---
title: "Magma V2.10-20 Patch Notes"
canonical: "https://docs.magma-maths.org/patchnotes/2.10-20.html"
source: "https://docs.magma-maths.org/patchnotes/2.10-20.md"
---

<a id="magma-v2-10-20-patch-notes"></a>
# Magma V2.10-20 Patch Notes

## Elliptic Curves

- A bug that caused the Mordell-Weil group calculation to hang under rare circumstances has been fixed. Reported by Kaori Suzuki.
- The `RootNumber` intrinsic is now available.

## Geometry

- Magma level printing of products of projective schemes has been corrected.
- A error in the checking of input to the function `DirectProduct` when applied to the ambient spaces of schemes has been fixed.

## Groups

- An error in the isomorphism returned by the function `PCGroup` applied to an abelian group has been corrected. Reported by Jon Carlson.
- An error that occurred in the function `LowIndexSubgroups` in the case in which not all of the composition factors are in the database of maximal subgroups of almost simple groups was fixed. Reported by Markus Grassl.
- An error which caused the `Subgroups` function to miss some groups when the `IsElementaryAbelian` flag was set was fixed.

## Incidence Structures

- A bug in the function [`IsHadamard`](../Combinatorics/HadamardMatrices/hadamard.md#function-ishadamard-algmatelt) that made the function fail to recognise that some matrices over finite fields were not Hadamard has been corrected.

## Lie Groups

- A bug in the function `RootSubdatum` which occurred when applied to the standard root datum of type $F_4$. Reported by K Andersen.

## Modules

- The function `Matrix``(R, vector)` now correctly returns a matrix.

## Rings and Fields

- An error which caused the different of a relative maximal order of a number field to die unexpectedly has been fixed.
- The `/` operator when applied to ideals of orders of number fields now returns fractional ideals when each argument is an integral ideal.
- The `pSelmerGroup` function now works correctly when applied to typed empty sets.
- A bug for `SUnitGroups` of rank 0 was fixed: formerly Magma would die in this case.
- A bug in [`IsProbablyPermutationPolynomial`](../BasicRings/FiniteFields/permutation-polynomials.md#function-isprobablypermutationpolynomial-rngupolelt) when applied to large finite fields has been fixed.

## Sets and Sequences

- A bug with in for sets and sequences with non-standard universes has been fixed.