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

Basic Examples  (3)

Plus threads element-wise over lists:

Explicit FullForm:

Scope  (6)

If any number is approximate, the whole result will be as follows:

Complex numbers add their components:

Plus threads element-wise over lists:

Matrices add element-wise:

Create mixed fractions by typing a whole number, +, and a fraction:

Sum two mixed fractions:

Plus can be used with Interval and CenteredInterval objects:

Properties & Relations  (10)

Plus sorts its arguments:

Display terms in a sum in a traditional order:

Display a sum without evaluation:

Display the FullForm of a sum:

Find the length of a sum:

Total applies Plus to a list:

Pattern matching works with Plus:

Distribute a function over Plus:

Distribute Plus through a head:

Accumulate makes a cumulative sum: