2015-03-05 03:03:18 UTC+1, felix34: I need to define a periodic function of a variable t (for time) > that can be integrated like a symbolic function. > > I have no idea how to do that with sagemath and even if it is possible. > > An example would be an periodic triangle function or periodic square > function. >
A few basic tricks can help to define periodic functions. Trick one: a(x) = arcsin(sin(x)) is a periodic triangle function, (it is 2*pi-periodic, increasing on [-pi/2,pi/2], where it equals x). Its derivative b(x) = diff(a(x),x) is a periodic square function (it is 2*pi-periodic, equal to 1 on (-pi/2,pi/2), -1 on (pi/2,3*pi/2)). The product ab(x) = a(x) * b(x) is a periodic sawtooth function of period pi, which equals x on (-pi/2,pi/2). Trick two: c(x) = x - floor(x) is a sawtooth function with period 1, which equals x on [0,1). Given a sawtooth function, cooking up periodic functions is easy. Indeed, suppose some function f is defined over (-pi/2,pi/2), then g(x) = f(ab(x)) is the corresponding pi-periodic function. Or if f is defined over [0,1) and you want a 1-periodic function based on f, then you can use g(x) = f(c(x)). Of course, if you prefer some other period, say, some t > 0, notice that cc(x) = t*c(x/t) is a t-periodic sawtooth function, and if you have some function f defined over [0,t), then the corresponding t-periodic function is just g(x) = f(cc(x)). -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
