Coercion is a fundamental concept in Magma. Given a structures A and B, there is often a natural mathematical mapping from A to B (e.g., embedding, projection), which allows one to transfer elements of A to corresponding elements of B. This is known as coercion. Natural and obvious coercions are supported in Magma as much as possible; see the relevant chapters for the coercions possible between various structures.
Given a structure S and an object x, attempt to coerce x into S and return the result if successful. If the attempt fails, an error ensues.
Given a structure S and an object x, attempt to coerce x into S; if successful, return true and the result of the coercion, otherwise return false.