A bug im simplify in the new Symbolic Toolbox?

Dear developpers Recently I run my codes in my book in the new versions of MATLAB

if true
A=[-7,2,0,-1; 1,-4,2,1; 2,-1,-6,-1; -1,-1,0,-4];
syms t, A1=(expm(A*1j*t)-expm(-A*1j*t))/(2*1j);
A2=(expm(A*1j*t)+expm(-A*1j*t))/2;
simplify(A1), simplify(A2)
end

I found that the results are not the same as the ones in the earlier versions such as R2011a, R2008a, which yield the saame results as funm(A*t,'sin'). Obviously the simplify function in the new Symbolic Math Toolbox did not apply Euler's formula.

[Dingyu Xue]

Also, another problem in simplify function, the new result is not the same as in the R2008a version, which are simpler

if true
   syms t; f=t^2*exp(-2*t)*sin(t+pi); F=simplify(laplace(f))
end

In 2008a, the simplified result is -2*(3*s^2+12*s+11)/(s^2+4*s+5)^3

[Star Strider]

If I remember correctly, until 2010, the symbolic math engine was Maple. Beginning in 2010 and for later releases, MuPad is the symbolic engine.

Answer 1

[Jan]

You do not reach "the developers" here, because this is the public forum of all Matlab users. Please use the "Contact Us" link on this page for an official enhancement request of bug report.

Answer 2

[John BG]

Hi Dingyu Xue

this is John BG <mailto:[e-mail] [e-mail]>

Both expressions are the same

t=[-10:.1:10];
y1=2./((t + 2).^2 + 1).^2 - (2*(2*t + 4).^2)./((t + 2).^2 + 1).^3;
y2=-2*(3*t.^2+12*t+11)./(t.^2+4*t+5).^3;

.

Despite the logical evaluation returns null

isequal(y1,y2)

ans =

    logical

     0

but it's because of really small decimals discrepancy

when plotting

plot(t,y1,t,y2)

both curves fall right on same place, y1 is same as y2.

MATLAB help for simplify suggests

Simplification of mathematical expression is not a clearly defined subject. There is no universal idea as to which form of an expression is simplest. The form of a mathematical expression that is simplest for one problem might be complicated or even unsuitable for another problem.

Kind of, the function has probably undergone some kind of improvement, the resulting simplification is now split into different fractions, perhaps helping spot poles and zeros, yet the comment clearly remarks that symbolic simplification is not like finding zeros.

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thanks in advance

John BG

<mailto:[e-mail] [e-mail]>

[Jan]

The problem concerned the symbolic simplification. Of course both expressions reply the same values except for rounding errors, but the symbolic expressions have changed with the Matlab version. See Star Strider's comment.