So bruno and simon agree that lcm(1/4,1/6) = 1/2 (lcm(numerators)/
gcd(denominators)) is the most logical. It also seems to satisfy dough
wanted relation up to units. I like it because it makes sense if you
think in terms of fractional ideals. And I suggest we switch to that
convention.
When trying fun stuff with fractional ideals in sage to give nice
examples I ran in to the following worrysome results.
First I tried to define a fractional ideal over QQ but I failed
misserabely. Does anybody know how to do it without the following ugly
trick (i.e. make a field extension of QQ of degree 1)?
sage: var('x')
sage: K=QQ.extension(x,'x')
sage: K*(1/4)
Fractional ideal (1/4)
sage: QQ*(1/4)
Principal ideal (1) of Rational Field
But this is not the most terrible thing yet. Look at what happens if I
intersect the rational ideal in K by itself!
sage: (K*(1/4)).intersection(K*(1/4))
Fractional ideal (1/16)
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