restart;

Mit der Eingabe des Intervals werden mit Hilfe des Intervallschachtelung die Nullstellen berechnet.DAS VERFAHREN KANN NUR REELLE NULLSTELLEN FINDEN

bisect := proc(a,b,TOL,N,f) local aa,bb,p,i; Digits := 50; aa := a; bb := b; p := (a+b)/2; i := 0; print(evalf(aa),evalf(bb),evalf(p),evalf(f(p))); while(evalf(abs(f(p)))>TOL and i<=N) do i := i+1; if(evalf(f(aa)*f(p))<0)then bb := p; else aa := p; end if; p := (aa+bb)/2; printf("i = %d a = %12.10f b = %12.10f p = %12.10f f(p) := %12.10f\n",i,evalf(aa),evalf(bb),evalf(p),evalf(f(p))); end do; print(p); print(evalf(p)); end proc:

f := (x) -> x^3+4*x^2-10;

NiM+SSJmRzYiZio2I0kieEdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCgqJDkkIiIkIiIiKiRGLiIiIyIiJSEjNUYwRiVGJUYl

bisect(1,2,0.0005,20,f);

NiYkIiIiIiIhJCIiI0YlJCJTKysrKysrKysrKysrKysrKysrKysrKysrOiEjXCQiUysrKysrKysrKysrKysrKysrKysrKysrdkJGKg==i = 1 a = 1.0000000000 b = 1.5000000000 p = 1.2500000000 f(p) := -1.7968750000 i = 2 a = 1.2500000000 b = 1.5000000000 p = 1.3750000000 f(p) := 0.1621093750 i = 3 a = 1.2500000000 b = 1.3750000000 p = 1.3125000000 f(p) := -0.8483886719 i = 4 a = 1.3125000000 b = 1.3750000000 p = 1.3437500000 f(p) := -0.3509826660 i = 5 a = 1.3437500000 b = 1.3750000000 p = 1.3593750000 f(p) := -0.0964088440 i = 6 a = 1.3593750000 b = 1.3750000000 p = 1.3671875000 f(p) := 0.0323557854 i = 7 a = 1.3593750000 b = 1.3671875000 p = 1.3632812500 f(p) := -0.0321499705 i = 8 a = 1.3632812500 b = 1.3671875000 p = 1.3652343750 f(p) := 0.0000720248 NiMjIiQqcCIkNyY=NiMkIlMrKysrKysrKysrKysrKysrKysrK3ZWQmw4ISNc

Digits:=10;

NiM+SSdEaWdpdHNHNiIiIzU=

g1 := (x) -> x**4-5*x**3+5*x**2+5*x-6;

NiM+SSNnMUc2ImYqNiNJInhHRiVGJTYkSSlvcGVyYXRvckdGJUkmYXJyb3dHRiVGJSwsKiQ5JCIiJSIiIiokRi4iIiQhIiYqJEYuIiIjIiImRi5GNiEiJ0YwRiVGJUYl

plot(g1(x),x=-5..5,y=-10..5);

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

bisect(-2,0,10**(-8),20,g1);

NiYkISIjIiIhJEYlRiUkISIiRiVGJg==NiMhIiI=NiMkISIiIiIh

bisect(0,1.5,10**(-8),40,g1);

NiYkIiIhRiQkIiM6ISIiJCJTKysrKysrKysrKysrKysrKysrKysrKysrdiEjXSQhUysrKysrKysrKysrKysrKysrKysrXShvL0IiISNci = 1 a = 0.7500000000 b = 1.5000000000 p = 1.1250000000 f(p) := 0.4357910156 i = 2 a = 0.7500000000 b = 1.1250000000 p = 0.9375000000 f(p) := -0.2653656006 i = 3 a = 0.9375000000 b = 1.1250000000 p = 1.0312500000 f(p) := 0.1210641861 i = 4 a = 0.9375000000 b = 1.0312500000 p = 0.9843750000 f(p) := -0.0634726882 i = 5 a = 0.9843750000 b = 1.0312500000 p = 1.0078125000 f(p) := 0.0310053863 i = 6 a = 0.9843750000 b = 1.0078125000 p = 0.9960937500 f(p) := -0.0156859753 i = 7 a = 0.9960937500 b = 1.0078125000 p = 1.0019531250 f(p) := 0.0077972338 i = 8 a = 0.9960937500 b = 1.0019531250 p = 0.9990234375 f(p) := -0.0039100638 i = 9 a = 0.9990234375 b = 1.0019531250 p = 1.0004882812 f(p) := 0.0019521712 i = 10 a = 0.9990234375 b = 1.0004882812 p = 0.9997558594 f(p) := -0.0009768009 i = 11 a = 0.9997558594 b = 1.0004882812 p = 1.0001220703 f(p) := 0.0004882216 i = 12 a = 0.9997558594 b = 1.0001220703 p = 0.9999389648 f(p) := -0.0002441555 i = 13 a = 0.9999389648 b = 1.0001220703 p = 1.0000305176 f(p) := 0.0001220666 i = 14 a = 0.9999389648 b = 1.0000305176 p = 0.9999847412 f(p) := -0.0000610361 i = 15 a = 0.9999847412 b = 1.0000305176 p = 1.0000076294 f(p) := 0.0000305173 i = 16 a = 0.9999847412 b = 1.0000076294 p = 0.9999961853 f(p) := -0.0000152588 i = 17 a = 0.9999961853 b = 1.0000076294 p = 1.0000019073 f(p) := 0.0000076294 i = 18 a = 0.9999961853 b = 1.0000019073 p = 0.9999990463 f(p) := -0.0000038147 i = 19 a = 0.9999990463 b = 1.0000019073 p = 1.0000004768 f(p) := 0.0000019073 i = 20 a = 0.9999990463 b = 1.0000004768 p = 0.9999997616 f(p) := -0.0000009537 i = 21 a = 0.9999997616 b = 1.0000004768 p = 1.0000001192 f(p) := 0.0000004768 i = 22 a = 0.9999997616 b = 1.0000001192 p = 0.9999999404 f(p) := -0.0000002384 i = 23 a = 0.9999999404 b = 1.0000001192 p = 1.0000000298 f(p) := 0.0000001192 i = 24 a = 0.9999999404 b = 1.0000000298 p = 0.9999999851 f(p) := -0.0000000596 i = 25 a = 0.9999999851 b = 1.0000000298 p = 1.0000000074 f(p) := 0.0000000298 i = 26 a = 0.9999999851 b = 1.0000000074 p = 0.9999999963 f(p) := -0.0000000149 i = 27 a = 0.9999999963 b = 1.0000000074 p = 1.0000000019 f(p) := 0.0000000074 NiMkIlMrKysrKysrKysrREpxJjRCXF5raT0rKysrIiEjXA==NiMkIlMrKysrKysrKysrREpxJjRCXF5raT0rKysrIiEjXA==

bisect(1.5,2.5,10**(-8),40,g1);

NiYkIiM6ISIiJCIjREYlJCJTKysrKysrKysrKysrKysrKysrKysrKysrPyEjXCQiIiFGLA==NiMkIlMrKysrKysrKysrKysrKysrKysrKysrKys/ISNcNiMkIlMrKysrKysrKysrKysrKysrKysrKysrKys/ISNc

bisect(2.5,4,10**(-8),40,g1);

