-- -*- M2-comint -*- {* hash: 1089792485 *}

i1 : e = 1e-11;

i2 : M = random(RR^4,RR^4)

o2 = | .142767  .650468  .34431  .831079 |
     | .344396  .477573  .35125  .50691  |
     | .249144  .62852   .344489 .741366 |
     | .0586825 .0463371 .60071  .690786 |

                4          4
o2 : Matrix RR    <--- RR
              53         53

i3 : M * (M + 1) + 1 - M^2 - M

o3 = | 1           0            0            -1.11022e-16 |
     | 0           1            1.11022e-16  0            |
     | 5.55112e-17 -1.11022e-16 1            1.11022e-16  |
     | 2.77556e-17 0            -1.11022e-16 1            |

                4          4
o3 : Matrix RR    <--- RR
              53         53

i4 : clean_e oo

o4 = | 1 0 0 0 |
     | 0 1 0 0 |
     | 0 0 1 0 |
     | 0 0 0 1 |

                4          4
o4 : Matrix RR    <--- RR
              53         53

i5 : CC[x];

i6 : f = product(5,j -> x - exp(2*pi*j*ii/5))

      5                                  4                   3     
o6 = x  + (2.22045e-16 - 1.11022e-16*ii)x  - 1.11022e-16*ii*x  + (-
     ------------------------------------------------------------------------
                                   2
     1.11022e-16 - 1.11022e-16*ii)x  - 1.11022e-16*ii*x - 1 + 5.55112e-16*ii

o6 : CC  [x]
       53

i7 : clean_e f  

      5
o7 = x  - 1

o7 : CC  [x]
       53

i8 :