monoid(...,Local=>...) -- specify local or global monomial order

Synopsis

Usage:

monoid[x,y,z, Local => P, Global => Q]

Description

The optional argument Global specifies whether all variables are larger than 1 in the monomial order. The default value Global => true means that rings in Macaulay2 are by default global rings. If set to true, and the option Inverses => true is not specified, an error is raised if any of the variables are not greater than 1 in the monomial ordering, as required by the standard theory of Gröbner bases.

i1 : QQ[x,y, Weights => {-1,1}, Global => false]

o1 = QQ[x..y]

o1 : PolynomialRing

i2 : 1 > x

o2 = true

i3 : 1 < y

o3 = true

i4 : leadTerm matrix{{x+x^2, y+y^2}}

o4 = | x y2 |

                      1               2
o4 : Matrix (QQ[x..y])  <-- (QQ[x..y])

The optional argument Local specifies whether all variables are smaller than 1 in the monomial order. Providing Local => true induces a local monomial ordering and in particular implies Global => false. A shortcut for indicating a local monomial ordering is to use a List to provide the variables.

i5 : QQ[x,y, Local => true]

o5 = QQ {x..y}

o5 : PolynomialRing

i6 : 1 > x

o6 = true

i7 : 1 > y

o7 = true

i8 : QQ{x,y}

o8 = QQ {x..y}

o8 : PolynomialRing

i9 : leadTerm matrix{{x+x^2, y+y^2}}

o9 = | x y |

                       1                2
o9 : Matrix (QQ {x..y})  <-- (QQ {x..y})

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

Further information

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

Functions with optional argument named Local :

monoid(...,Local=>...) -- specify local or global monomial order
newRing(...,Local=>...) -- see newRing -- make a copy of a ring, with some features changed
symmetricAlgebra(...,Local=>...) -- see symmetricAlgebra -- the symmetric algebra of a module
tensor(Monoid,Monoid,Local=>...) -- see tensor(Monoid,Monoid) -- tensor product of monoids
tensor(Ring,Ring,Local=>...) -- see tensor(Monoid,Monoid) -- tensor product of monoids

monoid(...,Local=>...) -- specify local or global monomial order

Synopsis

Description

Further information

See also

Functions with optional argument named Local :