Re: An open letter
- To: mathgroup at smc.vnet.net
- Subject: [mg16588] Re: An open letter
- From: "Allan Hayes" <hay at haystack.demon.co.uk>
- Date: Wed, 17 Mar 1999 23:55:01 -0500
- References: <7cleqb$9oh@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Jack,
I have struggled with the same problems for many years.
In my package IntegralManipulation for demonstrating the usual
manipulations, I use my own integral sign, int, format it to look like
traditional math (see Help>Add-ons > Extra Utilites > Notation) and
programme it to do what I want. I turn on the inbuilt function when needed
with /.int->Integrate.
It would be useful to me to standard versions of functions that format but
do not automatically evaluate; that I can programme as I want and turn on to
inbuilt evaluation as needed. Perhaps also that hold their parts
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
Jack Goldberg wrote in message <7cleqb$9oh at smc.vnet.net>...
>Hi Group,
>
>I am a Mathematica enthusiast who has dabbled in programming
>Mathematica for enough years that I feel free to complain. Here's
>my gripe:
>
>My main purpose in using Mathematica is help students learn mathematics.
>So for my purposes the fact that Mathematica evaluates everything in sight
>is a major drawback. Let me be explicit. I want to illustrate
>"Integration by Parts". So I try to define
>
>ByParts[Integrate[f_*g_,x_],g_] := ????
>
>What I would like as an output of ByParts is this
>
>Integrate[f*g,x] == f*Integrate[g,x] -
> Integrate[D[f,x]*Integrate[g,x],x]
>
>where the integration on the left IS NOT performed, the integration of
>g in the two integrals on the right is performed but the last integral
>on the right is unevaluated. Put in other words, I would like Mathematica
to
>display the kind of formula the student would get using integration by
>parts. I have found this surprisingly difficult to do. I have used
>various combinations of Evaluate, Hold, HoldFirst and HoldForm with
>only partial success. I have gotten to the point where I don't even
>understand why my last effort failed! Perhaps someone could explain why
>the following does not work.
>
>ByParts[ f_*g_,x_,g_] := Module[ {int, dif, li1},
> int = Integrate[g,x];
> dif = D[f,x];
> li1 = int*dif;
> HoldForm[Integrate[f*g,x]] == f*int-
> HoldForm[Integrate[li1,x]]
> ]
>
>(I hope I have the right number of left and right brackets!)
>The problem is that the very last HoldForm seems to prevent
>li1 from providing int*dif as the integrand. What's going on?
>
>Now back to my open letter. This example is only one of three or
>four that I have fell prey to. All of them are based on Mathematica's
propensity
>to evaluate. I offer only one more example and I will be brief
>in my description.
>
>I want to explain why e^x*e^x = e^(2x) by using
>the power series expansion of e^x. I
>define the Cauchy product of series for the students and would like
>Mathematica to exhibit the nth coefficient of the product as a finite sum.
>
>Sum[ x^n/n!, {n,0,Infinity} ]*Sum[ x^n/n!, {n,0,Infinity} ] ==
> Sum[ Sum[ 1/(k!(n-k)!, {k,0,n}] x^n, {n,0,Infinity} ]
>
>There is not a single term in this expression that Mathematica will leave
>unevaluated! I could trick Mathematica by inserting spurious factors that
>would stop the evaluation process, but I don't want to have to figure
>out some clever way to do this or to introduce holds etc.
>
>I am fairly confident that this type of problem can be solved by
>a judicious combination of "holds" and "releaseholds" and "evaluates".
>The fact remains that it is something of a challange. It shouldn't
>be. I say this because at least one other CAS has an easy means for
>accomplishing this goal.
>
>What say yo'all?
>
>Jack
>
>
>