Coercion

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.

S ! x: Str, Elt -> Elt

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.

IsCoercible(S, x): Str, Elt -> Bool, Elt

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.