Re: Problem with Solve and O[x]

*To*: mathgroup at christensen.cybernetics.net*Subject*: [mg1257] Re: Problem with Solve and O[x]*From*: danl (Daniel Lichtblau)*Date*: Mon, 29 May 1995 02:38:49 -0400*Organization*: Wolfram Research, Inc.

In article <3q3mcr$mc5 at news0.cybernetics.net> steve at tweedledee.ucsb.edu (Steve Trainoff) writes: > It appears the Solve and O[x] don't mix. Consider the following. > > Mathematica 2.0 for NeXT > Copyright 1988-91 Wolfram Research, Inc. > > In[1]:= Solve[x+z==1,x] > > Out[1]= {{x -> 1 - z}} > > In[2]:= Solve[x+z==1+O[z],x] > > Out[2]= {{x -> 1}} (* I would prefer x -> 1 + O[z] *) > > In[3]:= Solve[x+z==1+O[z]^2,x] > > Out[3]= {} (* What is wrong with x -> 1 + z + O[z]^2 ??? *) > > -- > > ...STeve This is caused by the fact that Solve uses LogicalExpand, and LogicalExpand does not do what one might wish in these cases. In[1]:= LogicalExpand[x == 1+O[z]] Out[1]= -1 + x == 0 In[2]:= LogicalExpand[x+z==1+O[z]^2] Out[2]= False If I can fix this immediate problem without breaking Solve, I'll do so. Daniel Lichtblau, WRI