*To*: mathgroup@smc.vnet.net*Subject*: [mg11869] Thread*From*: Des Penny <penny@suu.edu>*Date*: Fri, 3 Apr 1998 03:45:28 -0500*Organization*: Southern Utah University

Hi Groupers: I've written a program to calculate the forces on charged particles. The program works well except that parts are less than elegant. The key questions I have concern the Thread function: ========================================== Question 1: ------------ In[1]:= Thread[f[a,{b,c}]] Out[1]= {f[a,b],f[a,c]} We see that if "a" does not have head "List" it is automatically replicated so that Thread works. Now if a, b and c are defined as follows: In[2]:= a={q1,{x1,y1,z1}};b={q2,{x2,y2,z2}};c={q3,{x3,y3,z3}}; I would LIKE to have the following output when I apply Thread: {f[{q1,{x1,y1,z1}},{q2,{x2,y2,z2}}],f[{q1,{x1,y1,z1}},{q3,{x3,y3,z3}]} However, since "a" now has head "List", Thread now gives me: In[3]:= Thread[f[a,{b,c}]] Out[3]= {f[q1,{q2,{x2,y2,z2}}],f[{x1,y1,z1},{q3,{x3,y3,z3}}]} Is there a way to force Thread to give me what I want? ================================================================ I can make a workaround but its not very elegant: In[ ]:= t=Table[a,{2}]; Thread[f[t,{b,c}]] Out[]= {f[{q1,{x1,y1,z1}},{q2,{x2,y2,z2}}],f[{q1,{x1,y1,z1}},{q3,{x3,y3,z3}}]} ================================================================ Question 2: ------------- I would like to be able to Thread g across two lists as follows: In[1]:= ccs={a,b}; oc={x,y}; Thread[g[ccs,oc]] Out[1]= {g[a,x],g[b,y]} But unfortunately, since ccs and oc are lists, and since g is designed to operate on lists, g executes before the thread takes place. If g is undefined everything is ok: In[3]:= a={a1,a2}; b={b1,b2}; x={x1,x2}; y={y1,y2}; Thread[g[ccs,oc]] Out[3]= {g[{a1,a2},{x1,x2}],g[{b1,b2},{y1,y2}]} If I now define g: In[4]:= g[x1_List,x2_List]:=x1+x2^2 I would now LIKE the output of the Thread statement to be: In[6]:= {g[{a1,a2},{x1,x2}],g[{b1,b2},{y1,y2}]} Out[6]= {{a1 + x1^2, a2 + x2^2}, {b1 + y1^2, b2 + y2^2}} Instead the Thread statement now gives me: In[7]:= Thread[g[ccs,oc]] Out[7]= {{a1 + x1^2, b1 + y1^2}, {a2 + x2^2, b2 + y2^2}} The reason (I believe) is that the g function executes before the Thread operates. The function "List" is threaded over the sublists as in the following: In[9]:= Thread[{{a1 + x1^2, a2 + x2^2}, {b1 + y1^2, b2 + y2^2}}] Out[9]= {{a1 + x1^2, b1 + y1^2}, {a2 + x2^2, b2 + y2^2}} Is there a way of forcing Thread to keep its argument unevaluated until after it operates? =============================================== I am currently using the following workaround, but I don't like it: In[10]:= Clear[f] Thread[f[ccs,oc]] /. f->g Out[11]= {{a1 + x1^2, a2 + x2^2}, {b1 + y1^2, b2 + y2^2}} =============================================== Is there a better way? Cheers, Des Penny Physical Science Dept. Southern Utah University Cedar City, UT 84720 Office: (435) 586-7708 FAX: (435) 865-8051 email: penny@suu.edu Home: (435) 586-2286 email: dpenny@iname.com