Re: Recursive Rules

*To*: mathgroup at smc.vnet.net*Subject*: [mg31152] Re: [mg31147] Recursive Rules*From*: Andrzej Kozlowski <andrzej at tuins.ac.jp>*Date*: Sun, 14 Oct 2001 04:11:45 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

I depends what you mean. The following are essentially equivalent In[1]:= f[t_] := a + b*f[t-1] In[2]:= f[1]=1; In[3]:= f[4]//Expand Out[3]= a + a*b + a*b^2 + b^3 and In[4]:= Clear[f] In[5]:= f[1]=1; In[6]:= a+b f[3]//.f[t_/;t>1]-> a + b*f[t-1]//Expand Out[6]= a + a*b + a*b^2 + b^3 On the other hand, the really important thing about your original example was "dynamic programming", produced by the construction f[t_]:=f[t] = ... I don't think there is any way to do this using Rule for after all Rule does not assign any global values. (Maybe someone can think of some fiendish trick to do so but if so it will probably involve some sort of cheating, like using = somewhere ) Andrzej Kozlowski Toyama International University JAPAN http://platon.c.u-tokyo.ac.jp/andrzej/ On Saturday, October 13, 2001, at 03:47 PM, Mark S. Coleman wrote: > Greetings, > > I know that a recurrent/recursive function can be written > > f[t_] := f[t] = a + b*f[t-1]. > > So that once an initial value is stipulated, e.g., f[0]=0, then the > function "remembers" past values and can correctly calculate f[] for > any t. > > I was wondering if it was possible to do the same thing with a Rule? > > Thanks, > > -Mark > >