Re: Solve and Reduce
- To: mathgroup at smc.vnet.net
- Subject: [mg52150] Re: [mg52128] Solve and Reduce
- From: DrBob <drbob at bigfoot.com>
- Date: Fri, 12 Nov 2004 02:14:09 -0500 (EST)
- References: <200411100834.DAA10359@smc.vnet.net> <200411110953.EAA28876@smc.vnet.net>
- Reply-to: drbob at bigfoot.com
- Sender: owner-wri-mathgroup at wolfram.com
Possibly this is the function you need: eq = 2500*c^2 - 25*c^3 + 3500*c*q - 320*c^2*q - 1104*c*q^2 - 1152*q^3 == 0; qroot[c_] = Which @@ Cases[Reduce[{eq, c > 0, q > 0}, q], And[a_, Equal[q, c_]] :> Sequence[a, c]] Which[Inequality[0, Less, c, LessEqual, (5*(-109199 + 1497* Sqrt[5489]))/2744], Root[-2500*c^2 + 25*c^3 - 3500*c*#1 + 320*c^2*#1 + 1104*c*#1^2 + 1152*#1^3 & , 3], (5*(-109199 + 1497* Sqrt[5489]))/2744 < c < 100, Root[-2500*c^2 + 25*c^3 - 3500*c*#1 + 320*c^2*#1 + 1104*c*#1^2 + 1152*#1^3 & , 1]] Plot[qroot@c, {c, 0, 100}] Bobby On Thu, 11 Nov 2004 04:53:03 -0500 (EST), Carol Ting <tingyife at msu.edu> wrote: > > Hello list, > > I want to find q as a function of c, q(c), given the following > equation: > > 2500*c^2 - 25*c^3 + 3500*c*q - 320*c^2*q - 1104*c*q^2 - 1152*q^3 == 0 > > However, each of the following three methods gives different results. > I check the Mathematica Book but still cannot figure out why there are > such differences. Could someone please explain this to me? Thanks a > lot! > > (1) Use "Reduce" > > In[5]:= > q1[c_] = Reduce[{2500*c^2 - 25*c^3 +3500*c*q - 320*c^2*q -1104*c*q^2 > -1152*q^3 == 0, c > 0,q > 0}, q] > > Out[5]= > 0<c<=(5*(-109199 + 1497*Sqrt[5489]))/2744] &&q == Root[-2500*c^2 + > 25*c^3 - 3500*c*#1 + 320*c^2*#1 + 1104*c*#1^2 + 1152*#1^3 & ,3] || > (5*(-109199 + 1497*Sqrt[5489]))/2744 < c < 100 && q ==Root[-2500*c^2 + > 25*c^3 -3500*c*#1 + 320*c^2*#1 + 1104*c*#1^2 + 1152*#1^3 & , 1] > > In[6]:= > Plot[Root[-2500*c^2 + 25*c^3 - 3500*c*#1 + 320*c^2*#1 + 1104*c*#1^2 + > 1152*#1^3 & ,1], {c, 0, 100}] > Plot[Root[-2500*c^2 + 25*c^3 - 3500*c*#1 + 320*c^2*#1 + 1104*c*#1^2 + > 1152*#1^3 & ,3], {c, 0, 100}] > > Out[6]= > Graphics[] > > Out[7]= > Graphics[] > > > (2) Use "Solve" and Immediate assignment > > In[32]:= > qdroot1[c_] = q /. Solve[2500*c^2 - 25*c^3 + 3500*c*q - 320*c^2*q - > 1104*c*q^2 - 1152*q^3 == 0,q][[1]] > qdroot3[c_] = q /. Solve[2500*c^2 - 25*c^3 + 3500*c*q - 320*c^2*q - > 1104*c*q^2 - 1152*q^3 == 0,q][[3]] > > In[34]:= > Plot[qiroot1[c], {c, 0, 100}] > > Out[34]= > Graphics[] > > In[35]:= > Plot[qiroot3[c], {c, 0, 100}] > > Out[35]= > Graphics[] > > (3) Use "Solve" and delayed assignment > > In[28]:= > qdroot1[c_] := q /. Solve[2500*c^2 - 25*c^3 + 3500*c*q - 320*c^2*q - > 1104*c*q^2 - 1152*q^3 == 0,q][[1]] > qdroot3[c_] := q /. Solve[2500*c^2 - 25*c^3 + 3500*c*q - 320*c^2*q - > 1104*c*q^2 - 1152*q^3 == 0,q][[3]] > > In[30]:= > Plot[qdroot1[c], {c, 0, 100}] > > Out[30]= > Graphics[] > > In[31]:= > Plot[qdroot3[c], {c, 0, 100}] > > Out[31]= > Graphics[] > > > Carol > > > > -- DrBob at bigfoot.com www.eclecticdreams.net
- References:
- Solve and Reduce
- From: "Carol Ting" <tingyife@msu.edu>
- Solve and Reduce