NiYkIiNEISIiJCIiJSIiISQiUysrKysrKysrKysrKysrKysrKysrKysrXUshI1wkIlIrKysrKysrKysrKysrKysrKysrK0QiRykpSCEjWw==i = 1 a = 2.5000000000 b = 3.2500000000 p = 2.8750000000 f(p) := -0.7946777344 i = 2 a = 2.8750000000 b = 3.2500000000 p = 3.0625000000 f(p) := 0.5564117432 i = 3 a = 2.8750000000 b = 3.0625000000 p = 2.9687500000 f(p) := -0.2365407944 i = 4 a = 2.9687500000 b = 3.0625000000 p = 3.0156250000 f(p) := 0.1284447312 i = 5 a = 2.9687500000 b = 3.0156250000 p = 2.9921875000 f(p) := -0.0616488419 i = 6 a = 2.9921875000 b = 3.0156250000 p = 3.0039062500 f(p) := 0.0314640405 i = 7 a = 2.9921875000 b = 3.0039062500 p = 2.9980468750 f(p) := -0.0155716464 i = 8 a = 2.9980468750 b = 3.0039062500 p = 3.0009765625 f(p) := 0.0078258580 i = 9 a = 2.9980468750 b = 3.0009765625 p = 2.9995117188 f(p) := -0.0039029130 i = 10 a = 2.9995117188 b = 3.0009765625 p = 3.0002441406 f(p) := 0.0019539596 i = 11 a = 2.9995117188 b = 3.0002441406 p = 2.9998779297 f(p) := -0.0009763539 i = 12 a = 2.9998779297 b = 3.0002441406 p = 3.0000610352 f(p) := 0.0004883334 i = 13 a = 2.9998779297 b = 3.0000610352 p = 2.9999694824 f(p) := -0.0002441276 i = 14 a = 2.9999694824 b = 3.0000610352 p = 3.0000152588 f(p) := 0.0001220736 i = 15 a = 2.9999694824 b = 3.0000152588 p = 2.9999923706 f(p) := -0.0000610343 i = 16 a = 2.9999923706 b = 3.0000152588 p = 3.0000038147 f(p) := 0.0000305178 i = 17 a = 2.9999923706 b = 3.0000038147 p = 2.9999980927 f(p) := -0.0000152587 i = 18 a = 2.9999980927 b = 3.0000038147 p = 3.0000009537 f(p) := 0.0000076294 i = 19 a = 2.9999980927 b = 3.0000009537 p = 2.9999995232 f(p) := -0.0000038147 i = 20 a = 2.9999995232 b = 3.0000009537 p = 3.0000002384 f(p) := 0.0000019073 i = 21 a = 2.9999995232 b = 3.0000002384 p = 2.9999998808 f(p) := -0.0000009537 i = 22 a = 2.9999998808 b = 3.0000002384 p = 3.0000000596 f(p) := 0.0000004768 i = 23 a = 2.9999998808 b = 3.0000000596 p = 2.9999999702 f(p) := -0.0000002384 i = 24 a = 2.9999999702 b = 3.0000000596 p = 3.0000000149 f(p) := 0.0000001192 i = 25 a = 2.9999999702 b = 3.0000000149 p = 2.9999999925 f(p) := -0.0000000596 i = 26 a = 2.9999999925 b = 3.0000000149 p = 3.0000000037 f(p) := 0.0000000298 i = 27 a = 2.9999999925 b = 3.0000000037 p = 2.9999999981 f(p) := -0.0000000149 i = 28 a = 2.9999999981 b = 3.0000000037 p = 3.0000000009 f(p) := 0.0000000074 NiMkIlMrKysrKysrKytdaTomeWFodURLSjQrKysrJCEjXA==NiMkIlMrKysrKysrKytdaTomeWFodURLSjQrKysrJCEjXA==

solve(g1(x)=0,x);

NiYhIiIiIiIiIiMiIiQ=

g2 := x -> exp(x)-x**2+3*x-2;

NiM+SSNnMkc2ImYqNiNJInhHRiVGJTYkSSlvcGVyYXRvckdGJUkmYXJyb3dHRiVGJSwqLUkkZXhwR0YlNiM5JCIiIiokRjAiIiMhIiJGMCIiJCEiI0YxRiVGJUYl

plot(g2(x),x=-10..10,y=-5..5);

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

bisect(0,1,10**(-8),40,g2);

NiYkIiIhRiQkIiIiRiQkIlMrKysrKysrKysrKysrKysrKysrKysrKytdISNdJCJTNTUyNXdQbHJOOzl5eV0nW285RyxxcTdzKSopRik=i = 1 a = 0.0000000000 b = 0.5000000000 p = 0.2500000000 f(p) := -0.0284745833 i = 2 a = 0.2500000000 b = 0.5000000000 p = 0.3750000000 f(p) := 0.4393664146 i = 3 a = 0.2500000000 b = 0.3750000000 p = 0.3125000000 f(p) := 0.2066816912 i = 4 a = 0.2500000000 b = 0.3125000000 p = 0.2812500000 f(p) := 0.0894331962 i = 5 a = 0.2500000000 b = 0.2812500000 p = 0.2656250000 f(p) := 0.0305642341 i = 6 a = 0.2500000000 b = 0.2656250000 p = 0.2578125000 f(p) := 0.0010663677 i = 7 a = 0.2500000000 b = 0.2578125000 p = 0.2539062500 f(p) := -0.0136986837 i = 8 a = 0.2539062500 b = 0.2578125000 p = 0.2558593750 f(p) := -0.0063148068 i = 9 a = 0.2558593750 b = 0.2578125000 p = 0.2568359375 f(p) := -0.0026238823 i = 10 a = 0.2568359375 b = 0.2578125000 p = 0.2573242188 f(p) := -0.0007786731 i = 11 a = 0.2573242188 b = 0.2578125000 p = 0.2575683594 f(p) := 0.0001438683 i = 12 a = 0.2573242188 b = 0.2575683594 p = 0.2574462891 f(p) := -0.0003173971

i = 13 a = 0.2574462891 b = 0.2575683594 p = 0.2575073242 f(p) := -0.0000867631 i = 14 a = 0.2575073242 b = 0.2575683594 p = 0.2575378418 f(p) := 0.0000285530 i = 15 a = 0.2575073242 b = 0.2575378418 p = 0.2575225830 f(p) := -0.0000291050 i = 16 a = 0.2575225830 b = 0.2575378418 p = 0.2575302124 f(p) := -0.0000002760 i = 17 a = 0.2575302124 b = 0.2575378418 p = 0.2575340271 f(p) := 0.0000141385 i = 18 a = 0.2575302124 b = 0.2575340271 p = 0.2575321198 f(p) := 0.0000069313 i = 19 a = 0.2575302124 b = 0.2575321198 p = 0.2575311661 f(p) := 0.0000033276 i = 20 a = 0.2575302124 b = 0.2575311661 p = 0.2575306892 f(p) := 0.0000015258 i = 21 a = 0.2575302124 b = 0.2575306892 p = 0.2575304508 f(p) := 0.0000006249 i = 22 a = 0.2575302124 b = 0.2575304508 p = 0.2575303316 f(p) := 0.0000001745 i = 23 a = 0.2575302124 b = 0.2575303316 p = 0.2575302720 f(p) := -0.0000000508 i = 24 a = 0.2575302720 b = 0.2575303316 p = 0.2575303018 f(p) := 0.0000000619 i = 25 a = 0.2575302720 b = 0.2575303018 p = 0.2575302869 f(p) := 0.0000000055 NiMjIilsREc8IilrKTNyJw==NiMkIlMrKysrKysrKysrKytEIkdRIz4oXCIzcEdJdkQhI10=

fsolve(g2(x)=0,x);

