Answer to myself: some real algebraic number need sqrt(-1) to
represent them (e.g. some root of degree 3 polynomial).
So RealClosure can't handle them I guess.

- Qian

On 11/20/23 07:45, Qian Yun wrote:
Does RealClosure work with Expression? (e.g doing integration)
Currently we can't do so in FriCAS.  Is that possible in theory?

- Qian

On 11/19/23 23:12, Waldek Hebisch wrote:
On Sun, Nov 19, 2023 at 10:50:17PM +0800, oldk1331 wrote:
Then is there a way to specify the algebraic number
which square is 2 and is near +1.41421?

(1) -> rC := RealClosure(Fraction(Integer))

    (1)  RealClosure(Fraction(Integer))
Type: Type
(2) -> s2 := sqrt(2)$rC

          +-+
    (2)  \|2
                                          Type: RealClosure(Fraction(Integer))
(3) -> approximate(s2, 1/10000)

         46341
    (3)  -----
         32768
                                                       Type: Fraction(Integer)
(4) -> 2 - (%)^2

              4633
    (4)  - ----------
           1073741824
                                                       Type: Fraction(Integer)
(5) -> sqrt(-s2)$rC
    >> Error detected within library code:
    no roots

ATM roots in Complex(rC) remain unimplemented.


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