Mathematica 9 is now available
Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
1994
*January
*February
*March
*April
*May
*June
*July
*October
*November
*December
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 1994

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: Listable attribute (was Re: eval differential expressions)

  • To: mathgroup at yoda.physics.unc.edu
  • Subject: Re: Listable attribute (was Re: eval differential expressions)
  • From: Count Dracula <lk3a at kelvin.seas.virginia.edu>
  • Date: Sat, 25 Jun 1994 12:30:55 -0400

   <> Here is just one solution, using the listability, which ends with another
   <> question:
   <> 
   <> In[1]:= Diff[fun_,var_] := D[fun,var]^2 + fun
   <> 
   <> In[2]:= Diff[ { Cos[x], Sin[x], Tan[x] }, x ]
   <> 
   <>                         2        2                 4
   <> Out[2]= {Cos[x] + Sin[x] , Cos[x]  + Sin[x], Sec[x]  + Tan[x]}
   <> 
   <> Et voila, it can probably do what Geoff asked. But at my first try, I
   <> thought at the Listable attribute, but I have discovered that since the
   <> Plus[], D[] and Power[] have it, it is useless. In fact, it is not useless,
   <> it is worse than that:
   <> 
   <> In[3]:= Diff[ Exp[x+y^2], {x, y}]
   <> 
   <>               2           2
   <>          x + y       x + y          2
   <> Out[3]= E       + D[E      , {x, y}]
   <> 
   <> In[4]:= SetAttributes[Diff, Listable]
   <> 
   <> In[5]:= Diff[ Exp[x+y^2], {x, y}]
   <> 
   <>                2             2        2               2
   <>           x + y     2 x + 2 y    x + y       2 x + 2 y   2
   <> Out[5]= {E       + E          , E       + 4 E           y }
   <> 
   <> 
   <> At that point, the "listability" seems extended to the second argument,
   <> which can be nice. Alas, one can not pull the line too much:
   <> 
   <> In[6]:= Diff[{1,x,x y},{x,y}]
   <> 
   <> Thread::tdlen: Objects of unequal length in Diff[{1, x, x y}, {x, y}]
   <>      cannot be combined.
   <> 
   <>                             2             (y,0)      2
   <> Out[6]= {1, x + D[x, {x, y}] , x y + Times     [x, y] }
   <> 
   <> 
   <> Thus my question: does somebody know how to limit the Listable attribute to
   <> one of the arguments (a kind of "ListableOnFirstArg" attribute), or does
   <> one have to explicit rules with Thread and so on ?
   <> 
   <> 
   <> =====[   Eric LEWIN - lewin at ipgp.jussieu.fr - IPGP Geochimie  ]=====
   <> = Labo de Geochimie et Cosmochimie / Institut de Physique du Globe =
   <> ========================== Paris - FRANCE ==========================

Hello Eric,

Listability can be limited to the first argument by the device given
by Roman Maeder:

f[fun_List, args___] := Map[ f[#, args]&, fun]
f[fun_, ....] := (* code for usual case where fun is not a list*)

For the example above, if you define

     diff[fun_List, var_List] := Plus[ fun , #1] & /@ Transpose[Outer[D, fun, var]^2]

then you would have a kind of listability over the two lists, e.g.,

      diff[{x y, x^3, x^2 y^2, y^3}, {x, y}]  will give


                  2   3      4   2  2      2  4   3     2         3   2  2      4  2   3      4
         {{x y + y , x  + 9 x , x  y  + 4 x  y , y }, {x  + x y, x , x  y  + 4 x  y , y  + 9 y }

 _______________________________________________________________
  Levent Kitis                                                 
  Department of Mechanical, Aerospace and Nuclear Engineering  
  Thornton Hall  McCormick Road
  University of Virginia                                       
  Charlottesville, Virginia 22903  USA                         
  804-924-6230      lk3a at cars.mech.virginia.edu              
  804-924-3291      lk3a at kelvin.seas.virginia.edu
 _______________________________________________________________











  • Prev by Date: v2.2.2 for Windows and remote kernels
  • Next by Date: Re: Defining a predicate
  • Previous by thread: Listable attribute (was Re: eval differential expressions)
  • Next by thread: Power PC performance comparisons