monoid(...,Weights=>...) -- specify weights of the variables

Usage:

monoid[a,b,c, Weights => {w1, w2, w3}]

Description

This option specifies the weights of the variables in the monoid. The orderings by these weight vectors is prepended to the list of orderings provided by the monoid(...,MonomialOrder=>...) option. The value must be a list integers when the degree length is one, or a list of lists of integers otherwise.

i1 : R = QQ[x,y]

o1 = R

o1 : PolynomialRing

i2 : leadTerm matrix {{x+y, x^2+y}}

o2 = | x x2 |

             1      2
o2 : Matrix R  <-- R

i3 : R = QQ[x,y, Weights => {1,2}]

o3 = R

o3 : PolynomialRing

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

o4 = | y x2 |

             1      2
o4 : Matrix R  <-- R

i5 : R = QQ[x,y, Weights => {1,3}]

o5 = R

o5 : PolynomialRing

i6 : leadTerm matrix {{x+y, x^2+y}}

o6 = | y y |

             1      2
o6 : Matrix R  <-- R

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 Weights:

betti(...,Weights=>...) -- see betti(BettiTally) -- view and set the weight vector of a Betti diagram
minimalBetti(...,Weights=>...) -- see minimalBetti -- minimal betti numbers of (the minimal free resolution of) a homogeneous ideal or module
monoid(...,Weights=>...) -- specify weights of the variables
newRing(...,Weights=>...) -- see newRing -- make a copy of a ring, with some features changed
regularity(...,Weights=>...) -- see regularity -- compute the Castelnuovo-Mumford regularity
symmetricAlgebra(...,Weights=>...) -- see symmetricAlgebra -- the symmetric algebra of a module
tensor(Monoid,Monoid,Weights=>...) -- see tensor(Monoid,Monoid) -- tensor product of monoids
tensor(Ring,Ring,Weights=>...) -- see tensor(Monoid,Monoid) -- tensor product of monoids

Further information

Default value: {}
Function: monoid -- make or retrieve a monoid
Option key: Weights -- assigning weights to the variables

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

monoid(...,Weights=>...) -- specify weights of the variables

Description

See also

Functions with optional argument named Weights:

Further information