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12h
answered ParametricNDSolve KKT Constraint Directly
12h
comment finding eigenvectors of a n*n symbolic matrix
Yes, it's possible. In Mathematica go to Help > Documentation Center, enter "Eigenvalues" or "Eigensystem". That will show the command syntax.
1d
comment Numerical integration with NIntegrate
It worked for me. But I had some formatting issues when I cut-pasted your input and I may have guessed incorrectly as to which sigmas went where. I did get the memory exception with default handling, and I did get numerical results with that explicit method setting. Best I can suggest is maybe try other methods and see if things improve.
1d
comment Numerical integration with NIntegrate
Could set Method->"NewtonCotesRule". The default behavior is not pretty. I'll file a bug report on it. (I'm not certain it's a bug but seems like it's worth a report at least.)
1d
comment One of the factors greater than $x$
FactorInteger starts with trial division and then moves to Pollard methods, ECM, and MPQS. In principle several of those can deliver a nonprime factor. When the optional second argument is set, I'm not sure if any factor is guaranteed to be prime.
1d
comment Defining a custom Plus for a specific class of arguments
Actually I now realize UpValues is not a good idea in this specific situation. The reason is that they would be put on List, which is another object so critical to internals that it will likely mess up performance.
2d
comment ParametricNDSolve KKT Constraint Directly
I'm not convinced about this closing. The question is very much connected to Mathematica computations. They are difficult, granted. A basic restatement is this: Can ParametricNDSolveValue, or a surrogate, be made to respect the constraint? I don't know the answer but I think the question at least fits the general scope of this site. Too localized? Maybe. I'm not sure though.
2d
comment Bug in Operator Form of StringCases
The documentation should have been set to a later version (in this case, by me). Sorry about that.
2d
comment Defining a custom Plus for a specific class of arguments
If you put DownValues on Plus you will slow down anything that has a Plus in it, by a considerable amount. Either define a new operation myNewListPlus, or do this with UpValues.
2d
comment Solving a system of nonlinear equations
(1) I created the characteristic polynomial using x as the variable. To get the constant term I simply substitute 0 for x. In Mathematica that is done as whatever /. x->0. There are of course other ways to get that constant term. (2) It is generally good practice to comment on a response under that response rather than under the original note. As it was, I nearly missed this question.
Sep
28
answered Solving a system of nonlinear equations
Sep
28
comment Solving a system of nonlinear equations
Where you have Root[...,2] you probably want Sqrt.
Sep
28
comment Vigenere ciphertext encrypted with another vigenere cipher
A Vignenere of a Vignenere is still a Vignenere, albeit with a longer key.
Sep
28
comment What is the recommended way to define numeric function with special cases?
If/Which and conditional pattern methods will not be handled well by either the algebra (Solve family) or calculus (continuous and discrete) functions.
Sep
28
comment How to make a new analytic function work seamlessly with Mathematica's analysis functions?
I really cannot say whether or to what extent UpValues might be useful in FunctionExpand. I think it will depend on exactly what you are trying to do. As for internal usage, yes, FunctionExpand is used in several places inside Limit, Integrate, and I think elsewhere as well.
Sep
27
comment Verify positive definiteness using random numbers
Yes, I use Or, in order to get a counterexample. If either eigenvalue is nonpositive then the matrix is not positive definite. If either is strictly negative then it is not positive semidefinite. It need not be negative (semi)definite in order to not be pos def.
Sep
25
comment Finding related roots to a polynomial
(1) A specific example might make this more amenable to analysis. Withouty an example it's a bit difficult to follow. (2) You might try this. Remove the constants a1,b1,c1 (I suspect they are not really needed). Set a2=b3=c4=1. Expand the polynomial. One term in this should be f(x,y,z,v,w), which you can set to zero. Now look for nonzero parameter values that force what remains to vanish.
Sep
25
comment Substitution of a function in a differential equation
I believe there will be but I am not certain. (You noticed the comment in time; I was giving it only 5 minutes before deleting).
Sep
25
comment Different results of a definite integral $\int_0^{\cosh ^{-1}(a)} \frac{1}{\sqrt{a^2 \text{sech}^2(x)-1}}\, dx$
Well, it would be a bug. I get Pi/2 though, which is correct. I also get -Pi/2 when I approach from the other direction (again correct). I see this in versions 9 (running on Windows) and 10 (Linux).
Sep
24
comment Indeterminate expression 0^0 encountered
Could add alpha as a symbolic parameter, and eval symbolically before substituting a value. d[i_, j_, alf_] := Module[{aa}, Sum[aa^(i + j - 2 k)*(-1)^(-k)*Sqrt[i!] *Sqrt[j!]/((i - k)!*(j - k)!*k!), {k, 0, Min[i, j]}] /. aa->alf] In[16]:= d[0,0,0] Out[16]= 1