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Let $p(t)\in \mathbb{Z}_{\geq 0}[t]$. Write $p(t)=\sum_i a_i t^i$. Then we say $p(t)$ is unimodal if $a_0 \leq a_1 \leq ... \leq a_k \geq a_{k+1} \geq ... \geq a_n$ i.e, the sequence of coefficients increase at first and then decrease, they don't 'jump around' ; there is no phenomenon like increase then decrease then increase again. Given such a polynomial, how can we check unimodality in sage?

Let $p(t)\in \mathbb{Z}_{\geq 0}[t]$. Write $p(t)=\sum_i a_i t^i$. Then we say $p(t)$ is unimodal if $a_0 \leq a_1 \leq ... \leq a_k \geq a_{k+1} \geq ... \geq a_n$ i.e, the sequence of coefficients increase at first and then decrease, they don't 'jump around' ; there is no phenomenon like increase then decrease then increase again. Given such a polynomial, how can we check unimodality in sage? sage?

Let $p(t)\in \mathbb{Z}_{\geq 0}[t]$. Write $p(t)=\sum_i a_i t^i$. Then we say $p(t)$ is unimodal if $a_0 \leq a_1 \leq ... \leq a_k \geq a_{k+1} \geq ... \geq a_n$ i.e, the sequence of coefficients increase at first and then decrease, they don't 'jump around' ; there is no phenomenon like increase then decrease then increase again. Given such a polynomial, how can we check unimodality in sage?