Re: Re: With[{software=Mathematica}, Frustration]

*To*: mathgroup at smc.vnet.net*Subject*: [mg24721] Re: [mg24486] Re: [mg24308] With[{software=Mathematica}, Frustration]*From*: "Allan Hayes" <hay at haystack.demon.co.uk>*Date*: Wed, 9 Aug 2000 02:31:19 -0400 (EDT)*References*: <8mdjv6$51n@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Hartmut, I wonder if using With is the best way to deal with the original problem: >What I really want is as follows. I'm entering a bunch of functional relations > like c = a b, using direct assignments (=, not :=) and being careful not to > give values to the independent variables like a and b as I go along > > At various points I'd like to print out numerical test values or check values > of these functions With Block, in place of With, we can meet the need to avoid giving global values to the variables without any problems due to holding: c = a b; Block[{a = 2., b = 3., c = a b}, Print["a = ", a, ", b = ", b, ", c = ", c, ", Sin[c] = ", Sin[c]]] a = 2., b = 3., c = 6., Sin[c] = -0.279415 And a checking function might be convenient: chk[va_, vb_] := Block[{a = va, b = vb}, Print["a = ", va, ", b = ", vb, ", c = ", c, ", Sin[c] = ", Sin[c]]] chk[2., 3.] a = 2., b = 3., c = 6., Sin[c] = -0.279415 Allan --------------------- Allan Hayes Mathematica Training and Consulting Leicester UK www.haystack.demon.co.uk hay at haystack.demon.co.uk Voice: +44 (0)116 271 4198 Fax: +44 (0)870 164 0565 "Wolf Hartmut" <hwolf at debis.com> wrote in message news:8mdjv6$51n at smc.vnet.net... > > > > -----Original Message----- > > From: AES [SMTP:siegman at stanford.edu] To: mathgroup at smc.vnet.net > > Sent: Wednesday, July 19, 2000 7:22 AM > > To: mathgroup at smc.vnet.net > > Subject: [mg24721] [mg24486] Re: [mg24308] With[{software=Mathematica}, > > Frustration] > > > > In article <8l0ovj$dpf at smc.vnet.net>, Mark Fisher > > <me.fisher at atl.frb.org> wrote: > > > > > I'm probably not paying enough attention, but what's wrong with the > > > following? > > > > > > Print[ > > > With[{a = 2., b = 3.}, > > > Evaluate[StringForm["a = `1`, b = `2`, c = `3`, Sin[c] = `4`", > > > a, b, c, Sin[c]]] > > > ] > > > ] > > > > ------------------------------ > > > > The problem, to answer the question straightforwardly, is that an > > ordinary user [1] learns about Print[ ] and uses it lots of places in > > his notebooks; and then he learns about With[ ] and uses it a few > > places; and they work, and both seem like reasonably simple, intuitive, > > useful commands. > > > > So then he, very reasonably, tries to put the two together by using > > Print[] inside With[] -- and it doesn't work. > > > > So, he starts groping around, and after some searching gets introduced > > to Evaluate[]; and Evaluate[], though it's a somewhat messy and > > mysterious command, does work -- sometimes, that is -- within With[]. > > > > But, it doesn't work with Print[] inside With[] to accomplish the rather > > elementary objective outline above [2]. > > > > So, after a lot of time-wasting trial and error, a person obviously > > pretty expert in Mathematica is finally able to accomplish the objective > > by using StringForm[], which is a really obscure and esoteric command, > > seldom needed by the ordinary user [3] > > > > Don't get me wrong: I'm a Mathematica fan; regard it (along with TeX) > > as a true work of genius; understand its need to have some real > > complexity to accomplish all the things it does; and appreciate that > > many design decisions had to be made in creating it. > > > > But it's primary target, or one of its primary targets, is supposed to > > be the "ordinary user" [1]; and for the ordinary user who tries to move > > even slightly beyond the elementary things that he knows how to use, or > > who tries to make two apparently elementary things work together (like > > Wiht[] and Print[]) Mathematica can become *maddeningly* frustrating. > > > > --AES > > > > -------------- > > [1] An ordinary user is someone who just wants to get useful > > calculations done using