Re: Very very basic question about Mathematica expressions

*To*: mathgroup at smc.vnet.net*Subject*: [mg111166] Re: Very very basic question about Mathematica expressions*From*: Sam Takoy <sam.takoy at yahoo.com>*Date*: Thu, 22 Jul 2010 05:44:18 -0400 (EDT)*References*: <i23k1j$epv$1@smc.vnet.net> <i26kq8$9c8$1@smc.vnet.net>

Thanks to all who responded! May I belabor this point a little. I understand how to make Manipulate work and I understand functions. (I am a product of Scheme from with Mathematica seems to have borrowed a few ideas.) My question is much more formal: What are the building blocks of Mathematica, the formal language. When you say s = x+h what is s? Is it an "expression"? Does s represent x+h wherever it appears (assuming x and h are unassigned at the time of s=x+h)? Apparently not always: yes in s/.h->5, but not in Manipulate. So here, then is my "model" of Mathematica: In s = x+h, s is an "Expression" In s[x_, h_]:=x+h, s is a "Function" Manipulate expects a "Function" so that answers my question. Then what is s[h_] := x + h? Is it an "Expression" or a "Function" of h with a parameter x? Would then Manipulate[Plot[s[h], {x, 0, 1}, PlotRange -> {0, 1}], {h, 0, 1}] work? (The answer is yes.) So apparently, Plot is happy with an "Expression", but Manipulate wants a "Function"? Why? Also, in Manipulate[Plot[x+h, {x, 0, 1}, PlotRange -> {0, 1}], {h, 0, 1}], x+h is no longer an "Expression", but is once again a "Function", because of the context? Even though it's inside Plot which is happy with an "Expression"? A personal note: I guess I'm a little frustrated that after a few months of working with Mathematica, I still have to try things before I know whether they'll work or not. I'm used to having a clear picture of the grammar of the language that I'm working with, but I'm struggling here. On 7/21/2010 7:14 AM, dr DanW wrote: > I ran into this problem yesterday. I don't know exactly why it > happens, I think it has something to do with the way Manipulate > localizes variables. To solve it, I use a trick I found that lets me > take an expression built up of global symbols and localize the > symbols. Your trivial example: > > s = x + h > > Make a function out of it. The Evaluate[] is necessary to evaluate s, > which replaces it with x+h > > sfnc = Function[{x, h}, Evaluate[s]] > > Now the Manipulate[] works fine > > Manipulate[Plot[sfnc[x, h], {x, 0, h}], {h, 0.1, 1}] > > I find myself using this trick a lot. > > Regards, > Daniel >