// -- a binary operator, usually used for quotient

Synopsis

Usage:

x // y

Description

For ring elements in the integers, polynomial rings, and other rings, there are two types of division: exact division, whose result is often in a larger field, such as the rationals or a function field, and division with remainder, whose result is in the same ring. In Macaulay2, '/' denotes the first kind of division, while '//' denotes the latter kind. The following example shows the difference between // and /.

i1 : 4/2

o1 = 2

o1 : QQ

i2 : 4//2

o2 = 2

i3 : R = QQ[x];

i4 : (x^2-3)//(x-1)

o4 = x + 1

o4 : R

i5 : (x^2-3)%(x-1)

o5 = -2

o5 : R

i6 : (x^2-3)/(x-1)

      2
     x  - 3
o6 = ------
      x - 1

o6 : frac R

Ways to use symbol // :

CC // CC
CC // QQ
CC // RR
CC // ZZ
InfiniteNumber // QQ
InfiniteNumber // RR
InfiniteNumber // ZZ
Matrix // Number
Number // InfiniteNumber
Number // Matrix
Number // RingElement
QQ // QQ
QQ // ZZ
RingElement // Number
RR // QQ
RR // RR
RR // ZZ
ZZ // MonomialIdeal
ZZ // ZZ
Constant // InfiniteNumber (missing documentation)
InexactNumber // RingElement (missing documentation)
InfiniteNumber // CC (missing documentation)
InfiniteNumber // Constant (missing documentation)
InfiniteNumber // InfiniteNumber (missing documentation)
List // Number (missing documentation)
List // RingElement (missing documentation)
Matrix // GroebnerBasis -- see Matrix // Matrix -- factor a map through another
Matrix // Matrix -- factor a map through another
Matrix // MonomialIdeal -- see Matrix // Matrix -- factor a map through another
Matrix // RingElement -- see Matrix // Matrix -- factor a map through another
RingElement // GroebnerBasis -- see Matrix // Matrix -- factor a map through another
RingElement // Matrix -- see Matrix // Matrix -- factor a map through another
RingElement // MonomialIdeal -- see Matrix // Matrix -- factor a map through another
RingElement // RingElement -- see Matrix // Matrix -- factor a map through another
RingElement // InexactNumber (missing documentation)
Thing // Command -- see Thing // Function -- apply a function
Thing // Function -- apply a function
Thing // SelfInitializingType -- see Thing // Function -- apply a function

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.

// -- a binary operator, usually used for quotient

Synopsis

Description

See also

Ways to use symbol // :

For the programmer