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MathGroup Archive 2000

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Re:Modification to Thread or MapThread

  • To: mathgroup at smc.vnet.net
  • Subject: [mg26419] Re:[mg26380] Modification to Thread or MapThread
  • From: "Ersek, Ted R" <ErsekTR at navair.navy.mil>
  • Date: Wed, 20 Dec 2000 00:21:41 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

Chris Johnson wanted to make Thread work a certain way.  Thread and many
other programming constructs in Mathematica are very versatile.  In all the
examples below any other head could have been used instead of Plus.  The
first example is the simplest way of using thread.

In[1]:=
  Thread[{x1,x2,x3}+{y1,y2,y3}]

Out[1]=
  {x1+y1,x2+y2,x3+y3}

Unless Thread is given another argument indicating otherwise it threads over
lists. That explains the result of the next example.

In[2]:= 
Thread[{x1,x2,x3,x4}+h[a,b]]

Out[2]
{x1+h[a,b], x2+h[a,b], x3+h[a,b], x4+h[a,b]}

In the next example nothing at level 1 is a List so we have to tell the
kernel to thread over (g). We do that by giving Thread (g) as a second
argument.

In[3]:=
Thread[g[x1,x2,x3]+h[a,b], g]

Out[3]=
g[x1+h[a,b], x2+h[a,b], x3+h[a,b]]

In the next case we thread over (g) but only over the first 3 occurrences of
(g).

In[4]:=
Thread[g[w1,w2]+g[x1,x2]+g[y1,y2]+g[z1,z2], g, 3]

Out[4]=
g[w1+x1+y1+g[z1,z2], w2+x2+y2+g[z1,z2]]

In the next example we thread over the last 3 occurrences of (g).

In[5]:=
Thread[g[w1,w2]+g[x1,x2]+g[y1,y2]+g[z1,z2], g, -3]

Out[5]=
g[x1+y1+z1+g[w1,w2], x2+y2+z2+g[w1,w2]]


Next we thread over the first occurrence through to the 2nd from the last
occurrence of (g).

In[6]:=
Thread[g[w1,w2]+g[x1,x2]+g[y1,y2]+g[z1,z2], g, {1,-2}]

Out[6]=
g[w1+x1+y1+g[z1,z2], w2+x2+y2+g[z1,z2]]


-------
Download lots of other Mathematica tips, tricks from 
http://www.verbeia.com/mathematica/tips/Tricks.html


--------------------
Regards,
Ted Ersek



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