Jason Grout wrote:

> 
> sage: x=polygen(QQ)
> sage: A=matrix([[0,1,1],[2,2,-2],[-1,x,3]])
> sage: A.echelon_form()
> 
> [     2      2     -2]
> [     0     -1     -1]
> [     0      0 -x + 1]
> 
> 

Incidentally (while I'm still working on the echelon_form/hermite_form 
patch, where echelon_form will always assume that we want to assume the 
matrix is over a field), this gives one reason why having echelon_form 
not automatically assume the fraction field is nice:

sage: x=polygen(QQ)
sage: A=matrix([[0,1,1],[2,2,-2],[-1,x,3]])
sage: ring=A.base_ring()
sage: field=ring.fraction_field()
sage: A.echelon_form()

[     2      2     -2]
[     0     -1     -1]
[     0      0 -x + 1]
sage: b=A.change_ring(field)
sage: b.echelon_form()

[1 0 0]
[0 1 0]
[0 0 1]

Jason


-- 
Jason Grout


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