# + -- a unary or binary operator, usually used for addition

• Usage:
+y
x+y

## Description

In most cases, this operator refers to standard addition.

In many cases, the integer 1 can be used as the identity, and scalars function as multiples of the identity. For example, the 1 below refers to the identity matrix and the 2 to twice the identity matrix.

 ```i1 : M = matrix{{1,2,3},{2,3,4},{3,4,6}} o1 = | 1 2 3 | | 2 3 4 | | 3 4 6 | 3 3 o1 : Matrix ZZ <--- ZZ``` ```i2 : M+1, M+2 o2 = (| 2 2 3 |, | 3 2 3 |) | 2 4 4 | | 2 5 4 | | 3 4 7 | | 3 4 8 | o2 : Sequence```

• sum -- compute the sum

## Ways to use + :

• + CC
• + Constant
• + QQ
• + RR
• + ZZ
• CC + CC
• CC + QQ
• CC + RR
• CC + ZZ
• ChainComplexMap + ChainComplexMap
• ChainComplexMap + RingElement
• ChainComplexMap + ZZ
• Constant + Constant
• Constant + InexactNumber
• Constant + Number
• Ideal + RingElement
• InexactNumber + Constant
• InfiniteNumber + InfiniteNumber
• InfiniteNumber + Number
• Matrix + Matrix
• Matrix + Number
• Matrix + RingElement
• MonomialIdeal + MonomialIdeal
• MutableMatrix + MutableMatrix
• Number + Constant
• Number + InfiniteNumber
• Number + Matrix
• ProjectiveHilbertPolynomial + ProjectiveHilbertPolynomial
• QQ + CC
• QQ + QQ
• QQ + RR
• QQ + ZZ
• RingElement + ChainComplexMap
• RingElement + Matrix
• RingElement + RingElement
• RR + CC
• RR + QQ
• RR + RR
• RR + ZZ
• Vector + Vector
• ZZ + CC
• ZZ + ChainComplexMap
• ZZ + QQ
• ZZ + RR
• ZZ + ZZ
• + RingElement (missing documentation)
• CC + InfiniteNumber (missing documentation)
• Constant + RingElement, see Constant
• RingElement + Constant, see Constant
• Constant + InfiniteNumber (missing documentation)
• Expression + Expression, see Expression -- the class of all expressions
• Expression + Holder, see Expression -- the class of all expressions
• Expression + Thing, see Expression -- the class of all expressions
• Holder + Expression, see Expression -- the class of all expressions
• Holder + Holder, see Expression -- the class of all expressions
• Thing + Expression, see Expression -- the class of all expressions
• Ideal + Ideal -- sum of ideals
• Ideal + MonomialIdeal, see Ideal + Ideal -- sum of ideals
• MonomialIdeal + Ideal, see Ideal + Ideal -- sum of ideals
• Ideal + Number (missing documentation)
• IndexedVariable + IndexedVariable (missing documentation)
• InexactNumber + RingElement (missing documentation)
• InfiniteNumber + CC (missing documentation)
• InfiniteNumber + Constant (missing documentation)
• List + List -- sum of two vectors
• Module + Module -- sum of submodules
• Number + Ideal (missing documentation)
• ProjectiveHilbertPolynomial + ZZ (missing documentation)
• RingElement + Ideal (missing documentation)
• RingElement + InexactNumber (missing documentation)
• Set + Set -- set union
• Sum + Holder (missing documentation)
• Tally + Tally -- union of tallies
• VirtualTally + VirtualTally -- union of tallies
• ZZ + ProjectiveHilbertPolynomial (missing documentation)

## For the programmer

The object + is .

This operator may be used as a binary operator in an expression like x+y. The user may install binary methods for handling such expressions with code such as

`         X + Y := (x,y) -> ...`

where X is the class of x and Y is the class of y.

This operator may be used as a prefix unary operator in an expression like +y. The user may install a method for handling such expressions with code such as

`           + Y := (y) -> ...`

where Y is the class of y.