On expansion of algebraic functions in power and puiseux series, I
Journal of Complexity
On expansion of algebraic functions in power and Puiseux series, II
Journal of Complexity
The method of differentiating under the integral sign
Journal of Symbolic Computation
The method of creative telescoping
Journal of Symbolic Computation
An approach to the zero recognition problem by Buchberger algorithm
Journal of Symbolic Computation - Special issue on symbolic computation in combinatorics
Polynomial and matrix computations (vol. 1): fundamental algorithms
Polynomial and matrix computations (vol. 1): fundamental algorithms
The MAGMA algebra system I: the user language
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
Fundamental problems of algorithmic algebra
Fundamental problems of algorithmic algebra
Weyl closure of a linear differential operator
Journal of Symbolic Computation - Special issue on symbolic computation in algebra, analysis and geometry
Linear differential operators for polynomial equations
Journal of Symbolic Computation
Modern Computer Algebra
Lifting and recombination techniques for absolute factorization
Journal of Complexity
Complexity of creative telescoping for bivariate rational functions
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
Rational-functions telescopers: blending creative telescoping with hermite reduction
ACM Communications in Computer Algebra
Controlled non-uniform random generation of decomposable structures
Theoretical Computer Science
Fast computation of common left multiples of linear ordinary differential operators
ACM Communications in Computer Algebra
Good reduction of Puiseux series and applications
Journal of Symbolic Computation
Trading order for degree in creative telescoping
Journal of Symbolic Computation
Fast computation of common left multiples of linear ordinary differential operators
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
Order-degree curves for hypergeometric creative telescoping
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
Desingularization explains order-degree curves for ore operators
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
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It is classical that univariate algebraic functions satisfy linear differential equations with polynomial coefficients. Linear recurrences follow for the coefficients of their power series expansions. We show that the linear differential equation of minimal order has coefficients whose degree is cubic in the degree of the function. We also show that there exists a linear differential equation of order linear in the degree whose coefficients are only of quadratic degree. Furthermore, we prove the existence of recurrences of order and degree close to optimal. We study the complexity of computing these differential equations and recurrences. We deduce a fast algorithm for the expansion of algebraic series.