How come that solve doesn't solve this?
sage: solve(sqrt(sqrt(4*x^2 + 1) - x^2 - 1), x)
[x == -sqrt(sqrt(4*x^2 + 1) - 1), x == sqrt(sqrt(4*x^2 + 1) - 1)]
sage: axiom.solve(sqrt(sqrt(4*x^2 + 1) - x^2 - 1), x)
+-+ +-+
[x= 0,x= \|2 ,x= - \|2 ]
Furthermore, is there a way to convince integrate to do
sage: integrate(sqrt(sqrt(4*x^2 + 1) - x^2 - 1), x,0,sqrt(2))
integrate(sqrt(sqrt(4*x^2 + 1) - x^2 - 1), x, 0, sqrt(2))
sage: axiom.integrate(sqrt(sqrt(4*x^2 + 1) - x^2 - 1), "x=0..sqrt(2)",
'"noPole"')
1
-
2
a third question: how do I get a power series expansion of, say, x^(1/3)?
sage: axiom.series(sin(x)^(1/3),x=0)
1 7
- -
3 1 3 4
x - -- x + O(x )
18
(I know how to do it with FriCAS, but I'd like to know how I can show my
students how to do these things with sage. Actually, sage-3.1.2, that is
what's installed.)
Martin
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