symbolic expantion in matlab

hi,

I need to expand [1- (a1+b1)B ] / (1-b1B) and get a polynomial.

Can someone help me with this please?

Thanks.

[Azzi Abdelmalek]

What should be the result?

Answer 1

[Walter Roberson]

A polynomial in which variable? A finite polynomial or an infinite one?

If you need an infinite polynomial in B, then the expression is, using MuPAD notation,

1-a1*(sum(B^n*b1^(n-1), n = 1 .. infinity))

There is no finite version unless you want an approximation.

The above was deduced by examining the taylor expansion around B=0

[dav]

Thanks .

when I typed it however, I get an error. Can u please help me with it?

syms a1 b1 B
y= 1-a1*(sum(B^n*b1^(n-1), n = 1 .. infinity))
y= 1-a1*(sum(B^n*b1^(n-1), n = 1 .. infinity))
                           |
Error: The expression to the left of the equals sign is not a valid target for an assignment.

[Walter Roberson]

I did say "using MuPAD notation". MATLAB notation would be (ummm)

syms a1 b1 B
y = 1 - a1 * symsum(B^n*b1^(n-1), n, 1, inf)

Note that the answer would be your original expression. The infinite polynomial is

   1 - a1*B - a1*B^2*b1 - a1*B^3*b1^2 - a1*B^4*b1^3 ....

so that is the polynomial form of your expression with respect to B.

[dav]

Can you tell me how you got that last polynomial. All I got was,

y =

piecewise([B*b1 == 1, 1 - a1*(Inf/b1 - 1/b1)], [B*b1 ~= 1, a1*(B/(B*b1 - 1) - limit((B^n*b1^n)/(b1*(B*b1 - 1)), n == Inf)) + 1])

[Walter Roberson]

Try simple(y)

When I do it:

>> syms a1 b1 B n
>> 1-a1*(symsum(B^n*b1^(n-1), n, 1, inf))

ans =

                                         B a1
                                   1 + --------
                                       B b1 - 1

but I am using the Maple symbolic engine.

[dav]

I am sorry to bother you this much but I need to express it a s a polynomial.. Cam matlab do it?

thanks

[Walter Roberson]

What are you expecting the polynomial might look like? And which variable should it be in? Are you looking for an exact polynomial or an approximation? If an approximation, then how close does it need to be? Are there constraints on the values of a1, b1, or B ?

[dav]

I need a polynomial with at least 20 terms. I am actually tying to print a few terms of the infinite ar representation of the arma model in time series.

Also its better if I could have a constraint that a,b>0 and a+b<1 in it.

Finally i would like the code to print something like

1 - a1*B - a1*B^2*b1 - a1*B^3*b1^2 - a1*B^4*b1^3 ....

Again, Tanks a lot for all the help!