# Comap

Comap[{f1,f2,},x]

gives {f1[x],f2[x],}.

Comap[fs,x,levelspec]

applies parts of fs specified by levelspec to x.

Comap[fs]

represents an operator form of Comap that can be applied to an expression.

# Details and Options

• Comap is typically used to apply each of a list of functions to a single common argument. »
• Comap uses standard level specifications:
•  n levels 1 through n Infinity levels 1 through Infinity {n} level n only {n1,n2} levels n1 through n2
• The default value for levelspec in Comap is {1}.
• A positive level n consists of all parts of fs specified by n indices.
• A negative level -n consists of all parts of fs with depth n.
• Level 1 consists of numbers, symbols and other objects that do not have subparts.
• Level 0 corresponds to the whole expression.
• With the option setting , Comap includes heads of expressions and their parts. »
• Comap always effectively constructs a complete new expression and then evaluates it. »
• The head of fs in Comap[fs,x,] need not be List.
• If fs is an Association object, Comap[fs,x] applies the values in the association to x. »
• Comap[fs][x] is equivalent to Comap[fs,x].
• Parallelize[Comap[fs,x]] computes Comap[fs,x] in parallel on all subkernels. »

# Examples

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## Basic Examples(4)

Wrap x with each element of a list:

Use the operator form of Comap:

Comap on level 2:

Comap an expression under values in an association:

## Scope(6)

Use explicit pure functions:

Comap can be used on expressions with any head:

Comap on the second level of a nested Association:

Comap on level -1:

Positive and negative levels can be mixed:

## Options(1)

By default, the expression is not comapped into the heads:

## Applications(3)

Apply a sum of functions by forming the sum of the individual applications:

Apply a differential operator:

Tabulate square roots of values without using auxiliary variables:

## Properties & Relations(9)

Comap wraps parts of an expression around another expression:

Map wraps an expression around parts of another expression:

Query[list] is equivalent to Comap[list]:

Query[assoc] is also equivalent to Comap[assoc]:

Through[p[f,g,][x]] is equivalent to Comap[p[f,g,],x]:

Compare this to the operator form of Comap:

Comap[p[f,g,],x] can be used even when p[f,g,][x] has a value:

When p[f,g,][x] has a value, Through cannot be used:

Comap[{f1,f2,},x] is equivalent to Map[f|->f[x],{f1,f2,}] when the fi have no attributes:

Comap can apply parts inside held expressions to an expression without allowing evaluation to proceed:

Use ReleaseHold to allow evaluation to proceed:

If only some arguments are held, only those arguments will not evaluate further:

Use Unevaluated to apply a list of functions to an expression without evaluating it first:

The expression is evaluated first by default:

Use Unevaluated to comap an expression into the parts of an expression without evaluating it first:

The expression is evaluated first by default:

Comap can be parallelized automatically:

## Possible Issues(1)

Comap by default starts at level 1, so does not apply the whole expression to the expression:

Wolfram Research (2023), Comap, Wolfram Language function, https://reference.wolfram.com/language/ref/Comap.html.

#### Text

Wolfram Research (2023), Comap, Wolfram Language function, https://reference.wolfram.com/language/ref/Comap.html.

#### CMS

Wolfram Language. 2023. "Comap." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Comap.html.

#### APA

Wolfram Language. (2023). Comap. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Comap.html

#### BibTeX

@misc{reference.wolfram_2024_comap, author="Wolfram Research", title="{Comap}", year="2023", howpublished="\url{https://reference.wolfram.com/language/ref/Comap.html}", note=[Accessed: 21-April-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_comap, organization={Wolfram Research}, title={Comap}, year={2023}, url={https://reference.wolfram.com/language/ref/Comap.html}, note=[Accessed: 21-April-2024 ]}