how to transfer a function parameters to small degree

Hi fellows,

Somehow I get the function as below

f4 =

    -0.0699999999999999928 exp(0.0139999999999999986 x)

           - 0.0525000000000000050 exp(0.0140000000000000020 x)

           + 0.269999999999999962 exp(-0.0719999999999999946 x)

The parameters of the function is calculated in the previous steps. When I run

syms x
solve(f4,x);

there is an error message

??? Error using ==> sym.solve at 73
Error using ==> maplemex
Error, (in gcd/gcdchrem1) input polynomials have too large a degree

I guess it is becasue the parameters have too much degree of decimals. Is there any way to transfer f4 to something like

-0.07exp(0.014x)-0.052exp(0.014)+0.027exp(-0.072x)?

In fact, the parameter in the first part and the second part should equal since they are the same according to the way they being calculated. But somehow the result shows there is a very small difference. I dont understand why this either...

Is anyone could help with this? Thanks!

Answer 1

[Walter Roberson]

I notice you are using Maple as your symbolic engine. I never got a chance to play with Maple as the MATLAB symbolic engine, just with Maple itself. Inside Maple itself, this is easily handled as

solve(convert(f4, rational), x)

but I do not know if you have access to Maple's "convert" function. Experiment with

feval(symengine, 'convert', '0.0699999999999999928', 'rational')

and see if it complains about convert or if it returns 7/100

In general the difficulty you are running into is mixing floating point computation at the MATLAB level with calculations at the Symbolic Toolbox level. When you are going to be making symbolic computations, then for accuracy purposes is is best to switch over to symbolic form as soon as possible. For example, instead of using

3.52 * exp(pi/2) * x

you would use

sym('3.52') * exp(sym('Pi/2')) * x

Notice how I have converted every constant in the place it occurs. Do not get lazy and do things like

sym(3.52 * exp(pi/2)) * x

because you will already have lost precision through the floating point calculations at the MATLAB level. For example,

cos(pi/2)

will not be exactly 0 due to round-off error, but

cos(sym('Pi/2'))

will be exactly 0.

[xueqi]

yeah I just installed Maple today and somehow associate them together! I just unistalled Maple and then there is no problem any more! haha...