[sage-support] Re: units and absolute fields

2009-07-24 Thread mac8090
I'm using version 3.4 - this probably explains it! thanks On Jul 22, 12:21 pm, davidloeffler dave.loeff...@gmail.com wrote: On Jul 21, 6:01 pm, mac8090 bonzerpot...@hotmail.com wrote: For a field extension over Q of 2 values, for example M=QQ(i, sqrt (2)), it is possible to find an

[sage-support] Re: units and absolute fields

2009-07-23 Thread John Cremona
On Jul 22, 12:21 pm, davidloeffler dave.loeff...@gmail.com wrote: On Jul 21, 6:01 pm, mac8090 bonzerpot...@hotmail.com wrote: For a field extension over Q of 2 values, for example M=QQ(i, sqrt (2)), it is possible to find an absolute field X by the following L.b=NumberField(x^2-2)

[sage-support] Re: units and absolute fields

2009-07-22 Thread John Cremona
M.units() will give a set of units which are a Z-basis for the units modulo roots of unity. There is no canonical basis, so there's no reason why (even if the unit ranks are the same) you should get the same generators. For more functionality with units construct U=X.unit_group() and look at

[sage-support] Re: units and absolute fields

2009-07-22 Thread davidloeffler
On Jul 21, 6:01 pm, mac8090 bonzerpot...@hotmail.com wrote: For a field extension over Q of 2 values, for example M=QQ(i, sqrt (2)), it is possible to find an absolute field X by the following L.b=NumberField(x^2-2) R.t=L[] M.c=L.extension(t^2+1) (this gets M) X.d=M.absolute_field()