# - -- a unary or binary operator, usually used for negation or subtraction

• Usage:
-y
x-y

## Description

In most cases, this operator refers to standard negation or subtraction.

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 = (| 0 2 3 |, | -1 2 3 |) | 2 2 4 | | 2 1 4 | | 3 4 5 | | 3 4 4 | o2 : Sequence

### Intervals

If one of the inputs is an RRi, the output is an interval containing all differences of pairs in the inputs.

 i3 : 2-interval(1,3) o3 = [-1,1] o3 : RRi (of precision 53) i4 : interval(1,3)-interval(-1,2) o4 = [-1,4] o4 : RRi (of precision 53) i5 : interval(-1,1)-interval(-1,1) o5 = [-2,2] o5 : RRi (of precision 53)

## Ways to use symbol - :

• "- CC"
• "- ChainComplexMap"
• "- Constant"
• "- Holder"
• "- InfiniteNumber"
• "- Matrix"
• "- Minus"
• "- MutableMatrix"
• "- ProjectiveHilbertPolynomial"
• "- QQ"
• "- RingElement"
• "- RR"
• "- RRi"
• "- ZeroExpression"
• "- ZZ"
• "CC - CC"
• "CC - QQ"
• "CC - RR"
• "CC - ZZ"
• "ChainComplexMap - ChainComplexMap"
• "ChainComplexMap - RingElement"
• "Constant - Constant"
• "Constant - InexactNumber"
• "Constant - Number"
• "InexactNumber - Constant"
• "InfiniteNumber - InfiniteNumber"
• "InfiniteNumber - Number"
• "Matrix - Matrix"
• "Matrix - Number"
• "Matrix - RingElement"
• "MutableMatrix - MutableMatrix"
• "Number - Constant"
• "Number - InfiniteNumber"
• "Number - Matrix"
• "ProjectiveHilbertPolynomial - ProjectiveHilbertPolynomial"
• "QQ - CC"
• "QQ - QQ"
• "QQ - RR"
• "QQ - RRi"
• "QQ - ZZ"
• "RingElement - ChainComplexMap"
• "RingElement - Matrix"
• "RingElement - RingElement"
• "RR - CC"
• "RR - QQ"
• "RR - RR"
• "RR - RRi"
• "RR - ZZ"
• "RRi - QQ"
• "RRi - RR"
• "RRi - RRi"
• "RRi - ZZ"
• "Vector - Vector"
• "ZZ - CC"
• "ZZ - QQ"
• "ZZ - RR"
• "ZZ - RRi"
• "ZZ - ZZ"
• - Expression (missing documentation)
• - List -- negation of a vector
• - String (missing documentation)
• - String = Thing (missing documentation)
• - Tally (missing documentation)
• - Vector -- negation of a Vector
• - VirtualTally -- negation of a VirtualTally
• 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
• InexactNumber - RingElement (missing documentation)
• InfiniteNumber - CC (missing documentation)
• InfiniteNumber - Constant (missing documentation)
• List - List -- difference of two vectors
• MonomialIdeal - MonomialIdeal -- monomial ideal difference
• RingElement - InexactNumber (missing documentation)
• "List - Set" -- see Set - Set -- set difference
• "Set - List" -- see Set - Set -- set difference
• Set - Set -- set difference
• Tally - Tally -- difference of tallies
• Thing - Minus (missing documentation)
• "VirtualTally - VirtualTally" -- see VirtualTally

## 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.