monoid -- make a monoid

monoid -- make a monoid

monoid [a,b,c,Degrees=>{2,3,4}] -- makes a free ordered commutative monoid on the variables listed, with degrees 2, 3, and 4, respectively.

monoid [a,b,c,Degrees=>{{1,2},{3,-3},{0,4}}] -- makes a free ordered commutative monoid on the variables listed, with multi-degrees as listed.

monoid [a,b,c,Degrees=>{{},{},{}}] -- makes a free ordered commutative monoid on the variables listed, ungraded.

The variables listed may be symbols or indexed variables. The values assigned to these variables (with assign) are the corresponding monoid generators. The function baseName may be used to recover the original symbol or indexed variable.

The class of all monoids created this way is GeneralOrderedMonoid.

See also:

OrderedMonoid -- the class of all ordered monoids

IndexedVariable -- the class of all indexed variables

Symbol -- the class of all symbols

The function monoid is a member of the class Function.

Ways to use monoid :

monoid QuotientRing

monoid Ring -- get the monoid from a monoid ring

monoid [...] -- make a polynomial ring or monoid ring