* then we divide this row of A by the common factor, unless gcd(A_i) = 0.
* In the later case, we simply drop the row (in both A and d).
*
- * If there are no rows left in A, the G is the identity matrix. Otherwise,
+ * If there are no rows left in A, then G is the identity matrix. Otherwise,
* for each row i, we now determine the lattice of integer vectors
* that satisfies this row. Let U_i be the unimodular extension of the
* row A_i. This unimodular extension exists because gcd(A_i) = 1.
*
* M x - c = 0
*
- * this function computes unimodular transformation from a lower-dimensional
+ * this function computes a unimodular transformation from a lower-dimensional
* space to the original space that bijectively maps the integer points x'
* in the lower-dimensional space to the integer points x in the original
* space that satisfy the equalities.
*
- * The input is given as a matrix B = [ -c M ] and the out is a
+ * The input is given as a matrix B = [ -c M ] and the output is a
* matrix that maps [1 x'] to [1 x].
* If T2 is not NULL, then *T2 is set to a matrix mapping [1 x] to [1 x'].
*