Re: Sage 5.4 determinant is very slow

[P Purkayastha]

On 11/14/2012 06:59 AM, platane wrote:
> In Sage 5.4 determinant for dense matrix is very slow. For the following Hankel determinant calculation, Sage 4.6.1 is 100000 time more fast than Sage 5.4 (!!):
>
> Sage 5.4, Sparse = False, Time=117.49
>
> Sage 4.6.1, Sparse=False, Time=0.0011
>
> # --------------------
> import time
>
> def test(K, SP):
> n=100
> f=taylor(prod((1-x**i) for i in range(1,n)),x,0,n)
> A=[f.coefficient(x,i) for i in range(n)]
> cf= [[A[i+j] for i in range(K)] for j in range(K)]
> m= matrix(ZZ, cf, sparse=SP)
> #
> t0=time.time()
> print " K =", K, ", result =", m.det()
> t_det= time.time()-t0
> print " ",version()
> print " sparse= ", SP
> print " time = ", t_det
>
> KK=30
> test(KK, True)
> print
> test(KK, False)
>
>
> # --------------------
>

It happened some time in between 4.7.2 and 4.8: (det.sage) is the above
code.


----------------------------------------------------------------------
| Sage Version 4.7.2, Release Date: 2011-10-29 |
| Type notebook() for the GUI, and license() for information. |
----------------------------------------------------------------------
sage: attach det.sage
K = 30 , result = -9
Sage Version 4.7.2, Release Date: 2011-10-29
sparse= True
time = 0.260323047638

K = 30 , result = -9
Sage Version 4.7.2, Release Date: 2011-10-29
sparse= False
time = 0.026487827301
sage:
Exiting Sage (CPU time 0m1.77s, Wall time 0m29.31s).
Exiting spawned Gap process.


----------------------------------------------------------------------
| Sage Version 4.8, Release Date: 2012-01-20 |
| Type notebook() for the GUI, and license() for information. |
----------------------------------------------------------------------
sage: attach det.sage
K = 30 , result = -9
Sage Version 4.8, Release Date: 2012-01-20
sparse= True
time = 0.011904001236

K = 30 , result = -9
Sage Version 4.8, Release Date: 2012-01-20
sparse= False
time = 122.02807498

[platane]

Thank you for finding the exact version having the determinant problem. 

Maybe we can compare the source codes of those two versions

to solve the problem.