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Testing polynomials

1990
*
Journal of symbolic computation
*

We show that any set of evaluations (a

doi:10.1016/s0747-7171(08)80033-8
fatcat:ktu6znvqbze75ni5w6tqm45xwa
*testing*set) for a*polynomial*with k terms has to contain at least k members, and we construct such a set with precisely k members. ... This construction relies on knowing the exponents, but not the coefficients, of the*polynomial*being*tested*. We leave to others the task of converting this theorem into algorithms." ...##
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Test polynomials

2000
*
Journal of Pure and Applied Algebra
*

We also give examples of strong

doi:10.1016/s0022-4049(98)00135-2
fatcat:2ojcsty33vclnewo2ozgvdtbxi
*test**polynomial*in the class of all endomorphisms of C[x1; : : : ; xn]. ... In this paper we show that a generic*polynomial*p ∈ C[x 1; : : : ; xn] of degree greater than n is a strong*test**polynomial*for monomorphisms of C[x1; : : : ; xn]. ... If deg p ≥ 4 then a*polynomial*p is a*test**polynomial*; otherwise it is not a*test**polynomial*. Proof. First assume that a*polynomial*p is of degree ≥ 4. We show that p is a*test**polynomial*. ...##
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Tests of Symmetric Polynomials

1911
*
The American mathematical monthly
*

The above remarks apply directly to all rational func- tions of the n variables as well as to the more special functions which are commonly (but not universally) called

doi:10.1080/00029890.1911.11997604
fatcat:byj65ssvzrgovej56h322nifty
*polynomials*. ...##
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Tests of Symmetric Polynomials

1911
*
The American mathematical monthly
*

Although the last theorem requires n-1

doi:10.2307/2973677
fatcat:dtq3vxtsrveehlbrs4e5pxg5mm
*tests*to prove the symmetry of a*polynomial*, each of these*tests*is so very simple that the total number of them involve about the same amount of labor as each of ...*TESTS*OF SYMMETRIC*POLYNOMIALS*. By DR. G. A. MILLER, University of Illinois. * Dyck, Mathematische Annalen, Vol. 22 (1883), p. 89. t Mathematische Annalen, Vol. 33 (1889), p. 587. ...##
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Polynomial Time Algorithm for Graph Isomorphism Testing
[article]

2013
*
arXiv
*
pre-print

This article deals with new

arXiv:1004.1808v6
fatcat:kdahgyrdijaojmizcjayac3jaa
*polynomial*time algorithm for graph isomorphism*testing*. ... At present many effective algorithms for graph isomorphism*testing*were proposed and there are number of investigations with attempts to prove*polynomial*complexity of some of these algorithms. ... Now we can consider the following algorithm, where function Verify*tests*found mapping by procedure P1. ...##
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Counting and testing dominant polynomials
[article]

2015
*
arXiv
*
pre-print

In this paper, we concentrate on counting and

arXiv:1407.2789v2
fatcat:ibp2lbwy6zavfb4j5ybvtarluu
*testing*dominant*polynomials*with integer coefficients. ... Finally, we will design some algorithms to*test*whether a given*polynomial*with integer coefficients is dominant or not without finding the*polynomial*roots. ...*Testing*dominant*polynomials*In this section, we will design some algorithms to*test*whether a given*polynomial*f ∈ Z[X] is dominant or not without finding the*polynomial*roots. ...##
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Testing hyperbolicity of real polynomials
[article]

2018
*
arXiv
*
pre-print

Hyperbolic

arXiv:1810.04055v2
fatcat:4qcuvrjntrdvfae3mnccpnu5sm
*polynomials*are real multivariate*polynomials*with only real roots along a fixed pencil of lines.*Testing*whether a given*polynomial*is hyperbolic is a difficult task in general. ... We examine different ways of translating hyperbolicity into nonnegativity conditions, which can then be*tested*via sum-of-squares relaxations. ... Finally, it should also be pointed out that we always*test*hyperbolicity of a*polynomial*with respect to a fixed point e. ...##
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Test complexity of generic polynomials

1992
*
Journal of Complexity
*

INTRODUCTION Given a

doi:10.1016/0885-064x(92)90022-4
fatcat:3j3xkv37ofawzeujun2uuej4lm
*polynomial*f: Cm + C we may check whether f(t) = 0 by evaluating fat 4. But*testing*for zero may be easier than evaluating. ... 0) such that for any*polynomial*f E k[x, , . . . , x,] of degree d ~*.k[xl(f) 5 j& (1 + Pd). ...##
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Read-once polynomial identity testing

