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Extremal Sparse Polynomial Systems Over Local Fields
Extremal Sparse Polynomial Systems Local Fields
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2010/11/23
Consider a system F of n polynomials in n variables, with a total of n+k distinct exponent vectors, over any local field L of characteristic 0. We discuss conjecturally tight upper and lower bounds o...
alphaCertified: certifying solutions to polynomial systems
alphaCertified certifying polynomial systems
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2010/11/11
Smale's alpha-theory uses estimates related to the convergence of Newton's method to give criteria implying that Newton iterations will converge quadratically to solutions to a square polynomial syste...
Root Isolation of Zero-dimensional Polynomial Systems with Linear Univariate Representation
Zero-dimensional polynomial system linear univariate representation local generic position root isolation
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2013/9/9
In this paper, a linear univariate representation for the roots of a zero-dimensional polynomial equation system is presented, where the roots of the equation system are represented as linear combinat...
Explicit non-algebraic limit cycle for polynomial systems of degree seven
Planar polynomial differential system Algebraic solution
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2010/9/13
Explicit non-algebraic limit cycle for polynomial systems of degree seven.
Ritt-Wu's Characteristic Set Method For Ordinary Di®erence Polynomial Systems With Arbitrary Ordering
dierence polynomial ascending chain characteristic set Ritt-Wu's zero decomposition theorem
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2013/9/9
In this paper, a new Ritt-Wu's characteristic set method for ordinary di®erence systems is proposed, which is valid for any admissible ordering. New deˉnition for irreducible chains and new zero ...
A Characteristic Set Method For Ordinary Di®erence Polynomial Systems
di® erence polynomial ascending chain characteristic set coherence irreducibility zero decomposition theorem automated theorem proving
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2013/9/9
We prove several basic properties for di®erence ascending chains including a necessary and su±cient condition for an ascending chain to be the characteristic set of its saturation ideal and a nec...
Properties of Ascending Chains for Partial Difference Polynomial Systems
Ascending chain characteristic set coherent chain regular chain irreducible chain partial difference polynomial
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2013/9/9
A characteristic set theory for partial difference polynomial systems is proposed. We introduce the concept of coherent and regular ascending chains and prove that a partial difference ascending chain...
Number and Location of Limit Cycles in a Class of Perturbed Polynomial Systems
polynomial system limit cycles stability bifurcation
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2007/12/11
In this paper, we investigate the number, location andstability of limit cycles in a class of perturbed polynomialsystems with $(2n+1)$ or $(2n+2)$-degree by constructing detectionfunction and using q...
Characteristic set method for differential-difference polynomial systems
Characteristic set Differential and difference polynomial Regular ascending chain Irreducible ascending chain Zero decomposition algorithm Perfect ideal membership problem
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2013/9/9
In this paper, we present a characteristic set method for mixed differential and difference polynomial systems. We introduce the concepts of coherent, regular, proper irreducible, and strongly irreduc...
Characteristic Set Method for Dierential-Dierence Polynomial Systems
Characteristic set dierence and dierential polynomial coherent ascending chain regular ascending chain irreducible ascending chain zero decomposition algorithm
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2013/9/9
In this paper, we present a characteristic set method for mixed dierence and dierential polynomial systems. We introduce the concepts of coherent, regular,proper irreducible, and strong irreducible as...