monoid[a,b,c,...]
monoid{a,b,c,...}
The function monoid is called whenever a polynomial ring is created, see Ring Array, or when a local polynomial ring is made, see Ring List. Some of the options provided when making a monoid don't take effect until the monoid is made into a polynomial ring.
Let's make a free ordered commutative monoid on the variables a,b,c, with degrees 2, 3, and 4, respectively.
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Call use to assign the variables their values in the monoid.
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The options used when the monoid was created can be recovered with options.
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The variables listed may be symbols or indexed variables. The values assigned to these variables are the corresponding monoid generators. The function baseName may be used to recover the original symbol or indexed variable.
The monoid(...,Heft=>...) option is used, for instance, by Ext(Module,Module).
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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.
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That behavior can be overridden with the monoid(...,Join=>...) option.
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The object monoid is a method function with a single argument.
The source of this document is in Macaulay2Doc/functions/monoid-doc.m2:563:0.