# / -- a binary operator, usually used for division

• 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)

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

## Ways to use symbol / :

• "CC / CC"
• "CC / QQ"
• "CC / RR"
• "CC / ZZ"
• "QQ / CC"
• "QQ / QQ"
• "QQ / RR"
• "QQ / ZZ"
• "RR / CC"
• "RR / QQ"
• "RR / RR"
• "RR / ZZ"
• "ZZ / CC"
• "ZZ / QQ"
• "ZZ / RR"
• "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
• "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 .

This operator may be used as a binary operator in an expression like x/y. The user may install binary methodsfor 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.