avoided by using the option Unsimplified:

misc::maprec(hold(a+3+4), {DOM_INT} = 10, Unsimplified)

Example 2

Now we give an example where the selector is a function. We want to eleminate all the prime numbers from an expression.

misc::maprec(hold(_plus)(i $ i=1..20), isprime= null(), PostMap)

Here isprime returns TRUE for every prime number between 1 and 20. Every prime number between 1 and 20 is replaced by null() (since null()(p) gives null()) which means the above call computes the sum of all non-prime numbers between 1 and 20.

Example 3

Normally, misc::maprec recurses also into the operators of subexpressions. This may be unwanted in many cases:

misc::maprec(a+b, {DOM_IDENT}= (x -> x.1))

We just wanted to replace the summands, but not the operator. Using the option NoOperators helps:

misc::maprec(a+b, {DOM_IDENT}= (x -> x.1), NoOperators)

Parameters

ex

Any MuPAD object

selector

Any MuPAD object

funci

Any MuPAD object

Options

PreMap

For each subexpressions s of ex, the selector is applied to it after visiting all of its subexpressions; s may have changed at that time due to substitutions in the subexpressions.

PostMap

For each subexpressions s of ex, the selector is applied to it before visiting its subexpressions. If s is selected by selector, it is replaced by funci(s), and misc::maprec is not recursively applied to the operands of funci(s); otherwise, misc::maprec is recursively applied to the operands of s.

NoOperators

The selector is not applied to the operator of ex.

Unsimplified

The resulting expressions are not further simplified.

Return Values

misc::maprec may return any MuPAD object.

Overloaded By

ex

See Also

MuPAD Functions

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