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I am very new to Mathematica. I have this code of Bisection Method for finding a root of a polynomial.

Bisection[a0_, b0_, e0_, n_] := Module[{},
       a = N[a0];
       b = N[b0];
       e = N[e0];
       i = 0;
       f[x_] := x^2 - x - 12;
       Output = {{i, a, b, }};
       While[i < n,
        c = (a + b)/2;
         Output = Append[Output, {i + 1, a, b, c}];
        If[Sign[f[b]] == Sign[f[c]], b = c, a = c];
        If[(b - a)/2 < e, Print["Condition Exists at ", i + 1, " . "]; 
         Break[] ];
        i = i + 1;
        ];
       Print[NumberForm[TableForm[Output,
          TableHeadings -> {None, {"i", "a{i}", "b{i}", "c{i}"}}], 16]];
       Print["Root p = ", NumberForm[c, 16] ];
       Print[f[x]] ;
       Plot[f[x], {x, -4, 5}]
       ]

Bisection[-4, 2, 10^-5, 10]

It works fine for an example then if I want to use it for other example I have to change the code or copy it for other examples. How can I modify this code so that it takes an equation as an input and I can just used the command (or something like this)

Bisection[x^2 - x - 12,-4, 2, 10^-5, 10]
Bisection[x^3 + x,-4, 2, 10^-5, 10]

which should work for any equation.

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  • $\begingroup$ Remove the f[x_]... line and pass f in as an argument like Bisection[f_, a0_, b0_, e0_, n_] := Module[{}, ... . You can then define poly = Function[{x}, x^3 -x^2 + .... ] or whatever outside and pass in poly. $\endgroup$
    – flinty
    Apr 30, 2023 at 7:19
  • $\begingroup$ I tried that, doesn’t work. $\endgroup$
    – Learner
    Apr 30, 2023 at 7:24
  • $\begingroup$ 'doesn't work' how? $\endgroup$
    – flinty
    Apr 30, 2023 at 7:26
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    $\begingroup$ It should work. Sounds like you didn't define poly as a function poly[x_]:= or using Function as a I described or you have not cleared the old definition. $\endgroup$
    – flinty
    Apr 30, 2023 at 7:30
  • 1
    $\begingroup$ You don't need the extra function call if you're going to define poly that way. poly[u_]:=u^3-u-12 is enough. $\endgroup$
    – flinty
    Apr 30, 2023 at 9:31

1 Answer 1

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Here is you changed code that should work:

poly[x_] = x^2 - x - 12;
Bisection[f_, a0_, b0_, e0_, n_] := Module[{}, a = N[a0];
   b = N[b0];
   e = N[e0];
   i = 0;
   Output = {{i, a, b}};
   While[i < n, c = (a + b)/2;
    Output = Append[Output, {i + 1, a, b, c}];
    If[Sign[f[b]] == Sign[f[c]], b = c, a = c];
    If[(b - a)/2 < e, Print["Condition Exists at ", i + 1, " . "];
     Break[]];
    i = i + 1;];
   Print[
    NumberForm[
     TableForm[Output, 
      TableHeadings -> {None, {"i", "a{i}", "b{i}", "c{i}"}}], 16]];
   Print["Root p = ", NumberForm[c, 16]];
   Print[f[x]];
   Plot[f[x], {x, -4, 5}]];

Now, e.g. for your first polynomial:

Bisection[poly, -4, 2, 10^-5, 10]

enter image description here

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  • $\begingroup$ Thanks its working now. $\endgroup$
    – Learner
    Apr 30, 2023 at 8:21
  • $\begingroup$ is there anything else that can be changed in the code so that it works better or faster? $\endgroup$
    – Learner
    Apr 30, 2023 at 8:21
  • $\begingroup$ You could replace "Append" by "Reap" and "Sow" $\endgroup$ Apr 30, 2023 at 9:43

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