On Tuesday, January 16, 2018 at 3:23:16 AM UTC+1, saad khalid wrote:
>
> Hello everyone:
>
> So, I was just messing around with the assume command, and did:
>
> var('i')
> assume(abs(x) < 1)
> f(x) = sum(x^i, i, 0, oo )
>
> This is just 1/(1-x). I wanted to see what would happen when I tried using
> x > 1, and it still evaluates properly
>
I cannot confirm that, I get:
sage: forget()
sage: assume(x-1>0)
sage: f(x) = sum(x^i, i, 0, oo )
...
ValueError: Sum is divergent.
> , even though the sum should be divergent for x > 1. How does this happen
> behind the scenes exactly? Is Sage/Maxima substituting 1/(1-x) for my sum?
> Further, I took the integral from 0 to 2:
>
> integrate(f(x),x,0,2)
>
> which returned -I*pi.
>
I cannot confirm that either for f(x) = 1/(1-x) because I get
sage: integrate(1/(1-x),x,0,2)
...
ValueError: Integral is divergent.
regardless of assumptions.
My guess is you have done operations with f(x) in the meantime that change
what you think you are doing.
Regards,
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