Mathematica Looping Help: Find 'v' for 10 Different Values of 't

[suraj goyal]

pl help
Here I have written a mathematica code. It is a small example of my actual problem. In this code, 't' is an arbitrary constant which is being fixed at the top of the programme by assigning a value. All the other variables 'a','b','c' depend upon 't' . and 'h1','h2' are the roots of quadratic equation with coefficients a,b,c.
Further, 'f' is a function in an unknown variable 'p' and involves 'h1' and 'h2'.. We can determine 'p' by solving f(p)=0, giving two roots. Finally I calculated 'v' from the from assigned 't' and calculated second root of equation f(p)=0.
Thus 'v' depends upon 't' both explicitly and implicitly.. With change in 't', "v" will change. I want to draw a graph between 't' and 'v'.. For this I need looping or some other command to assign different values to 't' at the top of the programme.. Me unable to do that.. Pl if possible , help me in this regard
t := 3
a := t^2
b := (t + 1)*I
c := t^2 + 2*t*I + 1
h1 = (-b + Sqrt[b^2 - 4*a*c])/(2*a)
h2 = (-b - Sqrt[b^2 - 4*a*c])/(2*a)
a11 := Sqrt[p]*h1
a12 := h1*2
a21 := 3*h2^2
a22 := 4 + p
f[p_] = a11*a22 - a21*a12
h = sols = NSolve[f[p] == 0, p]
d = p /. sols[[2]]
v = t/Re[d]
Suppose I want to calculate my final answer for ten values of 't' (say 1,2,3...10) and finally to plot a graph between the final values of 'v' and the ten assigned values for 't'. I have tried a lot in this regard and have defined a function, used array and table commands too.. But unable to pick those ten values by my for loop command and to draw graph...

 

[Dale]

You should not set t at the beginning. It seems that t is the argument to a function, so you should express everything in terms of functions of t:

a[t_] := t^2
b[t_] := (t + 1)*I
c[t_] := t^2 + 2*t*I + 1
h1[t_] := (-b[t] + Sqrt[b[t]^2 - 4*a[t]*c[t]])/(2*a[t])
...

 

[suraj goyal]

Now I have tried the following

For[t = 1, t < 100, t = t + 10,
a = t^2;
b = (t + 1)*I;
c = t^2 + 2*t*I + 1;
h1 = (-b + Sqrt[b^2 - 4*a*c])/(2*a);
h2 = (-b - Sqrt[b^2 - 4*a*c])/(2*a);
a11 = Sqrt[p]*h1;
a12 = h1*2;
a21 = 3*h2^2;
a22 = 4 + p;
S = {{a11, a22}, {a21, a22}};
f[p_] = Det;
h = sols = NSolve[f[p] == 0, p];
d = p /. sols[[2]];
v = t/Re[d] ;
data = {{v, t}} // TableForm;
Print[data];
]
The output is
{{2.41743, 1}}
{{-2.75, 11}}
{{-5.25, 21}}
{{-7.75, 31}}
{{-10.25, 41}}
{{-12.75, 51}}
{{-15.25, 61}}
{{-17.75, 71}}
{{-20.25, 81}}
{{-22.75, 91}}
But problem is to plot.. In plotting command, it willl take the final value i.e. -22.75 and 91.. So still having the problem.. Want to plot a graph between 't' and 'v...'Pl help

 

[Dale]

Don't do it that way. Make everything into functions of t. Avoid explicit looping structures in interpreted languages whenever possible.

The reason you are unable to plot the data is because you never set anything equal to the data, you simply printed it. Printing it displays it but does not store it in a variable.

Instead of using For you should use Table to actually build up a table of values.

 

[alphy]

Thank you for sharing your Mathematica code and explaining your problem. It seems like you are trying to plot a graph of 'v' against different values of 't'. To do this, you can use a for loop to iterate through the ten different values of 't' and calculate the corresponding 'v' for each value. Here is an example code:

tValues = Range[1, 10]; (*assigning ten values to t*)
vValues = {}; (*creating an empty list to store v values*)

For[t = 1, t <= 10, t++, (*for loop to iterate through t values*)
a = t^2;
b = (t + 1)*I;
c = t^2 + 2*t*I + 1;
h1 = (-b + Sqrt[b^2 - 4*a*c])/(2*a);
h2 = (-b - Sqrt[b^2 - 4*a*c])/(2*a);
a11 = Sqrt[p]*h1;
a12 = h1*2;
a21 = 3*h2^2;
a22 = 4 + p;
f[p_] = a11*a22 - a21*a12;
h = sols = NSolve[f[p] == 0, p];
d = p /. sols[[2]];
v = t/Re[d];
AppendTo[vValues, v]; (*adding calculated v value to the list*)
]

ListPlot[Transpose[{tValues, vValues}], PlotStyle -> PointSize[Large],
AxesLabel -> {"t", "v"}] (*plotting the values as a scatter plot*)

I hope this helps you in plotting your desired graph. If you face any further difficulties, please do not hesitate to ask for help. Good luck with your research!