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documentation:language_reference:objects:operator:methods:chop [2016/09/25 13:59] – created Maurits W. Haverkortdocumentation:language_reference:objects:operator:methods:chop [2025/11/20 04:20] (current) – external edit 127.0.0.1
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 +====== 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 ====
 +<code Quanty 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)
 +</code>
 +
 +==== Result ====
 +<file Quanty_Output>
 +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
 +</file>
 +
 +===== Available methods =====
 +{{indexmenu>.#1}}

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