monoid(...,Inverses=>...) -- allow negative exponents in monomials

Usage:

monoid[X,Y, Inverses => P]

Description

The optional argument Inverses specifies whether negative exponents will be allowed, making the monoid into a group. This option is mainly used by degreesMonoid and degreesRing functions to allow negative exponents in the monomials.

i1 : S = QQ[x,y, Inverses => true, MonomialOrder => Lex]

o1 = S

o1 : PolynomialRing

i2 : S_{1,-1} + S_{-1,1}

        -1    -1
o2 = x*y   + x  y

o2 : S

This option may also be used when creating a new ring from an existing ring, creating a tensor product ring, or symmetric algebra.

Functions with optional argument named Inverses:

monoid(...,Inverses=>...) -- allow negative exponents in monomials
newRing(...,Inverses=>...) -- see newRing -- make a copy of a ring, with some features changed
symmetricAlgebra(...,Inverses=>...) -- see symmetricAlgebra -- the symmetric algebra of a module
tensor(Monoid,Monoid,Inverses=>...) -- see tensor(Monoid,Monoid) -- tensor product of monoids
tensor(Ring,Ring,Inverses=>...) -- see tensor(Monoid,Monoid) -- tensor product of monoids

Further information

Default value: false
Function: monoid -- make or retrieve a monoid
Option key: Inverses -- an optional argument

The source of this document is in Macaulay2Doc/functions/monoid-doc.m2:563:0.

monoid(...,Inverses=>...) -- allow negative exponents in monomials

Description

See also

Functions with optional argument named Inverses:

Further information