Roots of a function: Difference between revisions

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=={{header|Lua}}==

<lang Lua>~~function~~ ~~f (x) return x^3 -~~ ~~3*x^2~~ + ~~2*x~~ ~~end~~

<lang Lua>-- Function to have roots found

function f (x) return x^3 - 3*x^2 + 2*x end

-- Finds roots of f within range x=[start, stop] or approximations thereof

function root (f, start, stop, step)

local roots, x, sign, foundExact, value = {}, start, f(start) > 0, false

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table.insert(roots, {val = x, err = 0})

foundExact = true

~~elseif value > 0 ~= sign then~~

end

if value > 0 ~= sign then

if foundExact then

foundExact = false

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end

-- Main procedure

print("Root (to 12DP)\tMax. Error\n")

for _, r in pairs(root(f, -1, 3, 10^-6)) do

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2.000000999934 1e-06</pre>

Note that the roots found are all near misses because fractional numbers that seem nice and 'round' in decimal (such as 10^-6) often have some rounding error when represented in binary. To increase the chances of finding exact integer roots, try using an integer start value with a step value that is a power of two.