/ -- 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
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) -> ...

where X is the class of x and Y is the class of y.