Quadratic numbers in matlab

5 次查看（过去 30 天）
Mayur Punekar
Mayur Punekar 2015-5-18
评论： Mayur Punekar 2015-5-24
I inverted a matrix H with entries from quadratic field, e.g., Q(sqrt(3)) and the inverted matrix G gives me entries also from Q(sqrt(3)), e.g., entry at (1,1) is 12 - 8*3^(1/2). However, is there a way to decouple integer coefficient 12 and -8? I want to store these integer values separately.
In fact I want to generate two integer matrices G1 and G2 from G which contains integer coefficients of each entry in G.
Can anyone suggest how can I do it??
Thanks in advance !

请先登录，再回答此问题。

回答（1 个）

Nalini Vishnoi
Nalini Vishnoi 2015-5-20
Hi Mayur,
I can think of one way to do what you asked by using Symbolic Math toolbox. It has a function coeffs which can return the coefficients of a polynomial. I have included a small example below demonstrating how to do it.
syms x; % Create a symbolic variable
G = repmat(12-8*x, 10,2); % Create a matrix of polynomials
for i = 1:size(G,2), % Use coeffs column by column
[C(:,i)] = arrayfun(@(z) coeffs(z,x), G(:,i),'Uniformoutput', false);
end
G1 = cellfun(@(x) double(x(1)), C, 'UniformOutput', false); % extract the coefficients as doubles
G1 = cell2mat(G1); % Convert the cell to a matrix
G2 = cellfun(@(x) double(x(2)), C, 'UniformOutput', false);
G2 = cell2mat(G2);
Please note that you can use subs to substitute symbolic variable 'x' with sqrt(3).
I hope this helps.
Nalini
  1 个评论
Mayur Punekar
Mayur Punekar 2015-5-24
Hello Nalini,
Thanks for the reply but unfortunately it didn't solve my problem.
I state my problem more explicitly here. I have a matrix H which has entries from quadratic field Q(3^(1/2)) i.e., entries are in form of h(i,j) = a+b*3^(1/2), where a,b are integers.
H = [0, 0, 1/x, 0, 0, 1/x, 0, 1; 1/x, 0, 0, 0, 0, 1, 0, 1/x; 0, 0, 1, 1/x, 0, 0, 1/x, 0; 0, 1/x, 0, 1, 1/x, 0, 0, 0; 1/x, 1, 0, 0, 0, 1/x, 0, 0; 0, 1/x, 0, 0, 1/x, 0, 1, 0; 0, 0, 0, 1/x, 1, 0, 0, 1/x; 1, 0, 1/x, 0, 0, 0, 1/x, 0];
Now I want to invert this matrix in such a way that the inverted matrix G still has entries of the form G(i,j) = a+b*3^(1/2).
As far as I know, theory suggests that any matrix with entries in Q(3^(1/2)) (or in general Q(D^(1/2)) can be inverted so that the inverted matrix also contains entries from the same field.
I tried many methods but couldn't find a way to get desired results with matlab. Can you suggest a method to solve this problem?
Thanks !

请先登录，再进行评论。

类别

在 Help Center 和 File Exchange 中查找有关 Conversion Between Symbolic and Numeric 的更多信息

标签

产品

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by