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location Champaign, IL
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visits member for 2 years, 9 months
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7h
comment Pull out scalars from NonCommutativeMultiply in commutator of SU2 spin algebra
There is a section in this that gives some approaches to working with commutators. Also available here as a notebook.
7h
comment Ovals of plane curves (and esoteric surfaces in space)
The 3D example in no way conflicts with connectivity, it's the outcome of Reduce using cylindrical decomposition.
11h
comment Strange integration
Definitely a bug.
15h
comment Solving an equation for rational modulus 1
If you post a representative example you are more likely to get a viable response.
15h
answered Partial fraction decomposition of $1/(e^x-1)$
15h
comment Solving a system of nonlinear equations 2
By "bad" solutions I mean the ones that satisfy 6 but not all 7 equations. As for which equation you might initially discard, that's not so easy. I think it could be any but the last in this case (I have not checked that though). Might be a trial-and-error situation, I'm not sure.
22h
awarded  Necromancer
1d
comment Solving an equation for rational modulus 1
Yes, taking logs to make it linear would be better. But where do you get the constraint that these must be roots of unity?
1d
comment NMinimize ignores constraints
Looks like you have a function such as Sqrt that can be complex-valued in some places near the region. If so, then definitely this is the same issue as in the posts linked to by @MichaelE2. This could also explain why it might give up in a bad place in the parameter space.
1d
comment How to make a real number parameter go 2 decimal precision?
Possibly something like NumberForm[...,{Infinity,2}]. See also AccountingForm.
2d
comment Solving a system of nonlinear equations 2
My thought is that for now the method of @MichaelE2 is the best I can think of. Solve for all but the first equation (so it's neither over nor under determined), then use the first equation to rule out "bad" solutions. The problem is the system is not what's called a "complete intersection", and NSolve is not able to discern that it is consistent within a certain tolerance. If I get time I'll look into that but in any case NSolve is not now able to handle the full system.
2d
comment Minimization of a non-linear objective function subject to linear constraints
You can define something like vars=Array[x,Length[b]] and form constraints automatically using something like m.vars>=0 and maybe use MapThread on vars and the lower/upper bounds list to get the ranges.
Oct
19
comment How to tell Eigensystem the type of the elements comprising a matrix I would like to diagonalize
What @Jens said. Especially if dimension is in the several hundreds or more.
Oct
19
comment What is the algorithm behind Mathematicas Reduce in this equation?
(3) I think this is a reasonable question even if I don't have a particularly good answer. Granted, as worded it might require knowledge of Solve internals. A modest reinterpretation is "Can anyone explain why this is apparently out of range for solving?" and that seems like a fair thing to request (and a reasonable variant to address).
Oct
19
comment What is the algorithm behind Mathematicas Reduce in this equation?
(2) "Galois theory" is two words.
Oct
19
comment What is the algorithm behind Mathematicas Reduce in this equation?
(1) Reduce is looking to create a "polynomial" is some exponential of x. It will be represented internally in a dense manner at least for some preprocessing (involving polynomial gcds). When the exponents of those numerators gets large this polynomial will be too big and PolynomialGCD code will give up with that message.
Oct
19
comment Counting the permuted forms of a list with repeated members under a permutation group
If all you want is the count, use Multinomial. Multinomial[5,1,1] Out[18]= 42
Oct
18
comment Solving a system of nonlinear equations 2
I think I know how to use it. I just can't beat a better result out of it. Alas.
Oct
18
comment Solving a system of nonlinear equations 2
Very nice (I think I am the first upvote). At some point I may need to investigate why the Tolerance method is coming up short. (I had of course also tried that, and got nowhere.)
Oct
18
comment Solving a system of nonlinear equations 2
Very minor improvement on @MichaelE2 approach: First create expressions by subtracting right sides from left sides of the equations. Then can do NSolve[Flatten[{Thread[Rest[exprs] == 0], First[exprs]^2 < 10^(-4)}], vars]. Advantage is it filters out the "parasite" solutions automatically.