I have two matrices A and B with same number of rows. Consider a Lattice generated by the rows of B. I want to reduce B and during the reduction change A accordingly. That is if i-th row and j-th row of B interchanges, need to sweep i-th row and j-th row of A also, similarly other elementary row operations. How can I do these?
Also is there very simple C or C++-implementation of the LLL algorithm?
This is the source code to sage, a FOSS symbolic math program. It has an implementation of the triple-L that you could use provided you're willing to GPL the code once it's done. This is another standalone implementation.