solving equations: systems that use Round cannot be solved with the available methods

I have a simple system for which I would like a solution:

$ text {round} (a cdot x ^ 2 + b cdot x + c) = text {round} (x ^ 2) $

Even simpler (for debugging purposes), consider this special case:

$ text {round} (a cdot x ^ 2) = text {round} (x ^ 2) $

But both Solve and NSolve don't seem to work.

Solve ( Round(a * x^2) == Round(x^2), x )

Returns Solve: This system cannot be solved with the methods available to Solve.

NSolve ( Round(a * x^2) == Round(x^2), x )

Returns NSolve: This system cannot be solved with the methods available to NSolve.

What is the correct way to solve this system?

How can I make a solitaire game that can be solved?

It was not difficult to mix the cards and make them alone.

But sometimes there are games that cannot be solved. (For example, in 3 shifts mode)

How can I make sure that the game can be solved?

Can this quadratic program be solved analytically?

I have a convex quadratic program that is structured as follows:
begin {align *}
argmin_ {p} & hspace {0.5em} p & # 39; A p – 2 p & # 39; b \
mathrm {s.t.} & hspace {0.5em} Ep = f \
& hspace {0.5em} 0 le p_i le 1 ; forall i
end {align *}

Any hypothesis:

  • Matrix $ A $ is a $ n times n $ diagonal matrix, with strictly positive diagonal elements and adding to one (then it is pos def e invertible)
  • The vector $ b $ it is not negative
  • Matrix $ E $ is a $ m times n $ matrix such that $ m <n $, making the number of restrictions smaller than the number of variables. Ellements in $ E $ they are in $ (0.1) $

  • The QP solution without restrictions, $ p ^ * = A – 1 b $, is within the constraints of inequality but do not within the constraint $ Ep = f $.

  • Be a point, let's call it $ p_ {eq} $such that $ Ep_ {eq} = f $ and such that $ 0 le p_ {ep} le 1 $.
  • If you look closely at the previous points, you will see that we have a convex problem, within a non-empty convex domain and, therefore, the existence and uniqueness of a minimum.

Some of this information may not be relevant, and others may, so I gave him everything I have;)

I know I can express the problem again using the block matrix $ ((A, E & # 39;), (E, 0)) $, but this did not help me.

What you think ? Will these hypotheses be sufficient to find a closed form expression for the solution? If there is no closed solution, can you think of a smarter way to solve it than using a standard QP solver?

Algorithms: What problems does a university / college have that can be solved in the form of software development?

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Algorithms: Formalizing $ x in Bbb {Z} $ cannot be solved for a divisor using arithmetic unless you already "know" a divisor.

We say a formula $ f (x) $, for $ x in Bbb {Z} $ a given compound, factors $ x $ Yes $ gcd (f (x), x) notin {1, x } $.

Suppose that $ gcd (f (x), x) = d $and take any rational formula, including radicals, to $ f (x) $and you will find that yes $ f $ you cannot write in less operations, then there is a constant $ c $ what factors $ x $ or $ gcd (x, c) mid x $ and it is not one of the trivial divisors.

Intuitively, this says that an optimal formula for a divisor does not make sense because to arrive at a formula it is necessary to have "seen" a divisor. If you are not only doing a linear search through the integers (as in naive factorization), then your factoring method is calculating some formula for a divisor. I find it interesting

By rational, including radicals formula I mean any formula in the variable $ x $ come to take $ sqrt (a) {x} $ where $ a in Bbb {N} $, adding or subtracting, or multiplying or dividing a finite, constant number of times.

So for example yes $ x = $ 33. We have $ f (x) = dfrac {x – 1} {2} – 1 = $ 15 however, further reducing the number of operations we have $ f (x) = dfrac {x – 3} {2} $ then there is a constant term $ geq 3 $ In the optimal expression.

by $ x = 4 $. You really can't get to $ 2, 6, 8, $ or $ dots $ no first meeting 2.

Try this for different numbers.

