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P-adic constraint solving

1999
*
Proceedings of the 1999 international symposium on Symbolic and algebraic computation - ISSAC '99
*

We automatically cheek for t.lie feasibility of arbitrary hoolcan cou~hinatious of IiIICilr parametric

doi:10.1145/309831.309894
dblp:conf/issac/DolzmannS99
fatcat:u2hptbxbtjhpvednmq6ta6ajuu
*p*-*adic*coustraints using a quant.ifier elimination nwthotl. ... ThCse*p*-aclic solutions ('il.11 then 1x1 easily lifted t,o Z. As a wry iniport.ant. fcat,ure, our approach can*solve*prohlcxns uniformly for all*p*-*adic*valuations. ... Our goal is to*solve*the svstenl for concret~e*p*over the integers Z. *' The system is f&siblc over Z if and ouly if it is feasible over blic*p*-*adic*iiitcgcrs R,.,. ...##
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Parametric Systems of Linear Congruences
[chapter]

2001
*
Computer Algebra in Scientific Computing CASC 2001
*

*p*-

*adic*solutions for given primes, and simultaneous lifting strategies for finite sets of primes. ... This includes determining integer solutions for sets of moduli which are all power of a fixed prime, uniform

*p*-

*adic*integer solutions for parametric prime power moduli, lifting strategies for these uniform ... Our notion of

*solving*thus resembles the standard notion used in

*constraint*

*solving*. ...

##
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Physical degrees of freedom of non-local theories

2004
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Nuclear Physics B
*

*P*-

*adic*string theory for spatially homogeneous configurations has two fixed points. The physical phase space around $q=0$ is trivial, instead around $q=\frac 1g$ is infinite dimensional. ... ii) the symplectic two form in the surface on

*constraints*. ... used to

*solve*( q j ,

*p*j ), (j ≥ 4). ...

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A dyadic solution of relative pose problems
[article]

2009
*
arXiv
*
pre-print

A hierarchical interval subdivision is shown to lead to a

arXiv:0908.1919v3
fatcat:q4vpokgd5jegfg4wwxhhahyolm
*p*-*adic*encoding of image data. ... This allows in the case of the relative pose problem in computer vision and photogrammetry to derive equations having 2-*adic*numbers as coefficients, and to use Hensel's lifting method to their solution ...*p*-*adic*numbers The*p*-*adic*numbers were first described by Hensel in [8] . ...##
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Verification of arithmetic datapaths using polynomial function models and congruence solving

2008
*
2008 IEEE/ACM International Conference on Computer-Aided Design
*

We devise a decision procedure using Newton's

doi:10.1109/iccad.2008.4681562
dblp:conf/iccad/TewKSG08
fatcat:l6t4n4wsjfgtxoyyp6p53cvy64
*p*-*adic*iteration to*solve*such arithmetic with composite moduli, while properly accounting for the word-sizes of the operands. ... We describe our implementation and show how the basic*p*-*adic*approach can be improved upon. ... We are unaware of any approach that can directly*solve*such arithmetic with composite moduli. However, these*constraints*can be scaled to a uniform modulus and then*solved*using a*p*-*adic*approach. ...##
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A p-adic RANSAC algorithm for stereo vision using Hensel lifting

2010
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P-Adic Numbers, Ultrametric Analysis, and Applications
*

A

doi:10.1134/s2070046610010048
fatcat:uvdaucjksbdbvjgm66aqz3ctta
*p*-*adic*variation of the Ran(dom) Sa(mple) C(onsensus) method for*solving*the relative pose problem in stereo vision is developped. ... From two 2-*adically*encoded images a random sample of five pairs of corresponding points is taken, and the equations for the essential matrix are*solved*by lifting solutions modulo 2 to the 2-*adic*integers ... Acknowledgements The author would like to thank the organisers of the wonderful Fourth International Conference on*p*-*Adic*Mathematical Physics*p*-*ADIC*MATHPHYS.2009 which took place near Grodna, Belarus ...##
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p-adic Methods in Stereo Vision
[chapter]

2012
*
Studies in Classification, Data Analysis, and Knowledge Organization
*

Together with recent

doi:10.1007/978-3-642-24466-7_18
fatcat:2rb4urou35e6pdn252kdxgomg4
*p*-*adic*classification methods, this leads to RanSaC*p*, a*p*-*adic*version of the classical RANSAC in stereo vision. ... This approach is motivated by the observation that using*p*-*adic*numbers often leads to more efficient algorithms than their real or complex counterparts. ... The point is that a sequence of linear congruences modulo*p*k is iteratively*solved*, which makes the procedure to a*p*-*adic*version of Newton's method. ...##
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p-adic CFT is a holographic tensor network
[article]

