# clean -- Set to zero elements that are approximately zero

## Synopsis

• Usage:
clean(epsilon,M)
clean_epsilon M
• Inputs:
• epsilon,
• M, , or a
• Outputs:
• , or

## Description

If the input is or , 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 = | .986302 .607834 .717856 .283321 | | .737509 .0520427 .650032 .302656 | | .384985 .754548 .367082 .00851019 | | .849452 .510433 .232858 .464759 | 4 4 o2 : Matrix RR <--- RR 53 53``` ```i3 : M * (M + 1) + 1 - M^2 - M o3 = | 1 1.11022e-16 2.22045e-16 -1.11022e-16 | | 4.44089e-16 1 2.22045e-16 0 | | 2.22045e-16 1.11022e-16 1 0 | | 2.22045e-16 3.33067e-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```