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6h
comment Vector form using NDSolve
Help > Documentation Center > NDSolve > Examples > Scope > Ordinary Differential Equations > "Solve for a vector-valued function:". To answer the next question, yes, I really did drill down that far to find out how to do this. Also there is an example "Use matrix-valued variables to compute the fundamental matrix solution:"
1d
comment Vector form using NDSolve
It's a vectorial interpretation of the dependent variable. Documented, actually. Just sometimes frustrating to get working if the ode is nonlinear.
1d
comment How to speed up auxilary DooliitleDecomposite function?
Might try changing the sums to dot products. Also Table probably should be Do. For the machine real case you could run it through Compile.
1d
comment Vector form using NDSolve
@MichaelE2 I am not sure I follow your suggestion, but it looks like it is the sort of improvement, in terms of naturalness of input, that had eluded me. I will encourage you to either elaborate or edit my post or post a separate response with this feature.
1d
comment Convert a list of hexadecimal numbers to decimal
Probably a bad idea to hex a decimal anyway.
1d
comment Is this 30% slowdown in Mathematica 10 due to DownValues lookup time?
(1) It would be helpful if you could send Support a minimal example that shows the slowdown. (2) Version 5.2 remains my all time favorite. An absolute gem, that one was. And 4.1/4.2 were the releases that, to my mind, really stabilized the front end.
1d
comment Vector form using NDSolve
The colon is a way of giving the pattern that follows it a name (in this case, vals). That's so it can be used on the right side of the SetDelayed. The ?NumberQ (no space before Q) is a predicate test; if the input is not an explicit number then the pattern does not match. The .. makes it into a "repeated" form of the pattern; it will match one or more NumberQ items. A good place to read up on this might be the documentation e.g. for NDSolve, since there are a good number of examples therein. Not sure any show quite this approach but maybe some are similar.
2d
comment How to define a nested function like this?
Very nice, now that I look at it lo these many months later.
2d
answered Vector form using NDSolve
2d
comment Problems finding intersection points between line and generic function
You can define at least the line parametrically, e.g. as p+t*p2` where p1, p2 are the points it goes through. Then set ``p+t*p2=={x,g[x]} and solve for x (you have two eqn in two unknowns).
2d
comment How can I solve my easy system of equations?
Solve first two for {l1, t1} and plug solution(s) into third.
2d
comment General function for the expansion of a polynomial of operators
(1) It often pays to define rules on NonCommutativeMultiply for this sort of thing. (2) There is a section that shows ways of handling such operators here. There is a notebook version at library.wolfram.com.
2d
comment How can I verify double integral solution?
The divergence was from the incorrectly formulated integrand. I expect that the updated one converges, though have not checked that carefully.
Mar
29
comment Proving positive definiteness or semi-definiteness of a matrix
Over the reals,no less. One can try GenericCylindricalDecomposition[res, {a, b, w, x, y, z}] where res is the result of that Resolve. But that brought my laptop to its knees and I had to kill the kernel.
Mar
29
comment How can I verify double integral solution?
Check the grouping of products. It appears the code is missing a layer of parens in two places.
Mar
28
revised Optimizing matrix inequalities over trace
added 1498 characters in body
Mar
28
comment How can I simplify a triple integral with exponentials?
ii = Integrate[ 1/(R G) Exp[-p (1 + R a) - b q ((1 + R a)/(1 + G x))] Exp[-a/ R] Exp[-b] Exp[-x/G], {a, 0, \[Infinity]}, {x, 0, \[Infinity]}, {b, 0, \[Infinity]}, Assumptions -> G > 0 && R > 0 && p > 0 && q > 0]. This takes around 25 minutes on my machine, mostly for the final integration.
Mar
28
answered Proving positive definiteness or semi-definiteness of a matrix
Mar
28
comment Solve reports it can't handle my equation
For numeric ϵ you could use FindRoot.
Mar
28
comment Proving positive definiteness or semi-definiteness of a matrix
Probably too slow to be practical, but here is another formulation that avoid roots/radicals. cpol = CharacteristicPolynomial[kmat, t]; Resolve[ForAll[t, And @@ {w > 0, x > 0, y > 0, z > 0}, Implies[cpol == 0, t >= 0]], Reals]