How to further utilize the "simplify" function for simplification?

I was simplifying the trigonometric function, but despite using the "simplify" function, the result I obtained is as follows.

However, this result can still be further simplified. Could you please tell me where the problem lies?

[Torsten]

Could you include your code and describe why you think the result could further be simplified ?

You could try simplify with the 'steps' option:

simplify(expression,'steps',50)

e.g. Sometimes it simplifies further.

[John D'Errico]

When you incude only a picture of your expression, we cannot even copy and paste it into MATLAB to try to do something ourselves. And that makes it considerably more difficult to help you. Surely you don't want to make it more difficult to get help?

A picture may paint a thousand words, but not here.

Anyway, simple in your eyes need not be simple in the eyes of a computer.

[Star Strider]

The 'steps' name-value pair is correct, however I usually give it at least 500 iterations.

theta = sym('theta', [1 5]);
ans = (cos(theta(4))*sin(theta(1)) - prod(cos(theta(1:3)))*sin(theta(4)) + cos(theta(1))*prod(sin(theta(2:4))) *sin(theta(5)))

ans = 

ans = simplify(ans, 500)

ans = 

It doesn't appear to be able to be simplified further.

If you want it in a different form, experiment with collect or rewrite.

.

[John D'Errico]

Actually, I would add that asking for all responses is my preference. Then I take the one that makes me happy, as opposed to what simplify likes.

theta = sym('theta', [1 5]);
thing = (cos(theta(4))*sin(theta(1)) - prod(cos(theta(1:3)))*sin(theta(4)) + cos(theta(1))*prod(sin(theta(2:4))) *sin(theta(5)))

thing = 

simplethings = simplify(thing,steps = 20,all=true)

simplethings = 

simplethings(6)

ans = 

simplethings(8)

ans = 

But to be honest, I've not seen anything that seems very simple.

[Steven Lord]

However, this result can still be further simplified.

Can you show us the further simplification of that expression? It's possible that the simplification you're thinking of is incorrect or incomplete, or that you need to apply certain additional assumptions (real, positive, integer, etc.) to one or more of the variables in order to satisfy your simplification.

For example:

syms x
f = simplify(sqrt(x^2))

f = 

You might say "Shouldn't f just be x?" No, as you can see by substituting x = -1 into f.

shouldBeX = subs(f, x, -1)

shouldBeX = 

1

Now if you added the assumption that the variable was real:

syms y real
f = simplify(sqrt(y^2))

f = 

or that the variable was positive, MATLAB can simplify the expression further:

syms z positive
f = simplify(sqrt(z^2))

f = 

z

Answer 1

[David Goodmanson]

How did an overall factor of theta_dot5 in the question later become sin(theta_5) in the comments ?!? Taking the original posting as correct, and ignoring theta_dot5, this is

sin(th1)*cos(th4) - cos(th1)*cos(th2)*cos(th3)*sin(th4) ...
                  + cos(th1)*sin(th2)*sin(th3)*sin(th4)

I did the following calculuation by hand since it's straightforward AND because going to symbolic variables, Matlab seems incapable of simplifying this expression at all. Highly disappointing, although I don't think many people contend that Matlab symbolics is very adept at its job.

By inspection the expression becomes

ans1 = sin(th1)*cos(th4) - cos(th1)*cos(th2+th3)*sin(th4)

which already makes progress because it shows that th2,th3 only come in as their sum.

With d = cos(th2+th3), ans1 is of the form

a - b*d  =  (1/2)((a+b)*(1-d) + (a-b)*(1+d))

and throwing in some basic trig identities you can arrive at

ans2 =   sin(th1+th4)*sin((th2+th3)/2)^2 ...
       + sin(th1-th4)*cos((th2+th3)/2)^2   .                    

ans2 has a symmetric kind of form but whether it is simpler than ans1 is a matter of opinion. I doubt that further simplification is in the cards.