Dear Sage mailing list
I am having a hard time to get the maximum value
(numerically/analytically) to one equation. In concrete I want to solve:
sage: t= var('t') # dependent variable
sage: taum, tauh, m = var('taum, tauh, m') # parameters
sage: f(t) = ((1-e^(-t/taum))^m)*(e^(-t/tauh))
Now i describe my particular equation:
sage: myHH = f(t).subs(taum=0.1, tauh=1.0, m=3)
and got the maximum numerically
sage: myHH.find_maximum_on_interval(0, 3,t)
sage: (0.64289864921516393, 0.34339871886734297)
1) Is there any way to solve this maximum (or minimum), withouth giving
an interval?.
Besides that, if I now want to get this value analytically (getting the
the value at which it's first derivative is zero:
sage: Tmax = solve(diff(myHH,t)==0,t)
Tmax is
[t == log(31^(1/10)*e^(1/5*I*pi)), t == log(31^(1/10)*e^(2/5*I*pi)), t
== log(31^(1/10)*e^(3/5*I*pi)), t == log(31^(1/10)*e^(4/5*I*pi)), t ==
log(-31^(1/10)), t == -4/5*I*pi + 1/10*log(31), t == -3/5*I*pi +
1/10*log(31), t == -2/5*I*pi + 1/10*log(31), t == -1/5*I*pi +
1/10*log(31), t == 1/10*log(31)]
Which one of these values is the right one? Are all true? Should I
simply take the one without symbolic variables (e.g t==1/10*log(31))
Using Sage4.7 under Linux.
Thanks a lot in advance for your care!
Jose.
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