R. Perry, July 2018

corvids/diophantine.py is modified from Diophantine-master/diophantine.py:
carriage returns added at end of line, range() changed to xrange(), 
class and OO stuff added, self, etc., getBasis() added (similar to solve())

bug in corvids lllhermite() ?

diff -w corvids/diophantine.py corvids/Diophantine-master/diophantine.py
...
142,145c125,128
<         A, B, L, D = self.initialise_working_matrices(G)
<         if self.first_nonzero_is_negative(A):
<             B[m, m] = -1
<             A[m, :] *= -1
---
>     A, B, L, D = initialise_working_matrices(G)
>     if first_nonzero_is_negative(A):
>         B[m - 1, m - 1] = -1
>         A[m - 1, :] *= -1

if self.first_nonzero_is_negative(A) returns True, B[m,m] and A[m,:] are indexed out of range

###

Changes in corvids-RP/

diophantine.py modified from ../corvids/ for python3, and removed ^M

  xrange() -> range()

  zip() -> list(zip())

###

% diff -w diophantine.py ../corvids/diophantine.py
1d0
< # slightly modified copy of diophantine.py from https://github.com/katherinemwood/corvids
56c55
<         return [(i, j) for i, j in product(range(m.shape[0]), range(m.shape[1]))
---
>         return [(i, j) for i, j in product(xrange(m.shape[0]), xrange(m.shape[1]))
103,104c102
<                 solutions = []; solutions.append(-P[r,:-1].T) # RP, list of Matrix
<                 # raise NotImplementedError("Ax=B has unique solution in integers")
---
>                 raise NotImplementedError("Ax=B has unique solution in integers")
146,147c144,145
<             B[m-1, m-1] = -1
<             A[m-1, :] *= -1
---
>             B[m, m] = -1
>             A[m, :] *= -1
159c157
<                 for i in reversed(range(k - 1)):
---
>                 for i in reversed(xrange(k - 1)):
163c161
<             rank = A.shape[0] - next(i for i in range(A.shape[0])
---
>             rank = A.shape[0] - next(i for i in xrange(A.shape[0])
189c187
<         nonzero_columns = list(zip(*self.nonzero(A)))[1]  # Should always be nonzero
---
>         nonzero_columns = zip(*self.nonzero(A))[1]  # Should always be nonzero
199c197
<         nonzero_i_elems = list(zip(*self.nonzero(A[i, :])))
---
>         nonzero_i_elems = zip(*self.nonzero(A[i, :]))
208c206
<         nonzero_k_elems = list(zip(*self.nonzero(A[k, :])))
---
>         nonzero_k_elems = zip(*self.nonzero(A[k, :]))
263c261
<         for i in range(m):
---
>         for i in xrange(m):
298c296
<                         for j in range(i, m):
---
>                         for j in xrange(i, m):
326,327c324,325
<         for i in range(m - 1):
<             for j in range(i + 1, m):
---
>         for i in xrange(m - 1):
>             for j in xrange(i + 1, m):
332,333c330,331
<             for k in range(i + 1, m):
<                 for l in range(k, m):
---
>             for k in xrange(i + 1, m):
>                 for l in xrange(k, m):
345,346c343,344
<         for i in range(m):
<             for j in range(m):
---
>         for i in xrange(m):
>             for j in xrange(m):
438c436
<         for j in range(n):
---
>         for j in xrange(n):
%