A program for computing Puiseux expansions

1990 ◽  
Vol 24 (4) ◽  
pp. 33-41
Author(s):  
V. Baladi ◽  
J.-P. Guillement
Keyword(s):  
Puiseux Expansions

scholarly journals An algebraically closed field

1968 ◽  
Vol 9 (2) ◽  
pp. 146-151 ◽  
Author(s):  
F. J. Rayner
Keyword(s):  
Positive Integer ◽  
Power Series ◽  
Formal Power Series ◽  
Characteristic Zero ◽  
Closed Field ◽  
Algebraically Closed Field ◽  
Zero Characteristic ◽  
Image Position ◽  
Formal Power ◽  
Puiseux Expansions

Letkbe any algebraically closed field, and denote byk((t)) the field of formal power series in one indeterminatetoverk. Letso thatKis the field of Puiseux expansions with coefficients ink(each element ofKis a formal power series intl/rfor some positive integerr). It is well-known thatKis algebraically closed if and only ifkis of characteristic zero [1, p. 61]. For examples relating to ramified extensions of fields with valuation [9, §6] it is useful to have a field analogous toKwhich is algebraically closed whenkhas non-zero characteristicp. In this paper, I prove that the setLof all formal power series of the form Σaitei(where (ei) is well-ordered,ei=mi|nprt,n∈ Ζ,mi∈ Ζ,ai∈k,ri∈ Ν) forms an algebraically closed field.

scholarly journals Universal axion backreaction in flux compactifications

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Thomas W. Grimm ◽  
Chongchuo Li
Keyword(s):  
Flux Compactifications ◽  
Complex Structure ◽  
Boundary Structure ◽  
Type Ii ◽  
Newton Polygons ◽  
String Compactifications ◽  
Axion Field ◽  
Field Excursion ◽  
Scalar Potentials ◽  
Puiseux Expansions

Abstract We study the backreaction effect of a large axion field excursion on the saxion partner residing in the same $$ \mathcal{N} $$ N = 1 multiplet. Such configurations are relevant in attempts to realize axion monodromy inflation in string compactifications. We work in the complex structure moduli sector of Calabi-Yau fourfold compactifications of F-theory with four-form fluxes, which covers many of the known Type II orientifold flux compactifications. Noting that axions can only arise near the boundary of the moduli space, the powerful results of asymptotic Hodge theory provide an ideal set of tools to draw general conclusions without the need to focus on specific geometric examples. We find that the boundary structure engraves a remarkable pattern in all possible scalar potentials generated by background fluxes. By studying the Newton polygons of the extremization conditions of all allowed scalar potentials and realizing the backreaction effects as Puiseux expansions, we find that this pattern forces a universal backreaction behavior of the large axion field on its saxion partner.

scholarly journals Analytic Continuation for Solutions to the System of Trinomial Algebraic Equations

2020 ◽  
pp. 114-130
Author(s):  
Irina A. Antipova ◽  
Ekaterina A. Kleshkova ◽  
Vladimir R. Kulikov
Keyword(s):  
Integral Representation ◽  
Analytic Continuation ◽  
Algebraic System ◽  
Extension Problem ◽  
Algebraic Equations ◽  
Puiseux Expansions

In the paper, we deal with the problem of getting analytic continuations for the monomial function associated with a solution to the reduced trinomial algebraic system. In particular, we develop the idea of applying the Mellin-Barnes integral representation of the monomial function for solving the extension problem and demonstrate how to achieve the same result following the fact that the solution to the universal trinomial system is polyhomogeneous. As a main result, we construct Puiseux expansions (centred at the origin) representing analytic continuations of the monomial function

An algorithm for the inversion of Laplace transforms using Puiseux expansions

2017 ◽  
Vol 78 (1) ◽  
pp. 107-132 ◽  
Author(s):  
Tongke Wang ◽  
Yuesheng Gu ◽  
Zhiyue Zhang
Keyword(s):  
Laplace Transforms ◽  
Puiseux Expansions

On Average Behaviour of Regular Expressions in Strong Star Normal Form

2019 ◽  
Vol 30 (06n07) ◽  
pp. 899-920 ◽  
Author(s):  
Sabine Broda ◽  
António Machiavelo ◽  
Nelma Moreira ◽  
Rogério Reis
Keyword(s):  
Normal Form ◽  
Generating Functions ◽  
Finite Automata ◽  
Regular Expressions ◽  
Large Set ◽  
Asymptotic Estimates ◽  
Analytic Combinatorics ◽  
Average Complexity ◽  
Average Behaviour ◽  
Puiseux Expansions

For regular expressions in (strong) star normal form a large set of efficient algorithms is known, from conversions into finite automata to characterisations of unambiguity. In this paper we study the average complexity of this class of expressions using analytic combinatorics. As it is not always feasible to obtain explicit expressions for the generating functions involved, here we show how to get the required information for the asymptotic estimates with an indirect use of the existence of Puiseux expansions at singularities. We study, asymptotically and on average, the alphabetic size, the size of the [Formula: see text]-follow automaton and of the position automaton, as well as the ratio and the size of these expressions to standard regular expressions.

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