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Good bases for tame polynomials

2005
*
Journal of symbolic computation
*

An algorithm to compute a

doi:10.1016/j.jsc.2004.10.001
fatcat:euiltgtkergtflucu5ghmtcha4
*good*basis of the Brieskorn lattice of a cohomologically*tame**polynomial*is described. This algorithm is*based*on the results of C. ... Douai*for*convenient Newton non-degenerate*polynomials*. ... Acknowledgements The author is grateful to Claude Sabbah*for*drawing his attention to the subject and to Gert-Martin Greuel*for*valuable hints and discussions. ...##
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Efficient Resource Allocation in Hybrid Wireless Networks Increase the Capacity

2021
*
International Journal of Scientific Research in Computer Science Engineering and Information Technology
*

In this project we implemented a new technique with an algorithm named GNDA

doi:10.32628/cseit21715
fatcat:kza4wlwm3zerzmxszjqo4hujge
*Good*Node Detection Algorithm*Based*Approach technique with Wireless Sensor Networks. ... This project describes a*polynomial*pool*based*approach hybrid three-tier general framework that permits the use of any pairwise key predistribution scheme as its basic component. ...*Tame*-*based*key pre-distribution approach, where we exploit*tame*auto orphisms to get symmetric and two-one bivariate maps*for*the pairwise key establishment. ...##
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Tame Pool-Based Pairwise Key Predistribution for Large-Scale Sensor Networks

2009
*
GLOBECOM 2009 - 2009 IEEE Global Telecommunications Conference
*

It turns out that this

doi:10.1109/glocom.2009.5425302
dblp:conf/globecom/LiaoLWT09
fatcat:m4y2uxaawrezdilorfvey5zfca
*tame*map can substitute the conventional*polynomial*in any existing*polynomial*-*based*scheme to offer deterministic authentication service. ... This*tame*-*based*approach can provide deterministic authentication between two parties. We then present a general framework*for*the key predistribution, on the basis of the*tame*-*based*approach. ... Due to the use of conventional*polynomials**for*key predistribution, the*polynomial*pool-*based*schemes (The basic scheme [7] is a special case of the*polynomial*pool-*based*approach.) have collision problem ...##
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Page 4836 of Mathematical Reviews Vol. , Issue 93i
[page]

1993
*
Mathematical Reviews
*

If a

*polynomial*is not*good*then the map g is generally not a fibration. The paper under review introduces a large class of*polynomials*, semi-*tame**polynomials*,*for*which the mapping @ is a fibration. ... Like many of the other types of*polynomials*the definition is*based*on a gradient condition: f is semi-*tame*if*for*every sequence {z,} such that ||z;,|| - oo and grad f(z;,) = A,z, we have gradf(z,) — ...##
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Taming Reasoning in Temporal Probabilistic Relational Models
[article]

2019
*
arXiv
*
pre-print

To counteract groundings over time and to keep reasoning

arXiv:1911.07040v1
fatcat:6vsxusczqfbnvmxiyylddxvte4
*polynomial*by restoring a lifted representation, we present temporal approximate merging (*TAMe*), which incorporates (i) clustering*for*grouping ... In exchange*for*faster runtimes,*TAMe*introduces a bounded error that becomes negligible over time. ... do converge, allowing*TAMe*to keep reasoning*polynomial*. ...##
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Automorphisms of Weyl Algebra and a Conjecture of Kontsevich
[article]

2018
*
arXiv
*
pre-print

Our proof uses lifting of

arXiv:1802.01225v1
fatcat:r5b5knyytnbedgk3yya7jv4kwa
*polynomial*symplectomorphisms to Weyl algebra automorphisms by means of approximation by*tame*symplectomorphisms and gauging of the lifted morphism. ... Approximation by*tame*symplectomorphisms is the symplectic version of the well-known theorem of D. Anick and is a result of our prior work. ... This statement provides the*base*case*for*the processing of the higher-order terms. The gauging acts upon the term at 2 . ...##
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Locally tame plane polynomial automorphisms

2012
*
Journal of Pure and Applied Algebra
*

*For*automorphisms of a

*polynomial*ring in two variables over a domain R, we show that local

*tameness*implies global

*tameness*provided that every 2-generated locally free R-module of rank 1 is free. ... The last author is funded by Veni-grant of council

*for*the physical sciences, Netherlands Organisation

*for*Scientific Research (NWO). ... Acknowledgements The first author is funded by a free competition grant of the Netherlands Organisation

*for*Scientific Research (NWO). ...

