On Tue, Feb 9, 2010 at 5:41 PM, zsharon <[email protected]> wrote: >> >> What is wrong with this? >> > > Thanks for replying. > > Well, the indicator function I want should have f(1)=1, not f(1)=1/2. > It would be nice to be able to define the indicator function > correctly, but since I'm integrating that's not really a problem. > > I can integrate the indicator functions just fine, but I need to > compute convolutions, which requires composing functions. I need to
But convolutions are already implemented for functions in the Piecewise class. Is there a problem you were having with that? > compute the following: > > Given f and g, I want (f*g)(x)=integral(f(x-y)g(y),y,-oo,oo) <----- > (convolution) > > So, I need to compose f(x) with h(y)=x-y to get f(x-y). > > But, the way I constructed the indicator function doesn't seem to be > compatible with composing functions. I get this error: > > f1(x) = 1 > f2(x) = 0 > f = Piecewise([[(-oo,0),f2],[(0,1),f1],[(1,oo),f2]]) > g = Piecewise([[(-oo,0),f2],[(0,1),f1],[(1,oo),f2]]) > h(x) = f(x-y)g(y) > integral(f(x-y)g(y),y,-10,10 > #Syntax Error: > integral(f(x-y)g(y),y,-10,10) > > Another way I thought of doing that is to have the composition > redefine the set defining the indicator function. So if > f(x)=indicator([0,1]), then *as a function of y* f(x- > y)=indicator([-1+x,x]). But, I can't think of a clean way to do that. > > I tried doing it manually, but I get an error: > > g1(y) = 1 > g2(y) = 0 > f = Piecewise([[(-oo,0),g2],[(0,1),g1],[(1,oo),g2]]) > g = Piecewise([[(-oo,-1+x),g2],[(-1+x,x),g1],[(x,oo),g2]]) > integral(f*g,y,-10,10) > #Traceback (click to the left for traceback) > ... > ValueError: Function not defined outside of domain. > > I don't understand what that error means in the context of what I > tried to do. > > Thanks > > -- > To post to this group, send email to [email protected] > To unsubscribe from this group, send email to > [email protected] > For more options, visit this group at > http://groups.google.com/group/sage-support > URL: http://www.sagemath.org > -- To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
