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

Synopsis

• Usage:

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

Description

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

Further information

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

See also

• monoid -- make or retrieve a monoid
• newRing -- make a copy of a ring, with some features changed
• tensor(Ring,Ring) -- tensor product of monoids
• symmetricAlgebra -- the symmetric algebra of a module
• leadTerm -- get the greatest term
• monoid(...,MonomialOrder=>...) -- specify the monomial ordering

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