Programs and data for "The primitive solutions of seven small generalized Fermat equations"

This package contains the programs (PARI/GP and Python) that produce and check the computational statements of the paper "The primitive solutions of seven small generalized Fermat equations", with their inputs and outputs. Section, statement, table and appendix numbers are those of the paper. Table 7 (Appendix C.1) lists the statements that rest on machine computation; the README gives, for each of them, the programs, the commands that run them and the output files, and also the computations behind Remark 9.5 and the other remarks, which the proofs do not use. All arithmetic is exact (integers, rationals, number fields given by explicit polynomials, finite fields, and p-adic numbers whose precision the programs track), except that the first programs evaluate signs at real places numerically; the paper proves these signs, and the second programs compute them by interval analysis. Requirements: PARI/GP 2.17.3; Python 3.12 with NumPy, SymPy and python-flint 0.8.