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Total degree reverse lexicographic order is currently generally regarded asmost often fastest for computing Groebner bases. This article describes analternate less mysterious algorithm for computing this order using exponentsubtotals and describes why it should be very nearly the same speed thetraditional algorithm, all other things being equal. However, experimentalevidence suggests that subtotal order is actually slightly faster for theMathematica Groebner basis implementation more often than not. This is probablybecause the weight vectors associated with the natural subtotal weight matrixand with the usual total degree reverse lexicographic weight matrix aredifferent, and Mathematica also uses those the corresponding weight vectors tohelp select successive S polynomials and divisor polynomials: Those selectionheuristics appear to work slightly better more often with subtotal weightvectors.  However, the most important advantage of exponent subtotals is pedagogical.It is easier to understand than the total degree reverse lexicographicalgorithm, and it is more evident why the resulting order is often the fastestknown order for computing Groebner bases.  Keywords: Term order, Total degree reverse lexicographic, tdeg, grevlex,Groebner basis

Subtotal ordering -- a pedagogically advantageous algorithm for computing total degree reverse lexicographic order