##
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Page 7806 of Mathematical Reviews Vol. , Issue 2001K
[page]

2001
*
Mathematical Reviews
*

, calculate inverses, or determine

*tameness*over certain*base*rings. ... Emphasis is given to two topics: (1) Questions of*tameness*and stable*tameness*of particular automor- phisms; (2) Algorithms (which use Grdbner*bases*), e.g., decide whether an endomorphism is an automorphism ...##
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Tame torsion, the tame inverse Galois problem, and endomorphisms

2020
*
Manuscripta mathematica
*

As an application, we consider the

doi:10.1007/s00229-020-01213-2
fatcat:vjb6fx655vhtbdcr2w5bwdhzmi
*tame*inverse Galois problem and are able to realise general symplectic groups as Galois groups of*tame*extensions of Q. ... We prove the existence of a genus g curve C/Q such that the mod p representation of its Jacobian is*tame*by imposing conditions on the endomorphism ring. ... Acknowledgements I would like to thank Vladimir Dokchitser*for*suggesting this approach and helpful conversations. I am also indebted to the referee*for*suggesting the proof of Theorem 5.2. ...##
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Locally tame plane polynomial automorphisms
[article]

2010
*
arXiv
*
pre-print

*For*automorphisms of a

*polynomial*ring in two variables over a domain R, we show that local

*tameness*implies global

*tameness*provided that every 2-generated invertible R-module is free. ... This could suggest that, at least

*for*plane

*polynomial*automorphisms,

*tameness*is a property that can be checked locally on the

*base*ring. ... A

*good*starting point would be to have in general an effective algorithmic way to recognize

*tame*automorphisms. ...

##
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Tame torsion and endomorphisms
[article]

2019
*
arXiv
*
pre-print

We prove the existence of a genus g curve C/Q such that the mod p representation of its Jacobian is

arXiv:1912.08033v1
fatcat:rx46ysi4tnallkjxqagtb76eve
*tame*by imposing conditions on the endomorphism algebra. ...*For*primes ℓ 2g+1, ℓ = p choose a*polynomial*f ℓ (x) of degree 2g+2 such that C f ℓ has*good*reduction at ℓ (in the case of ℓ = 2, explicit conditions are given in [AD19, Lemma 7.7]). ... Observe that*for*p = 2, the hyperelliptic curve C n has*good*reduction at p*for*p ∤ n. ...##
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Page 4991 of Mathematical Reviews Vol. , Issue 92i
[page]

1992
*
Mathematical Reviews
*

A

*good*measure of knot complexity is defined to be a function F from the equivalence classes of (*tame*) knots to [0, 00) such that F(unknot) = 0 and*for*which there exists a class k, with F (nk,#k) > nF ... In this paper, the author presents new state models*for*a special- ization of the Kauffman*polynomial*. ...##
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An Algebraic Proof of Thurston's Rigidity for a Polynomial
[article]

2012
*
arXiv
*
pre-print

We provide an algebraic proof of this fact

arXiv:1201.1969v2
fatcat:z3bikc4hrncuvnfla76jdfdlha
*for**tamely*ramified maps*for*which at least one of the critical points is periodic. We also produce wildly ramified counterexamples. ... The situation*for**polynomials*is much simpler. Not only do we not need S in the proof of Theorem 2.4, but also we obtain: Theorem 3.7. Let f (z) be an absolutely*tamely*ramified PCF*polynomial*. ... The case of*polynomials*is already known: Theorem 1.9. [2] Rigidity holds*for**polynomials*whenever their reduction after any coordinate change is still*tamely*ramified, which is the case if they are of ...##
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Page 979 of Mathematical Reviews Vol. , Issue 2000b
[page]

2000
*
Mathematical Reviews
*

Ultimately, the authors formulate Conjecture 2.7, which makes an assertion about the face

*polynomials*of a 3-dimensional*tame*automorphism. ... In the modular case, it can be computed by a Molien-type formula, and it gives fairly*good*con- straints on the possible degrees of the elements of a homogeneous set of parameters*for*k[V]°, i.e., of a ...##
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Tame Galois Realizations of over

2010
*
International mathematics research notices
*

In this paper we obtain realizations of the 4-dimensional general symplectic group over a prime field of characteristic ℓ > 3 as the Galois group of a

doi:10.1093/imrn/rnq144
fatcat:d3g3heb6k5fbzoqy5lxa6bduqu
*tamely*ramified Galois extension of Q. ... We obtain an explicit family of curves of genus 2 such that the Galois representation attached to the ℓ-torsion points of their Jacobian varieties provide*tame*Galois realizations of the desired symplectic ... representation yielding a finite Galois extension K/Q,*tamely*ramified, with Galois group GSp 4 (F ℓ ), thus providing an affirmative answer to the*Tame*Inverse Galois Problem*for*this group. ...
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