Timeline for What's going on with this system of equations?
Current License: CC BY-SA 3.0
9 events
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| May 20, 2017 at 18:44 | comment | added | Daniel Lichtblau |
@Artes Sorry, I may have added to the confusion. What I should have stated is that the "polynomialized" system has dimensional components in its solution set. This is the system one obtains by replacing radicals by new variables and their defining polynomial equations. You are correct that the dimensional components are all parasite solutions. Problem for solvers, especially such as NSolve, is that the methods used rely on polynomialization and that is problematic if dimensional components are thus introduced, even if they are parasite solutions.
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| May 20, 2017 at 16:19 | comment | added | Artes | @DanielLichtblau If this is the case I hope you add another answer. | |
| May 20, 2017 at 16:17 | comment | added | Artes |
@DanielLichtblau Thanks for a reliable comment. I don't insist there is a bug behind the warning when evaluated Reduce[system, {ct, EAx, EAy, EBx, EBy}]; (see my answer) and I find you've slightly enlightened the issue. Nonetheless I can't see any full dimensional component of the solution set even when all variables are complex. Evaluating e.g. {ToRules@Reduce[system, {ct, EBx, EBy, EAy, EAx}]} clarifies that there is only a finite set of solutions, therefore the results of Solve[system, {ct, EAx, EAy, EBx, EBy}] is correct, unless I overlooked something.
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| May 20, 2017 at 15:45 | comment | added | Daniel Lichtblau |
@Artes (2) If there is are parametrized roots then in general one or another might lead to a parasite solution for different values of the parameter. In this example it might be the case that one branch always is a parasite but this is not so easy to assess in general (and in particular it is problematic for the verifier used in Solve to remove parasite solutions).
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| May 20, 2017 at 15:43 | comment | added | Daniel Lichtblau |
@Artes (1) The ideal in question has mixed dimension and most solver methods will find the highest dimensional component (Reduce will find all of them). The "generic" solution set is the highest dimensional component.
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| May 20, 2017 at 11:45 | comment | added | Artes |
@DanielLichtblau The system takes it as such but it's not, evaluate e.g. Reduce[Rationalize[system], {ct, EAx, EAy, EBx, EBy}, Reals,Backsubstitution -> True] or assume only ct to be real. Curiously, the system without specifying the domain does not resolve a simple equation 0==-(1/2) Sqrt[1+12 EAx^2] which seems to be a bug.
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| May 19, 2017 at 21:02 | comment | added | Daniel Lichtblau | @Artes One cannot solve for all variables; it is a parametrized solution set. | |
| May 19, 2017 at 15:36 | comment | added | Artes | Would you explain what you mean by "infinite set of the solutions of the system". There is only a finite set of solutions, unless you refer to an (incorrect) warning of the system. | |
| May 19, 2017 at 10:09 | history | answered | user64494 | CC BY-SA 3.0 |