Plus
x+y+z
represents a sum of terms.
Details
- Plus has attributes Flat, Orderless, and OneIdentity.
- The default value for arguments of Plus, as used in x_. patterns, is 0. »
- Plus[] is taken to be 0.
- Plus[x] is x.
- x+0 evaluates to x, but x+0.0 is left unchanged.
- In mixed fractions such as 1
, the implicit addition can be entered as 1 
+
or 1 \[ImplicitPlus] 
. This evaluates to 1+
, but implicit addition is an operator with much higher precedence than +. - Unlike other functions, Plus applies built‐in rules before user‐defined ones. As a result, it is not possible to make definitions such as 2+2=5.
- Plus can be used with Interval and CenteredInterval objects. »
Background & Context
- Plus is a function that does addition (summation) of expressions. The expression Plus[a,b,c,…] is commonly represented using the shorthand syntax a+b+c+…. Special cases include Plus[], which is taken to be 0, and Plus[x], which is taken to be x.
- Plus sorts its arguments and collapses any terms of the same type. Plus also threads element-wise over lists.
- To perform summation at a particular level of a list or to apply compensative summation to reduce numerical error for inexact summands, the function Total can be used. Accumulate gives a list of the successive accumulated totals of elements in a list. AddTo, Increment, and PreIncrement can be used to increase the value of a given variable. Minus gives the arithmetic negation of an expression, and Subtract gives the difference of two numbers.
- Summation of a function over a range or list of arguments is done using the function Sum.
Examples
open all close allBasic Examples (3)
Scope (6)
If any number is approximate, the whole result will be as follows:
1. + 2 + 3 / 4Complex numbers add their components:
(2 + I) + (3 - 7I)Plus threads element-wise over lists:
{a, b} + {c, d}{a, b, c} + x{{a, b}, {c, d}} + x{{1, 2}, {3, 4}} + {{a, b}, {c, d}}Create mixed fractions by typing a whole number, 
+
, and a fraction:
1(1/2)1(1/2) + 2(1/4)Plus can be used with Interval and CenteredInterval objects:
Interval[{0, 1}] + Interval[{-1, 1}]CenteredInterval[0, 1 + I] + CenteredInterval[1, 1 + I]Interval[{1, 2}] + CenteredInterval[2 + 3I, 1 + I]Properties & Relations (10)
Plus sorts its arguments:
b + c + aSum[x ^ n, {n, 0, 5}]Sum[x ^ i y ^ j, {i, 3}, {j, 3}]Display terms in a sum in a traditional order:
TraditionalForm[Sum[x ^ n, {n, 0, 5}]]TraditionalForm[Sum[x ^ i y ^ j, {i, 3}, {j, 3}]]Display a sum without evaluation:
HoldForm[1 + 3 + 2]Display the FullForm of a sum:
FullForm[a + b + c + d]Length[a + b + c + d]Apply[Plus, {a, b, c, d}]Total[{a, b, c, d}]Pattern matching works with Plus:
a + b + c + d /. a + d -> xa + b + c + d /. a + c + x_ -> f[x]{a, a + b, a + b + c} /. a + x_. -> f[x]Distribute a function over Plus:
f[a + b, c + d]Distribute[f[a + b, c + d]]Distribute Plus through a head:
(f + g)[x]Through[(f + g)[x]]Starting from f+g, use Comap to distribute the sum across an argument:
Comap[f + g][x]Accumulate makes a cumulative sum:
FoldList[Plus, 0, {a, b, c}]Accumulate[{a, b, c}]
An Elementary Introduction to the Wolfram Language
An Elementary Introduction to the Wolfram Language
NKS|OnlineText
Wolfram Research (1988), Plus, Wolfram Language function, https://reference.wolfram.com/language/ref/Plus.html (updated 2021).
CMS
Wolfram Language. 1988. "Plus." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2021. https://reference.wolfram.com/language/ref/Plus.html.
APA
Wolfram Language. (1988). Plus. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Plus.html