On Wed, Nov 22, 2023 at 08:29:11AM +0800, Qian Yun wrote:
> Now I understand most of your points.
>
> So what are the possible improvements regarding algebraic number
> in the future?
I do not think about deep changes to AlgebraicNumber or Expression,
at least in reasonably near future. Rather,
Now I understand most of your points.
So what are the possible improvements regarding algebraic number
in the future?
For example, in a "locally breaking symmetry" use case, a "real?"
function to determine if an algebraic number is real, is that useful?
(e.g.
On Tue, Nov 21, 2023 at 08:38:49PM +0800, Qian Yun wrote:
>
>
> On 11/21/23 20:26, Waldek Hebisch wrote:
> > On Tue, Nov 21, 2023 at 06:35:57PM +0800, Qian Yun wrote:
> > >
> > > If so, I want to confirm that is 'nthRoot already a kind of
> > > algebraic number?
> >
> > I am not sure what you
On 11/21/23 20:26, Waldek Hebisch wrote:
On Tue, Nov 21, 2023 at 06:35:57PM +0800, Qian Yun wrote:
If so, I want to confirm that is 'nthRoot already a kind of
algebraic number?
I am not sure what you want to say here: 'nthRoot is in
AlgebraicNumber which under right conditions models
On Tue, Nov 21, 2023 at 06:35:57PM +0800, Qian Yun wrote:
>
> If so, I want to confirm that is 'nthRoot already a kind of
> algebraic number?
I am not sure what you want to say here: 'nthRoot is in
AlgebraicNumber which under right conditions models
algebraic numbers and in Expression, where we
On 11/21/23 10:02, Waldek Hebisch wrote:
On Tue, Nov 21, 2023 at 08:24:39AM +0800, Qian Yun wrote:
On 11/20/23 20:48, Waldek Hebisch wrote:
Extra remark: it should be possible to get much of effect
of RealClosure by considering pairs of AlgebraicNumber
and floating point approximation.
On Tue, Nov 21, 2023 at 08:24:39AM +0800, Qian Yun wrote:
>
>
> On 11/20/23 20:48, Waldek Hebisch wrote:
> >
> > Extra remark: it should be possible to get much of effect
> > of RealClosure by considering pairs of AlgebraicNumber
> > and floating point approximation. Namely, we can compute
> >
On 11/20/23 20:48, Waldek Hebisch wrote:
Extra remark: it should be possible to get much of effect
of RealClosure by considering pairs of AlgebraicNumber
and floating point approximation. Namely, we can compute
minimal polynomial of algebraic number and moderately
accurate floating point
On Mon, Nov 20, 2023 at 12:48 PM Waldek Hebisch wrote:
>
> On Mon, Nov 20, 2023 at 06:20:45PM +0800, Qian Yun wrote:
> > 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.
>
> No,
On Mon, Nov 20, 2023 at 06:20:45PM +0800, Qian Yun wrote:
> 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.
No, this is not a problem. RealClosure can handle real roots of
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
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
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))
Then is there a way to specify the algebraic number
which square is 2 and is near +1.41421?
- Qian
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On Sun, Nov 19, 2023 at 09:49:10PM +0800, Qian Yun wrote:
>
>
> On 11/19/23 21:36, Waldek Hebisch wrote:
> > On Sun, Nov 19, 2023 at 07:58:50PM +0800, Qian Yun wrote:
> > > "real? sqrt (-sqrt 2)" returns "true" by default.
> >
> > You mean should return false? We get this when working
> > with
On 11/19/23 21:36, Waldek Hebisch wrote:
On Sun, Nov 19, 2023 at 07:58:50PM +0800, Qian Yun wrote:
"real? sqrt (-sqrt 2)" returns "true" by default.
You mean should return false? We get this when working
with expressions:
(2) -> real? sqrt (-sqrt 2::EXPR(INT))
(2) false
Because
On Sun, Nov 19, 2023 at 07:58:50PM +0800, Qian Yun wrote:
> "real? sqrt (-sqrt 2)" returns "true" by default.
You mean should return false? We get this when working
with expressions:
(2) -> real? sqrt (-sqrt 2::EXPR(INT))
(2) false
> Because interpreter prefers CTRIGMNP over TRIGMNIP
> as
"real? sqrt (-sqrt 2)" returns "true" by default.
Because interpreter prefers CTRIGMNP over TRIGMNIP
as shown by ")set mes bot on":
Function Selection for real?
Arguments: AN
[1] signature: EXPR(COMPLEX(INT)) -> BOOLEAN
implemented: slot (Boolean)(Expression (Complex
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