Opened 9 years ago

Last modified 5 years ago

## #15712 new defect

# Fix determinant for RR — at Initial Version

Reported by: | ppurka | Owned by: | |
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Priority: | major | Milestone: | sage-6.4 |

Component: | linear algebra | Keywords: | |

Cc: | Merged in: | ||

Authors: | Reviewers: | ||

Report Upstream: | N/A | Work issues: | |

Branch: | Commit: | ||

Dependencies: | Stopgaps: |

### Description

Refer to this sage-devel post

A = matrix([[ 1.0, -1.50614628068, 2.26847661882, -3.41665762226, 5.14598617013, -7.7506079306, 11.6735493077, -17.5820728722], [ 1.0, -0.936702701875, 0.877411951699, -0.821874145813, 0.769851732984, -0.721122198329, 0.675477111557, -0.632721235449], [ 1.0, -0.443181140009, 0.19640952286, -0.0870449962496, 0.03857670067, -0.0170964661807, 0.00757683137208, -0.00335790876514], [ 1.0, 0.352786603689, 0.124458387743, 0.0439072519123, 0.0154898902795, 0.00546462578321, 0.00192784677049, 0.000680118514595], [ 1.0, 0.647213396311, 0.418885180364, 0.271108100248, 0.175464794329, 0.11356316547, 0.07349960202, 0.0475699270508], [ 1.0, 1.44318114001, 2.08277180288, 3.00581698486, 4.33793838286, 6.26043086067, 9.03493574645, 13.0390488705], [ 1.0, 1.93670270187, 3.75081735545, 7.26421810653, 14.0686308339, 27.2467553477, 52.7688646993, 102.197602838], [ 1.0, 2.50614628068, 6.28076918019, 15.7405263208, 39.4480614948, 98.8626125954, 247.764168855, 620.933250262]]) B = A.change_ring(RDF) print "det(A) = {}, det(B) = {}".format(A.determinant(), B.determinant()) det(A) = -4.19430400000000e6, det(B) = 16801.7979988

According to Peter Bruin, a possible fix is to use pari:

*Well, it should also be fixed for a RealField? of higher precision. An easy solution for that is to use PARI, which uses a numerically more stable algorithm (Gaussian elimination, choosing pivots of maximal absolute value; I don't know about proven error bounds). Example:*

sage: A._pari_().matdet() 16801.7979988279 # same as when doing the computation over QQ

*Sage's determinant() already uses PARI over Z/nZ for n less than the machine word size; it would be trivial to adapt it to work also over the reals.*

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