NiMkIithR0l2RCEjNQ==

restart;

Mit der Eingabe eines Startwertes werden mit Hilfe des Newton-Verfahrens die Nullstellen berechnet. DAS VERFAHREN KANN NUR REELLE NULLSTELLEN FINDEN

newton := proc(p0,TOL,N,f) local converging,fprime,i,pold,p; Digits := 50; fprime := (x) -> D(f)(x); converging := true; i := 0; pold := p0; while converging do i := i+1; p := pold-f(pold)/fprime(pold); printf("i = %d p = %12.10f f(p) := %12.10f\n",i,p,f(p)); pold := p; converging := evalf(abs(f(p)))>TOL and i<N; end do; print(pold); print(evalf(pold)); end proc:

f:=(x)->x**3+4*x**2-10;

NiM+SSJmRzYiZio2I0kieEdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCgqJDkkIiIkIiIiKiRGLiIiIyIiJSEjNUYwRiVGJUYl

newton(1,10**(-5),20,f);

i = 1 p = 1.4545454545 f(p) := 1.5401953418 i = 2 p = 1.3689004011 f(p) := 0.0607196886 i = 3 p = 1.3652366002 f(p) := 0.0001087706 i = 4 p = 1.3652300134 f(p) := 0.0000000004 NiMjIkdoIj5LL1onSCJIYkFBeWFNKT1IPiUqIkdjZVI3RCopXEgweU9eRkZGdlQqKm8=NiMkIlNuaThBRjAoRydRUVJ1bnhiKDRtT05NLElfTyIhI1w=

g1 := (x) -> 2 + cos(exp(x)-2)-exp(x);

NiM+SSNnMUc2ImYqNiNJInhHRiVGJTYkSSlvcGVyYXRvckdGJUkmYXJyb3dHRiVGJSwoIiIjIiIiLUkkY29zR0YlNiMsJi1JJGV4cEdGJTYjOSRGLiEiI0YuRi5GMyEiIkYlRiVGJQ==

plot(g1(x),x=0.5..1.5);

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

newton(0.5,10**(-10),30,g1);

i = 1 p = 1.6930961157 f(p) := -4.3931772870 i = 2 p = 0.5541812360 f(p) := 1.2260070011 i = 3 p = 1.5016880067 f(p) := -3.2839308758 i = 4 p = 1.0464985875 f(p) := -0.1859255651 i = 5 p = 1.0091840503 f(p) := -0.0071639902 i = 6 p = 1.0076266534 f(p) := -0.0000122934 i = 7 p = 1.0076239717 f(p) := -0.0000000000 NiMkIlM4N0B1YV0kPSJcJUg6Ulk0RWo9M207KFJpMjUhI1w=NiMkIlM4N0B1YV0kPSJcJUg6Ulk0RWo9M207KFJpMjUhI1w=

fsolve(g1(x)=0,x);

NiMkIitzUmkyNSEiKg==

g2 := (x) -> x*cos(x)-2*x**2+3*x-1;

NiM+SSNnMkc2ImYqNiNJInhHRiVGJTYkSSlvcGVyYXRvckdGJUkmYXJyb3dHRiVGJSwqKiY5JCIiIi1JJGNvc0c2JEkqcHJvdGVjdGVkR0YzSShfc3lzbGliR0YlNiNGLkYvRi8qJEYuIiIjISIjRi4iIiQhIiJGL0YlRiVGJQ==

plot(g2(x),x=0.2..0.3);

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

plot(g2(x),x=1.2..1.3);

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

newton(0.2,10**(-10),20,g2);

i = 1 p = 0.2904320371 f(p) := -0.0191366106 i = 2 p = 0.2974851310 f(p) := -0.0001208223 i = 3 p = 0.2975302318 f(p) := -0.0000000050 i = 4 p = 0.2975302337 f(p) := -0.0000000000 NiMkIlNjOl5Kak1wcjpqIUh2cFMqUm9Ra3JPQkl2SCEjXQ==NiMkIlNjOl5Kak1wcjpqIUh2cFMqUm9Ra3JPQkl2SCEjXQ==

newton(1.2,10**(-10),5,g2);

i = 1 p = 1.2605727329 f(p) := -0.0115520206 i = 2 p = 1.2566400219 f(p) := -0.0000486390 i = 3 p = 1.2566233228 f(p) := -0.0000000009 i = 4 p = 1.2566233225 f(p) := -0.0000000000 NiMkIlMnKmVXJEdcVVR3JzM+XWVuIlJCKm9iXUFMaWM3ISNcNiMkIlMnKmVXJEdcVVR3JzM+XWVuIlJCKm9iXUFMaWM3ISNc

fsolve(g2(x)=0,x=0..1);

NiMkIitQQkl2SCEjNQ==

fsolve(g2(x)=0,x=1..2);

NiMkIitCTGljNyEiKg==

restart;

Mit der Eingabe von 3 Werten werden mit Hilfe des M\374ller-Verfahrens die Nullstellen berechnet.DAS VERFAHREN KANN AUCH KOMPLEXE NULLSTELLEN FINDEN

mueller := proc (p0in,p1in,p2in,TOL,N,f) local p0,p1,p2,n,converging,det,a,b,c,p; Digits := 50; p0 := p0in; p1 := p1in; p2 := p2in; printf("p0 = %12.20f p1 = %12.20f p2 = %12.20f\n",p0,p1,p2); n := 2; converging := true; while converging do n := n+1; det := (p0-p2)*(p1-p2)*(p0-p1); a := ((p1-p2)*(f(p0)-f(p2))-(p0-p2)*(f(p1)-f(p2)))/det; b := ((p0-p2)^2*(f(p1)-f(p2))-(p1-p2)^2*(f(p0)-f(p2)))/det; c := f(p2); p := evalf(p2-2*c/(b+(abs(evalf(Re(b)))/evalf(Re(b)))*sqrt(b^2-4*a*c))); printf("n = %a p = %a f(p) = %a\n",n,p,f(p)); converging := abs(evalf(f(p)))>TOL and n<N; p0 := p1; p1 := p2; p2 := p; end do; print(evalf(p)); end proc:

f:=(x)->16*x**4-40*x**3+5*x**2+20*x+6;

