Analytic equations and singularities of plane curves
Trans. Amer. Math. Soc., 245 (1978), 409-417.
Trans. Amer. Math. Soc., 245 (1978), 409-417.
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In the paper Deformations and Analytic Equations, I showed that, for a system of analytic equations to have a
solution, it is enough that the system have a solution up to order n for n sufficiently large. The current paper considers the case of one equation in two variables. It marks my first exposure to the
use of a computer in algebra. The computer was a IBM-5100 desktop programmed in APL I used the computer to carry out the lengthy algebraic computations involved in the steps in "blowing up" by
monoidal transformations. I was able to connect the number n with the complexity of the singularity and, eventually, with measures of the singularity like the Newton Polygon.
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