might be useful

*To*: mathgroup at smc.vnet.net*Subject*: [mg110293] might be useful*From*: Peter Pein <petsie at dordos.net>*Date*: Sat, 12 Jun 2010 05:31:33 -0400 (EDT)

As apology for my silly question, I'd like to provide a code snippet I wrote a while ago. Sometimes the problem arises to solve an equation/a set of equations not for a variable, but for an expression. Examples: In[1]:= Isolate[eqn:(_Equal|{_Equal ..}),expr_,elim_:{}]:= Block[{tmp}, Solve[GroebnerBasis[Subtract@@@Flatten[{eqn,tmp==expr}],tmp, Flatten[{First[Variables[expr]],elim}]]==0,tmp][[1]]/.{Rule->Equal,tmp->expr}] In[2]:= Isolate[{x^2+3y^2==1,y-x==1/2},2x+y] Out[2]= {2 x+y==1/8 (-5-3 Sqrt[13])} In[3]:= Isolate[x^2+3y^2==1,2x+y] Out[3]= {2 x+y==y-2 Sqrt[1-3 y^2]} In[4]:= Isolate[{x^2+y^2+z^2==1,r Cos[t]+r Sin[t]==1},x+y,{r,t}] Out[4]= {x+y==y-Sqrt[1-y^2-z^2]} or Isolate[{x^2+y^2+z^2==1,3z-(x+y)^2/2==0},x+y,z] eliminates z but the answer is a bit lengthy. If one or some of you want to improve it (and do this successfully), please let me know. Cheers, Peter