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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 = | .529038 .923911  .361789  .960494 |
     | .468082 .0415044 .458991  .347108 |
     | .671525 .64417   .430639  .443024 |
     | .808195 .14406   .0553286 .664635 |

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

o3 = | 1            1.11022e-16 0 -3.33067e-16 |
     | -1.11022e-16 1           0 1.11022e-16  |
     | 3.33067e-16  2.22045e-16 1 0            |
     | 2.22045e-16  0           0 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 :