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Journal of Symbolic Computation - Special issue: parametric algebraic curves and applications
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Journal of Symbolic Computation
Journal of Symbolic Computation
Automated simplification of large symbolic expressions
Journal of Symbolic Computation
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We present two algorithms for simplifying rational expressions modulo an ideal of the polynomial ring k[x1, . . . , xn]. The first method generates the set of equivalent expressions as amodule over k[x1, . . . , xn] and computes a reduced Gröbner basis. From this we obtain a canonical form for the expression up to our choice of monomial order for the ideal. The second method constructs equivalent expressions by solving systems of linear equations over k, and conducts a global search for an expression with minimal total degree. Depending on the ideal, the algorithms may or may not cancel all common divisors. We also provide some timings comparing the efficiency of the algorithms in Maple.