Dear all,
I just tried calculating this integral (I defined inf ==> %plusInfinity)
integrate(exp(-a^2*x^2),x=-inf..inf)
in FriCAS 1.3.4 and it failed. Why?
Best regards,
Marduk
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"FriCAS - computer algebra system"
Interesting. I did some experiments and it seems that limit(erf(M*x),
x=inf) returns 1
whenever FriCAS can determine that M > 0. In particular M=a^2 and M=exp(a)
work,
whereas M=a does not. However, M = abs(a) does not work either.
Now I have some questions:
1) Why does not sqrt(a^2) return
> 1) Why does not sqrt(a^2) return abs(a)?
OK, let's try with a being the imaginary unity.
(4) -> sqrt(%i^2)
(4) %i
Type:
Expression(Complex(Integer))
(5) -> abs(%i)
(5) abs(%i)
FriCAS does not simplify abs(%i). So it's left unspecified.
You
> In particular, there must be a way of defining a type for an
> exponential of a factored polynomial.
Of course, there is. However, I guess, you don't want to program this
just for the following.
> I am not interested in factorizing the exponential for doing a
> calculation, it is just for
>
> PS: BTW, what does have TeXmacs have to do with this FriCAS question?
>
I use TeXmacs as a frontend for FriCAS. I would like to be able to use the
expressions
generated by the CAS directly in my notes, papers, etc. But apparently, it
takes some
work to get that done.
Thanks anyway for
Hi Marduk,
> I would like to convert exp(-a^2*x^2 - a^2*y^2) into exp(-a^2*(x^2 +
> y^2)).
I don't know either. Maybe it would be easier to help if you explain the
actual problem you want to solve. Perhaps this factorization is not
really necessary.
It might even be that your rule (whatever it
I suspect, the problem lies in the limit computation.
Ralf
(1) -> i := integrate(exp(-a^2*x^2),x)::Expression(Integer)
+--+
+---+ | 2
\|%pi erf(x\|a )
(1) -
+--+
| 2
2 \|a
>
> OK, let's try with a being the imaginary unity.
>
I thought that by default FriCAS assumes that variables are real.
> Because it is just an operator and a can be anything.
Fair enough. Then one should be able to specify on which domain an operator
is acting
and abs(a) | a is real
Hi Ralf,
Thank you for your prompt reply. I understand that FriCAS works different
from
other CA systems. To me it is like using Haskell for doing computer
algebra.
And I think that is a very interesting approach.
I am not a computer scientist, but I think it should be possible to do the
Dear all,
I would like to convert exp(-a^2*x^2 - a^2*y^2) into exp(-a^2*(x^2 + y^2)).
However,
it seems that exp converts its argument presumably to Expression Integer,
and
since FriCAS always expands products the factorization is lost.
For more general expressions, I would like to write a
> I must say that it is highly disappointing that to this date there
> is no serious free-software alternative to Mathematica.
It all depends on what you want to do.
> The three programs mentioned above have been developed for about
> 40-50 years by very capable computer scientists and
I was also having some thoughs about factoring Expression.
I think it's doable, especially for displaying purpose.
We can use "paren"/"box" to keep the factors.
A quick sketch:
(25) -> exp map(x+->box(x::EXPR INT),factor numer first argument
mainKernel exp(-a^2*x^2 - a^2*y^2))
2
> We can use "paren"/"box" to keep the factors.
I was thinking about "box", but not in such a sophisticated way as you
did. Comes probably from my dislike of Expression(X). ;-)
Ralf
> (25) -> exp map(x+->box(x::EXPR INT),factor numer first argument
> mainKernel exp(-a^2*x^2 - a^2*y^2))
>
>
1) Why does not sqrt(a^2) return abs(a)?
IIUC:
When operating on a symbolic expression x in Expression R,
the operator sqrt "represents an arbitrary (but always the same through the code)
solution y of the algebraic equation y^2=x".
Even when R = Integer, there are still 2 real roots y that
I think it's doable.
First, by default, "limit" is for real expression (there are
accompanying "complexLimit"), so it knows "sqrt(a)" is positive:
(8) -> limit(sqrt(a)*x,x=%plusInfinity)
(8) + infinity
So in theory, it should also compute for "erf(sqrt(a)*x)", but:
(9) ->
On 11/8/18 1:05 PM, Marduk wrote:
3) How can one tell FriCAS that a>0 in the Gaussian integral?
Write a=A^2 :
(1) -> inf ==> %plusInfinity; integrate(exp(-A^4*x^2),x=-inf..inf)
┌───┐
\│%pi
(1) ──
2
A
Type: Union(f1:
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