On Feb 22, 2:37 am, JamesHDavenport <[email protected]> wrote:> "Canonical form" and "simplify" aren't the same thing (necessarily).> See Carette,J., Understanding Expression Simplification. > Proc. ISSAC 2004 (ed. J. Gutierrez), ACM Press, New York, 2004, pp. 72-79. I don't have access to that source but I completely agree, noting that the passage you quoted discusses the results of full_simplify(). What I've reported is primarily a bug in Sage simplification. However, the underlying cause appears to be an issue with the GiNaC canonical form, which apparently tends to proliferate radicals of small integers. Given Sage's dependence upon GiNaC's canonical form, unless Sage aggressively simplifies such expressions, Sage users will see many more expressions like -(3*sqrt(-2/3*(2*(3*sqrt(-2*sqrt(5) + 5) - 2*sqrt(5) +3)/ (sqrt(-2*sqrt(5) + 5) - sqrt(5) + 2) - 3)*el + 1/9*(3*sqrt(-2*sqrt(5)+ 5) - 2*sqrt(5) + 3)^2/(sqrt(-2*sqrt(5) + 5) - sqrt(5) + 2)^2) - (3*sqrt(-2*sqrt(5) + 5) - 2*sqrt(5) + 3)/(sqrt(-2*sqrt(5) + 5) - sqrt(5)+ 2))/(2*(3*sqrt(-2*sqrt(5) + 5) - 2*sqrt(5) + 3)/ (sqrt(-2*sqrt(5) + 5)- sqrt(5) + 2) - 3) My system engineering gut feel is that it would be desirable to address this particular simplification issue closer to the source rather than to try to engineer around it on the simplification end. When I get some free time, I'm going to raise this issue on GiNaC- list. I'm not sure how soon that will be though. -Mark
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