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Consider the following rational expression in $t$,

$$f(t)=\frac{(1-t^q)^{m-k}((1-t^2)^m}{(1-t)^{m-k+1}((1-t^{2q})^m}$$ where $q=4,m=33, k=31$.

I want to find the first power of $t$ with a non-positive coefficient. How can I proceed? The hint given in the book is that

$$f(t)=1 + 26t + 295t^2 + 1820t^3 + 5610t^4 − 1560t^5+\dots$$

How did the author of the book arrived at this approximation? Kindly give some hints. Is it possible to do it in SageMath.

Thanks for reading

Consider the following rational expression in $t$,

$$f(t)=\frac{(1-t^q)^{m-k}((1-t^2)^m}{(1-t)^{m-k+1}((1-t^{2q})^m}$$ where $q=4,m=33, k=31$.

I want to find the first power of $t$ with a non-positive coefficient. How can I proceed? The hint given in the book is that

$$f(t)=1 + 26t + 295t^2 + 1820t^3 + 5610t^4 − 1560t^5+\dots$$

How did the author of the book arrived at this approximation? Kindly give some hints. Is it possible to do it in SageMath.

Thanks for reading

Consider the following rational expression in $t$,

$$f(t)=\frac{(1-t^q)^{m-k}((1-t^2)^m}{(1-t)^{m-k+1}((1-t^{2q})^m}$$ where $q=4,m=33, k=31$.

I want to find the first power of $t$ with a non-positive coefficient. How can I proceed? The hint given in the book is that

$$f(t)=1 + 26t + 295t^2 + 1820t^3 + 5610t^4 − 1560t^5+\dots$$

How did the author of the book arrived at this approximation? Kindly give some hints. Is it possible to do it in SageMath.

Thanks for reading