[sage-support] Re: question on using integral() in sage. Fourier transform of unit step function.
Surprinsingly, SAGE 3.1.2 is more ignorant than 3.1.1:
./sage
---
| SAGE Version 3.1.2 ...
| Type notebook() ...
--
sage: var('a b t x')
(a, b, t, x)
sage: assume(exp(b*pi)1)
sage: expr(x)=integral(exp(-2*I*pi*(a+I*b)*t),t,0,x)
sage: factor(limit(expr(x),x=infinity))
-1*I/(2*pi*(I*b+a))
SAGE doesn't know anymore that exp() is strictly ascending.
(assume(b0) doesn't work anymore)
On 22 sep, 12:30, kkwweett [EMAIL PROTECTED] wrote:
you can indirectly get
./sage
---
| SAGE Version 3.1.1 ...
| Type notebook() ...
--
sage: var('a b t x')
(a, b, t, x)
sage: assume(b0)
sage: expr(x)=integral(exp(-2*I*pi*(a+I*b)*t),t,0,x)
sage: factor(limit(expr(x),x=infinity))
-1*I/(2*pi*(I*b+a))
--~--~-~--~~~---~--~~
To post to this group, send email to sage-support@googlegroups.com
To unsubscribe from this group, send email to [EMAIL PROTECTED]
For more options, visit this group at
http://groups.google.com/group/sage-support
URLs: http://www.sagemath.org
-~--~~~~--~~--~--~---
[sage-support] Re: question on using integral() in sage. Fourier transform of unit step function.
On Sep 21, 10:34 pm, Nasser Abbasi [EMAIL PROTECTED] wrote: Let me rewrite what I wrote in last post again, since it did not format well. I think it is still not clear, so I wrote it in latex via SW, here it is again as screen image and PDF file http://12000.org/tmp/092108/eq.gif http://12000.org/tmp/092108/eq.pdf I hope this is more clear. Nasser --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: question on using integral() in sage. Fourier transform of unit step function.
you can indirectly get
./sage
---
| SAGE Version 3.1.1 ...
| Type notebook() ...
--
sage: var('a b t x')
(a, b, t, x)
sage: assume(b0)
sage: expr(x)=integral(exp(-2*I*pi*(a+I*b)*t),t,0,x)
sage: factor(limit(expr(x),x=infinity))
-1*I/(2*pi*(I*b+a))
--~--~-~--~~~---~--~~
To post to this group, send email to sage-support@googlegroups.com
To unsubscribe from this group, send email to [EMAIL PROTECTED]
For more options, visit this group at
http://groups.google.com/group/sage-support
URLs: http://www.sagemath.org
-~--~~~~--~~--~--~---
[sage-support] Re: question on using integral() in sage. Fourier transform of unit step function.
(where is my my last post ?)
you can indirectly get :
./sage
--
| SAGE Version 3.1.1 ...
| Type notebook()
--
sage: var('a b t x')
(a, b, t, x)
sage: assume(b0)
sage: expr(x)=integral(exp(-2*I*pi*(a+I*b)*t),t,0,x)
sage: factor(limit(expr(x),x=infinity)
-1*I/(2*pi*(I*b+a))
--~--~-~--~~~---~--~~
To post to this group, send email to sage-support@googlegroups.com
To unsubscribe from this group, send email to [EMAIL PROTECTED]
For more options, visit this group at
http://groups.google.com/group/sage-support
URLs: http://www.sagemath.org
-~--~~~~--~~--~--~---
[sage-support] Re: question on using integral() in sage. Fourier transform of unit step function.
David Joyner wrote: sage: assume(x0) sage: integral( cos(2 * pi * x * t), t , 0 , Infinity) ind What is ind? I guess this is coming from Maxima, where ind = indeterminate. Btw und = undefined if ever you run across that, and don't forget inf = positive real infinity, minf = negative real infinity, infinity = complex infinity. best Robert Dodier --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: question on using integral() in sage. Fourier transform of unit step function.
On Sat, Sep 20, 2008 at 11:58 PM,NasserAbbasi[EMAIL PROTECTED] wrote:
Hello;
I am a sage newbie. I'd like to find out how to make Sage give me
this same result that I get in Mathematica.
This is what I typed (I do not know how to cut/paste from the VMWare
player console to her yet, so if there is a typo it is because of
this).
f=var('f')
assume(f0)
integral( e^(-I * 2 * pi * f * t), t , 0 , Infinity)
The answer I get starts with
limit(sin(2*pi*f*t),t, etc...etc...
Is there a way to tell Sage to give me this answer I get from
Mathematica?
Assuming[Im[f] 0, Integrate[Exp[(-I)*2*Pi*f*t], {t, 0, Infinity}]]
-(I/(2*f*Pi))
Thanks,
Nasser
On Sep 21, 2:49 pm, David Joyner [EMAIL PROTECTED] wrote:
This integral doesn't converge. Why do you think Sage should return
what Mma does?
I think it does converge.
int( exp(-I 2 Pi f t),{t,0,infinity) =
infinity
1/(-I 2 Pi f) * [ exp(-I 2 Pi f t) }
0
Let f be complex in general, say (a+ I b) then the above becomes
infinity
1/(-I 2 Pi f) * [ exp(-I 2 Pi (a +I b) t) }
0
or
infinity
1/(-I 2 Pi f) * [ exp(-I 2 Pi a t) exp (2 Pi b t) }
0
Since b0, then the above becomes
1/(-I 2 Pi f) * [ 0 - 1 }
or
1/(I 2 Pi f)
or
-I/(2 Pi f)
which is what Mathematica gave.
Did I make a mistake in the above somewhere? Could you explain why
you think the integral does not converge?
Nasser
--~--~-~--~~~---~--~~
To post to this group, send email to sage-support@googlegroups.com
To unsubscribe from this group, send email to [EMAIL PROTECTED]
For more options, visit this group at
http://groups.google.com/group/sage-support
URLs: http://www.sagemath.org
-~--~~~~--~~--~--~---
[sage-support] Re: question on using integral() in sage. Fourier transform of unit step function.
Let me rewrite what I wrote in last post again, since it did not
format well.
I think it does converge.
int( exp(-I 2 Pi f t),{t,0,infinity) =
infinity
1/(-I 2 Pi f) * [ exp(-I 2 Pi f t) }
0
Let f be complex in general, say (a+ I b) then the above becomes
infinity
1/(-I 2 Pi f) * [ exp(-I 2 Pi (a +I b) t) }
0
or
infinity
1/(-I 2 Pi f) * [ exp(-I 2 Pi a t) exp (2 Pi b t) }
0
Since b0 (this is the assumption that Im(f)0 ), then the above
becomes
1/(-I 2 Pi f) * [ 0 - 1 }
or
1/(I 2 Pi f)
or
-I/(2 Pi f)
Nasser
--~--~-~--~~~---~--~~
To post to this group, send email to sage-support@googlegroups.com
To unsubscribe from this group, send email to [EMAIL PROTECTED]
For more options, visit this group at
http://groups.google.com/group/sage-support
URLs: http://www.sagemath.org
-~--~~~~--~~--~--~---
