--- title: "Magma V2.21-3 Patch Notes" canonical: "https://docs.magma-maths.org/patchnotes/2.21-3.html" source: "https://docs.magma-maths.org/patchnotes/2.21-3.md" --- # Magma V2.21-3 Patch Notes ## Commutative Algebra - An bug in `IsPrime` for positive-dimensional ideals over finite fields of medium characteristic has been fixed. Reported by N. Bruin. ## Dirichlet and Hecke Characters - The creation intrinsics `DirichletCharacter` and `HeckeCharacter` can now take a list as an argument instead of a tuple. - The intrinsic [`GrossenTwist`](../GlobalFields/DirichletAndHeckeCharacters/introduction.md#function-grossentwist-grossenchar-list) has been expanded to include twists by Hecke characters of the same modulus, and also returns a kernel corresponding to characters that are trivial on the given data. ## Elliptic Curves - A crash with large degrees in `FrobeniusMap` is now avoided. - A problem with computing Euler factors at good primes (over a number field) which divide the denominator of the a-invariants has been fixed. Reported by F. Brunault. ## Groups - A crash in `IsCyclic` when applied to the trivial matrix group has been fixed. Bug reported by Andrew Sutherland. - A crash to do with [`HomomorphismsProcess`](../FinitelyPresentedGroups/FPGroups/homomorphism.md#function-grpfp-1-homomorphismsprocess), when no homomorphisms are found, has been fixed. Bug reported by Jan Karabas. ## Number Fields - The `meet` of 2 number fields which are defined as extensions of different coefficient fields has been fixed. ## Polynomials - A problem with multiplication of polynomials whose trailing terms were inexact elements of an exact ring, for instance a constant coefficient O(t^4) in a power series ring of fixed precision 20 over GF(3), has been fixed. Reported by B. Allombert in the context of factorization of polynomials over Laurent series rings. - A crash when taking `GCD` of polynomials over a [`GaloisRing`](../LocalFields/GaloisRings/creation.md#function-galoisring-rngintelt-rngintelt) has now been disallowed. - A crash in factorization of multivariate polynomials over a number field with a non-monic defining polynomial has been fixed. ## Sparse Matrices - A missing error check in `Echelonize` has been inserted. Reported by R. Zeier. ## Symmetric Function Algebras - Taking the characteristic of a symmetric function algebra no longer crashes. - Polynomial arithmetic over symmetric function algebras no longer crashes. Reported by A. Duncan. ## System - The description of [`GetDefaultRealField`](../BasicRings/RealAndComplexFields/introduction.md#function-getdefaultrealfield) now has the correct return type. - The deprecated `FldPr` and `FldPrElt` types have been removed. Note: As a consequence, workspaces saved before this patch release will not be able to be properly restored by it.