Mathematica in his or her own area of expertise, > > not spend his life becoming an expert in the arcane esoterica that you > > can get involved in with Mathematica, if you're unlucky or not careful. > > > > [2] Challenge: Accomplish the above task using *only* Print[], With[] > > and Evaluate[] -- no other Mathematica functions. > > > > [3] Note that StringForm[] is not discussed at all in The Beginners > > Guide to Mathematica by Glynn and Gray, and isn't treated except for a > > passing mention on page 715 of Mathematica for Scientists and Engineers > > by Thomas Bahder. > > > [Hartmut Wolf] > > Hello A E (Siegman), > > I was on vacation for a while, so now let me respond to your "[2] > challenge": > > In[14]:= > With[{a = 2., b = 3.}, > Evaluate[Hold[Print]["a = ", a, ", b = ", b, ", c = ", c, ", Sin[c] = ", > > Sin[c]]]] // ReleaseHold > > >From In[14]:= > a = 2., b = 3., c = 6., Sin[c] = -0.279415 > > > Why all this Hold and ReleaseHold ? > > Well if you try: > > In[9]:= > With[{a = 2., b = 3.}, > Evaluate[Print["a = ", a, ", b = ", b, ", c = ", c, ", Sin[c] = ", > Sin[c]]]] > > >From In[9]:= > a = a, b = b, c = a*b, Sin[c] = Sin[a*b] > > then this happens: > > (1) Print is executed, giving "From In[9]", no substitution has occurred so > far. The result of this operation is Null. > > (2) then With[{a = 2., b = 3.}, Null] is executed, giving Null (which is not > printed) > > > On the other side if you don't Evaluate then > > In[12]:= > With[{a = 2., b = 3.}, > Print["a = ", a, ", b = ", b, ", c = ", c, ", Sin[c] = ", Sin[c]]] > > >From In[12]:= > a = 2., b = 3., c = a*b, Sin[c] = Sin[a*b] > > Here standalone a and b have been visible to With, and hence substituted > with numerical values, not so as components of c (which has not yet been > evaluated when With did its work). > > > So what we have to do is to Evaluate the arguments of Print, but not Print > itself: this is suppressed by Hold; now With works on the evaluated > arguments, returns the held Print expression (with evaluated and substituted > arguments) and ReleaseHold then gives way to Printing. > > Of course Hold, ReleaseHold is not the only (yet a clear) way to suppress > printing while being exposed to With. Another one would be > > In[16]:= > With[{a = 2., b = 3.}, > Evaluate[printlater["a = ", a, ", b = ", b, ", c = ", c, ", Sin[c] = ", > Sin[c]]]] /. printlater -> Print > > >From In[16]:= > a = 2., b = 3., c = 6., Sin[c] = -0.279415 > > "printlater" is just an undefined symbol. > > > You can also work within the Print command, directly on the calling sequence > (of Print): > > In[23]:= > Print[With[{a = 2., b = 3.}, > Evaluate[s["a = ", a, ", b = ", b, ", c = ", c, ", Sin[c] = ", > Sin[c]]]] /. s -> Sequence] > > >From In[23]:= > a = 2., b = 3., c = 6., Sin[c] = -0.279415 > > Again here s has no function at all, just to contain the (evaluated) > arguments of Print for the operation of With, thereafter s is made to a > Sequence, such that Print gets its proper arguments. Having understood this > idea, of course you would just Apply Print to s to get the same effect: > > In[26]:= > Print @@ With[{a = 2., b = 3.}, > Evaluate[s["a = ", a, ", b = ", b, ", c = ", c, ", Sin[c] = ", Sin[c]]]] > > >From In[26]:= > a = 2., b = 3., c = 6., Sin[c] = -0.279415 > > > This all can be achieved by simple, pure logical thinking, once you fully > understand the basics. No wizards nor geniuses needed. However, I understand > your point. The way out -- to my opinion -- is not to read books over books > so many, but try to achieve a solid understanding of the basics (these are > about 200 Mathematica functions). Try to use what you know, make use of the > ressources you have (primarily Help and The Mathematica Book), try examples > and learn to cut problems done to the essentials. And finally there is this > friendly and inspiring community. > > Kind regards, Hartmut > >

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**RE: Re: With[{software=Mathematica}, Frustration]**

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