Re: How to remove curly brackets and arrow symbols from a list.

*To*: mathgroup at smc.vnet.net*Subject*: [mg58223] Re: How to remove curly brackets and arrow symbols from a list.*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>*Date*: Thu, 23 Jun 2005 05:34:03 -0400 (EDT)*Organization*: The Open University, Milton Keynes, England*References*: <d9av83$10a$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

T. K. Ghosh wrote: > Hi Math Guru, > > I will be very happy if you could help me to solve the following problem. > The simplified version of my problem is the following. > I have a quadratic equation with a parameter, say "p". > > Define the function: > f[x_] := A*X^2 + B*X*p + D with A, B and D are given. > "p" is a parameter. > I solve this equation for a given p: > w = Solve[f[x]] == 0, X]. > Now I want to make a Table for the solutions of this > quadratic equation for different values of "p". > So I write, > Table[{p,sol},{p,0,10,1}. > I will get a table which will look like, > 0 {w -> a} {w -> -a} > 1 {w -> b} {w -> -b} > 2 {w -> c} {w -> -c} > and so on......... > > How can I remove the curly brackets and the arrow symbol > from the TableForm? I would like to plot the 1st column > vs. 2nd or 3rd column. I must remove those brackets. > and I wish to get the following form: > 0 a -a > 1 b -b > 2 c -c > > > Hope this can be done easily which I am not aware. > Any suggestion/solution to this problem is most welcome. > Thanking you in advance. > TKG. > Hi, I am not sure that I have fully understood what you wanted; however, I hope that the following lines will help you. First we define the function f and solve the equation for the variable X In[1]:= f[x_] := A*X^2 + B*X*p + D In[2]:= w = Solve[f[x] == 0, X] Out[2]= {{X -> ((-B)*p - Sqrt[-4*A*D + B^2*p^2])/(2*A)}, {X -> ((-B)*p + Sqrt[-4*A*D + B^2*p^2])/(2*A)}} Since we have not defined any values for A, B and D yet, we get symbolic solutions that we use in the next line to compute the table. In[3]:= sol = Table[w, {p, 0, 10}] Out[3]= {{{X -> -(Sqrt[(-A)*D]/A)}, {X -> Sqrt[(-A)*D]/A}}, {{X -> (-B - Sqrt[B^2 - 4*A*D])/(2*A)}, {X -> (-B + Sqrt[B^2 - 4*A*D])/(2*A)}}, {{X -> (-2*B - Sqrt[4*B^2 - 4*A*D])/(2*A)}, {X -> (-2*B + Sqrt[4*B^2 - 4*A*D])/(2*A)}}, {{X -> (-3*B - Sqrt[9*B^2 - 4*A*D])/(2*A)}, {X -> (-3*B + Sqrt[9*B^2 - 4*A*D])/(2*A)}}, {{X -> (-4*B - Sqrt[16*B^2 - 4*A*D])/(2*A)}, {X -> (-4*B + Sqrt[16*B^2 - 4*A*D])/(2*A)}}, {{X -> (-5*B - Sqrt[25*B^2 - 4*A*D])/(2*A)}, {X -> (-5*B + Sqrt[25*B^2 - 4*A*D])/(2*A)}}, {{X -> (-6*B - Sqrt[36*B^2 - 4*A*D])/(2*A)}, {X -> (-6*B + Sqrt[36*B^2 - 4*A*D])/(2*A)}}, {{X -> (-7*B - Sqrt[49*B^2 - 4*A*D])/(2*A)}, {X -> (-7*B + Sqrt[49*B^2 - 4*A*D])/(2*A)}}, {{X -> (-8*B - Sqrt[64*B^2 - 4*A*D])/(2*A)}, {X -> (-8*B + Sqrt[64*B^2 - 4*A*D])/(2*A)}}, {{X -> (-9*B - Sqrt[81*B^2 - 4*A*D])/(2*A)}, {X -> (-9*B + Sqrt[81*B^2 - 4*A*D])/(2*A)}}, {{X -> (-10*B - Sqrt[100*B^2 - 4*A*D])/(2*A)}, {X -> (-10*B + Sqrt[100*B^2 - 4*A*D])/(2*A)}}} Say that the values of A, B and D are 2, 3 and 5, respectively. In[4]:= sol = sol /. {A -> 2, B -> 3, D -> 5} Out[4]= {{{X -> (-I)*Sqrt[5/2]}, {X -> I*Sqrt[5/2]}}, {{X -> (1/4)*(-3 - I*Sqrt[31])}, {X -> (1/4)*(-3 + I*Sqrt[31])}}, {{X -> -(3/2) - I/2}, {X -> -(3/2) + I/2}}, {{X -> (1/4)*(-9 - Sqrt[41])}, {X -> (1/4)*(-9 + Sqrt[41])}}, {{X -> (1/4)*(-12 - 2*Sqrt[26])}, {X -> (1/4)*(-12 + 2*Sqrt[26])}}, {{X -> (1/4)*(-15 - Sqrt[185])}, {X -> (1/4)*(-15 + Sqrt[185])}}, {{X -> (1/4)*(-18 - 2*Sqrt[71])}, {X -> (1/4)*(-18 + 2*Sqrt[71])}}, {{X -> (1/4)*(-21 - Sqrt[401])}, {X -> (1/4)*(-21 + Sqrt[401])}}, {{X -> (1/4)*(-24 - 2*Sqrt[134])}, {X -> (1/4)*(-24 + 2*Sqrt[134])}}, {{X -> (1/4)*(-27 - Sqrt[689])}, {X -> (1/4)*(-27 + Sqrt[689])}}, {{X -> (1/4)*(-30 - 2*Sqrt[215])}, {X -> (1/4)*(-30 + 2*Sqrt[215])}}} Now we have numerical solutions expressed as _replacement rules_. To get an array of numbers only, we use these rules to replace X by its values in sol. In[5]:= sol = X /. sol Out[5]= {{(-I)*Sqrt[5/2], I*Sqrt[5/2]}, {(1/4)*(-3 - I*Sqrt[31]), (1/4)*(-3 + I*Sqrt[31])}, {-(3/2) - I/2, -(3/2) + I/2}, {(1/4)*(-9 - Sqrt[41]), (1/4)*(-9 + Sqrt[41])}, {(1/4)*(-12 - 2*Sqrt[26]), (1/4)*(-12 + 2*Sqrt[26])}, {(1/4)*(-15 - Sqrt[185]), (1/4)*(-15 + Sqrt[185])}, {(1/4)*(-18 - 2*Sqrt[71]), (1/4)*(-18 + 2*Sqrt[71])}, {(1/4)*(-21 - Sqrt[401]), (1/4)*(-21 + Sqrt[401])}, {(1/4)*(-24 - 2*Sqrt[134]), (1/4)*(-24 + 2*Sqrt[134])}, {(1/4)*(-27 - Sqrt[689]), (1/4)*(-27 + Sqrt[689])}, {(1/4)*(-30 - 2*Sqrt[215]), (1/4)*(-30 + 2*Sqrt[215])}} Then we transpose the matrix sol to plot easily one or the other column. In[6]:= sol = Transpose[sol] Out[6]= {{(-I)*Sqrt[5/2], (1/4)*(-3 - I*Sqrt[31]), -(3/2) - I/2, (1/4)*(-9 - Sqrt[41]), (1/4)*(-12 - 2*Sqrt[26]), (1/4)*(-15 - Sqrt[185]), (1/4)*(-18 - 2*Sqrt[71]), (1/4)*(-21 - Sqrt[401]), (1/4)*(-24 - 2*Sqrt[134]), (1/4)*(-27 - Sqrt[689]), (1/4)*(-30 - 2*Sqrt[215])}, {I*Sqrt[5/2], (1/4)*(-3 + I*Sqrt[31]), -(3/2) + I/2, (1/4)*(-9 + Sqrt[41]), (1/4)*(-12 + 2*Sqrt[26]), (1/4)*(-15 + Sqrt[185]), (1/4)*(-18 + 2*Sqrt[71]), (1/4)*(-21 + Sqrt[401]), (1/4)*(-24 + 2*Sqrt[134]), (1/4)*(-27 + Sqrt[689]), (1/4)*(-30 + 2*Sqrt[215])}} Line 7 plots the first column with an index for the x-axes starting from 1 (so ranging from 1 to 11 in our case). Line 8 plots the same thing but with a range from 0 to 10 on the x-axes. In[7]:= ListPlot[sol[[1]]]; In[8]:= ListPlot[Transpose[{Range[0, 10], sol[[1]]}]]; Finally, we construct a nice table with 3 columns. In[9]:= TableForm[Transpose[{Range[0, 10], sol[[1]], sol[[2]]}]] Out[9]//TableForm= TableForm[{{0, (-I)*Sqrt[5/2], I*Sqrt[5/2]}, {1, (1/4)*(-3 - I*Sqrt[31]), (1/4)*(-3 + I*Sqrt[31])}, {2, -(3/2) - I/2, -(3/2) + I/2}, {3, (1/4)*(-9 - Sqrt[41]), (1/4)*(-9 + Sqrt[41])}, {4, (1/4)*(-12 - 2*Sqrt[26]), (1/4)*(-12 + 2*Sqrt[26])}, {5, (1/4)*(-15 - Sqrt[185]), (1/4)*(-15 + Sqrt[185])}, {6, (1/4)*(-18 - 2*Sqrt[71]), (1/4)*(-18 + 2*Sqrt[71])}, {7, (1/4)*(-21 - Sqrt[401]), (1/4)*(-21 + Sqrt[401])}, {8, (1/4)*(-24 - 2*Sqrt[134]), (1/4)*(-24 + 2*Sqrt[134])}, {9, (1/4)*(-27 - Sqrt[689]), (1/4)*(-27 + Sqrt[689])}, {10, (1/4)*(-30 - 2*Sqrt[215]), (1/4)*(-30 + 2*Sqrt[215])}}] Best regards, /J.M.