[sage-support] Re: splitting field vs. Galois closure

2017-02-22 Thread Johan S. H. Rosenkilde
On Sunday, January 8, 2017 at 10:14:32 AM UTC+1, Marc Mezzarobba wrote: > > Simon King wrote: > > Wouldn't it be better to [...] or change the > > arithmetic operations by *avoiding* a call to __init__()? > > That's what the branch I pointed to tries to do, to some extent at > least. But the st

[sage-support] Re: splitting field vs. Galois closure

2017-01-08 Thread Marc Mezzarobba
Simon King wrote: > Wouldn't it be better to [...] or change the > arithmetic operations by *avoiding* a call to __init__()? That's what the branch I pointed to tries to do, to some extent at least. But the structure of generic polynomial classes (with many operations implemented in an abstract

[sage-support] Re: splitting field vs. Galois closure

2017-01-07 Thread Simon King
Hi Marc, On 2017-01-07, Marc Mezzarobba wrote: > Another trick you can use if you are creating the polynomial rings > yourself and only need to do basic arithmetic is to define them by > > PolynomialRing_field(base, var, element_class=Polynomial_generic_dense) > > instead of PolynomialRing(base,

[sage-support] Re: splitting field vs. Galois closure

2017-01-07 Thread Marc Mezzarobba
Nils Bruin wrote: > polynomial aritmetic over ZZ and QQ is so much more optimized than > over number fields, Yes, polynomial arithmetic over number fields is painfully slow. The branch trac:u/mmezzarobba/speed_up_generic_polynomials (not fully tested yet) may help a little. Another trick you ca

Re: [sage-support] Re: splitting field vs. Galois closure

2017-01-06 Thread John Cremona
On 5 January 2017 at 20:01, Nils Bruin wrote: > On Thursday, January 5, 2017 at 11:27:05 AM UTC-8, John Cremona wrote: >> >> > I'm tempted to say: beware of memory leaks. Caching an extension on the >> > base >> > field would probably imply that both fields are now participating in a >> > referenc

Re: [sage-support] Re: splitting field vs. Galois closure

2017-01-05 Thread Nils Bruin
On Thursday, January 5, 2017 at 11:27:05 AM UTC-8, John Cremona wrote: > > > I'm tempted to say: beware of memory leaks. Caching an extension on the > base > > field would probably imply that both fields are now participating in a > > reference cycle, anchored in the global UniqueRepresentation

Re: [sage-support] Re: splitting field vs. Galois closure

2017-01-05 Thread John Cremona
On 5 January 2017 at 18:15, Nils Bruin wrote: > On Thursday, January 5, 2017 at 2:27:06 AM UTC-8, John Cremona wrote: >> >> I have a degree 5 polynomial whose Galois group is large (S_5): >> >> sage: x = polygen(QQ) >> sage: f = x^5 - 6*x^3 - x^2 + 6*x - 1 >> >> I can compute its splitting field e

[sage-support] Re: splitting field vs. Galois closure

2017-01-05 Thread Nils Bruin
On Thursday, January 5, 2017 at 2:27:06 AM UTC-8, John Cremona wrote: > > I have a degree 5 polynomial whose Galois group is large (S_5): > > sage: x = polygen(QQ) > sage: f = x^5 - 6*x^3 - x^2 + 6*x - 1 > > I can compute its splitting field easily, thanks to code written by > Jeroen Demeyer I