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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.
  • 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.
  • If lhs is of the form f[args], then args are evaluated.  »
  • 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.
EXAMPLESCLOSE ALL
Scope   (15)
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:
Ownvalues:
Downvalues:
Subvalues:
Upvalues:
Default values and options:
Numerical values:
Format values:
A definition for Attributes is associated with f, rather than Attributes:
Generalizations & Extensions   (5)
Set x and y to the same value:
Set x and y 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]:
New in 1
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