On Tue, Mar 11, 2025 at 11:22:23AM +0100, 'Ralf Hemmecke' via FriCAS - computer
algebra system wrote:
> Dear Waldek,
>
> On 3/7/25 19:16, Waldek Hebisch wrote:
> > AFAICS you are interested in _very_ special cases.
>
> Yes, of course. But this discussion helped me to realize,
> that I actually h
On 3/12/25 19:00, Waldek Hebisch wrote:
No, there is also 'rootOf'.
Ah, OK, that makes sense. And as you noted my code only makes sense for
radical expressions. But that is currently exactly what I need.
minPoly is in terms of lower oder kernels. For 'rootOf' minPoly is
not a binomial.
Ye
Dear Waldek,
On 3/7/25 19:16, Waldek Hebisch wrote:
AFAICS you are interested in _very_ special cases.
Yes, of course. But this discussion helped me to realize,
that I actually have a bit more freedom. I have to anyway investigate
all the conjugates where in the end I only care about real root
On Fri, Mar 07, 2025 at 04:47:04PM +0100, 'Ralf Hemmecke' via FriCAS - computer
algebra system wrote:
> Dear Waldek,
>
> thanks for the reply and apologies for being imprecise.
>
> Actually the algebraic numbers I talk about are rational expression of
> nested radicals. In fact, I get all roots
Dear Waldek,
thanks for the reply and apologies for being imprecise.
Actually the algebraic numbers I talk about are rational expression of
nested radicals. In fact, I get all roots of a polynomial via
radicalRoots $ RadicalSolvePackage(ZZ). Degree is <= 4 (mostly 2).
These roots undergo some
On Fri, Mar 7, 2025 at 7:30 AM Waldek Hebisch wrote:
>
> On Fri, Mar 07, 2025 at 01:39:53PM +0100, 'Ralf Hemmecke' via FriCAS -
> computer algebra system wrote:
> > I have given x: AlgebraicNumber and know already that the value is real.
>
> But how do you "know" this? We discussed several times
On Fri, Mar 07, 2025 at 01:39:53PM +0100, 'Ralf Hemmecke' via FriCAS - computer
algebra system wrote:
> I have given x: AlgebraicNumber and know already that the value is real.
But how do you "know" this? We discussed several times the problem:
algebraically conjugates of an algebraic number are
I have given x: AlgebraicNumber and know already that the value is real.
1) Is there a function that given x and an eps:Fraction(Integer) returns
two rational bounds l,u such that l<=x<=u and u-lI am actually interested only in (1), but while looking for it, I came
across RealClosure und foun
On Fri, Mar 22, 2024 at 08:11:31PM +0100, Ralf Hemmecke wrote:
> On 3/22/24 17:14, Waldek Hebisch wrote:
> > You asked almost the same thing on 6 Jul 2023.
>
> Do you see a problem?
Well, it was intended as gentl remaider that a lot of solutions
are in the mailing list archive. And if mailing li
On 3/22/24 17:14, Waldek Hebisch wrote:
You asked almost the same thing on 6 Jul 2023.
Do you see a problem?
I have at least 2.
(1) your solution was too complicated, i.e. hard to remember by heart,
(2) it involves InnerTrigonometricManipulations.
I consider an "Inner..." package as someth
On Fri, Mar 22, 2024 at 08:59:23PM +0800, Qian Yun wrote:
> Line 615 of expr.spad.
>
> (Related function: smp2an, k2an, R2AN).
This handles case of Expression(Integer). But to convert %i to
AlgebraicNumber one needs to do what ITRIGMNP is doing.
--
Waldek Hebisch
On Fri, Mar 22, 2024 at 01:22:23PM +0100, Ralf Hemmecke wrote:
> Suppose by some computation I get an expression like
>
> z := (10*sqrt(163)+11*%i)/13/sqrt(105)
>
> I would like to transform it into an element of AlgebraicNumber.
>
> Unfortunately, up to now I was unable to find a function that
Cool, Qian!
You are a genius. You seem to have digged out the right place.
Now, of course, the question is how to condition that part.
