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In "Congruence classes of presentations for the complex reflection groups $G(m, p, n)$", Paragraph 1.4, Shi provides explicit representatives for the root system of $G(m,p,n)$.
For what it's worth, here is an interesting quote of Arnold, relating to mathematics and experimentation. "Mathematics is a part of physics. Physics is an experimental science, a part of natural science. Mathematics is the part of physics where experiments are cheap."