T=x^3-6*x^2+11*x-6;
polrootsreal(T)
polrootsreal(T, [-oo,3/2])
polrootsreal(T, [3/2,6])
polrootsreal(T, [-oo,+oo])
polrootsreal(T, [2,3])
polrootsreal(T, [1,2])
polsturm(T, [-oo,3/2])
polsturm(T, [3/2,6])
polsturm(T, [-oo,+oo])
polsturm(T, [2,3])
polsturm(T, [1,2])
polsturm(T, [1,+oo])
polrootsreal(x^10 + 23*x^9 + 19*x^8 + 18*x^7 + 39*x^6 + 41*x^5 + 46*x^4 + 24*x^3 - 4*x^2 + 2*x + 42)
polrootsreal(polchebyshev(9))
polrootsreal(polchebyshev(10))
polrootsreal(x^0)
polrootsreal(1)
polrootsreal(0)
polrootsreal(Pol(0))
polrootsreal(Mod(1,2))
polrootsreal(x+0.) \\ #2196

polroots(T*x+0.)
polroots(1)
polrootsreal(T,[1,1])
polrootsreal(T,[0,0])
polsturm(T,[1,1])
polsturm(T,[2,1])
polsturm(-5500*x^4+440*x^3+21780*x^2-9680*x-29040,[-oo,-4])

U=(x^2-1)*(x-2);
polsturm(U)
polsturm(U,[-oo,1])
polsturm(U,[-1,+oo])

polrootsreal(x,[1,2])
polrootsreal(x,[-2,-1])
polrootsreal(x,[-1,1])

polrootsreal(x^3-2)
polrootsreal(x^3+2)
\\#1605
polsturm(33*x^2-4*x-1)
polrootsreal(4*x)
polsturm(-4*x)
polsturm((x^4-2)^2)

\\#1807
T=x^3+x^2-x+2;
polrootsreal(T)
polsturm(T)
polsturm(T,[-3,-1])
polsturm(T,[-2,-1])
polsturm(T,[-oo,-2])
polsturm(T,[-2,oo])
T=4*x^3-2*x^2-x-1;
polsturm(T,[0,oo])
polsturm(T,[0,1])
polsturm(T,[0,2])
polsturm(T,[1,3])
polsturm(x+0.)

\\#1808
polrootsreal(3*x^3-4*x^2+3*x-1)

\\#1809
polrootsreal(x^3-3*x^2-3*x+2)

\\#1810
polrootsreal(x^3-x^2)
polrootsreal((x^3-x^2)*(x-2)^3*(x-3)^2)

default(realprecision,19);
#polroots((x+1)^2 * (x-1)^7 * (x^2-x+1)^5 * 1.0)

\\#1884
default(realprecision,38);
polsturm(x^2-1,[-1,1])
polrootsreal(x^2-1,[-1,1])

polsturm((x-1)^2*(x+2)*1.)

\\#2112
pol=-x^4-2*x^3-x^2/3-x/100+1/2000;
polrootsreal(pol,[1/100,oo])

pol=-x^4-2*x^3-x^2/3-x/100+1/1000;
polrootsreal(pol,[1/10,oo])     \\ one extra root

\\ ERRORS: KEEP AT END OF FILE
polrootsreal(0.E25*x^2+0.E25*x+0.E25) \\ # 2516