2019
*
arXiv
*
pre-print

The

arXiv:1902.01411v2
fatcat:swpxpsv5srhbxekfol7mdv43cy
*p*-*adic*AdS/CFT correspondence relates a CFT living on the*p*-*adic*numbers to a system living on the Bruhat-Tits tree. ... Our rules give an explicit tensor network for any*p*-*adic*CFT (as axiomatized by Melzer), and can be applied not only to the*p*-*adic*plane, but also to compute any correlation functions on higher genus*p*-*adic*... Unfortunately, the wavefunction*constraints*are quadratic and contain a large number of*constraints*, making it difficult to*solve*them, if they can be*solved*at all. 2 We take a different approach in ...##
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Page 4336 of Mathematical Reviews Vol. , Issue 95g
[page]

1995
*
Mathematical Reviews
*

Summary: “We use the Euler-Lagrange equations of motion in order to

*solve*the*constraints*for various types of two-dimensional U(1) gauge theories. ... Phys. 33 (1994), no. 6, 1217-1228.*p*-*adic*quantum mechanics with*p*-*adic*valued wave functions is considered in terms of operator theory in*p*-*adic*Hilbert space. ...##
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Emergent Einstein Equation in p-adic CFT Tensor Networks
[article]

2021
*
arXiv
*
pre-print

We take the tensor network describing explicit

arXiv:2102.12022v2
fatcat:rwnlfr2n45eepdqbpei434f7mu
*p*-*adic*CFT partition functions proposed in [1], and considered boundary conditions of the network describing a deformed Bruhat-Tits (BT) tree geometry. ...*Solving**constraints*up to order λ 2 , we have 2b c = −*p*, A a = 0, Λ + 2a 1 = 0. x √ gΛ. The total test effective action is thus S tot = S EH + S cov m . ... Lightning review of*p*-*adic*CFTs A one dimensional*p*-*adic*CFT lives in the*p*-*adic*number field Q*p*for any given prime number*p*. i.e. coordinates x ∈ Q*p*.*p*-*adic*numbers Q*p*are field extensions of the ...##
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Page 6919 of Mathematical Reviews Vol. , Issue 91M
[page]

1991
*
Mathematical Reviews
*

*Solving*the string in terms of the above “times” and then relating the times according to the or- thonormal gauge, when the abelian

*constraints*are imposed the authors find, apart from the standard light-front ... The authors outline a multiloop generalization of

*p*-

*adic*string theory. Only basic definitions and results are presented. ...

##
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Non-linear non-local Cosmology

2008
*
arXiv
*
pre-print

Moreover, we show that this equation can be

arXiv:0810.5471v1
fatcat:wdhuvyneangpfkws2opktqbq4e
*solved*as an initial value problem once a set of non-trivial initial conditions that satisfy the boundary conditions is found. ... We then numerically*solve*the diffusion-like equation, and hence the non-local equations, as an initial value problem for the full non-linear potential and subsequently identify the cases when inflation ... THE*p*-*ADIC*STRING We will now look at two examples of the evolution of ψ(t). ...##
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Subspaces with well-scaled frames

1989
*
Linear Algebra and its Applications
*

Linear programming problems having

doi:10.1016/0024-3795(89)90450-3
fatcat:aymjrjtd45dprk3qw44ifk35ya
*constraint*matrices related to these subspaces can be*solved*rapidly by combinatorial methods after reformulating the programs. ... By letting d'= dD, A'= LAD, b'= Lb, I'= D-II, u'= D-h, and r'= D-lx, the program (8.5) can be*solved*instead: algorithms that exploit the structure of the null space of the*constraint*matrix may benefit ...##
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Euclidean (A)dS spaces over p-adic numbers
[article]

2021
*
arXiv
*
pre-print

With the help of Wick rotation over

arXiv:2105.10183v1
fatcat:3uurperzofdzbcbaufhbdmidsi
*p*-*adic*numbers ℚ_p, the*p*-*adic*version of Euclidean dS_2 space(noted as pdS_2) is obtained based on pAdS_2(*p*-*adic*version of Euclidean AdS_2 space), the latter of which ... The distances D(X,Y)'s on*p*(A)dS_1 and pAdS_2 have intuitive explanations. ... So we cannot use*constraint*x ′ 0 > 0 or x ′ 0 < 0 to make (x ′ 0 , x ′ 1 ) coordinate system only cover one half of pAdS 2 . This problem can be*solved*in another way. ...##
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p-adic CFT is a holographic tensor network

2019
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Journal of High Energy Physics
*

The

doi:10.1007/jhep04(2019)170
fatcat:4jwz5ax23jc2tb3v3qbzxt5bge
*p*-*adic*AdS/CFT correspondence relates a CFT living on the*p*-*adic*numbers to a system living on the Bruhat-Tits tree. ... Our rules give an explicit tensor network for any*p*-*adic*CFT (as axiomatized by Melzer), and can be applied not only to the*p*-*adic*plane, but also to compute any correlation functions on higher genus*p*-*adic*... The main obstacle for*solving*these*constraints*in a 2D CFT is that, in general, the OPE coefficients for arbitrary descendants are not known in closed form.*p*-*adic*CFT, on the other hand, is particularly ...
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