# The two examples in the paper "Nearest singular polynomial."
## Example 1:
f1:=evalf(x^5-x);
  N_m_1_2:=0.1763296120;
  N_m_1_3:=0.6261127476;
## Example 2:
  f2:=expand((x-0.89-0.03*I)*(x-0.88+0.02*I)*(x-0.87)*(x-1));
  N_m_2_2:=1.55738888907*10^(-13);
  N_m_2_3:=9.817251548*10^(-10);
  N_m_2_4:=1.958555857*10^(-5);

## The examples in the paper " Hybird method for computing Nearest Singular Polynomials".
## Example 3:
 f3:=x^4-0.960000*x^3-0.0401*x^2+0.000096*x+0.000004;
 N_m_3_2:=1.645038*10^(-11);
 N_m_3_3:=4.144531*10^(-7);
 N_m_3_4:=0.104999;
## Example 4:
f4:=x^5+2.03*x^4-0.9398*x^3-2.0296*x^2-0.0602*x-0.0004;
N_m_4_2:=2.460988*10^(-9);
N_m_4_3:=0.368179;
## Example 5:
f5:=x^6+1.99*x^5-9.0202*x^4-1.9104*x^3+8.0218*x^2-0.0796*x-0.0016;
N_m_5_2:=3.231668*10^(-6);
N_m_5_3:=5.766062;
#Example 6:
f6:=x^6+2.04*x^5-0.9199*x^4-2.039806*x^3-0.080112*x^2-0.000194*x+0.000012;
N_m_6_2:=3.009789*10^(-12);
N_m_6_3:=7.453849*10^(-7);
N_m_6_4:=0.444902;
## Example 7:
f7:=x^5+(0.909091+0.1*I)*x^4-10*x^3-(9.09091-I)*x^2+9.0*x+8.181818+0.9*I;
N_m_7_2:=0.0123884;
## Example 8:
f8:=x^21-1.142857*x^20-1.0*x^19+2.714286*x^18-4.0*x^17+4.1428714*x^16-2.571371*x^15+x^14+0.857143*x^13
    -3.142857*x^12+2.0*x^11+0.285714*x^10+0.571428*x^8-1.285600*x^7+2.857143*x^6-4.714286*x^5+2.142857*x^4
    +0.428571*x^3+0.857143*x^2-0.714286*x-0.285700;
N_m_8_2:=0.190477*10^(-8);
N_m_8_3:=0.0000963776;