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Computational Complexity in Polynomial Algebra
"... In recent years a number of algorithms have been designed for the "inverse" computational problems of polynomial algebra—factoring polynomials, solving systems of polynomial equations, or systems of polynomial inequalities, and related problems—with running time considerably less than tha ..."
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In recent years a number of algorithms have been designed for the "inverse" computational problems of polynomial algebra—factoring polynomials, solving systems of polynomial equations, or systems of polynomial inequalities, and related problems—with running time considerably less than
The Basic Polynomial Algebra Subprograms
"... Abstract. The Basic Polynomial Algebra Subprograms (BPAS) provides arithmetic operations (multiplication, division, root isolation, etc.) for univariate and multivariate polynomials over prime fields or with integer coefficients. The code is mainly written in CilkPlus [10] targeting multicore proce ..."
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Abstract. The Basic Polynomial Algebra Subprograms (BPAS) provides arithmetic operations (multiplication, division, root isolation, etc.) for univariate and multivariate polynomials over prime fields or with integer coefficients. The code is mainly written in CilkPlus [10] targeting mul
Automorphic orbit problem for polynomial algebras
 J. Algebra
"... Abstract. It is proved that every endomorphism preserving the automorphic orbit of a nontrivial element of the rank two polynomial algebra over the complex number field is an automorphism. ..."
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Cited by 3 (3 self)
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Abstract. It is proved that every endomorphism preserving the automorphic orbit of a nontrivial element of the rank two polynomial algebra over the complex number field is an automorphism.
Polynomial Algebras and Higher Spins by
, 1996
"... Polynomial relations for generators of su(2) Lie algebra in arbitrary representations are found. They generalize usual relation for Pauli operators in spin 1/2 case and permit to construct modified HolsteinPrimakoff transformations in finite dimensional Fock spaces. The connection between su(2) Lie ..."
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Polynomial relations for generators of su(2) Lie algebra in arbitrary representations are found. They generalize usual relation for Pauli operators in spin 1/2 case and permit to construct modified HolsteinPrimakoff transformations in finite dimensional Fock spaces. The connection between su(2
On constructing resolutions over the polynomial algebra
 HOMOLOGY, HOMOTOPY AND APPLICATIONS
, 2002
"... Let k be a field, and A be a polynomial algebra over k. Let I ⊆ A be an ideal. We present a novel method for computing resolutions of A/I over A. The method is a synthesis of Gröbner basis techniques and homological perturbation theory. The examples in this paper were computed using computer algebr ..."
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Cited by 3 (1 self)
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Let k be a field, and A be a polynomial algebra over k. Let I ⊆ A be an ideal. We present a novel method for computing resolutions of A/I over A. The method is a synthesis of Gröbner basis techniques and homological perturbation theory. The examples in this paper were computed using computer
Automorphisms of polynomial algebras and Dirichlet series
, 2008
"... Let Fq[x, y] be the polynomial algebra in two variables over the finite field Fq with q elements. We give an exact formula and the asymptotics for the number pn of automorphisms (f, g) of Fq[x, y] such that max{deg(f), deg(g)} = n. We describe also the Dirichlet series generating function p(s) = ..."
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Cited by 2 (1 self)
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Let Fq[x, y] be the polynomial algebra in two variables over the finite field Fq with q elements. We give an exact formula and the asymptotics for the number pn of automorphisms (f, g) of Fq[x, y] such that max{deg(f), deg(g)} = n. We describe also the Dirichlet series generating function p
Applications of Polynomial Algebras to 2Dimensional Deformed Oscillators
, 909
"... The polynomial algebra is a deformed SU(2) algebra. Here, we use polynomial algebra as a method to solve a series of deformed oscillators. Meanwhile, we find a series of physics systems for polynomial algebra. 1 ..."
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The polynomial algebra is a deformed SU(2) algebra. Here, we use polynomial algebra as a method to solve a series of deformed oscillators. Meanwhile, we find a series of physics systems for polynomial algebra. 1
On the Algebraic KTheory of Truncated Polynomial Algebras
 Cambridge University Press 15
, 2013
"... ar ..."
THE BOUSFIELD LATTICE FOR TRUNCATED POLYNOMIAL ALGEBRAS
, 802
"... Abstract. The global structure of the unbounded derived category of a truncated polynomial ring on countably many generators is investigated, via its Bousfield lattice. The Bousfield lattice is shown to have cardinality larger than that of the real numbers, and objects with large tensornilpotence h ..."
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Cited by 11 (0 self)
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Abstract. The global structure of the unbounded derived category of a truncated polynomial ring on countably many generators is investigated, via its Bousfield lattice. The Bousfield lattice is shown to have cardinality larger than that of the real numbers, and objects with large tensor
Results 1  10
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7,817