Hello sage-support, I'm a Sage newbie who just joined the group. Before I get to the meat of my post, I'd like to thank the open source math software community for all of your hard work! Nothing I say should be misinterpreted as a complaint. I have only admiration and gratitude.
I ran into an issue that I thought was worth reporting. As I worked on a relatively simple math problem, I noticed that my screen became filled with complicated expressions involving square roots of small integers. I knew the result couldn't be as complicated as it looked. Trying the various simplify methods didn't help. I scratched my head for a while and experimented. I eventually isolated the issue to the fact that Sage doesn't simplify "sqrt(5) / 5" to "1 / sqrt(5)". Worse, it dutifully replaces "1 / sqrt(5)" with "sqrt(5) / 5", implying that an underlying canonical form definition is systematically making expressions more complicated than necessary. I can imagine a theoretical argument about positive exponents being "simpler" than negative exponents of the same magnitude but that argument falls apart quickly in practice. The problem with keeping expressions like "sqrt(5) / 5" is that they grow uncontrollably with subsequent operations. For example, it keeps expressions like "-1/5*(sqrt(-2*sqrt(5) + 5) - sqrt(5))*sqrt(5)" from simplifying to "- sqrt(-2/sqrt(5) + 1) + 1". Several operations later, a screenful of unnecessary radicals completely obscures the underlying math. Given how common square roots of small integers are, particularly in newbie math problems, I expect this issue to be a significant stumbling block for many folks trying to learn Sage. I know that expression simplification is a black art so I can't pretend to know how to fix this issue. However, I'm certain that "1 / sqrt(5)" is simpler than "sqrt(5) / 5" in some important way. For what it's worth, I think that most of us would make that substitution if we were doing math without automated support. -Mark -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
