Hi everyone. I might be confused but I think I've found something not quite 
right.

The following code:

###############################
a(x) = x^2 - 5*x + 6
b(x) = x^2 - 8*x + 15

f(x) = lcm( a(x), b(x) )

print f

print f.rational_simplify()
###############################

produces the output

x |--> (x^2 - 5*x + 6)*(x^2 - 8*x + 15)/(x - 3)

x |--> x^3 - 10*x^2 + 31*x - 30

The latter is more my view of what f(x) should be. Am I wrong?
Should the lcm of two polynomials be a polynomial? 

In any case, I imagine the lcm is computed by multiplying a(x)
and b(x) together, and then dividing by their gcd. However,
shouldn't rational_simplify() be called on that quotient before
returning the solution?

Thoughts?
---Greg

p.s. While I have everyone's attention, is there a 
polynomial-long-division command in Sage? By polynomial long 
division, I mean the rote algorithm taught in College Algebra, 
not Groebner Bases. I searched for a while but didn't find one.

That's fine, it is a rare task, but I thought I'd double check...



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