MATLAB: I have an array of n elements like [1 2 4 8 16]. I want calculate frequency of all combinations. 1, 2 ,4 ,8, 16, 1+2, 1+4, 1+8, 1+16, 2+4, 2+8, 2+16, 4+8, 4+16, 8+16, 1+2+4, 1+2+8, 1+2+16, 1+2+4+8, 1+2+4+16, 1+2+4+8+16 How can i store output in arr

how can i do this

1, 2 ,4 ,8 ,16

1+2, 1+4, 1+8, 1+16,

2+4, 2+8, 2+16,

4+8, 4+16,

8+16,

1+2+4, 1+2+8, 1+2+16,

1+2+4+8, 1+2+4+16,

1+2+4+8+16

Best Answer

n=numel(yourVector);
mask=dec2bin(0:2^n-1,n)-'0';
   mask(1,:)=[];
   
 combs=  mask*yourVector(:) ;
 
 result = histcounts( combs  ,  1:max(combs)+1);

Related Solutions

MATLAB: Easily solved equation isn’t being solved by ‘solve’

There are 3 solutions, which you will find by setting the 'ReturnConditions' option to true:

syms x A alpha h2m
syms b positive rational
psi = A*exp(-(b*x^2));
V = alpha*x^4;
H = -h2m*diff(diff(psi)) + V*psi;
Hall = psi*H;
avgE=int(Hall,x,-inf,inf);
pretty(simplify(Hall))
pretty(simplify(avgE))
fmin = diff(avgE,b);
pretty(simplify(fmin));
eqn = (fmin == 0);
minb = solve(eqn,b ,'ReturnConditions',true);
minb.conditions
minb.b

results are:

