1 | initial version |

In case it saves anyone some time, I am using the following routine. Since this is for pedagogical purposes only, I restricted the matrices to rational entries. Bug reports welcome.

```
# Naive Gaussian reduction
def gauss_method(M,rescale_leading_entry=False):
"""Describe the reduction to echelon form of the given matrix of rationals.
M matrix of rationals e.g., M = matrix(QQ, [[..], [..], ..])
rescale_leading_entry=False boolean make the leading entries to 1's
Returns: None. Side effect: M is reduced. Note: this is echelon form,
not reduced echelon form; this routine does not end the same way as does
M.echelon_form().
"""
num_rows=M.nrows()
num_cols=M.ncols()
print M
col = 0 # all cols before this are already done
for row in range(0,num_rows):
# ?Need to swap in a nonzero entry from below
while (col < num_cols
and M[row][col] == 0):
for i in M.nonzero_positions_in_column(col):
if i > row:
print " swap row",row+1,"with row",i+1
M.swap_rows(row,i)
print M
break
else:
col += 1
if col >= num_cols:
break
# Now guaranteed M[row][col] != 0
if (rescale_leading_entry
and M[row][col] != 1):
print " take",1/M[row][col],"times row",row+1
M.rescale_row(row,1/M[row][col])
print M
change_flag=False
for changed_row in range(row+1,num_rows):
if M[changed_row][col] != 0:
change_flag=True
factor=-1*M[changed_row][col]/M[row][col]
print " take",factor,"times row",row+1,"plus row",changed_row+1
M.add_multiple_of_row(changed_row,row,factor)
if change_flag:
print M
col +=1
```

Copyright Sage, 2010. Some rights reserved under creative commons license. Content on this site is licensed under a Creative Commons Attribution Share Alike 3.0 license.