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

Synopsis

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
- GradedModuleMap
- 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
GradedModuleMap - GradedModuleMap
GradedModuleMap - RingElement
InexactNumber - Constant
InfiniteNumber - InfiniteNumber
InfiniteNumber - Number
Matrix - Matrix
Matrix - Number
Matrix - RingElement
MutableMatrix - MutableMatrix
Number - Constant
Number - InfiniteNumber
Number - Matrix
ProjectiveHilbertPolynomial - ProjectiveHilbertPolynomial
ProjectiveHilbertPolynomial - ZZ
QQ - CC
QQ - QQ
QQ - RR
QQ - RRi
QQ - ZZ
RingElement - ChainComplexMap
RingElement - GradedModuleMap
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 - ProjectiveHilbertPolynomial
ZZ - QQ
ZZ - RR
ZZ - RRi
ZZ - ZZ
- List -- negation of a vector
- SheafMap (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 -- see Expression -- the class of all expressions
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
VirtualTally - VirtualTally -- see VirtualTally

For the programmer

The object - is a keyword.

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) -> ...