Times

x*y*z, x×y×z, or x y z

represents a product of terms.

Details

  • The character × is entered as * or \[Times]. It is not the same as \[Cross].
  • Times has attributes Flat, Orderless, and OneIdentity.
  • The default value for arguments of Times, as used in x_. patterns, is 1.
  • Times[] is taken to be 1.
  • Times[x] is x.
  • 0x evaluates to 0, and 0.0x evaluates to 0.0.
  • Unlike other functions, Times applies builtin rules before userdefined ones. As a result, it is not possible to make definitions such as 2*2=5.

Background & Context

  • Times is a function that does multiplication (takes the product) of expressions. The expression Times[a,b,c,] is commonly represented using the shorthand syntax a*b*c*, a×b×c×, or simply a b c . Special cases include Times[], which is taken to be 1, and Times[x], which is taken to be x.
  • Times sorts its arguments and collapses any terms of the same type. Times also threads element-wise over lists. Expand can be used to expand out products of expressions not automatically multiplied out by Times.
  • TimesBy can be used to multiply the value of a given variable. Divide gives the division of two expressions.
  • Multiplication of a function over a range or list of arguments is done using the function Product. Other types of multiplication include Dot (for matrix or vector multiplication) and NonCommutativeMultiply (for non-commuting products).

Examples

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Basic Examples  (3)

Enter Times with spaces; × is added automatically between numbers:

Alternative form:

Times threads element-wise over lists:

Explicit FullForm:

Scope  (2)

Times threads element-wise:

Pattern matching works with Times:

Properties & Relations  (4)

Use Expand to expand out products:

Use Dot for matrix or vector multiplication:

Use Product for products of indexed elements:

As well as for closed forms of products:

Use NonCommutativeMultiply for non commuting products:

Introduced in 1988
 (1.0)
 |
Updated in 1996
 (3.0)