how i can show in matlab tha sqrt(x^2)=x in symbolic toolbox

Hi i use the symbolic tool box to simplify an expression I

receive that

((2*A*dhmax + B*h0)^2/h0^2)^(1/2)*(2*A^2*dhmax^2 + 2*A*B*dhmax*h0 + 6*C*A*h0^2 - B^2*h0^2))/(24*A^2*h0^2) - (((2*A*dhmax - B*h0)^2/h0^2)^(1/2)*(2*A^2*dhmax^2 - 2*A*B*dhmax*h0 + 6*C*A*h0^2 - B^2*h0^2))/(24*A^2*h0^2)

how i can say in matlab that ((2*A*dhmax + B*h0)^2/h0^2)^(1/2)= (2*A*dhmax+B*h0)/h0 ?

thank you

George

Answer 1

[Steven Lord]

That's not true in the general case.

A = 1;
h0 = 1;
dhmax = 2;
B = -5;
lhs = ((2*A*dhmax + B*h0)^2/h0^2)^(1/2)

lhs = 1

rhs = (2*A*dhmax+B*h0)/h0

rhs = -1

If you defined those variables to all be real and positive and used sqrt (so it's the principal square root):

syms A h0 dhmax B real positive
isAlways(sqrt((2*A*dhmax + B*h0)^2/h0^2) == (2*A*dhmax+B*h0)/h0)

ans = logical
   1

In that case, asking MATLAB to simplify the expression may allow it to perform the rewriting you want.

[Shubham]

If all the defined variables are not positive to begin, then atleast the entire expression should be positive:

syms A h0 dhmax B real;
expr = sqrt((2*A*dhmax + B*h0)^2/h0^2);
simplifiedExpr = simplify(expr);
disp(simplifiedExpr);
isAlways(simplifiedExpr == abs(  (2*A*dhmax+B*h0)/h0    ))

ans = logical
   1

Answer 2

[John D'Errico]

Except, that equality does NOT hold! The sqrt "function" has two branches. sqrt(x^2) can as easily be -x, as it is x. So you cannot simply replace sqrt(x^2) with x.

syms A dhmax B h0
expression = ((2*A*dhmax + B*h0)^2/h0^2)^(1/2)
simplify(expression)

As you can see, simplify refuses to do what you think is obvious. However, if you want, you can effectively tell simplify to play a little fast with the rules, to not be quite so picky.

simplify(expression,IgnoreAnalyticConstraints = true)

[John D'Errico]

Sadly, Answers is again bugged, and for some strange reason will not allow me to show the results of those operations. But it does do what you want. SIGH. It does not help if I change browsers. It does not help if I clear all history. It does not help if I empty the browser caches.

The IgnoreAnalyticConstraints flag does what you want, however.