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Monomial - Wikipedia, the free encyclopedia (307 words) |
 | The most obvious fact about monomials is that any polynomial is a linear combination of them, so they can serve as basis vectors in a vector space of polynomials - a fact of constant implicit use in mathematics. |
| In group representation theory, a monomial representation is a particular kind of induced representation. |
| In propositional logic, a monomial is a conjunction of literals. |
| Representation and Monomial Orders (1472 words) |
| Multivariate polynomial rings are constructed in Magma such that the monomials of any polynomial are sorted with respect to a specified monomial order, with the greatest monomial first. |
| A Gröbner basis of an ideal with respect to the graded reverse lexicographical order is usually the easiest to compute so it is recommended that this order be used when just any Gröbner basis for an ideal is desired. |
| Thus all variables but the i-th are "eliminated" so that a Gröbner basis of a zero-dimensional ideal I with this ordering will contain the unique monic generator of the elimination ideal consisting of all the polynomials in I containing the i-th variable alone. |
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