Set

lhs=rhs

evaluates rhs and assigns the result to be the value of lhs. From then on, lhs is replaced by rhs whenever it appears.

{l1,l2,…}={r1,r2,…}

evaluates the ri, and assigns the results to be the values of the corresponding li.

Details

  • lhs can be any expression, including a pattern.
  • f[x_]=x^2 is a typical assignment for a pattern. Notice the presence of _ on the left‐hand side, but not the right‐hand side.
  • An assignment of the form f[args]=rhs sets up a transformation rule associated with the symbol f.
  • Different rules associated with a particular symbol are usually placed in the order that you give them. If a new rule that you give is determined to be more specific than existing rules, it is, however, placed before them. When the rules are used, they are tested in order. »
  • New assignments with identical lhs overwrite old ones. »
  • You can see all the assignments associated with a symbol f using ?f or Definition[f].
  • If you make assignments for functions that have attributes like Flat and Orderless, you must make sure to set these attributes before you make assignments for the functions.
  • Set has attribute HoldFirst.
  • If lhs is of the form f[args], then args are evaluated. »
  • There are some special functions for which an assignment to s[f[args]] is automatically associated with f rather than s. These functions include: Attributes, Default, Format, MessageName, Messages, N, and Options. »
  • When it appears in an unevaluated symbolic form, Set is treated as a scoping construct so that variables in nested occurrences are renamed if necessary. »
  • lhs=rhs returns rhs even if for some reason the assignment specified cannot be performed.
  • Some global variables such as $RecursionLimit can only be assigned a certain range or class of values.

Background & Context

  • Set is a function that evaluates and assigns an expression to be the value of a variable. The expression Set[lhs,rhs] is commonly represented using the shorthand syntax lhs=rhs. After Set is evaluated, lhs is replaced by rhs whenever it appears. Depending on the form of lhs, the result is stored as in the associated OwnValues, DownValues, or a specialized data structure.
  • Set often contains patterns on the lhs that are assigned transformed values as indicated on the rhs, e.g. f[x_] = x^2. lhs=rhs evaluates rhs immediately, so in situations where rhs should be evaluated only after the assignment is made, SetDelayed (written in shorthand as :=) should be used instead.
  • The assignments associated with a given symbol can be seen using Definition[f]. Individual assignments may be removed from a symbol using Unset; Clear and ClearAll remove all definitions at once.

Examples

open allclose all

Basic Examples  (2)

Set a value for :

Unset :

Set multiple values:

Scope  (15)

Left-Hand Sides  (7)

Ordinary program variables:

Set values for "indexed variables":

Define a function from an expression:

Use Block to temporarily set variables:

Set part of a list:

Set part of an expression:

Replace a row of a matrix:

Replace a column of a matrix:

Different Kinds of Values  (8)

Ownvalues:

Downvalues:

Subvalues:

Upvalues:

Default values and options:

Numerical values:

Format values:

A definition for Attributes is associated with , rather than Attributes:

Generalizations & Extensions  (5)

Set and to the same value:

Set and to different values:

Interchange values:

Set part of a sparse array:

v is still a sparse array, with its second part changed:

Assign multiple return values of a function to individual variables:

A definition for a pattern with a specific head is associated with that head:

Applications  (6)

Compute the GCD of two numbers:

Find a fixed point:

Compute using Newton's method:

Use a variable as an abbreviation for a complicated expression used more than once:

A scalar implementation of backsubstitution in a system of linear equations:

A vector implementation of backsubstitution in a system of linear equations:

Properties & Relations  (9)

The right side of an immediate definition is evaluated when the definition is made:

The right side of a delayed definition is evaluated each time the definition is used:

The arguments of the left side of a definition are evaluated before the definition is made:

Definitions with the same left side overwrite earlier ones:

Make definitions for special and general cases using immediate and delayed assignments:

More specific definitions are put in front of more general ones:

The pattern variable is renamed if necessary inside a nested scope:

Module introduces new symbols, distinct from global ones:

Definition prints definitions associated with a symbol:

Information prints various information about a symbol, including any definitions:

OwnValues returns a list of rules corresponding to any downvalues defined:

Use Unset (=.) to clear definitions with a particular left-hand side:

Clear all definitions:

Possible Issues  (4)

In the presence of global variables, pattern variables may show unexpected behavior:

Delayed assignments behave as expected:

Runaway definitions:

Pattern variables are not symbols; you cannot normally assign to them:

Use local variables for this purpose:

Use upvalues to assign to subscripted variables:

Subscripted variables are distinct from indexed variables:

Neat Examples  (1)

Compute the arithmetic-geometric mean of two numbers [more info]:

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

Text

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

CMS

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

APA

Wolfram Language. (1988). Set. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Set.html

BibTeX

@misc{reference.wolfram_2024_set, author="Wolfram Research", title="{Set}", year="1988", howpublished="\url{https://reference.wolfram.com/language/ref/Set.html}", note=[Accessed: 22-December-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_set, organization={Wolfram Research}, title={Set}, year={1988}, url={https://reference.wolfram.com/language/ref/Set.html}, note=[Accessed: 22-December-2024 ]}