2016-10-09 13:55:31 +0100 received badge ● Famous Question (source) 2015-07-10 23:18:10 +0100 received badge ● Notable Question (source) 2014-06-09 11:02:29 +0100 received badge ● Popular Question (source) 2013-11-07 20:34:00 +0100 received badge ● Student (source) 2013-09-16 10:00:37 +0100 answered a question Defining a periodic function. Thank-you for the quick answer. frac() gives a function which is periodic on positive reals. I just adapted your solution to get it periodic on \RR. f = lambda x: 1 if (x - RR(x).floor()) < 1/2 else 0  I would have liked to be able to define a symbolic function though. Is it doable? I was also trying to get a function whose plot is correct (without asking it to be pointwise) as it is the case for Piecewise(). Below are some of the things (not chronologically ordred though) I had tried (just for completness as I guess they are just full of beginer's classical mistakes). f(x)=sum((-1)^k*unit_step(x-k),k,0,infinity)  which does not evaluate f1(x)=0 f2(x)=1 h=Piecewise([[(-oo,0),f1],[(0,1),f2],[(1,2),f1],[(2,+oo),f1]],x) h.plot()  returns ValueError: cannot convert float NaN to integer. f(x)=sum(h(x-2*k),k,0,infinity)  returns ValueError: Value not defined outside of domain. f(x)=sum(h(x-2*k),k,0,4)  also returns ValueError: Value not defined outside of domain. I also tried to redefine unit_step: def echelon_unite(x): # if x<0: hres=0 else: hres=1 return hres  problem integral(echelon_unite(x),x,-10,3) returns 13 numerical integral returns a coherent result. Other tentative with incoherent result (still with integrate and not numerical_integral)  def Periodisation_int(f,a,b): x = var('x') h0(x) = (x-b)-(b-a)*floor((x-b)/(b-a)) hres = compose(f,h0) return hres sage: g=Periodisation_int(sin,0,1) sage: integrate(g(x),x,0,2) -cos(1) + 2 sage: integrate(g(x),x,0,1) -cos(1) + 1 sage: integrate(g(x),x,1,2) -1/2*cos(1) + 1  My guess is I was using integrate on inappropriate objects. I would still like to know how to define corresponding symbolic function (if it is possible). Thanks again, best regards. 2013-09-15 06:57:16 +0100 asked a question Defining a periodic function. Hi, I am a new sage user. I'd like to define simple periodic maps over \R which plot and integrate correctly (eg. a square signal (which of course is discontinuous but which I would still like to be able to plot in a way that makes it clear that the function is not multivalued at discontinuity points)). I tried different approaches none of which gave satisfactory results. Any hint on how to do that nicely (or what would be the obstacles)? Thank you