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Fortunately, Buchberger himself described the context of his discovery, see Historical background to Gröbner's paper by Abramson. The method, in general outline, was known to Gröbner long before the Buchberger's thesis (1965). In the 1950 paper Über die Eliminationstheorie (Abramson's English translation) it is applied to finding bases of integrals of ...

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