"threads" f over any lists that appear in args.

threads f over any objects with head h that appear in args.

threads f over objects with head h that appear in the first n args.

# Details

• Functions with attribute Listable are automatically threaded over lists.
• All the elements in the specified args whose heads are h must be of the same length.
• Arguments that do not have head h are copied as many times as there are elements in the arguments that do have head h. »
• Thread specifies arguments using the standard sequence specification:
•  All all elements None no elements n elements 1 through n -n last n elements {n} element n only {m,n} elements m through n inclusive {m,n,s} elements m through n in steps of s

# Examples

open allclose all

## Basic Examples(3)

Convert equations for lists to lists of equations:

Apply a function to both sides of an equation:

## Scope(9)

### Sequence Specifications(7)

By default, thread over all arguments:

Do not thread at all:

Thread over the first two arguments only:

Thread over the last two arguments only:

Thread over argument 2 only:

Thread over arguments 2 through 4:

Thread over every other argument:

By default, thread over lists:

By default, does not thread over heads other than List:

Thread with respect to Plus:

## Generalizations & Extensions(1)

Elements that are not lists are repeated:

## Applications(3)

Build a list of rules:

Equate coefficients in a polynomial equation:

Alternatively, use SolveAlways:

Form pairs with a constant second element:

## Properties & Relations(3)

Functions with attribute Listable are threaded automatically over lists:

MapThread works like Thread, but takes the function and arguments separately:

The function to thread over can be List as well:

In this case, the result is the same as a transposition:

## Possible Issues(1)

Thread evaluates the whole expression before threading:

MapThread takes the function and its arguments separately:

Suppressing evaluation has a similar effect:

Wolfram Research (1988), Thread, Wolfram Language function, https://reference.wolfram.com/language/ref/Thread.html.

#### Text

Wolfram Research (1988), Thread, Wolfram Language function, https://reference.wolfram.com/language/ref/Thread.html.

#### CMS

Wolfram Language. 1988. "Thread." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Thread.html.