ans =
 
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      0 < (- 1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & in(((3^(1/2)*1i)/2 - 1/2)^2*((15*alpha)/(16*h2m))^(1/3), 'rational') & A ~= 0 & ((~0 < (1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & (signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1)) | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= -1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1)) & ~0 < alpha/h2m | ~in(((15*alpha)/(16*h2m))^(1/3), 'rational') & (~0 < (1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & (signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1)) | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= -1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1)) & 0 < alpha/h2m | 0 < (1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & ~in(((3^(1/2)*1i)/2 + 1/2)^2*((15*alpha)/(16*h2m))^(1/3), 'rational') & (~in(((15*alpha)/(16*h2m))^(1/3), 'rational') | ~0 < alpha/h2m) & (signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1))) | 0 < (- 1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & in(((3^(1/2)*1i)/2 - 1/2)^2*((15*alpha)/(16*h2m))^(1/3), 'rational') & in(((15*alpha)/(16*h2m))^(1/3), 'rational') & A ~= 0 & 0 < alpha/h2m & (~0 < (1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & (signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1)) | 0 < (1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & ~in(((3^(1/2)*1i)/2 + 1/2)^2*((15*alpha)/(16*h2m))^(1/3), 'rational') & (signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1)) | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= -1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1)) | 0 < (- 1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & 0 < (1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & in(((3^(1/2)*1i)/2 - 1/2)^2*((15*alpha)/(16*h2m))^(1/3), 'rational') & in(((3^(1/2)*1i)/2 + 1/2)^2*((15*alpha)/(16*h2m))^(1/3), 'rational') & (~in(((15*alpha)/(16*h2m))^(1/3), 'rational') | ~0 < alpha/h2m) & A ~= 0 & (signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1)) | 0 < (- 1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & 0 < (1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & in(((3^(1/2)*1i)/2 - 1/2)^2*((15*alpha)/(16*h2m))^(1/3), 'rational') & in(((3^(1/2)*1i)/2 + 1/2)^2*((15*alpha)/(16*h2m))^(1/3), 'rational') & in(((15*alpha)/(16*h2m))^(1/3), 'rational') & A ~= 0 & 0 < alpha/h2m & (signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1))
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                0 < (1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & in(((3^(1/2)*1i)/2 + 1/2)^2*((15*alpha)/(16*h2m))^(1/3), 'rational') & A ~= 0 & ((~0 < (- 1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & (signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1)) | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= -1 & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1)) & ~0 < alpha/h2m | ~in(((15*alpha)/(16*h2m))^(1/3), 'rational') & (~0 < (- 1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & (signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1)) | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= -1 & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1)) & 0 < alpha/h2m | 0 < (- 1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & ~in(((3^(1/2)*1i)/2 - 1/2)^2*((15*alpha)/(16*h2m))^(1/3), 'rational') & (~in(((15*alpha)/(16*h2m))^(1/3), 'rational') | ~0 < alpha/h2m) & (signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1))) | 0 < (1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & in(((3^(1/2)*1i)/2 + 1/2)^2*((15*alpha)/(16*h2m))^(1/3), 'rational') & in(((15*alpha)/(16*h2m))^(1/3), 'rational') & A ~= 0 & 0 < alpha/h2m & (~0 < (- 1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & (signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1)) | 0 < (- 1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & ~in(((3^(1/2)*1i)/2 - 1/2)^2*((15*alpha)/(16*h2m))^(1/3), 'rational') & (signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1)) | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= -1 & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1)) | 0 < (- 1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & 0 < (1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & in(((3^(1/2)*1i)/2 - 1/2)^2*((15*alpha)/(16*h2m))^(1/3), 'rational') & in(((3^(1/2)*1i)/2 + 1/2)^2*((15*alpha)/(16*h2m))^(1/3), 'rational') & (~in(((15*alpha)/(16*h2m))^(1/3), 'rational') | ~0 < alpha/h2m) & A ~= 0 & (signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1)) | 0 < (- 1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & 0 < (1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & in(((3^(1/2)*1i)/2 - 1/2)^2*((15*alpha)/(16*h2m))^(1/3), 'rational') & in(((3^(1/2)*1i)/2 + 1/2)^2*((15*alpha)/(16*h2m))^(1/3), 'rational') & in(((15*alpha)/(16*h2m))^(1/3), 'rational') & A ~= 0 & 0 < alpha/h2m & (signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1))
 in(((15*alpha)/(16*h2m))^(1/3), 'rational') & A ~= 0 & 0 < alpha/h2m & (0 < (- 1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & ~in(((3^(1/2)*1i)/2 - 1/2)^2*((15*alpha)/(16*h2m))^(1/3), 'rational') & (~0 < (1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & (signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1)) | 0 < (1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & ~in(((3^(1/2)*1i)/2 + 1/2)^2*((15*alpha)/(16*h2m))^(1/3), 'rational') & (signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1)) | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= -1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1)) | ~0 < (- 1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & ~0 < (1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & (signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1)) | 0 < (1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & ~in(((3^(1/2)*1i)/2 + 1/2)^2*((15*alpha)/(16*h2m))^(1/3), 'rational') & (~0 < (- 1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & (signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1)) | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= -1 & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1)) | ~0 < (- 1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= -1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1) | ~0 < (1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= -1 & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1) | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= -1 & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= -1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1) | 0 < (- 1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & in(((3^(1/2)*1i)/2 - 1/2)^2*((15*alpha)/(16*h2m))^(1/3), 'rational') & in(((15*alpha)/(16*h2m))^(1/3), 'rational') & A ~= 0 & 0 < alpha/h2m & (~0 < (1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & (signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1)) | 0 < (1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & ~in(((3^(1/2)*1i)/2 + 1/2)^2*((15*alpha)/(16*h2m))^(1/3), 'rational') & (signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1)) | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= -1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1)) | 0 < (1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & in(((3^(1/2)*1i)/2 + 1/2)^2*((15*alpha)/(16*h2m))^(1/3), 'rational') & in(((15*alpha)/(16*h2m))^(1/3), 'rational') & A ~= 0 & 0 < alpha/h2m & (~0 < (- 1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & (signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1)) | 0 < (- 1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & ~in(((3^(1/2)*1i)/2 - 1/2)^2*((15*alpha)/(16*h2m))^(1/3), 'rational') & (signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1)) | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= -1 & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1)) | 0 < (- 1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & 0 < (1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & in(((3^(1/2)*1i)/2 - 1/2)^2*((15*alpha)/(16*h2m))^(1/3), 'rational') & in(((3^(1/2)*1i)/2 + 1/2)^2*((15*alpha)/(16*h2m))^(1/3), 'rational') & in(((15*alpha)/(16*h2m))^(1/3), 'rational') & A ~= 0 & 0 < alpha/h2m & (signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1))
 
 
ans =
 
 ((3^(1/2)*1i)/2 - 1/2)^2*((15*alpha)/(16*h2m))^(1/3)
 ((3^(1/2)*1i)/2 + 1/2)^2*((15*alpha)/(16*h2m))^(1/3)
                          ((15*alpha)/(16*h2m))^(1/3)

MATLAB: Matrix with numerical sequence

N = 7; % must be odd
M = ones(N)*16;
M(1:2:N,:) = 4;
M(2:2:N*N) = 8;
M(:,[1,N]) = M(:,[1,N])/2;
M([1,N],:) = M([1,N],:)/2;

giving:

M =
  1    4    2    4    2    4    1
  4   16    8   16    8   16    4
  2    8    4    8    4    8    2
  4   16    8   16    8   16    4
  2    8    4    8    4    8    2
  4   16    8   16    8   16    4
  1    4    2    4    2    4    1

Best Answer

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