restart; First the Golden ratio program. evalf(.5*(1+sqrt(5)));

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Golden:=proc(N) Phi:=2: for j from 1 to N-2 do Phi:=evalf(1+1/Phi): end do: end:

Warning, `Phi` is implicitly declared local to procedure `Golden`

Warning, `j` is implicitly declared local to procedure `Golden`

Golden(3);

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Golden(4);

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Golden(10);

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Golden(11);

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Golden(12);

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Now the quadratic formula program. quadro:=proc(a,b,c): if (a=0) then if (b=0) then print(`Constant function: no roots.`): else x := -c/b: print(`Linear function: one root at `, x): end if: else disc := b^2-4*a*c: if (disc<0) then print(`Negative discriminant: no real roots.`): else if (disc=0) then x := -b/(2*a): print(`Zero discriminant: one repeated root at `, x): else sqd := sqrt(disc): if (b<0) then x1 := (-b+sqd)/(2*a): x2 := (-2*c)/(b-sqd): else if (b>0) then x1 := (-b-sqd)/(2*a): x2 := (-2*c)/(b+sqd): else x1 := sqrt(-c/a): x2 := -x1: end if: end if: print(`Two real roots at`, x1, ` and `, x2): end if: end if: end if: end:

Warning, `x` is implicitly declared local to procedure `quadro`

Warning, `disc` is implicitly declared local to procedure `quadro`

Warning, `sqd` is implicitly declared local to procedure `quadro`

Warning, `x1` is implicitly declared local to procedure `quadro`

Warning, `x2` is implicitly declared local to procedure `quadro`

quadro(1,2,1);

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quadro(1,2,2);

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Test that it works for four digits. Digits:=4;

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fsolve(2.1*x^2-42.6*x+1.0=0,x);

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quadro(2.1,-42.6,1.0);

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fsolve(2.0*x^2+55*x-1.0=0,x);

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quadro(2.0,55,-1.0);

NiZJMlR3b35yZWFsfnJvb3RzfmF0RzYiJCElX0YhIiNJJn5hbmR+R0YkJCIlPD0hIiY=