--- title: "Magma V2.26-12 Patch Notes" canonical: "https://docs.magma-maths.org/patchnotes/2.26-12.html" source: "https://docs.magma-maths.org/patchnotes/2.26-12.md" --- # Magma V2.26-12 Patch Notes ## Algebraic Number Fields - The algorithm used to compute `IsSubfield` for fields of degree more than 50 has been changed. Previously a root was computed by lifting but this showed to be unnecessarily expensive when for such degrees all roots can be computed in much less time. Reported by A. Pacetti. - A crash has been fixed in `MaximalOrder` when the `Ramification` parameter is specified and the number field is defined by a non-monic or non integral polynomial. Reported by J. Rouse. - `ValuationRing`s and `Localization`s of number fields can now be constructed. Requested by A. Markowitz. ## Algebraically Closed Fields - A crash involving algebraically closed fields defined over a small finite (arising from G-module computations) has been fixed. Reported by D. Benson. ## Elliptic Curves - A crash in [`TatePairing(P, Q, m)`](../ArithmeticGeometry/EllipticCurvesOverFiniteFields/pairings.md#function-tatepairing-ptell-ptell-rngintelt) where $P$ and $Q$ are equal has been fixed. Reported by M.R. Houben. ## Local Rings - $p$-adic rings constructed as a completion of the integers or rationals will now have default precision given by the `Precision` parameter, consistent with completions of number fields. Reported by T. Keller. ## Matrix Algebra - A crash in `Centre` for matrix algebras with large numbers of generators has been fixed. Reported by R. Zeier. ## Representation Theory - A crash in `DirectSumDecomposition(M)` for an $A$-module $M$ has been fixed. Reported by D. Gvirtz-Chen. ## Series Rings - Series rings constructed as a completion of a rational function field will now have default precision given by the `Precision` parameter, consistent with completions of function fields. Reported by T. Keller. ## System - A crash has been fixed when printing multisets whose elements are multisets containing tuples of sets. Reported by R. van Bommel. ## Valuation Rings - `ValuationRing`s of algebraic number fields and function fields can now be constructed.