NiM+SSJmRzYiZio2I0kieEdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCwqJDkkIiIlIiM7KiRGLiIiJCEjUyokRi4iIiMiIiZGLiIjPyIiJyIiIkYlRiVGJQ==

mueller(0.5,-0.5,0,0.00001,20,f);

p0 = 0.50000000000000000000 p1 = -0.50000000000000000000 p2 = 0.00000000000000000000 n = 3 p = -.55555555555555555555555555555555555555555555555554+.59835164523716711458341227683781439514390224018276*I f(p) = -29.400701112635269013869836915104404816338972717574-3.898724711764806302155292613140765949154369877732*I n = 4 p = -.13073118315071300785504162383161018420815905658972-.14956754323534346510796191103676277990753492302222*I f(p) = 3.0733838452095444042611946013548803048222401673705-2.6295176879783921124333716865655499258171529204591*I n = 5 p = -.23128905375721011870169176566162636672413198068180+.8595405442290481413068253191050344287144340213992e-1*I f(p) = 1.9033247133120719764500332069308353054817200899328+.93524770947281091929159666961126842955656736693478*I n = 6 p = -.31507131281149578773903324093698220683440119395779+.12066772361147685248131048413427389272683354914524*I f(p) = .8449875028574559682631382605988613155016224102687+.4598886169853518635876149898336476913564742213407*I n = 7 p = -.36651376267477837993578077954622396094297962918886+.16992710482895891248956126840474492786858168472329*I f(p) = -.1738923467600027079166659763763543096647432078692-.1875492944220974161211437045223282498253190074392*I n = 8 p = -.35573517122866975827255308740848106064631396818120+.16264027592358211745231877398874142681384843899203*I f(p) = .33596153257496637869870071290635995540530708870e-2+.58775577602647207438813630044982470947046120257e-2*I n = 9 p = -.35606093852130935890280282977680575008310104465926+.16275824830920855947178512248884844894930423811844*I f(p) = .53246914418689636376482249897313867158284855e-5+.153764248023111468495140884281327029909283460e-4*I n = 10 p = -.35606176173660153284191102885614965877210686193873+.16275838285677635497015129874228014042770908997519*I f(p) = -.681020949279284241600913254080354795220e-10+.2242212844258853897424761474828814720718e-9*I NiNeJCQhU3RRPidvNXMoZSdcaCYpRzUiPiVHYCxtdGg8MWMkISNdJCJTPnYqKjM0eFVTLEdVKClIXiwoXE53biZHUWVGO0Ym

mueller(0.5,1.0,1.5,0.00001,20,f);

p0 = 0.50000000000000000000 p1 = 1.00000000000000000000 p2 = 1.50000000000000000000 n = 3 p = 1.2878547375517568769626400820689161355864563001971 f(p) = -1.376274560795554110952686602778825932423123288318 n = 4 p = 1.2374587503613367315546312874014878573668489749844 f(p) = .126945398693346955430546602757849028826339662719 n = 5 p = 1.2416045140563090983668092999419715454102036343479 f(p) = .2193408761085774908280794108878168906719748854e-2 n = 6 p = 1.2416774637308543108470466441604372201037132613241 f(p) = -.570403633529792512392224646049426295256949e-6 NiMkIlNUS2hLci4sQVAvO1dtL1ozSmEzdGp1blQ3ISNc

mueller(2.5,2.0,2.25,0.00001,20,f);

p0 = 2.50000000000000000000 p1 = 2.00000000000000000000 p2 = 2.25000000000000000000 n = 3.00000000000000000000 p = 1.96059228847980796509 f(p) = -0.61130995432133935329 n = 4.00000000000000000000 p = 1.97056360203444227732 f(p) = 0.00745549876243339624 n = 5.00000000000000000000 p = 1.97044653852263668036 f(p) = 0.00002916094449518955 n = 6.00000000000000000000 p = 1.97044607873060158124 f(p) = 0.00000000004576660080 NiMkIlN3KVIjeU9lYG8oZmhlJClHbEIiZSwxdHlnV3E+ISNc

solve(f(x),x);

NiYtSSdSb290T2ZHNiRJKnByb3RlY3RlZEdGJkkoX3N5c2xpYkc2IjYkLCwqJEkjX1pHRigiIiUiIzsqJEYsIiIkISNTKiRGLCIiIyIiJkYsIiM/IiInIiIiL0kmaW5kZXhHRiVGNy1GJDYkRiovRjlGMy1GJDYkRiovRjlGMC1GJDYkRiovRjlGLQ==

evalf(%);

NiYkIitYdW5UNyEiKiQiK3pnV3E+RiVeJCQhKzx3aGdOISM1JCIrSFFlRjtGK14kRikkIStIUWVGO0Yr

g1 := x -> 16*x**4+88*x**3+159*x**2+76*x-240;

NiM+SSNnMUc2ImYqNiNJInhHRiVGJTYkSSlvcGVyYXRvckdGJUkmYXJyb3dHRiVGJSwsKiQ5JCIiJSIjOyokRi4iIiQiIykpKiRGLiIiIyIkZiJGLiIjdyEkUyMiIiJGJUYlRiU=

plot(g1(x),x=-5..5,y=-1000..1000);

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

mueller(0.8,0.81,0.82,10**(-8),20,g1);

p0 = 0.80000000000000000000 p1 = 0.81000000000000000000 p2 = 0.82000000000000000000 n = 3 p = .84675383070116093647243032652896687214641645279264 f(p) = .645594296671572825589078042450599994617257483e-2 n = 4 p = .84674256899773961333657124601065414588087772878268 f(p) = -.156220284651280925243999862742969050831115e-5 n = 5 p = .84674257172220042216952164116323780016914208872829 f(p) = -.11629155023232892954606751329563952e-12 NiMkIlNIRygpM1UicCwheUJqNmtAJnBAVStBc3JEdVkpISNd

mueller(-3.35,-3.355,-3.356,10**(-8),20,g1);

p0 = -3.35000000000000000000 p1 = -3.35500000000000000000 p2 = -3.35600000000000000000 n = 3 p = -3.3580444958803901622287184322316090716885997741978 f(p) = .634443905680292424604555122072096623033787e-5 n = 4 p = -3.3580444814069502118066870930914161919673302311869 f(p) = -.1142620392270066391754435453133660020e-10 NiMkIVNwPUotTG4+Pjs5NCQ0KG8xPUBdcFMiW1chZUwhI1w=

g11 := x -> g1(x)/((x-.84674257172220042216952164116323780016914208872829)*(x+3.3580444814069502118066870930914161919673302311869));

NiM+SSRnMTFHNiJmKjYjSSJ4R0YlRiU2JEkpb3BlcmF0b3JHRiVJJmFycm93R0YlRiUqKC1JI2cxR0YlNiM5JCIiIiwmRjBGMSQiU0hHKCkzVSJwLCF5Qmo2a0AmcEBVK0FzckR1WSkhI10hIiJGNiwmRjBGMSQiU3A9Si1Mbj4+Ozk0JDQobzE9QF1wUyJbVyFlTCEjXEYxRjZGJUYlRiU=

mueller(-1.3,-1.4,-1.5,10**(-8),20,g11);

p0 = -1.30000000000000000000 p1 = -1.40000000000000000000 p2 = -1.50000000000000000000 n = 3 p = -1.4943490451576009148207724196530847757239758985180-1.7442181428080398592241246800622221751564438031571*I f(p) = .42653115176082976908527085933359793503167003848252e-12-.62839887319413200214596251515005905515195591672908e-12*I NiNeJCQhUyE9JikqZShSc3ZaM2AnPkN4P1siNGdkXi9cVlwiISNcJCFTcjouUVdjXjxBQTEhb0NUQWYpUiEzRzk9VXUiRiY=

mueller(-1.5,-1.51,-1.52,10**(-8),20,g1);