How can I do a better job formalizing this concept in the context of integer factorization algorithms?

Soft question: What are some problems for research in functional analysis that can possibly be solved by someone with basic knowledge on the subject?

I wanted to know if there is a problem in Functional Analysis (FA) that can be successfully addressed by someone like me who has no experience in this area, but who is only familiar with some basic issues that you will find at most levels of undergraduate courses?

I wanted to mention that I searched the web before posting here. It seems that there is not much left for a university student to do in this area (or almost any other area), but sometimes I have seen documents from other researchers who at the end of their work mention how their work can be used to do something (usually they are concrete applications or suggestions to work on specific examples), but the author did not find the time or did not have the resources to carry out the work and left it to the interested reader. I wanted someone to help me find these kinds of problems that would be easy to work with if I had some time.

My goal is to write a research paper and publish it in a suitable magazine. I am out of school at the moment and I would like to enter a good doctoral program. It is very difficult for someone like me to get the attention of a professor to take me as a PhD student without first showing that I am motivated and that I can do the work in FA.

Thanks for your time and help.

Why can't this variable quadratic equation be solved?

I am trying to solve this following equation:
my code

Is there a general term for elimination grid logic puzzles and can they be solved with Bipartite Graph Matching?

There is a type of logical puzzle in which, taking a form of you, you are given some information about the things of especially two groups, then you are asked about the unclear relationships that do not occur.

For example, see or see

From time to time I encounter these questions and as I am familiar with the graphics theory of my computer science conferences, most of the time I tend to make a graph about relationships, but then I cannot understand how to continue. It seems like a bipartite graphical coincidence, but I can't be sure how Graph Theory can be technically applied to these types of questions.

I was looking for a general name for this kind of puzzle questions and what I could find are Elimination Grids and Logic Grid Puzzles.

I have found some documents on how to solve this type of puzzle and in one of them they were using logical programming with Prolog, but I am not interested in that aspect of them.

Also some popular puzzle questions like "Cheryl's birthday problem" look like puzzles and I found an article "I know now": Solve logical puzzles using Catherine Greenhill graphics.

Is there a general term (more technical than "logical grid") for this type of puzzle and can we apply graph theory to solve those riddles?

c ++: coding equipment located in the results table based on the tasks solved and the penalty time

I am trying to solve this problem using OOP:

Dice N Programming equipment


N lines that contain S, P. S denotes the number of tasks solved, P of note
penalty times


Order the equipment according to this condition:

  1. For the number of tasks solved in descending order
  2. When the amounts of tasks solved are equal, for the penalty time in
    ascending order
  3. When both amounts of tasks solved and penalty times are equal, according to the indexes of the teams in ascending order.

I have the following code that uses classification with a comparator. How can I use struct to simplify the solution?



using namespace std;

int n;
int *s = new int(n);
int *p = new int(n);

int mlt(int i, int j) {

    if (s(i) != s(j))
        return s(i) > s(j);
    else if (s(i) == s(j))
        if (p(i) != p(j))
            return p(i) < p(j);
            return i <  j;

int main() {

    freopen("input.txt", "r", stdin);
    freopen("output.txt", "w", stdout);

    cin >> n;

    int *A = new int(n);

    for (int i = 0; i < n; i++)
        A(i) = i;

    for (int i = 0; i < n; i++) {
        cin >> s(i);
        cin >> p(i);

    sort(A, A + n, mlt);

    for (int i = 0; i < n; i++)
        cout << A(i) + 1 << " ";

    delete() A;
    return 0;


5 5

3 50

5 720

1 7

0 0



5 2 1 3 4

p vs np: if a problem is in P solved by dynamic programming, is it also in NP?

Then I can solve a given problem using dynamic programming in $ O (n ^ 2k ^ 2) $ Complexity of time. This means that the problem is in P. But they ask me if it is in NP.

My answer is: "Since it can also be solved in polynomial time, the problem is also in $ NP $".

Is that a correct statement? If not, is a problem solved in P through dynamic programming also NP?