Reputation
Next tag badge:
98/100 score
31/20 answers
Badges
1 53 100
Newest
 Nice Answer
Impact
~701k people reached

16m
comment Class field theory of imaginary quadratic fields
recommend you add in the reference for this article you are reading
1h
comment How to solve this kind of recurrence relation in closed form? $F(n) = aF(n-1) + bF(n-2) + cF(n-3) + dF(n-4)$
You can solve it numerically, that gives some information, certainly. Depends upon what you hope to learn from the information.
1h
revised Generating vectors in a non-orthogonal 3D lattice with increasing magnitude
added 5644 characters in body
2h
comment How to solve this kind of recurrence relation in closed form? $F(n) = aF(n-1) + bF(n-2) + cF(n-3) + dF(n-4)$
no......................
2h
comment Generating vectors in a non-orthogonal 3D lattice with increasing magnitude
done..............................................
2h
revised Generating vectors in a non-orthogonal 3D lattice with increasing magnitude
added 1042 characters in body
3h
revised Generating vectors in a non-orthogonal 3D lattice with increasing magnitude
added 509 characters in body
3h
comment Generating vectors in a non-orthogonal 3D lattice with increasing magnitude
Yes, and the gradient of $X^T G X,$ written as a column vector, is $2 G X.$ The gradient of, say, $u,$ is $(1,0,0)^T.$ Anyway, the main computation for Lagrange is to find $G^{-1}$ and go from there. It is also fine to use the adjoint matrix for $G,$ as it is just a multiple of the inverse.
3h
comment Generating vectors in a non-orthogonal 3D lattice with increasing magnitude
I can finally make one substantial comment: in order to find all $|v|^2$ up to some bound $M,$ we get a guaranteed search by using lagrange multipliers to maximize $|u|,$ $|v|,$ $|w|,$ under the constraint i mentioned, $$ X^T G X \leq M $$
4h
comment Class field theory of imaginary quadratic fields
wiley.com/WileyCDA/WileyTitle/productCd-1118390180.html
4h
comment Class field theory of imaginary quadratic fields
K. S. Williams, D. Liu, Representation of primes by the principal form of negative discriminant ∆ when h(∆) is 4, Tamkang J. Math. 25 (1994)
4h
comment Class field theory of imaginary quadratic fields
Williams, Kenneth S.; Hudson, Richard H., Representation of primes by the principal form of discriminant $-D$ when the class number $h(-D)$ is $3$. Acta Arith. 57 (1991), no. 2, 131--153.
4h
comment Class field theory of imaginary quadratic fields
plentiful worked examples in Hudson and Williams 1991, then Liu and Williams 1994
4h
comment Class field theory of imaginary quadratic fields
Cox, Primes of the Form $x^2 + n y^2$
4h
comment Generating vectors in a non-orthogonal 3D lattice with increasing magnitude
Srikanth, I put a 3 by 3 Gram matrix in my answer. What this indicates, for basis vectors $a,b,c$ is that $a \cdot a = 2,$ $b \cdot b = 2,$ $c \cdot c = 5,$ $b \cdot c = 1,$ $c \cdot a = 1,$ $a \cdot b = 0.$ Please find the first ten items that you would want for your sequence, and edit those into your question. I currently have little idea what you want, and I suspect you are attempting to get an algorithm for a task you have never done by some slow method.
4h
revised Generating vectors in a non-orthogonal 3D lattice with increasing magnitude
added 256 characters in body
4h
comment Generating vectors in a non-orthogonal 3D lattice with increasing magnitude
@Srikanth, so, what is your actual major? And why do you want this sequence of vectors?
4h
comment $y^2 = x^3 - 26$, exist ideal satisfying conditions?
a method that works at math.blogoverflow.com/2014/08/23/…
5h
answered Generating vectors in a non-orthogonal 3D lattice with increasing magnitude
20h
comment Deriving expression for an integral that arose in Fourier analysis.
@CameronWilliams however, it should be arose, not arouse