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MathGroup Archive 2007

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Re: Re: Re: Hold and Equal

  • To: mathgroup at smc.vnet.net
  • Subject: [mg73804] Re: [mg73771] Re: [mg73747] Re: Hold and Equal
  • From: Murray Eisenberg <murray at math.umass.edu>
  • Date: Thu, 1 Mar 2007 06:07:01 -0500 (EST)
  • Organization: Mathematics & Statistics, Univ. of Mass./Amherst
  • References: <erufqm$s7j$1@smc.vnet.net> <200702271048.FAA24024@smc.vnet.net> <200702280929.EAA24225@smc.vnet.net> <acbec1a40702280457r5cd8708at59e67331d62326f5@mail.gmail.com>
  • Reply-to: murray at math.umass.edu

Almost!  Look at this:

   Attributes@formEquation=List@HoldFirst
   formEquation[expr_,op_]:=With[{result=op@expr},HoldForm[expr=result]]

   Table[formEquation[Integrate[x^n, x], Identity], {n, 1, 2}]//InputForm
{HoldForm[Integrate[x^n, x] = x^2/2], HoldForm[Integrate[x^n, x] = x^3/3]}

I used InputForm there so could copy as plain text from Mathematica to 
here.  The problem is that both entries in the list have x^n on the left 
side of the equations now.


Chris Chiasson wrote:
> In[1]:= Attributes@formEquation=List@HoldFirst(*or one could just
> supply Unevaluated arguments*)
> 
> Out[1]= {HoldFirst}
> 
> In[2]:= 
> formEquation[expr_,op_]:=With[{result=op@expr},HoldForm[expr=result]]
> 
> In[3]:= formEquation[Integrate[x^2,x],Identity]
> 
> Out[3]= \[Integral]x^2\[DifferentialD]x=x^3/3
> 
> On 2/28/07, Murray Eisenberg <murray at math.umass.edu> wrote:
>> Aha!  I believe this approach _almost_ allows me to accomplish what I
>> was REALLY trying to accomplish.  It certainly works in the example I
>> gave.  If I encapsulate this in a function...
>>
>>    formEquation[expr_, op_]:= HoldForm[expr=z]/.z\[Rule]op[expr]
>>
>> ... then
>>
>>    formEquation[(a+b)^2,Identity]
>>
>> will produce exactly what I want.
>>
>> However, if I try something like the example I was really after (which I
>> didn't mention in my original post, since I gave something simpler), it
>> works in the direct version...
>>
>>    HoldForm[Integrate[x^2,x] = z] /. z\[Rule]Integrate[x^2,x]
>>
>> but not with the encapsulating function:
>>
>>    formEquation[Integrate[x^2, x], Identity]
>>
>> The latter produces the equation
>>
>>    x^3/3 = x^3/2
>>
>> whereas I want the left-hand side to be the unevaluated integral 
>> expression.
>>
>> You can tell I'm struggling with Hold!  (One of the "last frontiers" in
>> my Mathematica education.)
>>
>> bghiggins at ucdavis.edu wrote:
>> > Murray,
>> >
>> > Try this
>> >
>> >
>> > HoldForm[(a + b)^2 = z] /. z -> Expand[(a + b)^2]
>> >
>> >
>> > (a + b)^2 = a^2 + 2*a*b + b^2
>> >
>> > Cheers,
>> >
>> > Brian
>> >
>> >
>> >
>> > On Feb 26, 3:20 am, Murray Eisenberg <mur... at math.umass.edu> wrote:
>> >> How can I produce in an Output cell (under program control) an
>> >> expression like the following,
>> >>
>> >>    (a+b)^2 = a^2+ 2 a b + b^2
>> >>
>> >> where instead of the usual Equal (==) I get a Set (=), as in 
>> traditional
>> >> math notation?  I want to input the unexpanded (a+b)^2 and have the
>> >> expansion done automatically.
>> >>
>> >> Of course, I can try something like the following:
>> >>
>> >>    (a+b)^2 == Expand[(a+b)^2])
>> >>
>> >> So how do I convert the == to =?  Of course
>> >>
>> >>    ((a + b)^2 == Expand[(a + b)^2]) /. Equal -> Set
>> >>
>> >> gives a Set::write error.  And
>> >>
>> >>    (Hold[(a + b)^2 == Expand[(a + b)^2]]) /. Equal -> Set
>> >>
>> >> doesn't actually evaluate the Expand part and leaves the "Hold" 
>> wrapper.
>> >>
>> >> --
>> >> Murray Eisenberg                     mur... at math.umass.edu
>> >> Mathematics & Statistics Dept.
>> >> Lederle Graduate Research Tower      phone 413 549-1020 (H)
>> >> University of Massachusetts                413 545-2859 (W)
>> >> 710 North Pleasant Street            fax   413 545-1801
>> >> Amherst, MA 01003-9305
>> >
>> >
>> >
>>
>> -- 
>> Murray Eisenberg                     murray at math.umass.edu
>> Mathematics & Statistics Dept.
>> Lederle Graduate Research Tower      phone 413 549-1020 (H)
>> University of Massachusetts                413 545-2859 (W)
>> 710 North Pleasant Street            fax   413 545-1801
>> Amherst, MA 01003-9305
>>
>>
> 
> 

-- 
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305


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