p0 = -1.50000000000000000000 p1 = -1.51000000000000000000 p2 = -1.52000000000000000000 n = 3 p = -2.0542080505860579888957433682911782850092535471931+3.1499778864743748086811550856208422675207313362976*I f(p) = 1155.9906811223932789621264005499680741294593250882+1301.9777354254422502942580952938029285692101351000*I n = 4 p = -1.3317503355181450373794495295137734361698523472468+1.0567693323430639815080829753673981722648147226754*I f(p) = -171.85839925185133772949149895716629254539700432381-35.435831189188497206767877243249898965397488259550*I n = 5 p = -1.3559110543130513344770463597625815903656770893354+1.4738132467107833113006325168848348525482949597767*I f(p) = -91.730169450226171836493380008382539713176493980298-47.18004399352157486135277694373096132422270931955*I n = 6 p = -1.4360822862170617522410505103365391922903271867491+1.7005819494368830627410253898445801046087947943739*I f(p) = -15.95737027483868628095464744914796170302216178808-24.59103877032071301177735068533006414779015726074*I n = 7 p = -1.4981143033039057311855877823827360723947885586488+1.7441623671223468751773533235187054548726598380843*I f(p) = -.20247042985723946208506292680091967839767816489+1.55300192496792653968913717478399520006507803215*I n = 8 p = -1.4943443990529728736430759053535353514339500406137+1.7442390266359531472767422144826788355360939936908*I f(p) = .884800572025854545837904164455978164606956157e-2-.94982284886363536756860972128569481762088715e-3*I n = 9 p = -1.4943490463832273737597021428991537216763516204293+1.7442181418314482054817270407586628533274705183924*I f(p) = -.46062075455181815714502493792461366683945e-6+.46119622437049856473010505666483043727814e-6*I n = 10 p = -1.4943490451576121874493070021349237559184323432974+1.7442181428080475320349526423876174095532654247048*I f(p) = .1213467427910978675823376017441571e-13+.723370373584227749189682895676330e-14*I NiNeJCQhU3VIVkJWPWZ2Qlw4LXFJXHU9N3c6WCFcVlwiISNcJCJTW3FDYUVgJjR1aChRVUUmXC5Ldi8zRzk9VXUiRiY=

solve(g1(x)=0,x);

NiYtSSdSb290T2ZHNiRJKnByb3RlY3RlZEdGJkkoX3N5c2xpYkc2IjYkLCwqJEkjX1pHRigiIiUiIzsqJEYsIiIkIiMpKSokRiwiIiMiJGYiRiwiI3chJFMjIiIiL0kmaW5kZXhHRiVGNy1GJDYkRiovRjlGMy1GJDYkRiovRjlGMC1GJDYkRiovRjlGLQ==

evalf(%);

NiYkIis8ZFVuJSkhIzVeJCQhK1ghXFZcIiEiKiQiK1YiPVV1IkYpJCErIltXIWVMRileJEYnJCErViI9VXUiRik=

g2 := x ->x**5+11*x**4-21*x**3-10*x**2-21*x-5;

NiM+SSNnMkc2ImYqNiNJInhHRiVGJTYkSSlvcGVyYXRvckdGJUkmYXJyb3dHRiVGJSwuKiQ5JCIiJiIiIiokRi4iIiUiIzYqJEYuIiIkISNAKiRGLiIiIyEjNUYuRjYhIiZGMEYlRiVGJQ==

plot(g2(x),x=-20..20,y=-100000..100000);

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

mueller(-0.2,-0.21,-0.22,10**(-8),20,g2);

p0 = -0.20000000000000000000 p1 = -0.21000000000000000000 p2 = -0.22000000000000000000 n = 3 p = -.25032712196331261692288289028578612129663139154107 f(p) = .18587299824375941072250494481077039253640907550e-2 n = 4 p = -.25023677662725375588830620700530328762873599739874 f(p) = -.33738259306330389920517649794433397336713834e-5 n = 5 p = -.25023694032445366234838598536696644364268849994059 f(p) = -.138774605494974064132622251141062582959e-10 NiMkIVNmUyoqXClvVU9XbXBPJilmUVtCbWBXS1NwQl0jISNd

mueller(3,3.1,3.2,10**(-8),20,g2);

p0 = 3.00000000000000000000 p1 = 3.10000000000000000000 p2 = 3.20000000000000000000 n = 3 p = 2.3530619486065173592249032160465388132877663707565+.37941096135594427697909308873701331535285217267556*I f(p) = -22.126270844899299328888708182965018237896458472452+109.96504098842650016950917514787644675101227000714*I n = 4 p = 2.3834243610979800512405775662600923963836367194833-.15585045315706023159679031783020478409204182811288*I f(p) = 27.208285075127756392183443503218628915839124651016-50.982231953674508872178371382563177480812584161920*I n = 5 p = 2.2188626987098155909302461365616073738198268112142-.3905576013796485742885018736829583544803618888813e-1*I f(p) = -10.255263056704204716381719897991699171535037187086-8.8314129226894652935449222192855856619125199594009*I n = 6 p = 2.2609111726732632804371287747241090216782492534398+.2294110490198183103277541408073320813963752175260e-2*I f(p) = .205372967330616631429097164168344084790200589417+.57560483973494645384929983533225187416478118576464*I n = 7 p = 2.2600926682166065490271015321873895851601650491349+.124618239556666532350853346217668653289864968106e-4*I f(p) = .1787935168290001433315158149941644198074630707e-2+.31206209846361666156137886792491209205116664467192e-2*I n = 8 p = 2.2600855270507721086793705433751141713214501800003+.115959625397097031167856564340356522227679164e-9*I f(p) = -.254130105988931372657793879541949845372565e-6+.29037470448740701839281408105986383954165968264875e-7*I n = 9 p = 2.2600855280656274353036816061598505452228023204729+.1535878369608935242166554255486924477386506e-16*I f(p) = -.2584356659786401533892398581465797e-14+.38459957701804378086456242090263757260011270921396e-14*I NiNeJCQiU0haP0IhR0FYMCYpZmhnIm8uYFZGYzFHYjNnQSEjXCQiTDFsUXhXI3BbYlVibUBDTiozJ3AkeWVgIiEjZg==

mueller(-12.0,-12.1,-12.2,10**(-8),20,g2);

p0 = -12.00000000000000000000 p1 = -12.10000000000000000000 p2 = -12.20000000000000000000 n = 3 p = -12.616796609345673034566771280286093997366577957301 f(p) = -124.42874631843264825740903419681428762631201195598 n = 4 p = -12.612397919666454319556182289307967316136807848640 f(p) = .89928890818257990684484747634341475973039974824 n = 5 p = -12.612429522943650966622714402829193850643427404830 f(p) = .5656305495536630791414997806336346248947143e-4 n = 6 p = -12.612429524931524816458594483580328086510738428630 f(p) = .27849107796604537803908693317247553e-12 NiMkIVNJJ0clUTJeJzNHLmUkWyVmZWsiW19KXF9IQ2g3ISNb

g22 := x -> g2(x) /((x-2.260085528)*(x+.2502369403)*(x+12.61242952));

