Opened 12 years ago

Closed 5 years ago

# Infinite matrix groups over QQ fail for is_finite()

Reported by: Owned by: rbeezer AlexGhitza minor sage-8.2 algebra vdelecroix Frédéric Chapoton Travis Scrimshaw N/A 9892a36 9892a36fe40dc681a3f5c00e278b200878a450ac

### Description

```sage: H=SL(2,QQ)
sage: H.is_finite()
---------------------------------------------------------------------------
NotImplementedError                       Traceback (most recent call last)

/sage/dev/<ipython console> in <module>()

/sage/dev/local/lib/python2.6/site-packages/sage/groups/matrix_gps/matrix_group.pyc in is_finite(self)
343         if self.base_ring().is_finite():
344             return True
--> 345         return self._gap_().IsFinite().bool()
346
347     def cardinality(self):

/sage/dev/local/lib/python2.6/site-packages/sage/groups/matrix_gps/matrix_group.pyc in _gap_(self, G)
217             return SageObject._gap_(self, G)
218         except TypeError:
--> 219             raise NotImplementedError, "Matrix group over %s not implemented."%self.__R
220
221     def __cmp__(self, H):

NotImplementedError: Matrix group over Rational Field not implemented.
```

GL fails similarly. Other rings (ZZ, finite fields) seem to work OK, so perhaps this is restricted to something peculiar to the rationals?

### comment:1 Changed 12 years ago by davidloeffler

From the Gap manual, I get the impression that Gap won't allow you to construct a group unless it is finitely generated (and it knows how to calculate a set of generators). That's why Gap will allow you to work with GL(2, ZZ) but not GL(2, QQ).

### comment:2 Changed 5 years ago by chapoton

• Authors set to Frédéric Chapoton
• Branch set to u/chapoton/8550
• Commit set to 9892a36fe40dc681a3f5c00e278b200878a450ac
• Status changed from new to needs_review

New commits:

 ​9892a36 `trac 8550 fix order of SL(2,QQ)`

### comment:4 Changed 5 years ago by tscrim

• Reviewers set to Travis Scrimshaw
• Status changed from needs_review to positive_review

LGTM.

### comment:5 Changed 5 years ago by chapoton

• Milestone set to sage-8.2

thanks

### comment:6 Changed 5 years ago by vbraun

• Branch changed from u/chapoton/8550 to 9892a36fe40dc681a3f5c00e278b200878a450ac
• Resolution set to fixed
• Status changed from positive_review to closed
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