For
map(x+->(real x + sqrt(-1)@AN*imag(x)), z)
to work R must provide "real" and "imag" and
their target should be coercible to AN.
I think, just testing "R
Line 615 of expr.spad.
(Related function: smp2an, k2an, R2AN).
- Qian
On 3/22/24 20:57, Ralf Hemmecke wrote:
Maybe this signature
retractIfCan : % -> Union(AlgebraicNumber,"failed")
should support it, when % is EXPR COMPLEX INT.
Implemented where?
Ralf
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You received this message bec
Maybe this signature
retractIfCan : % -> Union(AlgebraicNumber,"failed")
should support it, when % is EXPR COMPLEX INT.
Implemented where?
Ralf
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computer algebra system" group.
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Maybe this signature
retractIfCan : % -> Union(AlgebraicNumber,"failed")
should support it, when % is EXPR COMPLEX INT.
- Qian
On 3/22/24 20:38, Ralf Hemmecke wrote:
Oh, for my case I have found a simple trick.
First map to Expression(Complex Intger) to Expression(AN) and then retract.
i :=
Oh, for my case I have found a simple trick.
First map to Expression(Complex Intger) to Expression(AN) and then retract.
i := sqrt(-1)@AN;
za := map(x+->(real x + i*imag(x)), z)
Ralf
PS: Yes, Qian, your answer looks close.
On 3/22/24 13:22, Ralf Hemmecke wrote:
Suppose by some computation I
I can only think of this way:
(real z + sqrt(-1)*imag z)::AN
- Qian
On 3/22/24 20:22, Ralf Hemmecke wrote:
Suppose by some computation I get an expression like
z := (10*sqrt(163)+11*%i)/13/sqrt(105)
I would like to transform it into an element of AlgebraicNumber.
Unfortunately, up to now I
Suppose by some computation I get an expression like
z := (10*sqrt(163)+11*%i)/13/sqrt(105)
I would like to transform it into an element of AlgebraicNumber.
Unfortunately, up to now I was unable to find a function that helps to
to the retraction.
Does someone know a way for cases where I kno
>> P why is it always me that runs into bugs?
>
> I would not call the above a bug: this is fundamental limitation of
> AlgebraicNumber.
Well, I call it a bug if the specification doesn't match the
implementation. Even if the documentation is wrong (which obviously is
then), it's a bug.
Ralf Hemmecke wrote:
> On 06/10/2010 12:43 PM, Bertfried Fauser wrote:
>
> >> a := sqrt((sqrt(5) + 3)/2)
> >> b := (sqrt(5)+1)/2
> >>
> >> (51) -> (a=b)::Boolean
> >>
> >> (51) true
>
> >> c:= -(sqrt(5)+1)/2
> >> (4) -> (a=c)::Boolean
> >>
> >> (4) true
>
> >> (6) -> (b=c)::Boolean
> >>
>
On 06/10/2010 12:43 PM, Bertfried Fauser wrote:
>> a := sqrt((sqrt(5) + 3)/2)
>> b := (sqrt(5)+1)/2
>>
>> (51) -> (a=b)::Boolean
>>
>> (51) true
>> c:= -(sqrt(5)+1)/2
>> (4) -> (a=c)::Boolean
>>
>> (4) true
>> (6) -> (b=c)::Boolean
>>
>> (6) false
>>T
Hi Ralf,
> can someone simplify the following expression a to b
Not me, but...
> a := sqrt((sqrt(5) + 3)/2)
> b := (sqrt(5)+1)/2
>
> (51) -> (a=b)::Boolean
>
> (51) true
> Type: Boolean
define
> c:= -(sqrt(5)+1)/2
> (4) -> (a=c)::Boolean
>
> (4) true
>
Hello
can someone simplify the following expression a to b
a := sqrt((sqrt(5) + 3)/2)
b := (sqrt(5)+1)/2
I don't seem to be able to find an appropriate function in AN.
So maybe a better question is: Should it reduce to b? I think, it
should, since
(51) -> (a=b)::Boolean
(51) true
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