Re: Eliminate Complex Roots

*To*: mathgroup at smc.vnet.net*Subject*: [mg64361] Re: [mg64348] Eliminate Complex Roots*From*: Bob Hanlon <hanlonr at cox.net>*Date*: Tue, 14 Feb 2006 01:31:36 -0500 (EST)*Reply-to*: hanlonr at cox.net*Sender*: owner-wri-mathgroup at wolfram.com

Reduce[a^3+10*a^2-15*a+b==0,a,Reals] (b < (10/27)*(-335 - 29*Sqrt[145]) && a == Root[#1^3 + 10*#1^2 - 15*#1 + b & , 1]) || (b == (10/27)*(-335 - 29*Sqrt[145]) && (a == Root[#1^3 + 10*#1^2 - 15*#1 + b & , 1] || a == Root[#1^3 + 10*#1^2 - 15*#1 + b & , 3])) || ((10/27)*(-335 - 29*Sqrt[145]) < b < (10/27)*(-335 + 29*Sqrt[145]) && (a == Root[#1^3 + 10*#1^2 - 15*#1 + b & , 1] || a == Root[#1^3 + 10*#1^2 - 15*#1 + b & , 2] || a == Root[#1^3 + 10*#1^2 - 15*#1 + b & , 3])) || (b == (10/27)*(-335 + 29*Sqrt[145]) && (a == Root[#1^3 + 10*#1^2 - 15*#1 + b & , 1] || a == Root[#1^3 + 10*#1^2 - 15*#1 + b & , 2])) || (b > (10/27)*(-335 + 29*Sqrt[145]) && a == Root[#1^3 + 10*#1^2 - 15*#1 + b & , 1]) Reduce[{a^3+10*a^2-15*a+b\[Equal]0,b==(10/27)*(-335-29*Sqrt[145])},a] b == (10/27)*(-335 - 29*Sqrt[145]) && (a == (1/3)*(-10 - Sqrt[145]) || a == (2/3)*(-5 + Sqrt[145])) %//N b == -253.4097195499913 && (a == -7.347198192930765 || a == 4.6943963858615305) Plot[Root[#1^3+10*#1^2-15*#1+b&,1],{b,-500,25}]; Bob Hanlon > > From: bghiggins at ucdavis.edu To: mathgroup at smc.vnet.net > Subject: [mg64361] [mg64348] Eliminate Complex Roots > > Hi All, > > Suppose I have the following equation and I want to plot the real roots > using Plot as a function of the parameter b > > a^3 + 10*a^2 - 15*a + b == 0 > > For the problem I am interested I have a set of algebraic equations of > at least order 3, but this is simpler enough to explain what the issue > is. > > Now if I want just the Real root I can do the following: > > > Sol2[b_] := DeleteCases[Solve[a^3 + 10.*a^2 - 15*a + b == > 0, a], {___, x_ -> Complex[y_, z_], ___}] > > and evaluating > > Sol2[20] > > {{a -> -11.46104034060055}} > > Gives the desired result. So far so good. Now suppose I want to plot > the solutions asa function of b. My immediate thought was to try > > Plot[Evaluate[a /. Sol2[b]], {b, -10, 30}, PlotStyle -> {Red, Blue, > Magenta}] > > This does give the desired result, but gives error messages when it > tries to plot a complex quantity. That is the DeleteCases does not seem > to work within Plot, even though I wrapped everything with evaluate. > > Any suggestions? > > Thanks much > > Brian > >