- -- 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"
"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 - 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 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.