# Chop

Numerics inside a computer is not exact. Quanty represents numbers by doubles, which can store numbers with about 16 digits accuracy. The fact that you only have 16 digits can lead to number-loss and situations where numbers that should be zero are close to zero but not exactly zero. An example in base 10: If you represent $1/3$ by $0.3333333333333333$ then $1-3\times0.3333333333333333 = 0.00000000000000001$. In Quanty you can remove these small numbers with the command Chop().

For an operator O, O.Chop() or O.Chop($\epsilon$) Removes small (smaller than $\epsilon$) numbers from the operator. The standard value (when the argument is omitted) for $\epsilon = 2.2 \times 10^{−15}$. O.Chop() returns nil and changes the value of O.

## Example

We define: $$O=3.4+1.2a^{\dagger}_{0}\,a^{\phantom{\dagger}}_{0}+(2.5+0.0000000001I)a^{\dagger}_{1}\,a^{\phantom{\dagger}}_{2},$$ and remove the small complex part with the command Chop()

### Input

Example.Quanty
NF=3
NB=0
O = NewOperator(NF,NB,{{3.4},{0,-0,1.2},{1,-2,2.5+0.0000000001*I}})
print(O)
O.Chop(0.00001)
print(O)

### Result

Operator: Operator
QComplex         =          2 (Real==0 or Complex==1 or Mixed==2)
MaxLength        =          2 (largest number of product of lader operators)
NFermionic modes =          3 (Number of fermionic modes (site, spin, orbital, ...) in the one particle basis)
NBosonic modes   =          0 (Number of bosonic modes (phonon modes, ...) in the one particle basis)

Operator of Length   0
QComplex      =          0 (Real==0 or Complex==1)
N             =          1 (number of operators of length   0)
|  3.400000000000000E+00

Operator of Length   2
QComplex      =          1 (Real==0 or Complex==1)
N             =          2 (number of operators of length   2)
C  0 A  0 |  1.200000000000000E+00  0.000000000000000E+00
C  1 A  2 |  2.500000000000000E+00  1.000000000000000E-10

Operator: Operator
QComplex         =          0 (Real==0 or Complex==1 or Mixed==2)
MaxLength        =          2 (largest number of product of lader operators)
NFermionic modes =          3 (Number of fermionic modes (site, spin, orbital, ...) in the one particle basis)
NBosonic modes   =          0 (Number of bosonic modes (phonon modes, ...) in the one particle basis)

Operator of Length   0
QComplex      =          0 (Real==0 or Complex==1)
N             =          1 (number of operators of length   0)
|  3.400000000000000E+00

Operator of Length   2
QComplex      =          0 (Real==0 or Complex==1)
N             =          2 (number of operators of length   2)
C  0 A  0 |  1.200000000000000E+00
C  1 A  2 |  2.500000000000000E+00