---
title: "Magma V2.15-8 Patch Notes"
canonical: "https://docs.magma-maths.org/patchnotes/2.15-8.html"
source: "https://docs.magma-maths.org/patchnotes/2.15-8.md"
---

<a id="magma-v2-15-8-patch-notes"></a>
# Magma V2.15-8 Patch Notes

## Coding Theory

- A crash in [`LDPCDecode`](../CodingTheory/LowDensityParityCheckCodes/introduction.md#function-ldpcdecode-code-modtuprngelt) has been fixed.  Reported by M. Grassl.

## Elliptic Curves

- `TwoDescent` has been modified to also return maps. Similarly with [`TwoCover`](../ArithmeticGeometry/EllipticCurvesOverQAndNumberFields/mordell-weil.md#function-twocover-fldnumelt).
- [`DualIsogeny`](../ArithmeticGeometry/EllipticCurves/morphism.md#function-dualisogeny-map) has been rewritten.  Previously it was correct only up to an automorphism; now the composite of the given and its dual is guaranteed to equal multiplication by m, where m is the degree of the isogeny.
- Some errors in [`IsogenyFromKernel`](../ArithmeticGeometry/EllipticCurves/morphism.md#function-isogenyfromkernel-schgrpell) have been corrected.
- [`PushThroughIsogeny`](../ArithmeticGeometry/EllipticCurves/morphism.md#function-pushthroughisogeny-map-rngupolelt) now works faster.
- Improved the equality comparison of isogenies so that different presentations of the same isogeny are correctly identified as equal more often.
- Improved the speed of [`MultiplicationByMMap`](../ArithmeticGeometry/EllipticCurves/morphism.md#function-multiplicationbymmap-crvell-rngintelt) for larger values of `m`, and fixed several bugs in the characteristic 2 case.
- A change to the amount of real precision in [`QuarticReduce`](../ArithmeticGeometry/EllipticCurvesOverQAndNumberFields/mordell-weil.md#function-quarticreduce-rngupolelt) was made, which was a problem in some cases of using the descent machinery.
- An bug has been fixed concerning reduction of plane cubics (occurring as genus one models of degree 3, or as curves returned by [`ThreeDescent`](../ArithmeticGeometry/EllipticCurvesOverQAndNumberFields/mordell-weil.md#function-threedescent-crvell)).

## Function Fields

- Some incorrect answers from `Expand` and the application of completion maps have been fixed. Reported by G. Moehlmann.

## Galois Groups

- A crash in [`SolveByRadicals`](../GlobalFields/AlgebraicFunctionFields/galois.md#function-solvebyradicals-rngupolelt) has been fixed.  Reported by A. Previtali.

## Groups

- A crash when comparing two group homomorphisms for equality has been corrected. Bug reported by S. Guest.
- A bug when computing conjugacy classes of a matrix group has been corrected. Bug reported by S. Guest.
- A crash computing `NormalLattice` of a matrix group has been fixed. Bug reported by H. Coutts.

## Hilbert Modular Forms

- A serious oversight in the initial choices has been corrected. This would only have affected Hecke operators at primes dividing the level.  (The choice of right ideal classes for a definite quaternion order was not made carefully enough.)
- The precomputation phase is now massively faster for number fields of degree $\ge 8$, due to greater care in lattice searches.

## Hyperelliptic Curves

- The intrinsics taking a sequence of 3 G2 invariants now accept sequences of integers which are converted to rationals. The geometric autorphism groups returned for genus 2 curves are now permutation groups (`GrpPerm`) rather than finitely-presented groups (`GrpFP`).

## Invariant Theory

- A bug in `FundamentalInvariants` for invariant rings of reductive groups has been fixed.  Reported by M. Vogt.

## Lattices

- A long-standing bug in the 2-adic genus of a lattice was fixed; e.g., [`pAdicDiagonalization(LatticeWithGram(DiagonalMatrix([4,6])),2)`](../LatticesQuadraticForms/Lattices/genus.md#function-padicdiagonalization-lat-rngintelt) gave the wrong result. Reported by N. Scheithauer.
- A crash in `ShortestVectors` has been fixed.  Reported by R. Marinier.
- A crash when taking an `ActionGenerator` of a G-Lattice has been fixed. Bug reported by M. Watkins.

## Polynomial Rings

- A crash when creating polynomial rings over fields of fractions has been fixed.  Reported by K. Binder.
- A crash when computing the discriminant of the zero multivariate polynomial has been fixed.  Reported by A. Brumer.
- An incorrect result for squarefree factorization of bivariate polynomials in small characteristic has been fixed.  Reported by P. Lisonek.

## Real Numbers

- A convergence problem when using `Root` in fixed low-precision real fields has been fixed.  Reported by R. Cossett.

## Sparse Matrices

- A bug in [`ModularSolution`](../MatricesLinearAlgebra/SparseMatrices/solution.md#function-smat-modularsolution) would result in a crash whenever Lanczos was selected without also selecting verbose output. Reported by C. Diem.