NiM+SSRnMjJHNiJmKjYjSSJ4R0YlRiU2JEkpb3BlcmF0b3JHRiVJJmFycm93R0YlRiUqKi1JI2cyR0YlNiM5JCIiIiwmRjBGMSQiK0diM2dBISIqISIiRjYsJkYwRjEkIisuJXBCXSMhIzVGMUY2LCZGMEYxJCIrX0hDaDchIilGMUY2RiVGJUYl

mueller(-0.15,-0.16,-0.17,10**(-8),20,g22);

p0 = -0.15000000000000000000 p1 = -0.16000000000000000000 p2 = -0.17000000000000000000 n = 3 p = -.19870952948258453268972491512560366591816470372103+.81331253763712550593063190858893069639836179897284*I f(p) = .14912958571429945332071554347941418018046956398974e-7+.31262160664469203372943450879346760421442538797570e-8*I n = 4 p = -.19870953140448782369794858002287253107547940766716+.81331254680516225588670052467348222003892874871688*I f(p) = .87296885521594968850991274756176789677736774170491e-17-.19550393328466784429845731996210264804703284190348e-16*I NiNeJCQhUztud1N6YTJKRChHLSFlW3pwQnlbLzlgNCgpPiEjXSQiUylvclsoRypRK0EjW3RZXytuKWVEaV4hb2E3TCIpRiY=

solve(g2(x)=0,x);

NictSSdSb290T2ZHNiRJKnByb3RlY3RlZEdGJkkoX3N5c2xpYkc2IjYkLC4qJEkjX1pHRigiIiYiIiIqJEYsIiIlIiM2KiRGLCIiJCEjQCokRiwiIiMhIzVGLEY0ISImRi4vSSZpbmRleEdGJUYuLUYkNiRGKi9GOkY2LUYkNiRGKi9GOkYzLUYkNiRGKi9GOkYwLUYkNiRGKi9GOkYt

evalf(%);

NickIitHYjNnQSEiKl4kJCErOWA0KCk+ISM1JCIrb2E3TCIpRikkISsuJXBCXSNGKSQhK19IQ2g3ISIpXiRGJyQhK29hN0wiKUYp

restart;a0:=5.0;b:=3.0;f0:=0.1;

NiM+SSNhMEc2IiQiI10hIiI=NiM+SSJiRzYiJCIjSSEiIg==NiM+SSNmMEc2IiQiIiIhIiI=

g := x-> a0*exp(-x/3)*cos(2.0*Pi*f0*x)-(200.*Pi*f0*x);

NiM+SSJnRzYiZio2I0kieEdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCYqKEkjYTBHRiUiIiItSSRleHBHRiU2IywkOSQjISIiIiIkRi8tSSRjb3NHRiU2IyoqJCIjP0Y2Ri9JI1BpR0kqcHJvdGVjdGVkR0Y/Ri9JI2YwR0YlRi9GNEYvRi9GLyoqJCIkKyMiIiFGL0Y+Ri9GQEYvRjRGL0Y2RiVGJUYl

plot(g(x),x=-1..1,y=-10..10);

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

bisect := proc(a,b,TOL,N,f) local aa,bb,p,i; Digits := 50; aa := a; bb := b; p := evalf((a+b)/2); i := 0; print(evalf(aa),evalf(bb),evalf(p),evalf(f(p))); while(abs(evalf(f(p)))>TOL and i<=N) do i := i+1; if(evalf(f(aa)*f(p))<0)then bb := evalf(p); else aa := evalf(p); end if; p := evalf((aa+bb)/2); printf("i = %d a = %12.20f b = %12.20f p = %12.20f f(p) := %12.20f\n",i,evalf(aa),evalf(bb),evalf(p),evalf(f(p))); end do; print(p); print(evalf(p)); end proc:

bisect(0,0.5,10**(-10),40,g);

NiYkIiIhRiQkIiImISIiJCJTKysrKysrKysrKysrKysrKysrKysrKysrRCEjXSQhU1c4Y29qIzMvIXBQUks2bGI8MG1gQGN4Vjs2ISNbi = 1 a = 0.00000000000000000000 b = 0.25000000000000000000 p = 0.12500000000000000000 f(p) := -3.07281865334364030640 i = 2 a = 0.00000000000000000000 b = 0.12500000000000000000 p = 0.06250000000000000000 f(p) := 0.96614474882751874160 i = 3 a = 0.06250000000000000000 b = 0.12500000000000000000 p = 0.09375000000000000000 f(p) := -1.05272519435169513137 i = 4 a = 0.06250000000000000000 b = 0.09375000000000000000 p = 0.07812500000000000000 f(p) := -0.04313395736882851315 i = 5 a = 0.06250000000000000000 b = 0.07812500000000000000 p = 0.07031250000000000000 f(p) := 0.46154487952253342425 i = 6 a = 0.07031250000000000000 b = 0.07812500000000000000 p = 0.07421875000000000000 f(p) := 0.20921527976920297114 i = 7 a = 0.07421875000000000000 b = 0.07812500000000000000 p = 0.07617187500000000000 f(p) := 0.08304310934784935571 i = 8 a = 0.07617187500000000000 b = 0.07812500000000000000 p = 0.07714843750000000000 f(p) := 0.01995518721115951842 i = 9 a = 0.07714843750000000000 b = 0.07812500000000000000 p = 0.07763671875000000000 f(p) := -0.01158923237530475341 i = 10 a = 0.07714843750000000000 b = 0.07763671875000000000 p = 0.07739257812500000000 f(p) := 0.00418301560654398340 i = 11 a = 0.07739257812500000000 b = 0.07763671875000000000 p = 0.07751464843750000000 f(p) := -0.00370309883881807738 i = 12 a = 0.07739257812500000000 b = 0.07751464843750000000 p = 0.07745361328125000000 f(p) := 0.00023996077045250574 i = 13 a = 0.07745361328125000000 b = 0.07751464843750000000 p = 0.07748413085937500000 f(p) := -0.00173156843756026989 i = 14 a = 0.07745361328125000000 b = 0.07748413085937500000 p = 0.07746887207031250000 f(p) := -0.00074580368439514408 i = 15 a = 0.07745361328125000000 b = 0.07746887207031250000 p = 0.07746124267578125000 f(p) := -0.00025292141968124604 i = 16 a = 0.07745361328125000000 b = 0.07746124267578125000 p = 0.07745742797851562500 f(p) := -0.00000648031529180329 i = 17 a = 0.07745361328125000000 b = 0.07745742797851562500 p = 0.07745552062988281250 f(p) := 0.00011674022991099901 i = 18 a = 0.07745552062988281250 b = 0.07745742797851562500 p = 0.07745647430419921875 f(p) := 0.00005512995789225905 i = 19 a = 0.07745647430419921875 b = 0.07745742797851562500 p = 0.07745695114135742188 f(p) := 0.00002432482144589308 i = 20 a = 0.07745695114135742188 b = 0.07745742797851562500 p = 0.07745718955993652344 f(p) := 0.00000892225311346119 i = 21 a = 0.07745718955993652344 b = 0.07745742797851562500 p = 0.07745730876922607422 f(p) := 0.00000122096891993302 i = 22 a = 0.07745730876922607422 b = 0.07745742797851562500 p = 0.07745736837387084961 f(p) := -0.00000262967318365912 i = 23 a = 0.07745730876922607422 b = 0.07745736837387084961 p = 0.07745733857154846191 f(p) := -0.00000070435213129405 i = 24 a = 0.07745730876922607422 b = 0.07745733857154846191 p = 0.07745732367038726807 f(p) := 0.00000025830839446174 i = 25 a = 0.07745732367038726807 b = 0.07745733857154846191 p = 0.07745733112096786499 f(p) := -0.00000022302186838059 i = 26 a = 0.07745732367038726807 b = 0.07745733112096786499 p = 0.07745732739567756653 f(p) := 0.00000001764326304946 i = 27 a = 0.07745732739567756653 b = 0.07745733112096786499 p = 0.07745732925832271576 f(p) := -0.00000010268930266334 i = 28 a = 0.07745732739567756653 b = 0.07745732925832271576 p = 0.07745732832700014114 f(p) := -0.00000004252301980638 i = 29 a = 0.07745732739567756653 b = 0.07745732832700014114 p = 0.07745732786133885384 f(p) := -0.00000001243987837832 i = 30 a = 0.07745732739567756653 b = 0.07745732786133885384 p = 0.07745732762850821018 f(p) := 0.00000000260169233561 i = 31 a = 0.07745732762850821018 b = 0.07745732786133885384 p = 0.07745732774492353201 f(p) := -0.00000000491909302135 i = 32 a = 0.07745732762850821018 b = 0.07745732774492353201 p = 0.07745732768671587110 f(p) := -0.00000000115870034287 i = 33 a = 0.07745732762850821018 b = 0.07745732768671587110 p = 0.07745732765761204064 f(p) := 0.00000000072149599637 i = 34 a = 0.07745732765761204064 b = 0.07745732768671587110 p = 0.07745732767216395587 f(p) := -0.00000000021860217325 i = 35 a = 0.07745732765761204064 b = 0.07745732767216395587 p = 0.07745732766488799825 f(p) := 0.00000000025144691156 i = 36 a = 0.07745732766488799825 b = 0.07745732767216395587 p = 0.07745732766852597706 f(p) := 0.00000000001642236916 NiMkIlMrKysrKytdKD08XnVReSk+Z3EoZl9vd0tkdSghI14=NiMkIlMrKysrKytdKD08XnVReSk+Z3EoZl9vd0tkdSghI14=

