Gröbner bases and Diophantine analysis

DOI10.1016/j.jsc.2008.01.004zbMath1149.11057OpenAlexW1988541839MaRDI QIDQ950419

Mihai Cipu

Publication date: 22 October 2008

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jsc.2008.01.004

zbMATH Keywords

Gröbner basisDavenport's lemmageneralised Pell equation

Mathematics Subject Classification ID

Quadratic and bilinear Diophantine equations (11D09) Computer solution of Diophantine equations (11Y50) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Diophantine approximation, transcendental number theory (11J99)

Uses Software

• Magma
• PARI/GP

Cites Work

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• Simultaneous Pell equations
• On the number of solutions to systems of Pell equations
• Diophantine approximation
• Efficient computation of zero-dimensional Gröbner bases by change of ordering
• The Magma algebra system. I: The user language
• Converting bases with the Gröbner walk
• Linear forms in two logarithms and interpolation determinants
• Norm form equations
• An explicit lower bound for a homogeneous rational linear form in the logarithms of algebraic numbers. II
• The number of subspaces occurring in the p-adic subspace theorem in diophantine approximation.
• On the number of solutions of simultaneous Pell equations II
• THE EQUATIONS 3x²−2 = y² AND 8x²−7 = z²
• On the number of solutions of simultaneous Pell equations
• On the number of solutions of simultaneous Pell equations
• Algorithms in invariant theory