Check Machin-like formulas: Difference between revisions

== {{heder|GAP}} ==

The formula is entered as a list of pairs [k, x], where each pair means <math>k \mathrm{atan}(x)</math>, and all the terms in the list are summed. Like most other solutions, the program will only check that the tangent of the resulting sum is <math>1</math>. For instance, <code>Check([[5, 1/2], [5, 1/3]]);</code> returns also <code>true</code>, though the result is <math>\frac{5\pi}4</math>.

<lang gap>TanPlus := function(a, b)

return (a + b) / (1 - a * b);

end;

TanTimes := function(n, a)

local x;

x := 0;

while n > 0 do

if IsOddInt(n) then

x := TanPlus(x, a);

fi;

a := TanPlus(a, a);

n := QuoInt(n, 2);

od;

return x;

end;

Check := function(a)

local x, p;

x := 0;

for p in a do

x := TanPlus(x, SignInt(p[1]) * TanTimes(AbsInt(p[1]), p[2]));

od;

return x = 1;

end;

ForAll([

[[1, 1/2], [1, 1/3]],

[[2, 1/3], [1, 1/7]],

[[4, 1/5], [-1, 1/239]],

[[5, 1/7], [2, 3/79]],

[[5, 29/278], [7, 3/79]],

[[1, 1/2], [1, 1/5], [1, 1/8]],

[[5, 1/7], [4, 1/53], [2, 1/4443]],

[[6, 1/8], [2, 1/57], [1, 1/239]],

[[8, 1/10], [-1, 1/239], [-4, 1/515]],

[[12, 1/18], [8, 1/57], [-5, 1/239]],

[[16, 1/21], [3, 1/239], [4, 3/1042]],

[[22, 1/28], [2, 1/443], [-5, 1/1393], [-10, 1/11018]],

[[22, 1/38], [17, 7/601], [10, 7/8149]],

[[44, 1/57], [7, 1/239], [-12, 1/682], [24, 1/12943]],

[[88, 1/172], [51, 1/239], [32, 1/682], [44, 1/5357], [68, 1/12943]]], Check);

Check([[88, 1/172], [51, 1/239], [32, 1/682], [44, 1/5357], [68, 1/12944]]);</lang>