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P-adic constraint solving

Andreas Dolzmann, Thomas Sturm
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 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,.,.  ... 
doi:10.1145/309831.309894 dblp:conf/issac/DolzmannS99 fatcat:u2hptbxbtjhpvednmq6ta6ajuu

Parametric Systems of Linear Congruences [chapter]

Andreas Dolzmann, Thomas Sturm
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.  ... 
doi:10.1007/978-3-642-56666-0_12 fatcat:47p3rxpgybbrhjx5tquthfvzjm

Physical degrees of freedom of non-local theories

Joaquim Gomis, Kiyoshi Kamimura, Toni Ramírez
2004 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).  ... 
doi:10.1016/j.nuclphysb.2004.06.046 fatcat:ikolilep3jcq7gnsrsa4kosajm

A dyadic solution of relative pose problems [article]

Patrick Erik Bradley
2009 arXiv   pre-print
A hierarchical interval subdivision is shown to lead to a 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] .  ... 
arXiv:0908.1919v3 fatcat:q4vpokgd5jegfg4wwxhhahyolm

Verification of arithmetic datapaths using polynomial function models and congruence solving

Neal Tew, Priyank Kalla, Namrata Shekhar, Sivaram Gopalakrishnan
2008 2008 IEEE/ACM International Conference on Computer-Aided Design  
We devise a decision procedure using Newton's 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.  ... 
doi:10.1109/iccad.2008.4681562 dblp:conf/iccad/TewKSG08 fatcat:l6t4n4wsjfgtxoyyp6p53cvy64

A p-adic RANSAC algorithm for stereo vision using Hensel lifting

Patrick Erik Bradley
2010 P-Adic Numbers, Ultrametric Analysis, and Applications  
A 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  ... 
doi:10.1134/s2070046610010048 fatcat:uvdaucjksbdbvjgm66aqz3ctta

p-adic Methods in Stereo Vision [chapter]

Patrick Erik Bradley
2012 Studies in Classification, Data Analysis, and Knowledge Organization  
Together with recent 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.  ... 
doi:10.1007/978-3-642-24466-7_18 fatcat:2rb4urou35e6pdn252kdxgomg4

p-adic CFT is a holographic tensor network [article]

Ling-Yan Hung, Wei Li, Charles M. Melby-Thompson
2019 arXiv   pre-print
The 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  ... 
arXiv:1902.01411v2 fatcat:swpxpsv5srhbxekfol7mdv43cy

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.  ... 

Emergent Einstein Equation in p-adic CFT Tensor Networks [article]

Lin Chen, Xirong Liu, Ling-Yan Hung
2021 arXiv   pre-print
We take the tensor network describing explicit 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  ... 
arXiv:2102.12022v2 fatcat:rwnlfr2n45eepdqbpei434f7mu

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.  ... 

Non-linear non-local Cosmology

N. J. Nunes, D. J. Mulryne
2008 arXiv   pre-print
Moreover, we show that this equation can be 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).  ... 
arXiv:0810.5471v1 fatcat:wdhuvyneangpfkws2opktqbq4e

Subspaces with well-scaled frames

Jon Lee
1989 Linear Algebra and its Applications  
Linear programming problems having 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  ... 
doi:10.1016/0024-3795(89)90450-3 fatcat:aymjrjtd45dprk3qw44ifk35ya

Euclidean (A)dS spaces over p-adic numbers [article]

Feng Qu
2021 arXiv   pre-print
With the help of Wick rotation over 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.  ... 
arXiv:2105.10183v1 fatcat:3uurperzofdzbcbaufhbdmidsi

p-adic CFT is a holographic tensor network

Ling-Yan Hung, Wei Li, Charles M. Melby-Thompson
2019 Journal of High Energy Physics  
The 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  ... 
doi:10.1007/jhep04(2019)170 fatcat:4jwz5ax23jc2tb3v3qbzxt5bge
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