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Question: problems with solve - disjoint sets of solution despite same input

Question:problems with solve - disjoint sets of solution despite same input

Saalehorizontale 20 Maple 2024
solve inequality allsolutions
October 15 2024
2
restart;

{(-x-y+1)*t+n*y^2 = 0, -t*(x+y-1)*k+x = 0, (x+y-1)*(p-s)*k-p*(x-1) = 0, m*y^2+(n*x-m-t)*y-t*(x-1) = 0, n*x^2+(m*y-n-s)*x-s*(y-1) = 0, y*(n*x-n-s+1)+(1-x)*s+p*x-1 = 0, (x+y-1)*(p-s)*k+(-x-y+1)*p-m*x+s*y = 0, ((-x-y+1)*k+y)*t-m*y+m+x-1 = 0}

{0 < k, 0 < m, 0 < n, 0 < p, 0 < x, 0 < y, 0 < (-m*x+p)*t+(s-p)*(m*y-m+1), 0 < (n*x-n-p+1)*t+n*y*(p-s), 0 < (m*x-n*x+n-1)*t+(m*y-n*y-m+1)*s+(n*x-n+1)*(m*y-m+1)-n*y*m*x, 1 < x+y, k < 1, m < 1, n < 1, p < 1}

"solve(equalities union inequalities)", {k = .487116703, m = .656557610, n = .3562602382, p = .1863581607, s = .372716320, t = .8665379799, x = .4642487806, y = 1.635592831}

"------------------------------------------------------------------------------------------------------------------------------"

"solve(equalities)", {k = k, m = m, n = 0., p = 0., s = 0., t = 1., x = 0., y = 1.}, {k = 1., m = 0., n = 1., p = 0., s = 0., t = 1., x = 1., y = 1.}, {k = 2.130395435, m = 1.469396425, n = -1.299895929, p = 2.299895929, s = .8304995051, t = .1695004949, x = -.3611030805, y = .3611030805}, {k = .893308015, m = -1.942064138, n = .8632249760, p = -1.307713373, s = -2.615426746, t = 1.427148086, x = .5879938248, y = .8732201900}

"solve(solve(equalities) union inequalities"

"solve(solve(equalities) union inequalities"

"solve(solve(equalities) union inequalities"

"solve(solve(equalities) union inequalities"

 

NULL

Download problems_with_solve_15.10.24.mw

Hey guys, 

I'm working with Maple to solve sets of 8 equations and 14 inequalities. I use the command solve to get values for my 8 variables. Often there is no solution, sometimes we have one single solution or like a parametric solution. However sometimes this procedure fails to finish the calculation, that means I stop the calculation after a certain time (multiple houres). So now I am looking for some other ways to get the solution. For example I try a two-stage solve-attemp. In the first round I use the solve coammand only for the set of 8 equations. In the second round I take each of the solutions I found in the step before and combine them with the set of inequalities. Then I use solve again for this set. 

However I found out that the two ways I described above lead to diffrent solutions. In my opinion the solutions of solve(equations union inequalities) should be a subset of solve(equations), since all the solutions we find with equations union inequalities has to fullfill the 8 equations we want put into solve(equations). As you can see in the attached file that is not the case. The sets of solutions of solve(equalities union inequalites) and the set of solutions of solve(equalities) is disjoint, so no subset. 
Since I have disjoint sets in the step between, the solutions of solve(equations union inequalities) and the solutions of solve((solve equations) union inequalities) are disjoint as well, so I think the problem is already in the step before. 

I would be really glad if anyone can help me. Either explain me, where my argumentation above went wrong or why I find those solutions which dont fit together. 

Regards
Felix
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