How to generate a totally positive matrix randomly using software like Maple?

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A matrix $A$ is totally positive if all the minors of $A$ are positive. How to generate a totally positive matrix randomly using some software like Maple or any other CAS? Thank you very much.

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We can first generate a random sequence L. Let $A$ be the Vandermonde matrix generated by sort(L). Then $A$ is totally positive. Then we compute the Gaussian LDU decomposition of $A$: $A = utv$. The matrices $u, t, v$ are all totally positive. Let $B=vtu$. Then $B$ is totally positive. The matrix $B$ is a random totally positive matrix.