monoid(...,Join=>...) -- specify how to handle degrees in the coefficient ring

Synopsis

Usage:

monoid[a,b,c, Join => P]

Description

The Join option specifies whether the degrees in the new monoid ring will be obtained by joining the degrees in the coefficient with the degrees in the monoid.

By default, (multi)degrees are concatenated when forming polynomial rings over polynomial rings, as can be seen by examining the corresponding flattened monoid, which displays information about all of the variables.

i1 : QQ[x][y]

o1 = QQ[x][y]

o1 : PolynomialRing

i2 : oo.FlatMonoid

o2 = monoid[y, x, Degrees => {{1}, {0}}, Heft => {2:1}, MonomialOrder => {MonomialSize => 32}]
                              {0}  {1}                                   {GRevLex => {1}    }
                                                                         {Position => Up    }
                                                                         {GRevLex => {1}    }

o2 : GeneralOrderedMonoid

i3 : QQ[x][y][z]

o3 = QQ[x][y][z]

o3 : PolynomialRing

i4 : oo.FlatMonoid

o4 = monoid[z, y, x, Degrees => {{1}, {0}, {0}}, Heft => {3:1}, MonomialOrder => {MonomialSize => 32}]
                                 {0}  {1}  {0}                                   {GRevLex => {1}    }
                                 {0}  {0}  {1}                                   {Position => Up    }
                                                                                 {2:(GRevLex => {1})}

o4 : GeneralOrderedMonoid

That behavior can be overridden with the monoid(...,Join=>...) option.

i5 : QQ[x][y, Join => false]

o5 = QQ[x][y]

o5 : PolynomialRing

i6 : oo.FlatMonoid

o6 = monoid[y, x, Degrees => {2:1}, Heft => {1}, Join => false, MonomialOrder => {MonomialSize => 32}]
                                                                                 {GRevLex => {1}    }
                                                                                 {Position => Up    }
                                                                                 {GRevLex => {1}    }

o6 : GeneralOrderedMonoid

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: null
Function: monoid -- make or retrieve a monoid
Option key: Join -- an optional argument

Functions with optional argument named Join :

monoid(...,Join=>...) -- specify how to handle degrees in the coefficient ring
newRing(...,Join=>...) -- see newRing -- make a copy of a ring, with some features changed
symmetricAlgebra(...,Join=>...) -- see symmetricAlgebra -- the symmetric algebra of a module
tensor(Monoid,Monoid,Join=>...) -- see tensor(Monoid,Monoid) -- tensor product of monoids
tensor(Ring,Ring,Join=>...) -- see tensor(Monoid,Monoid) -- tensor product of monoids

monoid(...,Join=>...) -- specify how to handle degrees in the coefficient ring

Synopsis

Description

Further information

See also

Functions with optional argument named Join :