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 Apr 10 revised Applications of resolution of singularities edited tags Mar 29 comment Algorithmic computing kernel of a graded homomorpism @CaptainLama for example consider a hommorphism between two polynomial ring, for computing its kernel one can use Groebner basis and elimination which is a nice application of Groebner basis and one can see in many books about computational algebraic geometry or commutative algebra. Or the one I mentioned about SyZyGies. By computing I mean finding a generator explicitly. Mar 29 asked Algorithmic computing kernel of a graded homomorpism Jan 31 awarded Revival Jan 30 accepted Non-linear optimization programming Jan 30 comment Non-linear optimization programming So please check if my conclusion from your answer is right or not. If my constrains and target functions be twice differential which polynomials are, and I be in a box for my variables then "global optimization using interval analysis" is always working for my problem whether they be linear or not or whether they are convex or not. So just being in a box and twice differentiablity is enough for this method, yes? Jan 29 asked Non-linear optimization programming Jan 23 answered Matroid Direct Sum Jan 9 revised Depolarizing channel edited body Jan 9 comment Relation between ranks of submatrices of a matrix. In fact you only need to write the two computations for s_i,j and then using association of multiplication and distribution of multiplication on summation. It is easy to write it. ^_^ Jan 9 revised Relation between ranks of submatrices of a matrix. edited title Jan 9 comment Relation between ranks of submatrices of a matrix. The answer is too easy, but it seems they closed your question so I answer it here. By assuming '9', all s_k,j (k from 1 to i-1) is a linear combination of other columns and same but maybe different linear combination for s_i,k, now for the matrix S(i,j) you only don't know value of one entry which is S_i,j, S_i,j should satisfy the two linear relations using entries added in steps S(i-1,j) and S(i,j-1), obviously you can have at most one possible values conditioning to have a same results starting from linear relation of row or column, which is true.. Jan 9 revised Relation between ranks of submatrices of a matrix. deleted 34 characters in body Jan 4 revised Depolarizing channel added 30 characters in body; edited tags Dec 28 asked A reference containing computational examples for Quantum information Dec 21 comment limit of a simple complex function ِYou've missed "$-3i$" in nominator of the second fraction for $-f(i)$. And in sequel of your limit computation you can multiple complex conjugate of denominator to denom and nomin of your fraction, then following using lHopital. Dec 17 comment Prove That If $(x^{2}+y^{2})\cos^{2}\psi+z^{2}\cot^{2}\psi=A^2$ then $\nabla ^2 \psi=0$. @GiuseppeNegro really? So you checked and this equation failed to satisfy Laplacian? I'll try later when I found time, as I answered to Shushao Cao, this question was asked from me by a Physics student. Dec 13 awarded Revival Dec 13 revised How does one get this equation? added 1 character in body Dec 11 answered limit of a simple complex function