Re: FactorInteger Print Formatting

• To: mathgroup at christensen.cybernetics.net
• Subject: [mg725] Re: FactorInteger Print Formatting
• From: rubin at msu.edu (Paul A. Rubin)
• Date: 11 Apr 1995 20:49:02 GMT
• Organization: Michigan State University

```In article <3m4q93\$e47 at news0.cybernetics.net>,
Alan Powell <POWELLA at delphi.com> wrote:
->
->
->Could anyone suggest a neat way to reformat the output of
->FactorInteger into a more usable print format?
->
->FactorInteger[n] gives a list of prime factors of the integer n
->in ascending order, together with their exponents viz:
->
->  FactorInteger[900]    produces the list   {{2,2},{3,2},{5,2}}
->
->What I need is a function called say factorform[list] such that:
->
->  Print[ factorform[{{2,2},{3,2},{5,2}}] ]  produces  2^2*3^2*5^2
->
->Ideally exponents equal to 1 would be suppressed so that when
->
->  ff = FactorInteger[30]    produces    {{2,1},{3,1},{5,1}}    then
->
->  Print[factorform[ff]]  would give  2*3*5  instead of  2^1*3^1*5^1  and
->
->  Print[factorform[FactorInteger[2^6*3*5^2*7]]]  would give  2^6*3*5^2*7
->
->A procedural solution is possible, but I was unable to create a simple
->function which would give the desired result.
->
->
->Alan Powell          POWELLA at delphi.com

If you don't need your "factorform[ff]" to reduce to a list for purposes of
subsequent arithmetic, etc., you can do it with Format.

In[1]:= faclist[ x_Integer ] := ff[ FactorInteger[ x ] ]
In[2]:= Format[ ff[ {n_Integer, 1} ] ] := n
In[3]:= Format[ ff[ {n_Integer, m_Integer} ] ] := SequenceForm[ n, "^", m ]
In[4]:= Format[ ff[ x_List ] ] :=
SequenceForm[ ff[ x[[1]] ], "*", ff[ Rest[ x ] ] ]
In[5]:= Format[ ff[ {x_List} ] ] := ff[ x ]

This defines a function faclist that wraps the output of FactorInteger in a
dummy head "ff."  It would be a good idea to Protect[ ff ] so that the
symbol ff does not inadvertantly get assigned a value someplace else.  Now
faclist prints in the desired format automatically:

In[6]:= faclist[ 2400 ]
Out[6]= 2^5*3*5^2

Paul

**************************************************************************
* Paul A. Rubin                                  Phone: (517) 432-3509   *
* Department of Management                       Fax:   (517) 432-1111   *
* Eli Broad Graduate School of Management        Net:   RUBIN at MSU.EDU    *
* Michigan State University                                              *
* East Lansing, MI  48824-1122  (USA)                                    *
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Mathematicians are like Frenchmen:  whenever you say something to them,
they translate it into their own language, and at once it is something
entirely different.                                    J. W. v. GOETHE

```

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