I am trying to solve a system of equations with 90 equations in mathematica: https://www.wolframcloud.com/obj/484bbb56-7b5e-4278-8730-902844c8ccdd
Mathematica just refuses to run it after a while and it crashes. Does anyone have any tips or solutions for going around this problem?
Thank you!
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if so, how does it work? I tried to find information on z3 about differential equations but I didn't find anything.
I think dReal (http://dreal.github.io/) is the only solver that provides support for ODEs, though I’m not an expert on this.
Also, see this paper for further details: https://arxiv.org/pdf/1310.8278.pdf
I want to solve this system in mathematica and i have applied various functions such as Solve, NSolve, etc. but none of them worked. could you help me how could i find my answer?
I want to know that is there any difference between NP- hard problems and Computationally hard problems or are these two terms used for the same thing? I have tried to search the solution but cannot get some reasonable answer. Can anybody please help?
As of current knowledge (until that P=NP question is answered):
All NP-hard problems are computationally hard. But not all computationally hard problems are NP-hard (problems in P, with high exponents in the polynome, for example).
Note that "NP-hard" is a well defined class of problems in computer science.
"Computationally hard" on the other hand isn't, as far as I know.
I'm working on a ping-pong simulation program in which I have to calculate deflection angles based upon the angle of the paddle and incoming ball trajectory. I've developed a system of equations that calculates deflection. Unfortunately, it involves a system of at least thirty trig functions that can't really be simplified and must be run once during each draw function.
My question is: How much will this slow my program?
Without the functions implemented the program runs fine on my new iMac, but on any older computer it already has a great deal of lag as a result of OPENGL and probably some inefficiency on my part.
Will running that many trig functions substantially affect my framerate? If so, would replacing the trig functions with taylor polynomials and then simplifying be, in theory, any better?
After experimenting a little, I found that, as should probably have been obvious to me, running that many functions seriously affects frameRate. I tried simplification using Taylor Polynomials, but found that I couldn't really simplify my equations much without a great deal of error. The solution I settled on was a 3-dimensional array in my setup loop that precalculates a range of values suitable for my purposes. Thanks to everyone who replied for the help, I hope I didn't waste too much of your time.
I have started to solve PE problems a year ago, but within this year, I realised, that finding a problem which would be fun for me to think of is quite hard. I would like to solve problems more related with classic algorithms (graph theory, game theory, dynamic programming, divide and conquer...) and not so much of number theory and geometry (althought I like them too, but there was so much of them so far).
Any tips? (first 50 problems already solved and second half of first hudnred almost too, so I would like to get some tips for problems from 100-200. 200+ are quite hard for me, I think)
From 100+, intersected with the ones that I've solved, those that might be interesting to you are:
#107 (graph theory)
#114, #115, #116, #117 (combinatorics, dynamic programming)
#122 (some algebra, but hardly any)
#206 (numerics, but hardly number theory)
Try the following Project Euler questions:
185
186
212
215
237
314 - The Mouse on the Moon
There is PE page that lists details of all problems on one page, which may make it easier to find problems that suit your interests.