On 01/17/2012 04:54 AM, Jori Mantysalo wrote:
After saying
R.<t> = PolynomialRing(QQ)
both of these works:
expand ( (t-(5-sqrt(7))) * (t-(5+sqrt(7))) )
expand ( (t-(5-sqrt(7))) * (t-(5+sqrt(7))) )
and I got t^2 - 10*t + 18 and t^2 - 4*t + 1 as expected. However,
expand ( (t-(2-sqrt(3))) * (t-(2+sqrt(3))) * (t-(5-sqrt(7))) * (t-(5+sqrt(7))) )
does not work in a similar way. If I put ".simplify_full()" at the end of
the expression, I got simplified answer.
What is logic behind this?
Sometimes expanding a product simplifies it, and sometimes it doesn't.
This is the smallest example I could come up with.
sage: a,b = var('a,b')
sage: f = a*(a+b)
sage: f.expand()
a^2 + a*b
sage: f.simplify()
(a + b)*a
Furthermore, sage automatically simplifies some *really* easy
expressions like,
sage: 1*a + 2*a
3*a
That's why you get an answer with three terms in the first two cases. It
won't automatically combine square roots, though:
sage: sqrt(2)*a + sqrt(3)*a
sqrt(2)*a + sqrt(3)*a
So the "simplified" answer in the first two cases was just lucky. In
general you have to call simplify() or full_simplify().
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