How to represent and calculate the product of non disjoint cycles in SageMath

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Define the permutation for each cycle, and multiply them.

Of course the result depends on the order in which you multiply.

Example:

sage: prod(Permutation(c) for c in ("(3, 5)", "(1, 2)", "(2, 5)", "(1, 4)"))
[5, 4, 2, 1, 3]