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Using computer-aid approach to solve algebraic problems. Questions with this tag should typically include at least one other tag indicating what sort of algebraic problem is involved, such as ac.commutative-algebra or rt.representation-theory or ag.algebraic-geometry.
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efficient arithmetic with (short) Conway games?
There are indeed (relatively) efficient algorithms to do this (computing canonical form in particular, deciding equality etc.) They are implemented in the CGSuite software package written by Aaron Sie …