Well I guess doing symbolic computation in a clean fashion is never easy
...
I'm not unfimiliar with the notion of Picard-Vessiot extensions, but I will
have a second look into it. Thanks for the input.
On Friday, December 20, 2013 8:19:33 PM UTC+1, Nils Bruin wrote:
>
> On Friday, December 20
On Friday, December 20, 2013 2:58:51 AM UTC-10, maldun wrote:
>
> Another more careful approach would be to start at the field of rational
> functions and extend it step by step with algebraic and transcendental
> functions, till we reach a field which is maximal under the available
> symbolic e
Another more careful approach would be to start at the field of rational
functions and extend it step by step with algebraic and transcendental
functions, till we reach a field which is maximal under the available
symbolic expressions.
On Friday, December 20, 2013 9:26:22 AM UTC+1, maldun wrote
On Thursday, December 19, 2013 7:47:19 PM UTC+1, Nils Bruin wrote:
> On Wednesday, December 18, 2013 11:04:22 PM UTC-10, maldun wrote:
>>
>> What I mean is that we should only allow expressions of meromorphic
>> functions in the symbolic field, i.e. we would only allow variables,
>> trigonometri
And meromorphic functions are not stable under composition...
2013/12/19, Nils Bruin :
> On Wednesday, December 18, 2013 11:04:22 PM UTC-10, maldun wrote:
>>
>> What I mean is that we should only allow expressions of meromorphic
>> functions in the symbolic field, i.e. we would only allow variable
On Wednesday, December 18, 2013 11:04:22 PM UTC-10, maldun wrote:
>
> What I mean is that we should only allow expressions of meromorphic
> functions in the symbolic field, i.e. we would only allow variables,
> trigonometric functions and so on.
> SR should be then a superset where everything els
Sorry my Mistake, but if you look into the text you quoted, I already
corrected it:
...
> ... The ring of analytic
> functions is an Integral domain.
...
Continous is of course not sufficient.
On Thursday, December 19, 2013 10:12:15 AM UTC+1, John Cremona wrote:
>
> On 19 December 2013 09:04,
Sorry my Mistake, but if you look into the text you quoted, I already it:
...
> that the Kronecker delta is not a continuous function. The ring of
analytic
> functions is an Integral domain.
...
Continous is of course not sufficient.
On Thursday, December 19, 2013 10:12:15 AM UTC+1, John Crem
On 19 December 2013 09:04, maldun wrote:
> The fact, that SR is not a field is interesting, the Kronecker delta example
> on the ticket shows it quite well. But the problem originates from the fact,
> that the Kronecker delta is not a continuous function. The ring of analytic
> functions is an Int
The fact, that SR is not a field is interesting, the Kronecker delta
example on the ticket shows it quite well. But the problem originates from
the fact,
that the Kronecker delta is not a continuous function. The ring of analytic
functions is an Integral domain.
Question: Should we define a subs
This isn't exactly a question of mathematical correctness, but of usability.
Think of users who aren't mathematicians, but engineers or from physics.
Most of them even don't know the difference between a polynomial from ZZ or
RR.
So the goal should be a good default behavior which covers 70-90% o
This isn't exactly a question of mathematical correctness, but of usability.
Think of users who aren't mathematicians, but engineers or from physics.
Most of them even don't know the difference between a polynomial from ZZ or
RR.
So the goal should be a good default behavior which covers 70-90% o
The fact, that SR is not a field is interesting, the Kronecker delta
example on the ticket shows it quite well. But the problem originates from
the fact,
that the Kronecker delta is not a continuous function. The ring of
continuous functions is an Integral domain.
Question: Should we define a su
The fact, that SR is not a field is interesting, the Kronecker delta
example on the ticket shows it quite well. But the problem originates from
the fact,
that the Kronecker delta is not a continuous function. The ring of
continuous functions is an Integral domain.
Question: Should we define a su
On Wednesday, December 18, 2013 9:58:15 AM UTC-8, vdelecroix wrote:
>
> Users of polynomials should worry about the coefficient ring. What do
> someone should expect of
>
> sage: (6*x^2 - 12).factor()
>
> The answers are different in ZZ[x], QQ[x] and RR[x]. For a symbolic
> polynomial there
Users of polynomials should worry about the coefficient ring. What do
someone should expect of
sage: (6*x^2 - 12).factor()
The answers are different in ZZ[x], QQ[x] and RR[x]. For a symbolic
polynomial there is no way to make it coherent...
Moreover, I feel very uncomfortable having an extra
Why reinvent the wheel? A symbolic polynomal class should be capable of a
type checking of the coefficients and transform the polynomial internally
into the correct setting and then call the correct algorithms and methods.
The main purpose of such a class is that the user can work intuitively wi
Hi again,
On 2013-12-18, maldun wrote:
> 1) I think that applying Polynomial division by commands like
>
> sage: f(x)=3Dx^3+5*x^2-3*x+1
> sage: g(x)=3Dx+1
> sage: f.maxima_methods().divide(g)
> [x^2 + 4*x - 7, 8]
>
> are not very intuitive.
These aren't polynomials but symbolic expressions. If y
Hi,
On 2013-12-18, maldun wrote:
> --=_Part_1054_13775092.1387359867313
> Content-Type: text/plain; charset=ISO-8859-1
>
> And another thing: A more unified interface for polynomials.
>
> Currently we have, as you mentioned, three ways to define polynomials.
No, we have only one. The other t
And another thing: A more unified interface for polynomials.
Currently we have, as you mentioned, three ways to define polynomials. It
would enable us to design a class which provides a good default behavior
for the average user.
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1) I think that applying Polynomial division by commands like
sage: f(x)=x^3+5*x^2-3*x+1
sage: g(x)=x+1
sage: f.maxima_methods().divide(g)
[x^2 + 4*x - 7, 8]
are not very intuitive. This should be done by specific methods/operators for
polynomials, and this can only be done by a specific class f
Hi,
On 2013-12-17, maldun wrote:
> On ticket http://trac.sagemath.org/ticket/9706 for the orthogonal
> Polynomials Jeroen Demeyer came up with the the idea of a
> SymbolicPolynomial class. I think that's a great idea, because, if well
> designed, such a class has much potential to give very mu
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