Re: Simplify Log[ab] - Log[b] to Log[a] ?

*To*: mathgroup at smc.vnet.net*Subject*: [mg16050] Re: Simplify Log[ab] - Log[b] to Log[a] ?*From*: dreissBLOOP at bloop.earthlink.net (David Reiss)*Date*: Mon, 22 Feb 1999 01:44:31 -0500*Organization*: EarthLink Network, Inc.*References*: <7ao3po$rv0@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

In article <7ao3po$rv0 at smc.vnet.net>, "Simon Allfrey" <simon at allfrey13.freeserve.co.uk> wrote: > How do I persuade Mathematica to simplify > > Log[a b] - Log[b] to Log[a]? > > when processing algebraic expressions? In your simple example you could do the following with pattern matching in a repalcement rule: In[1]:= rules = {Log[x_ y_] :> Log[x] + Log[y]} Out[1]= {Log[(x_) (y_)] :> Log[x] + Log[y]} In[2]:= Log[a*b] - Log[b] /. rules Out[2]= Log[a] In the following case you need to use ReplaceRepeated (//.) so that the rule is applied until the expression no longer changes: In[3]:= Log[a*b*c] - Log[b] - Log[c] /. rules Out[3]= Log[a] - Log[b] - Log[c] + Log[b c] In[4]:= Log[a*b*c] - Log[b] - Log[c] //. rules Out[4]= Log[a] However, since a and b can be rather complicated, and because in such a case the product, a b, might be represented in its FullForm by something other than Times[a, b], you need to write transformation rules that cover all cases of interest. In[5]:= FullForm[a*b] Out[5]//FullForm= Times[a, b] Note that the following doesn't simplify to the degree that you want: In[6]:= Log[a*b/c] - Log[b] /. rules Out[6]= b Log[a] - Log[b] + Log[-] c This is because the FullForm of (a b/c) does not correspond to the rule: In[7]:= FullForm[a*b/c] Out[7]//FullForm= Times[a, b, Power[c, -1]] In[8]:= FullForm[b/c] Out[8]//FullForm= Times[b, Power[c, -1]] But, if we include another rule to cover this case, it does work: In[9]:= rules = {Log[(x_)*(y_)] :> Log[x] + Log[y], Log[(x_)/(y_)] :> Log[x] - Log[y]} Out[9]= {Log[(x_) (y_)] :> Log[x] + Log[y], Log[x_/y_] :> Log[x] - Log[y]} In[10]:= Log[a*b/c] - Log[b] //. rules Out[10]= 1 Log[a] + Log[-] c -- ---------------------------------------- Scientific Arts: Creative Services and Consultation for the Applied and Pure Sciences David Reiss Email: dreiss at !SPAMscientificarts.com ---------------------------------------- Remove the !SPAM to send email