I have found something a bit strange for me:

sage: xx=QQ(2)
sage: xx.parent()
Rational Field

ok...

sage: xxc=xx.sqrt()
sage: xxc.parent()
Symbolic Ring


Why not, but now:

sage: M1=matrix(QQ,1,1,[2])

sage: M1.parent()
Full MatrixSpace of 1 by 1 dense matrices over Rational Field


sage: M1C=M1.cholesky()
sage: M1C
[1.414213562373095?]
sage: M1C.parent()
Full MatrixSpace of 1 by 1 dense matrices over Algebraic Field

So, we have:

xxc: Symbolic Ring
M1C: Full MatrixSpace of 1 by 1 dense matrices over Algebraic Field

and also:
sage: mxx=M1C.row(0)[0]
sage: mxx.parent()
Algebraic Field
sage:  mxx==xxc
True

Why is xxc in Symbolic Ring and not in Algebraic Field?
mxx and xxc are essentialy the same thing, no ?

A bit strange for me...

Yours
 t.d.

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