How to simplify a symbolic matrix

Hello everyone,

I was trying the following code:

    clc
    clear all
    close all
    syms a k1 k2;
    A=[exp(-i*k1*a) 0; 0 exp(i*k1*a)];
    B=[k2+k1 k1-k2; k1-k2 k2+k1];
    C=[exp(i*k2*a) 0; 0 exp(-i*k2*a)];
    D=[exp(i*k2*a) 0; 0 exp(-i*k2*a)];
    E=[k2+k1 k2-k1; k2-k1 k2+k1];
    F=[exp(-i*k1*a) 0; 0 exp(i*k1*a)];
    T=((((A*B)*C)*D)*E)*F;
    T=T/(4*k1*k2);
    T=simplify(T);
    fprintf('T11=\n%s \n',char(T(1,1)));
    fprintf('T12=\n%s \n',char(T(1,2)));
    fprintf('T21= \n%s \n',char(T(2,1)));
    fprintf('T22= \n%s \n',char(T(2,2))); 

In this code, i am trying to evaluate T matrix;

I want to simplify the individual components of T matrix {i.e., T(1,1) , T(1,2) , T(2,1) & T(2,2) }

I searched it on internet and found "simplify" will perform the above task.

But , for the above code, the result is yet unsimplified,

i.e., i am getting T(1,1) output as

(exp(a*k1*(-i))*(exp(a*k1*(-i))*exp(a*k2*(2*i))*(k1 + k2)^2 - exp(a*k1*(-i))*exp(a*k2*(-2*i))*(k1 - k2)^2))/(4*k1*k2)

i.e.,

but we can see that from the inner bracket can be further taken out to simplify the result ;

hence how to simplify the results of the above code?

Answer 1

[Swatantra Mahato]

Hi Sourav,

As mentioned in the documentation for "simplify" there is no universal idea to the simplest form of an expression. You may want to try out different Name-Value Pair arguments mentioned in the documentation to get the desired form suitable for your use case

As an example,

executing

T=simplify(T,'Steps',20);

instead gives

T12=
-(exp(-a*k2*2i)*(k1^2 - k2^2)*(exp(a*k2*4i) - 1))/(4*k1*k2) 

while

T=simplify(T,'Steps',30);

gives the result

T12=
-(sin(2*a*k2)*(k1^2 - k2^2)*1i)/(2*k1*k2) 

Hope this helps