t_optimizer_attribute(model, "NonConvex", 2) Using JuMP with Gurobi it was only able to identify 1 fixed point while Homotop圜ontinuation was able to find all 3 (unless I have implemented something incorrectly). The system is governed by 14 parameters: kb1 = 0.01 Īnd is solved in the following way in Mathematica: Solve[Īs an aside: I ran a different parameter set that should produce 3 fixed points (2 stable and 1 unstable) as determined by Mathematica. The documentation provided a simple example that I wasn’t able to extrapolate to my Mathematica code (below) successfully. Is anyone able to comment on whether it would be possible to call Mathematica into Julia using MathLink.jl to solve the below system. FullSimplify).I’m currently using Mathematica to symbolically solve a system of non-linear ODEs (10 equations with 8 variables) as I believe this is not yet possible using Symbolics.jl. Reduce[ x^2 + y^2 83/84, y -> 31/18}, *)ģ) Solve tends to be less thorough than Reduce in order to return an answer faster (somewhat like Simplify vs. Solve::fdimc: When parameter values satisfy the condition r ∈ Reals, the solution setĬontains a full-dimensional component use Reduce for complete solution information. We have the same issue with Reduce.Įxample : Solve cannot find solutions in the real domainĬonsider a simple symbolic case in the real domain where Solve does not work even with Ma圎xtraConditions -> All : Solve Inequalities are real, while all other quantities are complex. Solve assumes by default that quantities appearing algebraically in Using Ma圎xtraConditions -> All in Solve provides complete solutions for algebraic equations, nevertheless we have to emphasize that sometimes we might better work with Reduce rather than Solve (regardless of any options added) because replacement rules may appear not a good fit in description of solutions in the real or complex domain to algebraic equations as well as to trancendental equations˛ Distinction between genericity and completness does not make sense in the Integers, an example provided below. Solve returns lists of replacement rules yielding generic solutions.Īn important step toward more complete description of solution sets was a new option of Solve in Mathematica 8, namely Ma圎xtraConditions (default value 0).Reduce returns results of computation as boolean formulae and gives complete description of solution sets.There is much more than a little difference between them. Reduce and related functions use about 350 pages of Mathematica code The code for Solve and related functions is about 500 pages long. In Some Notes on Internal Implementation especially in Algebra and Calculus one finds interesting subtleties and differences between these two functions, e.g.
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