Re: On Reduce

*To*: mathgroup at smc.vnet.net*Subject*: [mg72046] Re: On Reduce*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>*Date*: Sat, 9 Dec 2006 06:09:55 -0500 (EST)*Organization*: The Open University, Milton Keynes, UK*References*: <elbi51$k23$1@smc.vnet.net>

Virgil Stokes wrote: > I have the following small piece of Mathematica code that works fine for > my purposes. > > BInv = {{ 1/4, 1/4, 0}, > {-1/2, 1/2, 0}, > { 3/4, -5/4, 1}} > B = Inverse[BInv] > b = {4 + \[Delta], 8, 10}; > BInv.b // FullSimplify > Reduce[{%[[1]] >= 0, %[[2]] >= 0, %[[3]] >= 0}, {\[Delta]}] > % /. {\[Delta] -> b1 - 4} // FullSimplify > > which gives > > 0 <= b1 <= 8 > > which is of course correct. But, how can I use (access) the values 0 and 8? > That is, I would like to now use these values in some expressions that > would follow this. > > Thanks, > V. Stokes > Hi Virgil, In Mathematica, "Everything is an expression." Therefore, you can manipulate the result made of inequalities as any expression. In[1]:= BInv = {{1/4, 1/4, 0}, {-2^(-1), 1/2, 0}, {3/4, -5/4, 1}}; B = Inverse[BInv]; b = {4 + Î´, 8, 10}; FullSimplify[BInv . b]; Reduce[{%[[1]] >= 0, %[[2]] >= 0, %[[3]] >= 0}, {Î´}]; sol = FullSimplify[% /. {Î´ -> b1 - 4}] Out[6]= 0 <= b1 <= 8 In[7]:= FullForm[sol] Out[7]//FullForm= FullForm[Inequality[0, LessEqual, b1, LessEqual, 8]] In[8]:= lowval = First[sol] Out[8]= 0 In[9]:= upval = Last[sol] Out[9]= 8 Regards, Jean-Marc