Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The “predictable degree property”, a terminology introduced by Forney in 1970, is a property of polynomial matrices over a field F that has proven itself to be fundamentally useful for a range of applications.   strengthen this property into the “predictable leading monomial” property, and show that this PLM property is shared by minimal Grobner bases for any positional term order (here: TOP and POT) in F[x] q . The property is useful particularly for minimal interpolationtype problems. Because of the presence of zero divisors, minimal Grobner bases over a finite ring of the type ℤ p r (where p is a prime integer and r is an integer > 1) do not have the PLM property.  show how to construct, from an ordered minimal Grobner basis, a so-called minimal Grobner p-basis that does have a PLM property. The parametrization of all shortest linear recurrence relations of a finite sequence over ℤ p r is a type of problem for which this is useful and  include an illustrative example.
['Margreta Kuijper', 'Kristina Schindelar']
I am writing a research paper on a idea The predictable leading monomial property for polynomial vectors over a ring
[{"from": "human", "value": "I am writing a research paper on a idea The predictable leading monomial property for polynomial vectors over a ring"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The \u201cpredictable degree property\u201d, a terminology introduced by Forney in 1970, is a property of polynomial matrices over a field F that has proven itself to be fundamentally useful for a range of applications.   strengthen this property into the \u201cpredictable leading monomial\u201d property, and show that this PLM property is shared by minimal Grobner bases for any positional term order (here: TOP and POT) in F[x] q . The property is useful particularly for minimal interpolationtype problems. Because of the presence of zero divisors, minimal Grobner bases over a finite ring of the type \u2124 p r (where p is a prime integer and r is an integer > 1) do not have the PLM property.  show how to construct, from an ordered minimal Grobner basis, a so-called minimal Grobner p-basis that does have a PLM property. The parametrization of all shortest linear recurrence relations of a finite sequence over \u2124 p r is a type of problem for which this is useful and  include an illustrative example."}]