2008
*
Proceedings of the fourtieth annual ACM symposium on Theory of computing - STOC 08
*

In this paper we study the problems of giving deterministic identity

doi:10.1145/1374376.1374448
dblp:conf/stoc/ShpilkaV08
fatcat:h2nph4eyurfflnlpdcckgkfx3e
*testing*for models related to preprocessed ROFs. ... A preprocessed ROF (PROF for short) is a ROF in which we are allowed to replace each variable x i with a univariate*polynomial*T i (x i ). ... Introduction In this paper we study the*polynomial*identity*testing*problem for several models based on readonce formulas. ...##
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Read-once polynomial identity testing

2015
*
Computational Complexity
*

In this paper we study the problems of giving deterministic identity

doi:10.1007/s00037-015-0105-8
fatcat:qfbq4xbyd5fdfdh2hsfryzeuou
*testing*for models related to preprocessed ROFs. ... A preprocessed ROF (PROF for short) is a ROF in which we are allowed to replace each variable x i with a univariate*polynomial*T i (x i ). ... Introduction In this paper we study the*polynomial*identity*testing*problem for several models based on readonce formulas. ...##
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Likelihood ratio tests for positivity in polynomial regressions
[article]

2012
*
arXiv
*
pre-print

In this paper, we consider the likelihood ratio

arXiv:1108.1033v4
fatcat:3tzaxi7fcvdurcqr27s3lrozxq
*test*for the hypothesis of positivity that the estimand*polynomial*regression curve is a positive*polynomial*. ... A*polynomial*that is nonnegative over a given interval is called a positive*polynomial*. The set of such positive*polynomials*forms a closed convex cone K. ... likelihood ratio*test*(LRT) for*testing*H 1 against H 2 . ...##
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Polynomial Identity Testing for Low Degree Polynomials with Optimal Randomness

2020
*
International Workshop on Approximation Algorithms for Combinatorial Optimization
*

We give a randomized

doi:10.4230/lipics.approx/random.2020.8
dblp:conf/approx/BlaserP20
fatcat:soynqhsaqzgt5peas7wr52y7ia
*polynomial*time algorithm for*polynomial*identity*testing*for the class of n-variate poynomials of degree bounded by d over a field 𝔽, in the blackbox setting. ... We also collect two simple constructions of hitting sets with information theoretically optimal size against the class of n-variate, degree d*polynomials*. ... For a history on the progress on*polynomial*identity*testing*, we refer the readers to [47, 42, 43] . In this work, we are interested in blackbox*polynomial*identity*testing*. ...##
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T1 testing implies Tp polynomial testing: optimal cancellation conditions for CZO's
[article]

2019
*
arXiv
*
pre-print

The main result here is that the familiar T1

arXiv:1907.10734v2
fatcat:5kbliabv7rbadl6i3c6g6irqcy
*testing*conditions over indicators of cubes, together with the one-tailed A2 conditions, imply*polynomial**testing*. ... Controlling*polynomial**testing*conditions -main theorems. ... Introduction and definitions In Theorem 3 below, we show that for fractional Calderón-Zygmund operators, the κ-Cube*Testing*conditions over*polynomials*of degree less than κ times indicators of cubes, ...##
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Equivalence of Polynomial Identity Testing and Deterministic Multivariate Polynomial Factorization

2014
*
2014 IEEE 29th Conference on Computational Complexity (CCC)
*

In this paper we show that the problem of deterministically factoring multivariate

doi:10.1109/ccc.2014.25
dblp:conf/coco/KoppartySS14
fatcat:crhpkkfubvhitdpfn3jc56jdwi
*polynomials*reduces to the problem of deterministic*polynomial*identity*testing*. ... of f can be solved deterministically, given a deterministic algorithm for the*polynomial*identity*testing*problem (we require either a white-box or a black-box algorithm, depending on the representation ... Claim 3.5 The pair g k , h k obtained above is the unique pair of*polynomials*(mod T 2 k ) such that (a) f = g k h k mod T 2 k , (b) g k is monic in X, and (c) g k = g 0 mod T . ...##
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On testing the divisibility of lacunary polynomials by cyclotomic polynomials

2003
*
Mathematics of Computation
*

A running analysis shows that, for a fixed number of nonzero terms, the algorithm runs in

doi:10.1090/s0025-5718-03-01589-8
fatcat:6amujzwlbrhqhgbrqqjjqsaufa
*polynomial*time. ... The algorithm is intended to be used for sparse*polynomials*given as a sequence of coefficientexponent pairs. ... THE DIVISIBILITY OF LACUNARY*POLYNOMIALS*...
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