Partial fractions with generating functions

BigBoss22
Messages
2
Reaction score
0
Suppose that q(z) = 1, and p(z) = (1 + z)(1 + 3z).

We wish to express q(z)/p(z) in the form

where A and B are constants. To find them, we multiply through by p(z) =
(1 + z)(1 + 3z) and obtain
1 = A(1 + 3z) + B(1 + z)
= (A + B) + (3A + B)z

Im fine up to this point, But according to my notes it is obvious that A + B = 1 and (3A + B)z = 0.

I can not see why this is the case?

Any help would be greatly appreciated.
 
Physics news on Phys.org
Never mind figured it out:

1 + 0*z = ...
 
Two polynomials are equal iff their coefficients are equal.
 
Thread 'Use greedy vertex coloring algorithm to prove the upper bound of χ'
Hi! I am struggling with the exercise I mentioned under "Homework statement". The exercise is about a specific "greedy vertex coloring algorithm". One definition (which matches what my book uses) can be found here: https://people.cs.uchicago.edu/~laci/HANDOUTS/greedycoloring.pdf Here is also a screenshot of the relevant parts of the linked PDF, i.e. the def. of the algorithm: Sadly I don't have much to show as far as a solution attempt goes, as I am stuck on how to proceed. I thought...
Back
Top