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

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)

See also

Ways to use symbol -:

  • - CC
  • - Constant
  • - InfiniteNumber
  • - List
  • - Matrix
  • - MutableMatrix
  • - QQ
  • - RingElement
  • - RR
  • - RRi
  • - Tally
  • - Vector
  • - ZZ
  • CC - CC
  • CC - InfiniteNumber
  • CC - QQ
  • CC - RR
  • CC - ZZ
  • Constant - Constant
  • Constant - InexactNumber
  • Constant - Number
  • Constant - RingElement
  • InexactNumber - Constant
  • InexactNumber - RingElement
  • InfiniteNumber - CC
  • InfiniteNumber - InfiniteNumber
  • InfiniteNumber - Number
  • Matrix - Matrix
  • Matrix - Number
  • Matrix - RingElement
  • MutableMatrix - MutableMatrix
  • Number - Constant
  • Number - InfiniteNumber
  • Number - Matrix
  • Number - RingElement
  • Number - Vector
  • QQ - CC
  • QQ - QQ
  • QQ - RR
  • QQ - RRi
  • QQ - ZZ
  • RingElement - Constant
  • RingElement - InexactNumber
  • RingElement - Matrix
  • RingElement - Number
  • RingElement - RingElement
  • RingElement - Vector
  • RR - CC
  • RR - QQ
  • RR - RR
  • RR - RRi
  • RR - ZZ
  • RRi - QQ
  • RRi - RR
  • RRi - RRi
  • RRi - ZZ
  • Vector - Number
  • Vector - RingElement
  • Vector - Vector
  • ZZ - CC
  • ZZ - QQ
  • ZZ - RR
  • ZZ - RRi
  • ZZ - ZZ
  • - VirtualTally -- negation of a virtual tally
  • List - List -- difference of two vectors
  • MonomialIdeal - MonomialIdeal -- monomial ideal difference
  • 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

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) -> ...

where Y is the class of y.

The source of this document is in Macaulay2Doc/operators/minus.m2:113:0.