/ -- a binary operator, usually used for division

Synopsis

Usage:

x / y

Description

This operator is currently used in several ways in Macaulay2.

division in a ring, yielding a fraction
division in unevaluated expressions
quotient rings, modules and sheaves
applying a function or ring map to every element of a list or set

i1 : 2/3

     2
o1 = -
     3

o1 : QQ

i2 : 2./3

o2 = .666666666666667

o2 : RR (of precision 53)

Intervals

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

i3 : 2/interval(1,3)

o3 = [.666666666666667,2]

o3 : RRi (of precision 53)

i4 : interval(-1,2)/interval(1,3)

o4 = [-1,2]

o4 : RRi (of precision 53)

i5 : interval(1,2)/interval(1,2)

o5 = [.5,2]

o5 : RRi (of precision 53)

Ways to use symbol / :

CC / CC
CC / QQ
CC / RR
CC / ZZ
QQ / CC
QQ / QQ
QQ / RR
QQ / RRi
QQ / ZZ
RR / CC
RR / QQ
RR / RR
RR / RRi
RR / ZZ
RRi / QQ
RRi / RR
RRi / RRi
RRi / ZZ
ZZ / CC
ZZ / QQ
ZZ / RR
ZZ / RRi
ZZ / ZZ
CoherentSheaf / CoherentSheaf -- quotient of coherent sheaves
CoherentSheaf / Ideal -- see CoherentSheaf / CoherentSheaf -- quotient of coherent sheaves
Constant / Constant -- see Constant
Constant / InexactNumber -- see Constant
Constant / Number -- see Constant
Constant / RingElement -- see Constant
Holder / OneExpression -- see Constant
InexactNumber / Constant -- see Constant
Number / Constant -- 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
Ideal / Function -- apply a function to generators of an ideal
Ideal / Ideal -- quotient module
InexactNumber / RingElement (missing documentation)
InfiniteNumber / CC (missing documentation)
InfiniteNumber / Constant (missing documentation)
List / Thing -- vector division
Module / Ideal -- see Module / Module -- quotient module
Module / List -- see Module / Module -- quotient module
Module / Module -- quotient module
Module / RingElement -- see Module / Module -- quotient module
Module / Sequence -- see Module / Module -- quotient module
Module / Vector -- see Module / Module -- quotient module
MonoidElement / MonoidElement (missing documentation)
Ring / Ideal -- make a quotient ring
Ring / List -- see Ring / Ideal -- make a quotient ring
Ring / Module -- see Ring / Ideal -- make a quotient ring
Ring / MonomialIdeal -- see Ring / Ideal -- make a quotient ring
Ring / RingElement -- see Ring / Ideal -- make a quotient ring
Ring / Sequence -- see Ring / Ideal -- make a quotient ring
Ring / ZZ -- see Ring / Ideal -- make a quotient ring
RingElement / InexactNumber (missing documentation)
RingElement / RingElement -- fraction
Set / Command (missing documentation)
Set / Function (missing documentation)
List / Command -- see VisibleList / Function -- apply a function to elements of a list
List / Function -- see VisibleList / Function -- apply a function to elements of a list
List / RingMap -- see VisibleList / Function -- apply a function to elements of a list
String / Command -- see VisibleList / Function -- apply a function to elements of a list
String / Function -- see VisibleList / Function -- apply a function to elements of a list
VirtualTally / Command -- see VisibleList / Function -- apply a function to elements of a list
VirtualTally / Function -- see VisibleList / Function -- apply a function to elements of a list
VisibleList / Command -- see VisibleList / Function -- apply a function to elements of a list
VisibleList / Function -- apply a function to elements of a list
VisibleList / SelfInitializingType -- see VisibleList / Function -- apply a function to elements of a list

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) -> ...