The following session surprised me.
%%% (1) -> e7:=nthRoot((3*sqrt(7)::Expression(INT)+2*sqrt(3))/sqrt(3),3)
+---------------+
| +-+ +-+
|3 \|7 + 2 \|3
(1) |---------------
3| +-+
\| \|3
Type: Expression(Integer)
%%% (2) -> a7 := nthRoot((3*sqrt(7)+2*sqrt(3))/sqrt(3),3)
+---------------+
| +-+ +-+
|3 \|7 + 2 \|3
(2) |---------------
3| +-+
\| \|3
Type: AlgebraicNumber
%%% (3) -> b7 := nthRoot((3*sqrt(7)+5*sqrt(3))/sqrt(3),3)
+------------+
3| +-+ +-+
(3) \|\|3 \|7 + 5
Type: AlgebraicNumber
%%% (4) -> a5 := nthRoot((3*sqrt(5)+2*sqrt(3))/sqrt(3),3)
+------------+
3| +-+ +-+
(4) \|\|3 \|5 + 2
Type: AlgebraicNumber
When you remove the comment sign from the first line of the attached
file and execute foo.input in a fresh session, the output will look
different.
Well, of course, it shouldn't surprise me. There is caching done in FriCAS.
I did not manage to get a rational denominator of e7
%%% (5) -> ratDenom e7
+---------------+
| +-+ +-+
|3 \|7 + 2 \|3
(5) |---------------
3| +-+
\| \|3
Type: Expression(Integer)
And this I find somewhat user-unfriendly.
Ralf
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-- a7 := nthRoot((3*sqrt(7) +2*sqrt(3))/sqrt(3),3)
e7 := nthRoot((3*sqrt(7)::Expression(INT)+2*sqrt(3))/sqrt(3),3)
a7 := nthRoot((3*sqrt(7) +2*sqrt(3))/sqrt(3),3)
b7 := nthRoot((3*sqrt(7) +5*sqrt(3))/sqrt(3),3)
a5 := nthRoot((3*sqrt(5) +2*sqrt(3))/sqrt(3),3)