solve(g(x)=0,x);

NiMkIituRnRYeCEjNg==

restart;g := x-> sin(x)-exp(-x);

NiM+SSJnRzYiZio2I0kieEdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCYtSSRzaW5HRiU2IzkkIiIiLUkkZXhwR0YlNiMsJEYwISIiRjZGJUYlRiU=

plot(g(x),x=-1..10,y=-1.5..1.5);

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

fsolve(g(x)=0,x=0..2);

NiMkIitTdUsmKWUhIzU=

fsolve(g(x)=0,x=2..4);

NiMkIitLUk8nNCQhIio=

fsolve(g(x)=0,x=5..7);

NiMkIit0I1xdRychIio=

bisect := proc(a,b,TOL,N,f) local aa,bb,p,i; Digits := 50; aa := a; bb := b; p := (a+b)/2; i := 0; print(evalf(aa),evalf(bb),evalf(p),evalf(f(p))); while(evalf(abs(f(p)))>TOL and i<=N) do i := i+1; if(evalf(f(aa)*f(p))<0)then bb := p; else aa := p; end if; p := (aa+bb)/2; printf("i = %d a = %12.20f b = %12.20f p = %12.20f f(p) := %12.20f\n",i,evalf(aa),evalf(bb),evalf(p),evalf(f(p))); end do; print(p); print(evalf(p)); end proc:

bisect(0.0,2.0,10**(-8),20,g);

NiYkIiIhRiQkIiM/ISIiJCJTKysrKysrKysrKysrKysrKysrKysrKysrNSEjXCQiU2dtKEg+dndAOFEpbzlieXAwJj1ha2pWOmZ0JSEjXQ==i = 1 a = 0.00000000000000000000 b = 1.00000000000000000000 p = 0.50000000000000000000 f(p) := -0.12710512110843042333 i = 2 a = 0.50000000000000000000 b = 1.00000000000000000000 p = 0.75000000000000000000 f(p) := 0.20927220728231945960 i = 3 a = 0.50000000000000000000 b = 0.75000000000000000000 p = 0.62500000000000000000 f(p) := 0.04983584442147191285 i = 4 a = 0.50000000000000000000 b = 0.62500000000000000000 p = 0.56250000000000000000 f(p) := -0.03648015119490283644 i = 5 a = 0.56250000000000000000 b = 0.62500000000000000000 p = 0.59375000000000000000 f(p) := 0.00722068108434651232 i = 6 a = 0.56250000000000000000 b = 0.59375000000000000000 p = 0.57812500000000000000 f(p) := -0.01449455389526723927 i = 7 a = 0.57812500000000000000 b = 0.59375000000000000000 p = 0.58593750000000000000 f(p) := -0.00360307518162063126 i = 8 a = 0.58593750000000000000 b = 0.59375000000000000000 p = 0.58984375000000000000 f(p) := 0.00181727650089655876 i = 9 a = 0.58593750000000000000 b = 0.58984375000000000000 p = 0.58789062500000000000 f(p) := -0.00089078198344332919 i = 10 a = 0.58789062500000000000 b = 0.58984375000000000000 p = 0.58886718750000000000 f(p) := 0.00046377672676494983 i = 11 a = 0.58789062500000000000 b = 0.58886718750000000000 p = 0.58837890625000000000 f(p) := -0.00021337027743070541 i = 12 a = 0.58837890625000000000 b = 0.58886718750000000000 p = 0.58862304687500000000 f(p) := 0.00012523631440688129 i = 13 a = 0.58837890625000000000 b = 0.58862304687500000000 p = 0.58850097656250000000 f(p) := -0.00004405870932855206 i = 14 a = 0.58850097656250000000 b = 0.58862304687500000000 p = 0.58856201171875000000 f(p) := 0.00004059087061645209 i = 15 a = 0.58850097656250000000 b = 0.58856201171875000000 p = 0.58853149414062500000 f(p) := -0.00000173340234065905 i = 16 a = 0.58853149414062500000 b = 0.58856201171875000000 p = 0.58854675292968750000 f(p) := 0.00001942886339223562 i = 17 a = 0.58853149414062500000 b = 0.58854675292968750000 p = 0.58853912353515625000 f(p) := 0.00000884776283931164 i = 18 a = 0.58853149414062500000 b = 0.58853912353515625000 p = 0.58853530883789062500 f(p) := 0.00000355718832769945 i = 19 a = 0.58853149414062500000 b = 0.58853530883789062500 p = 0.58853340148925781250 f(p) := 0.00000091189501311253 i = 20 a = 0.58853149414062500000 b = 0.58853340148925781250 p = 0.58853244781494140625 f(p) := -0.00000041075315887530 i = 21 a = 0.58853244781494140625 b = 0.58853340148925781250 p = 0.58853292465209960938 f(p) := 0.00000025057105334312 NiMkIlMrKysrKysrKysrKysrK11QNCcqNF9ZI0hgKWUhI10=NiMkIlMrKysrKysrKysrKysrK11QNCcqNF9ZI0hgKWUhI10=

bisect(2.0,4.0,10**(-8),20,g);

