x*y*z, x×y×z, or x y z
represents a product of terms.
- 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).
Examplesopen allclose all
Basic Examples (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).
Wolfram Language. 1988. "Times." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2021. https://reference.wolfram.com/language/ref/Times.html.
Wolfram Language. (1988). Times. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Times.html