Conputation with symbolic elements

Question

pepito che 2021-5-17

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/832303-conputation-with-symbolic-elements

评论： pepito che 2021-5-17

Hello,

I'm trying to make symbolic computation with matlab. My problem is that, since the moment there is symbol in the expression, it doesn't want to compute the rest.

To be explicit I have this kind of probleme: let suppose 'eps' symbolic variable: my output are kind of: 213263172/3216586391302232716*eps while I would like it compute 213263172/3216586391302232716 and then multiply by 'eps'.

I heard it is because he take each element as string now and not as number... ??

Thank you for any help,

Here is the code:

expup=[0 1 0 0 0; 0 0 1 0 0; 0 0 0 1 0; 0 0 0 0 1; 1 0 0 0 0];
expdown=transpose(expup);
ket0=[1 0];
ket1=[0 1];
qx=[0 0 1 0 0];
qy=[0 0 1 0 0];
qz=[0 0 1 0 0];
point=kron(qx,qz);
syms alpha beta eps phi;
alpha=1/sqrt(2);
beta=1/sqrt(2);
phi=pi/4;
m=alpha*ket0+beta*ket1;
vec=kron(m,point).';
sigma_x=[0 1; 1 0];
sigma_y=[0 -i; i 0];
sigma_z=[1 0; 0 -1];
up_p=-i*eps*logm(expup)
down_p=i*eps*logm(expdown)
droite=expm(i*(kron(kron(sigma_x,up_p),eye(5))+kron(kron(sigma_z,eye(5)),up_p)));
gauche=expm(-i*(kron(kron(sigma_x,up_p),eye(5))+kron(kron(sigma_z,eye(5)),up_p)));

the result of up_p is:

up_p =
 
[ (eps*7998807863191437i)/10141204801825835211973625643008,               -(eps*4814164849790005i)/4503599627370496,                  (eps*5950635009230501i)/9007199254740992,                 -(eps*5950635009230503i)/9007199254740992,              (eps*4814164849790003i)/4503599627370496]
[                 (eps*2407082424895001i)/2251799813685248, (eps*1663548296596613i)/5070602400912917605986812821504,                 -(eps*4814164849790009i)/4503599627370496,                   (eps*743829376153813i)/1125899906842624,             -(eps*5950635009230501i)/9007199254740992]
[                -(eps*5950635009230499i)/9007199254740992,                  (eps*601770606223751i)/562949953421312, -(eps*6027246515204799i)/20282409603651670423947251286016,                 -(eps*4814164849790009i)/4503599627370496,              (eps*1487658752307625i)/2251799813685248]
[                 (eps*2975317504615257i)/4503599627370496,               -(eps*5950635009230511i)/9007199254740992,                  (eps*4814164849790011i)/4503599627370496, -(eps*6827359916614769i)/40564819207303340847894502572032,             -(eps*4814164849790005i)/4503599627370496]
[                -(eps*2407082424895003i)/2251799813685248,                (eps*5950635009230509i)/9007199254740992,                 -(eps*5950635009230503i)/9007199254740992,                  (eps*2407082424895001i)/2251799813685248, (eps*215792426952591i)/316912650057057350374175801344]
 

I would like he compute number and then times epsilon.

The next step is to get 'droite' (which is 50x50 matrix) in function of 'eps'