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2020-09-27 12:00:58 +0200 asked a question Unimodular transformation matrix of LLL algorithm

I also asked this question on sage-support.

I have a matrix M1 with integer entries with 90 rows and 6 columns. After applying the LLL algorithm to M1, I get M2 = M1.LLL(). I want to get the corresponding unimodular transformation matrix T such that T * M1 = M2.

We can find T by T = M2 * M1.pseudoinverse() or T = M1.solve_left(M2), but determinant of T becomes 0 i.e., T.det() equals 0. I want T.det() to equal 1.

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2019-10-20 13:22:12 +0200 asked a question How to find common solution of inequalities in Sage

I have few inequalities:

3 x1 + 5 x2 + 2 x3 + 5 x4 + 7 x5 <= 28

2 x1 + 0 x2 + 0 x3 + 8 x4 <= 14

4 x4 + 5 x5 <= 22
3 x2 <= 2
3 x4 >= 1

How to find common solution in Sage ? xi' s are either 0 or 1.