Hi
If you do
A.determinant(algorithm="DF")
it is much much faster.
Alastair
On 02/03/2012 14:21, firebird wrote:
Wrong conclusion in previous txn! The problem is with the matrix
routines and not with the Cyclotomics.
Wrote a couple of routines based on simple Gauss Seidel techniques
operating on a list of lists and produced the following results
F.<s>=CyclotomicField(29)
a=[[s^(i*j) for i in range(n)] for j in range(n)]
sage: time ai=gaussinv(a)
Time: CPU 0.72 s, Wall: 0.72 s
sage: x=matrix(a)
sage: time xi=x.inverse()
Time: CPU 2.74 s, Wall: 2.75 s
sage: time adet=gaussdet(a)
Time: CPU 0.33 s, Wall: 0.33 s
sage: time xdet=x.det()
Time: CPU 50.12 s, Wall: 50.14 s
sage: xi==matrix(ai)
True
sage: adet==xdet
True
So Cyclotomics looks fine. I will use my own routines for the time
being.
Graham
On Mar 1, 10:17 am, firebird<graham.gerr...@gmail.com> wrote:
Alastair
Thanks for the rapid reply.
Your Sage code is far superior to mine. Very interesting and
instructive! Looks as though GAP->Sage recipe conversion may be
easier than I thought.
Original is just an example... GAP array is nothing special.
All Sage Cyclotomics is very slow in comparison to GAP:-(
Finally, mat.<tab> looks very useful.
Graham
On Feb 29, 10:35 pm, Alastair Irving<alastair.irv...@sjc.ox.ac.uk>
wrote:
On 29/02/2012 19:54, firebird wrote:> I am having performance problems when
using SAGE matrices with
Cyclotomic Fields. Processing in GAP appears almost instant, whereas
the similar computation takes of the order of a minute in SAGE. Am I
missing something?
Sage:
F.<s>=CyclotomicField(29)
m=[]
n=20
for i in range(n):
row=[]
for j in range(n):
row.append(s**(i*j))
m.append(row)
mat=matrix(m)
There are shorter ways of creating this matrix. I did it with
mat=Matrix(20,20,[s^(i*j) for i in range(20) for j in range(20)])
This isn't the only way, do
Matrix?
to see the documentation if you're interested in other possibilities,
(useing a function to define the matrix entries might be even shorter).
print mat.det()
I agree this is slow, about 5 minutes on my system. I did a few smaller
matrices and the time gets worse very rapidly as you increase the number
of rows.
GAP:
n:=20;
m:=List([1..n],i->List([1..n],j->E(29)^(i*j)));
Print(Determinant(m),"\n");
This is incredibly fast. Is it possible that gap is recognising this as
a special determinant and just applying a standard formula? I changed a
couple of random elements in the matrix to small integers and then the
computation took a bit longer. It might be interesting to try a 20x20
matrix with random small entries over your field to see how long it takes.
If its not exploiting the structure of the matrix and is just much
quicker than sage then I suppose the question to answer would be if this
is caused by Sage taking many more field operations to do the
computation or if it is slower at doing the individual field operations.
I am new to Sage and still find negotiating the documentation tricky.
Where, for example, might I find a list of methods corresponding to
class matrix?
Once you've defined your matrix you can type "mat." and then press tab
and it will list all the available methods.
I hope this is of some use
Alastair
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