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I have a function which produces a polynomial in $t$ with positive integer coefficients, and I know that these factor as product of $t-$ numbers of the form $[k]_t = 1+t+...+t^{k-1}$ . Is there a way to factor the polynomials in sage which readily give the factorization in terms of the $t-$numbers?

For example, I have a polynomial $(t^2-t+1)(t^2+t+1)(t+1)$. I want the program to return $[6]_t$.

I have a function which produces a polynomial in $t$ with positive integer coefficients, and I know that these factor as product of $t-$ numbers of the form $[k]_t = 1+t+...+t^{k-1}$ . Is there a way to factor the polynomials in sage which readily give the factorization in terms of the $t-$numbers?

For example, I have a polynomial $(t^2-t+1)(t^2+t+1)(t+1)$. $(t^2-t+1)(t^2+t+1)(t+1)^2=(t^5+t^4+t^3+t^2+t+1)(t+1)$. I want the program to return $[6]_t$. $[6]_t[2]_t$.

I have a function which produces a polynomial in $t$ with positive integer coefficients, and I know that these factor as product of $t-$ numbers of the form $[k]_t = 1+t+...+t^{k-1}$ . Is there a way to factor the polynomials in sage which readily give the factorization in terms of the $t-$numbers?

For example, I have a polynomial $(t^2-t+1)(t^2+t+1)(t+1)^2=(t^5+t^4+t^3+t^2+t+1)(t+1)$. I want the program to return $[6]_t[2]_t$.