Hi guys,
I'm doing some work and I need to figure out some bounds on parameters to ensure that a solution to a differential equation exists. I have a few dozen inequalities to re-arrange and get bounds for, though a few among them should give me the strictest bounds and the rest should follow. My expressions vary from big to unreasonable. Something is wrong with the TeX editor, but to give you an idea:
I have some assumptions I can make, e.g. all parameters are positive, a_2 - a_1 > 0, etc. Probably the best way to handle this would be to try and factor out something that is always positive or negative and get rid of it, but doing that by hand is ... long, to say the least.-2a_1+2a_1nk_1^2+a_2+2a_1nk_2+2a_1k_1k_2-2a_2nk_2+2a_1nk_2^2
-2a_2nk_1^2-2a_2nk_2^2+2a_1mk_2+2a_1mk_1^2-3k_1a_1k_2^2+a_2nk_1^3
-2a_1mk_2^3-k_1a_2n-2a_1k_1^2k_2-a_1mk_1^3+a_1nk_1-a_1nk_1^3+k_1a_1m
+a_2k_1^2k_2+2a_2nk_2^3+a_2k_1k_2^2-2a_1nk_2^3-2k_2a_2m-2a_1m+a_1k_1
+2a_2n-2a_2k_2-2a_1n+3a_1k_2-a_2k_1+a_1k_1^2-a_1k_2^3+a_2k_2^2
-4a_2nk_1k_2+4a_1nk_1k_2-4a_1k_1^2mk_2-5k_1a_1mk_2^2
+4a_2nk_1^2k_2+5k_1a_2nk_2^2
-4a_1nk_1^2k_2-5k_1a_1nk_2^2+2k_2a_2mk_1 < 0
Do you guys have any ideas?
EDIT: To add: I've tried Maple and Mathematica, and a few other manipulators. None of them give me anything reasonable to work with. I've tried grouping terms that pop up often, but that still isn't good enough. I haven't been able to find anything useful online, googling using combinations of keywords like those in the title of this post.