NiYkIiM/ISIiJCIjU0YlJCJTKysrKysrKysrKysrKysrKysrKysrKysrSSEjXCQiU1pRMXNPQjpLXVshZXJRLTk3eksrI3BSSEwiKiEjXg==i = 1 a = 3.00000000000000000000 b = 4.00000000000000000000 p = 3.50000000000000000000 f(p) := -0.38098061111193834886 i = 2 a = 3.00000000000000000000 b = 3.50000000000000000000 p = 3.25000000000000000000 f(p) := -0.14696934236183038692 i = 3 a = 3.00000000000000000000 b = 3.25000000000000000000 p = 3.12500000000000000000 f(p) := -0.02734504139405951301 i = 4 a = 3.00000000000000000000 b = 3.12500000000000000000 p = 3.06250000000000000000 f(p) := 0.03223959436343070489 i = 5 a = 3.06250000000000000000 b = 3.12500000000000000000 p = 3.09375000000000000000 f(p) := 0.00249276273631884775 i = 6 a = 3.09375000000000000000 b = 3.12500000000000000000 p = 3.10937500000000000000 f(p) := -0.01241675930291451898 i = 7 a = 3.09375000000000000000 b = 3.10937500000000000000 p = 3.10156250000000000000 f(p) := -0.00495940433930240741 i = 8 a = 3.09375000000000000000 b = 3.10156250000000000000 p = 3.09765625000000000000 f(p) := -0.00123264119653457809 i = 9 a = 3.09375000000000000000 b = 3.09765625000000000000 p = 3.09570312500000000000 f(p) := 0.00063023456104065047 i = 10 a = 3.09570312500000000000 b = 3.09765625000000000000 p = 3.09667968750000000000 f(p) := -0.00030116035619886981 i = 11 a = 3.09570312500000000000 b = 3.09667968750000000000 p = 3.09619140625000000000 f(p) := 0.00016454790358780566 i = 12 a = 3.09619140625000000000 b = 3.09667968750000000000 p = 3.09643554687500000000 f(p) := -0.00006830353361129008 i = 13 a = 3.09619140625000000000 b = 3.09643554687500000000 p = 3.09631347656250000000 f(p) := 0.00004812285911150415 i = 14 a = 3.09631347656250000000 b = 3.09643554687500000000 p = 3.09637451171875000000 f(p) := -0.00001009016883779211 i = 15 a = 3.09631347656250000000 b = 3.09637451171875000000 p = 3.09634399414062500000 f(p) := 0.00001901638725472008 i = 16 a = 3.09634399414062500000 b = 3.09637451171875000000 p = 3.09635925292968750000 f(p) := 0.00000446311973607514 i = 17 a = 3.09635925292968750000 b = 3.09637451171875000000 p = 3.09636688232421875000 f(p) := -0.00000281352191918755 i = 18 a = 3.09635925292968750000 b = 3.09636688232421875000 p = 3.09636306762695312500 f(p) := 0.00000082479956639051 i = 19 a = 3.09636306762695312500 b = 3.09636688232421875000 p = 3.09636497497558593750 f(p) := -0.00000099436101191546 i = 20 a = 3.09636306762695312500 b = 3.09636497497558593750 p = 3.09636402130126953125 f(p) := -0.00000008478068164126 i = 21 a = 3.09636306762695312500 b = 3.09636402130126953125 p = 3.09636354446411132812 f(p) := 0.00000037000945265499 NiMkIlMrKysrKysrKysrKysrK0QiRzg2a1dhamo0JCEjXA==NiMkIlMrKysrKysrKysrKysrK0QiRzg2a1dhamo0JCEjXA==

bisect(5.0,7.0,10**(-8),20,g);

NiYkIiNdISIiJCIjcUYlJCJTKysrKysrKysrKysrKysrKysrKysrKysrZyEjXCQhU3QuUk0sJj52VTZGLzkxZ003QiNmdi5EJSo9RyEjXQ==i = 1 a = 6.00000000000000000000 b = 7.00000000000000000000 p = 6.50000000000000000000 f(p) := 0.21361654889483795185 i = 2 a = 6.00000000000000000000 b = 6.50000000000000000000 p = 6.25000000000000000000 f(p) := -0.03510967068378452612 i = 3 a = 6.25000000000000000000 b = 6.50000000000000000000 p = 6.37500000000000000000 f(p) := 0.08998212869437518796 i = 4 a = 6.25000000000000000000 b = 6.37500000000000000000 p = 6.31250000000000000000 f(p) := 0.02749700056526275105 i = 5 a = 6.25000000000000000000 b = 6.31250000000000000000 p = 6.28125000000000000000 f(p) := -0.00380636627796319422 i = 6 a = 6.28125000000000000000 b = 6.31250000000000000000 p = 6.29687500000000000000 f(p) := 0.01184721302700032508 i = 7 a = 6.28125000000000000000 b = 6.29687500000000000000 p = 6.28906250000000000000 f(p) := 0.00402065938642456075 i = 8 a = 6.28125000000000000000 b = 6.28906250000000000000 p = 6.28515625000000000000 f(p) := 0.00010717581072437914 i = 9 a = 6.28125000000000000000 b = 6.28515625000000000000 p = 6.28320312500000000000 f(p) := -0.00184959163783261358 i = 10 a = 6.28320312500000000000 b = 6.28515625000000000000 p = 6.28417968750000000000 f(p) := -0.00087120654981561275 i = 11 a = 6.28417968750000000000 b = 6.28515625000000000000 p = 6.28466796875000000000 f(p) := -0.00038201497051194727 i = 12 a = 6.28466796875000000000 b = 6.28515625000000000000 p = 6.28491210937500000000 f(p) := -0.00013741947287298431 i = 13 a = 6.28491210937500000000 b = 6.28515625000000000000 p = 6.28503417968750000000 f(p) := -0.00001512180341130480 i = 14 a = 6.28503417968750000000 b = 6.28515625000000000000 p = 6.28509521484375000000 f(p) := 0.00004602701068576135 i = 15 a = 6.28503417968750000000 b = 6.28509521484375000000 p = 6.28506469726562500000 f(p) := 0.00001545260538034998 i = 16 a = 6.28503417968750000000 b = 6.28506469726562500000 p = 6.28504943847656250000 f(p) := 0.00000016540141852998 i = 17 a = 6.28503417968750000000 b = 6.28504943847656250000 p = 6.28504180908203125000 f(p) := -0.00000747820088810719 i = 18 a = 6.28504180908203125000 b = 6.28504943847656250000 p = 6.28504562377929687500 f(p) := -0.00000365639970769085 i = 19 a = 6.28504562377929687500 b = 6.28504943847656250000 p = 6.28504753112792968750 f(p) := -0.00000174549913780254 i = 20 a = 6.28504753112792968750 b = 6.28504943847656250000 p = 6.28504848480224609375 f(p) := -0.00000079004885794137 i = 21 a = 6.28504848480224609375 b = 6.28504943847656250000 p = 6.28504896163940429688 f(p) := -0.00000031232371928192 NiMkIlMrKysrKysrKysrKysrK3ZvSC8lUjsnKltdRychI1w=NiMkIlMrKysrKysrKysrKysrK3ZvSC8lUjsnKltdRychI1w=