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Macaulay2Doc :: clean

clean -- Set to zero elements that are approximately zero

Synopsis

Description

If the input is a matrix or a ring element, then the result has the same type, where each real or complex number coefficient that is less than epsilon in absolute value is replaced with zero.

i1 : e = 1e-11;
i2 : M = random(RR^4,RR^4)

o2 = | .423277  .876329 .263563  .85297   |
     | .0269454 .763461 .420112  .227744  |
     | .421525  .987858 .0688942 .0120255 |
     | .724822  .142726 .928725  .0445929 |

                4          4
o2 : Matrix RR    <--- RR
              53         53
i3 : M * (M + 1) + 1 - M^2 - M

o3 = | 1            -2.22045e-16 0            1.11022e-16  |
     | 0            1            -1.11022e-16 2.77556e-17  |
     | -5.55112e-17 1.11022e-16  1            -1.11022e-16 |
     | -2.22045e-16 -1.11022e-16 -2.22045e-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
Cleaning a polynomial is a way to get rid of small terms.
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

See also

Ways to use clean :