I realize that my 4th paragraph (specifically "the implicit replacement...") is not very truthful. It may be a good first explanation, but there's a more technical answer if you (or anyone) cares for one.
when you try plot( foo, ...) then the first thing sage does is evaluate "foo" once. It has to evaluate to a function -- a python callable object with one parameter, to be more precise, so basically foo.__call__ must exist, and foo( value ) should return something. if that works, sage goes on, computing foo( v ) for a bunch of values v, and plots that. when x is a formal variable, then foo= sin(x) evaluates to itself, and it IS callable, which is what I declared was mildly weird. So for example sin(x)(0) works and gives you 0 -- mind you at the moment sage also warns you that this syntax is deprecated. But when plotting, people use this syntax all the time! Now, with your "def h(x, n):...", then "h" evaluates to a function, but is tqkes two parameters, not one. On the other hand h(x, 3) evaluates to 3*x - 2 when x is a formal variable (which it is by default). In turn 3*x - 2 is callable, by the reason i just give, hence the plot proceeds. finally "lambda x : h(x, 3)" evaluates precisely to the function that you want. And "lambda y : h(y, n)" would have worked, too, even if y is not a formal variable. On 10 avr, 10:48, Pierre <pierre.guil...@gmail.com> wrote: > "lambda x : f(x)" should read "the function which maps x to f(x)". It > has nothing to do with symbolic computations, and exists in Python. > > note that "lambda x : x^2" is exactly the same as "lambda y : y^2", > which is mathematically very sound. Using the symbolic ring however, > if x and y are formal variables then x^2 is not the same as y^2 > (though plotting them will give the same thing!) > > if you think about it, what is *really* a little weird, is that > "plot(sin(x), (-1, 1))" should work at all. It assumes you are talking > about the function which to x assigns sin(x) (and not, say, the > constant function which to anything assigns the formal expression > sin(x)). > > By the way if you fix a value for x, then "plot(sin(x), ...)" gives > you a constant plot -- so the trick (of replacing sin(x) by a > function) is context-dependent. By contrast, "plot(lambda x : > sin(x), ...)" always works. Oh, and the implicit replacement works for > symbolic expressions, like sin(x), and not your h(x,n) which is > defined as a python function (a very different thing). > > As you have discovered, these sorts of things become much, much > clearer when more than one variable is involved. "plot( x*y, ...)", or > "plot(h(x, n))" is just ambiguous. You want to plot the function which > to x assigns h(x, n), with n being fixed? well that is precisely > lambda x : h(x, n). > > hope this helps. > > Pierre > > On 10 avr, 06:08, ObsessiveMathsFreak <obsessivemathsfr...@gmail.com> > wrote: > > > Partial seems useful, thank you. The Lambda solutions also work. > > > But what IS lambda anyway? I don't see that its doing anything other > > than being syntactic verbose. > > > On Apr 9, 7:24 am, Jason Grout <jason-s...@creativetrax.com> wrote: > > > > On 4/8/11 2:00 PM, John H Palmieri wrote: > > > > > On Friday, April 8, 2011 11:03:14 AM UTC-7, ObsessiveMathsFreak wrote: > > > > > I have a python type function taking two variables is defined in > > > > such > > > > a say that accidental evaluation is a possibility. Here is a > > > > simplified version > > > > > def h(x,n): > > > > if x>2: > > > > return n-x > > > > else: > > > > return n*x-2 > > > > > How can functions like this be plotted over x for a constant value > > > > of > > > > n in sage? > > > > > sage: plot(lambda x: h(x,3), (x, 0, 4)) > > > > > works for me. > > > > Another approach that supplies default arguments for the *first* > > > variables is to use functools.partial: > > > > def h(x,n): > > > if x>2: > > > return n-x > > > else: > > > return n*x-2 > > > from functools import partial > > > plot(partial(h,1),(n,-1,1)) > > > > This effectively plots h(1,n), where n goes from -1 to 1. > > > > Note that we can't do > > > > plot(partial(h,x=1),(n,-1,1)) > > > > since plot calls the function by positional arguments, rather than > > > keyword arguments (i.e., this last plot calls h like this: > > > h(-.5434344,x=1), and so we get two values for x). I think this is a > > > bug; I think if the variable is specified in the plot range, the > > > function should be called with a keyword argument, so that the function > > > would be called as h(n=-.5434344,x=1). I believe I even have a patch > > > from late last year somewhere on my laptop that changes this behavior to > > > call a function using keyword arguments if the variable is specified in > > > the plot range. Once this bug is fixed, then doing plot(partial(h,x=1), > > > (n,-1,1)) would work. > > > > Thanks, > > > > Jason -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
