Looks like you re-implemented rational reconstruction with  
denominator, though its not quite as fast as what I had.

On Mar 6, 2007, at 2:12 PM, William Stein wrote:

> Hello,
>
> I have released SAGE-2.3: http://sage.math.washington.edu/sage
> This is a nontrivial upgrade in terms of new improved code in the
> SAGE core library, especially in terms of linear algebra.
>
> sage-2.4 will be released around March 15-20 after the
> Arizona Winter School.
>
> Summary of changes:
>          * inclusion and integration into SAGE of IML; this allows for
>            computing nullspaces.  E.g., if A is a 300x301 matrix with
>            32-bit integer entries it finds the kernel (a single  
> vector)
>            in about 1-2 seconds.  Also, system solving and in some  
> cases
>            echelon forms are computed using IML.
>          * David Roe et al.: a completely new implementation of p- 
> adics
>          * W Stein, Clement P, Soroosh Y, and Martin A.: lots of  
> optimization
>            work on linear algebra over QQ and GF(p); new optimized  
> compiled
>            sparse linear algebra over QQ and ZZ.  Speedups to  
> multimodular,
>            rational reconstruction, etc.
>          * W. Stein: lots of optimization of modular symbols  
> computation.
>          * Carl Witty: many many improvements to how floating point
>            arithmetic works in SAGE.
>          * David Harvey: improvements to p-adics heights code
>
> -- 
> William Stein
> Associate Professor of Mathematics
> University of Washington
>
> 

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