monomial ordering造句
造句與例句
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- Monomial orderings are most commonly used with multivariate division.
- The two monomial orderings change the calculations.
- Reduced Gr鯾ner bases are " unique " for any given ideal and any monomial ordering.
- The defining property of monomial orderings implies that the order of the terms is kept when multiplying a polynomial by a monomial.
- This is for instance the case when considering a monomial basis of a polynomial ring, or a monomial ordering of that basis.
- The "'leading term "'of a polynomial is thus the term of the largest monomial ( for the chosen monomial ordering.
- When using monomial orderings to compute Gr鯾ner bases, different orders can lead to different results, and the difficulty of the computation may vary dramatically.
- Multivariate division requires a monomial ordering, the basis depends on the monomial ordering chosen, and different orderings can give rise to radically different Gr鯾ner bases.
- Multivariate division requires a monomial ordering, the basis depends on the monomial ordering chosen, and different orderings can give rise to radically different Gr鯾ner bases.
- In most cases ( polynomials in finitely many variables with complex coefficients or, more generally, coefficients over any field, for example ), Gr鯾ner bases exist for any monomial ordering.
- It's difficult to see monomial ordering in a sentence. 用monomial ordering造句挺難的
- Although the dimension and the degree do not depend on the choice of the monomial ordering, the Hilbert series and the polynomial P ( t ) change when one changes of monomial ordering.
- Although the dimension and the degree do not depend on the choice of the monomial ordering, the Hilbert series and the polynomial P ( t ) change when one changes of monomial ordering.
- This is easily tested with a Gr鯾ner basis computation, because 1 belongs to an ideal if and only if 1 belongs to the Gr鯾ner basis of the ideal, for any monomial ordering.
- Explicitly, it is used to define the degree of a polynomial and the notion of homogeneous polynomial, as well as for graded monomial orderings used in formulating and computing Taylor series in several variables.
- Once a monomial ordering is fixed, the " terms " of a polynomial ( product of a monomial with its nonzero coefficient ) are naturally ordered by decreasing monomials ( for this order ).
- The quotient of a ring by an ideal depends only on the ring and the ideal, nothing else; monomial ordering only comes into the picture when looking for a basis . J . 13 : 26, 26 October 2010 ( UTC)
- When the number of zeros is finite, the Gr鯾ner basis for a lexicographical monomial ordering provides, theoretically, a solution : the first coordinates of a solution is a root of the greatest common divisor of polynomials of the basis that depends only of the first variable.
- Finally let " B " be a Gr鯾ner basis of " I " for a monomial ordering refining the total degree partial ordering and " G " the ( homogeneous ) ideal generated by the leading monomials of the elements of " B ".
- An ideal does not have any zero ( the system of equations is inconsistent ) if and only if 1 belongs to the ideal ( this is Hilbert's Nullstellensatz ), or, equivalently, if its Gr鯾ner basis ( for any monomial ordering ) contains 1, or, also, if the corresponding reduced Gr鯾ner basis is [ 1 ].
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