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Determinant Equivalence Test over Finite Fields and over Q

2019
*
International Colloquium on Automata, Languages and Programming
*

But, to our knowledge, the complexity of the problem

doi:10.4230/lipics.icalp.2019.62
dblp:conf/icalp/GargGK019
fatcat:xe3hhmbxxrclxb5v47akljjtjy
*over**finite**fields**and**over**Q*was not well understood. ... In this work, we give a randomized poly(n, log |F|) time*determinant**equivalence**test**over**finite**fields*F (under mild restrictions on the characteristic*and*size of F). ... The*test*for the permanent holds*over**finite**fields**and**Q*, but the same is not true for the*determinant**equivalence**test*in [16] . ...##
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Determinant equivalence test over finite fields and over $\mathbf{Q}$
[article]

2019
*
Electronic colloquium on computational complexity
*

In [Kay12], a randomized polynomial time

dblp:journals/eccc/GargGKS19
fatcat:f75f3eh5qrbqdcyictvc3ylpce
*determinant**equivalence**test*was given*over*F = C. But, to our knowledge, the complexity of the problem*over**finite**fields**and**over**Q*was not well understood. ... A polynomial f is*equivalent*to Det n (x)*over*a*field*F if there exists a*over*F,*and*if so then output a transformation matrix A ∈ GL(n 2 , F). ... The*test*for the permanent holds*over**finite**fields**and**Q*, but the same is not true for the*determinant**equivalence**test*in [Kay12] . ...##
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Giesbrecht's algorithm, the HFE cryptosystem and Ore's p^s-polynomials
[article]

2016
*
arXiv
*
pre-print

We also discuss the

arXiv:1611.04479v1
fatcat:3c23gi6vsbhhxbhoxu5dxzfg4a
*equivalence*between factoring polynomials in a skew-polynomial ring*and*decomposing p^s-polynomials*over*a*finite**field*,*and*how Giesbrecht's algorithm is outlined in some detail by ... We end with some observations on the security of the Hidden*Field*Equation (HFE) cryptosystem, where p-polynomials play a central role. ... Choose a*finite**field*F*q*,*q*= p e ,*and*a basis (β 1 , . . . , β e ) for F*q**over*F p . 2. ...##
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Detecting Infinitely Many Semisimple Representations in a Fixed Finite Dimension
[article]

2008
*
arXiv
*
pre-print

We describe an algorithmic

arXiv:0708.3190v3
fatcat:yxpdp252p5cbzljrsndpufo2by
*test*for*determining*whether or not a*finitely*presented k-algebra R has infinitely many*equivalence*classes of semisimple representations R → M_n(k'), where k' is the algebraic ... The*test*reduces the problem to computational commutative algebra*over*k, via famous results of Artin, Procesi,*and*Shirshov. The*test*is illustrated by explicit examples, with n = 3. ... Setup*and*Proof of*Test*In this section we develop*and*prove our*test*to*determine*whether a*finitely*presented algebra*over*a*field*has infinitely many distinct*equivalence*classes of ndimensional semisimple ...##
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Detecting infinitely many semisimple representations in a fixed finite dimension

2008
*
Journal of Algebra
*

We describe an algorithmic

doi:10.1016/j.jalgebra.2008.06.035
fatcat:dqyaurodvnfrtdkok7p2uecot4
*test*for*determining*whether or not a*finitely*presented k-algebra R has infinitely many*equivalence*classes of semisimple representations R → M n (k ), where k is the algebraic ... The*test*reduces the problem to computational commutative algebra*over*k, via famous results of Artin, Procesi,*and*Shirshov. The*test*is illustrated by explicit examples, with n = 3. ... Setup*and*proof of*test*In this section we develop*and*prove our*test*to*determine*whether a*finitely*presented algebra*over*a*field*has infinitely many distinct*equivalence*classes of n-dimensional semisimple ...##
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GIESBRECHT'S ALGORITHM, THE HFE CRYPTOSYSTEM AND ORE'S ps-POLYNOMIALS

2001
*
Computer Mathematics
*

We also discuss the

doi:10.1142/9789812799661_0004
fatcat:no5fe3ndxnb63omlmyvd43e6di
*equivalence*between factoring polynomials in a skew-polynomial ring*and*decomposing p s -polynomials*over*a*finite**field*,*and*how Giesbrecht's algorithm is outlined in some detail by ... We end with some observations on the security of the Hidden*Field*Equation (HFE) cryptosystem, where p-polynomials play a central role. ... Choose a*finite**field*F*q*,*q*= p e ,*and*a basis (β 1 , . . . , β e ) for F*q**over*F p . 2. ...##
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A test for additive decomposability of irreducibles over a finite field

