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 built‐in rules before user‐defined ones. As a result, it is not possible to make definitions such as 2*2=5.
  • Times can be used with Interval and CenteredInterval objects. »

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

open allclose all

Basic Examples  (3)

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

Alternative form:

Times threads element-wise over lists:

Explicit FullForm:

Scope  (3)

Times threads element-wise:

Pattern matching works with Times:

Times can be used with Interval and CenteredInterval objects:

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:

Wolfram Research (1988), Times, Wolfram Language function, https://reference.wolfram.com/language/ref/Times.html (updated 2021).

Text

Wolfram Research (1988), Times, Wolfram Language function, https://reference.wolfram.com/language/ref/Times.html (updated 2021).

CMS

Wolfram Language. 1988. "Times." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2021. https://reference.wolfram.com/language/ref/Times.html.

APA

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

BibTeX

@misc{reference.wolfram_2024_times, author="Wolfram Research", title="{Times}", year="2021", howpublished="\url{https://reference.wolfram.com/language/ref/Times.html}", note=[Accessed: 21-November-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_times, organization={Wolfram Research}, title={Times}, year={2021}, url={https://reference.wolfram.com/language/ref/Times.html}, note=[Accessed: 21-November-2024 ]}