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 Sep24 awarded Autobiographer Aug3 awarded Enlightened Aug3 awarded Nice Answer Aug27 awarded Yearling Jan12 answered Different ways to represent functions other than Laurent and Fourier series? Nov11 revised How can one efficiently generate n small relatively prime integers? added 150 characters in body Nov11 comment How can one efficiently generate n small relatively prime integers? @Qiaochu, OK but how does Latex work here? Any links? Nov11 revised How can one efficiently generate n small relatively prime integers? added 12 characters in body Nov11 awarded Editor Nov11 comment How can one efficiently generate n small relatively prime integers? @Moron, I was in a hurry when I typed it last night and messed it up. Read it now. About O(log n) bits, yes, some of these may not provide that. Nov11 revised How can one efficiently generate n small relatively prime integers? deleted 78 characters in body; added 4 characters in body Nov11 answered How can one efficiently generate n small relatively prime integers? Nov8 comment Intuition explanation of taylor expansion? See the graph @ en.wikipedia.org/wiki/Taylor_series. Also see en.wikipedia.org/wiki/Taylor_polynomial. Taylor's theorem is derived from the Mean Value Theorem Nov6 answered What does closed form solution usually mean? Nov3 answered Intuitive explanation of the difference between waves in odd and even dimensions Aug29 comment Using Gröbner bases for solving polynomial equations Aug29 comment Using Gröbner bases for solving polynomial equations The choice of Order is tied to running time/complexity. There are papers on this topic which I haven't read. On your second question, there is an underlying ideal-variety correspondence(i.e. comm. algebra to algebraic geometry). The Groebner basis Ideal I= you end up with may not contain the initial two polynomials you started with (due to S-poly reductions), therefore Variety(Ideal) can be a null set. This gets decided by the Extension Theorem books.google.com/… Aug28 awarded Teacher Aug28 answered Using Gröbner bases for solving polynomial equations