1989
*
Discrete Mathematics
*

This paper derives a

doi:10.1016/0012-365x(89)90289-6
fatcat:5ieb4tib7jbc3m6bagmbztq5iy
*test*for*determining*whether or not a given irreducible*over*a*finite**field*is additively decomposable. 0012-36W89/$3.50 @ 1989, Elsevier Science Publishers B.V. (North-Holland) ... A polynomial h*over*a*field*F is said to be additively decomposable*over*F if there exist polynomials f*and*g in F[x] each of degree ~1 sue% l h L at the roots of h are precisely all sums*Q*! ... Carlitz, Irreducibles*and*the composed product for polynomials*over*a*finite**field*, Discrete Math. 65 (1987) 115-139. [3] R. Lid1*and*H. ...##
###
Page 67 of Mathematical Reviews Vol. , Issue 83a
[page]

1983
*
Mathematical Reviews
*

There is a

*finite*set of polynomials in K which*determine*the Galois group by*testing*whether they are invariant under substitution of roots. ... Two extensions K,, K, of k are said to be Kronecker*equivalent**over*k if D(K,/k)*and*D( K,/k) differ by*finite*sets. W. Jehne has studied properties of these Kronecker*equivalence*classes [J. ...##
###
On the Symmetries of and Equivalence Test for Design Polynomials

2019
*
International Symposium on Mathematical Foundations of Computer Science
*

A useful example of such a polynomial, introduced in [34], is the following: where d is a prime, F d is the

doi:10.4230/lipics.mfcs.2019.53
dblp:conf/mfcs/GuptaS19
fatcat:46awkhafpfghhnr5p47z6kc4gq
*finite**field*with d elements,*and*k d. ... We give an efficient*equivalence**test*for N W in the case where the transformation A is a block-diagonal permutation-scaling matrix. ... We also thank anonymous reviewers for their comments. 53:11 Algorithm 3 Block-diagonal permutation*equivalence**test*for N W . Input: Black-box access to f ∈ F[x]. ...##
###
Randomized Polynomial-Time Equivalence Between Determinant and Trace-IMM Equivalence Tests

2020
*
International Symposium on Mathematical Foundations of Computer Science
*

The above result may appear a bit surprising as the complexity of

doi:10.4230/lipics.mfcs.2020.72
dblp:conf/mfcs/MurthyN020
fatcat:zrtouth5vrdlxocsieonwvio4q
*equivalence**testing*for IMM*and*that for Det are quite different*over**ℚ*: a randomized poly-time*equivalence**testing*for IMM*over**ℚ*is known ... We show that, despite the syntactic similarity between IMM*and*Tr-IMM,*equivalence**testing*for Tr-IMM*and*that for Det are randomized poly-time Turing reducible to each other*over*any*field*of characteristic ... Except for the*determinant*, the algorithms in [24, 25] work*over*C,*Q*,*and**finite**fields*6 ,*and*for the*determinant*it works only*over*C. ...##
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Page 6648 of Mathematical Reviews Vol. , Issue 99j
[page]

1999
*
Mathematical Reviews
*

The author

*determines*here all such curves*over*k =*Q*(/29)*and**Q*(V37). ... /K) (Ay =*finite*adéles of K). For Y a Mumford curve*over*K,. ...##
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Page 865 of Mathematical Reviews Vol. 31, Issue 5
[page]

1966
*
Mathematical Reviews
*

Then cd,(@) = 0 for all g#:p,

*and*to*determine*ed,(@), one need only*test*the cohomology of the module Z/p. ... closure) ; examples are R,*finite**fields*, C((¢)),*finite*exten- sions of*Q*,. ...##
###
Detecting complex multiplication

2005
*
Computational Aspects of Algebraic Curves
*

From this, we derive an algorithm to compute the endomorphism ring of an elliptic curve

doi:10.1142/9789812701640_0003
fatcat:guvuq35k3bfmnpn2sfkewcpfv4
*over*a number*field*. ... We give an efficient, deterministic algorithm to decide if two abelian varieties*over*a number*field*are isogenous. ... Algorithms for elliptic curves Detecting isogenous elliptic curves The isogeny class of an elliptic curve E*over*a*finite**field*κ is uniquely*determined*by |E(κ)|. ...##
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Conjugacy classes of centralizers in unitary groups
[article]

2019
*
arXiv
*
pre-print

Further, we count the number of z-classes in the

arXiv:1610.06728v2
fatcat:kic2woswbrfdnki5qf3cdusboq
*finite*unitary group U_n(*q*),*and*prove that this number is same as that of GL_n(*q*) when*q*>n. ... In this paper, we prove that the number of z-classes in the unitary group*over*such*fields*is*finite*. ... Special focus is on the unitary group*over**finite**field*F = F*q*2 of characteristic = 2 with σ given byx = x*q**and*F 0 = F*q*. ...##
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Deterministic irreducibility testing of polynomials over large finite fields

1987
*
Journal of symbolic computation
*

We present a sequential deterministic polynomial-time algorithm for

doi:10.1016/s0747-7171(87)80055-x
fatcat:m7cbqp7l4jbqvpmrnafsmb6tdu
*testing*dense multivariate polynomials*over*a large*finite**field*for irreducibility. ... Our deterministic solution is based on our algorithm for absolute irreducibility*testing*combined with Berlekamp's algorithm. ... Notation: ~:*q*denotes a*finite**field*with*q*elements; degx(f) denotes the highest degree of x inf~ IFq[y, xl*and*deg(f) the total degree off. ...
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