simplifying symbolic expressions using assumptions

Hi all,

I have a symbolic equation as follows:

A = X / (XY + 1);

I know that for my specific case XY >> 1

I wish to simplify this equation using this assumption such that the denominator simplifies to 1 + XY ~ XY and A becomes X/XY = 1/Y.

Are there tools/functions in the symbolic math toolbox that allow one to do these user defined simplifications on a symbolic expression?

If not then is there a way I can do this through some code?

Thanks, Bhupi

Answer 1

[Yu Jiang]

I don’t think there is a way to directly approximate a symbolic expression in MATLAB with another symbolic term.

However, here is a workaround for the example you provided. Since x*y >> 1, you may want to consider replace (x*y+1) with x*y by using the function sub (See Documentation) .

For example, the following code can be executed

>> syms x y
>> A = x/(x*y+1);
>> A = subs(A, 'x*y+1', 'x*y');

The result will be A = 1/y.

-Yu

[Bhupi]

Yu,

Thanks thats what I had in mind as an alternative but it gets a bit messy when I have too many of these substitutions.

I know MuCAD supports something like assume() where one can define assumptions to further simplify the expressions but it does not support something like A >> 1.

I wish MATLAB did have a much cleaner solution to this as many a times these symbolic equations get too lengthy and tedious and some heuristic/simplifications are required based on users knowledge of the system.

For now I guess I will go with your solution.

Thanks for your help.

-Bhupi

Answer 2

[Christopher Creutzig]

This approximation can be viewed as a special kind of truncated series:

>> syms X Y
>> A = X/(X*Y + 1);
>> taylor(A, Y, Inf, 'Order', 2)

ans =

1/Y

>> taylor(A, X, Inf, 'Order', 2)

ans =

1/Y - 1/(X*Y^2)

>> taylor(A, X, Inf, 'Order', 1)

ans =

1/Y