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13h
revised Why doesn't the decision problem for Presburger arithmetic demonstrate that $\mathsf{P} \neq \mathsf{NP}$
added author and citation for "other source"
13h
comment Why doesn't the decision problem for Presburger arithmetic demonstrate that $\mathsf{P} \neq \mathsf{NP}$
For a paper co-authored by Kuncak in 2005 that cites the 1974 paper by Fischer and Rabin, see here.
13h
comment Second order nonlinear differential equation $x''+Hx =A(1-J/(2x^2))$
Actually there are currently three votes to reopen, but I take your point.
14h
comment Second order nonlinear differential equation $x''+Hx =A(1-J/(2x^2))$
Actually the term with $x^{-4}$ has disappeared, leaving only $J/2x^2$.
14h
comment Why doesn't the decision problem for Presburger arithmetic demonstrate that $\mathsf{P} \neq \mathsf{NP}$
@BillCody: Have a look at the paper. The "quantifier-free" qualification applies to both the Boolean algebra and the Presburger arithmetic formulas. The author Viktor Kuncak has written previously on decision procedures for the full theory of Boolean algebra and Presburger arithmetic, and its reduction to a decision procedure for Presburger arithmetic, so it seems he would be fully aware of the literature.
14h
comment Why doesn't the decision problem for Presburger arithmetic demonstrate that $\mathsf{P} \neq \mathsf{NP}$
I've added a link to the "other source", a brief glance at which suggests that the fragment of Presburger arithmetic which is quantifier-free is there shown to be in NP, but avowedly not all of Presburger arithmetic is included in the theory considered there.
14h
revised Why doesn't the decision problem for Presburger arithmetic demonstrate that $\mathsf{P} \neq \mathsf{NP}$
corrected title and added link to "some other source"
15h
comment Second order nonlinear differential equation $x''+Hx =A(1-J/(2x^2))$
If the OP is still interested in this Question, as the recent edit seems to suggest, perhaps an explanation of the domain for $E$ could be added to the body of the Question.
15h
reviewed Close Find the number of ways in which $n$ identical items can be divided into $r$ groups
15h
reviewed Reject probability regarding three people throwing a die
15h
comment Why doesn't the decision problem for Presburger arithmetic demonstrate that $\mathsf{P} \neq \mathsf{NP}$
It isn't immediately clear that the decision problem for Presburger arithmetic is in NP. One first thinks of checking a proof for any statement in (the additive theory of natural numbers), which of course can be done in time polynomial in the length of the proof, but what would be required is a check that can be done in time polynomial in the length of the statement, a substantially higher bar.
16h
comment Efficient Test For Commuting Matrices
Note that since $A,B$ are Hermitian, one needs only compute (in exact precision) $AB$ and test it for being Hermitian. Still $O(n^3)$ (unless fast multiplication is used), but saves a constant factor.
16h
comment Efficient Test For Commuting Matrices
Simply multiplying both $AB,BA$ and testing for (numerical) equality would be an $O(n^3)$ computation.
23h
reviewed Close The sum of the multiples of 2 and 17 under 767
23h
comment Symmetric matrices and eigenvalues
It might be useful to clarify that $A$ is real symmetric.
1d
comment Interesting Combinatorial Identities; e.g. $\sum_{k=0}^n {n\choose k}^2 = {2n\choose n}$
Also the downloadable book "A-B" on methods for automatically discovering and proving combinatorial identities by Wilf, et al.
1d
revised Diameter of a 10-ball in a 10-box is larger than the side length of box?
added image to illustrate
1d
reviewed Reviewed Diameter of a 10-ball in a 10-box is larger than the side length of box?
1d
reviewed Close Density of probability in a square
1d
comment How do I prove this nice inequality $x+3\sqrt[3]{xy^2}\geq4\sqrt{xy} $?
For future reference, if direct manipulations seem to make things more complicated, look for a change of variables to eliminate some clutter.