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—documentation:language_reference:functions:partialoperator [2022/10/04 22:08] (current) – Maurits W. Haverkort
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 +====== PartialOperator ======
 +
 +###
 +PartialOperator(//op//,//indices//,//mode//) takes an operator and a list of indices and depending on //mode// removes or keeps specific terms.
 +###
 +
 +###
 +Mode //"include"// keeps all terms whereby at least one of the creation or annihilation operators acts on the orbitals included in the list //indices//.
 +###
 +
 +###
 +Mode //"exclude"// removes all terms whereby at least one of the creation or annihilation operators acts on the orbitals included in the list //indices//.
 +###
 +
 +###
 +Mode //"conserve"// removes all terms that do not keep the occupation conserved from the orbitals listed in the table //indices//. In this case the table //indices// is allowed to include tables. In the latter case the sum of the occupation all orbitals in the list needs to be conserved
 +###
 +
 +===== Input =====
 +
 +  * //op// : An Operator.
 +  * //indices// : A list of indices.
 +  * //mode// : either "include", "exclude", or "conserve"
 +
 +===== Output =====
 +
 +  * //partialOp// : The operator with a subset of terms of the original operator.
 +
 +===== Example =====
 +
 +==== Input ====
 +<code Quanty Example.Quanty>
 +NF = 3
 +NB = 0
 +
 +opp1cr = NewOperator(NF,NB, {{ 0,1},{ 1,1},{ 2,1}})
 +opp1an = NewOperator(NF,NB, {{-0,1},{-1,1},{-2,1}})
 +opp2 = opp1cr * opp1an
 +opp3 = opp1an * opp2
 +opp4 = opp1cr * opp3
 +
 +opp = 1 + opp1cr + opp1an + opp2 + opp3 + opp4
 +
 +-- The operatore contains strings of creation and annihilation operators of length 0 to 4
 +-- l=0  1 term
 +-- l=1  6 terms (3 creation, 3 annihilation)
 +-- l=2  9 terms (3 creation * 3 annihilation)
 +-- l=3  9 terms (cr an an) note that an0 an1 = - an1 an0
 +-- l=4  9 terms 
 +-- the full operator is
 +print("================ opp =============")
 +print(opp)
 +
 +-- We only keep terms that at least act once on orbital 1
 +print("================ PartialOperator  {1} include =============")
 +print(PartialOperator(opp,{1},"include"))
 +
 +-- We only keep terms that at least act once on orbital 0 or at orbital 1
 +print("================ PartialOperator  {0,2} include =============")
 +print(PartialOperator(opp,{0,2},"include"))
 +
 +-- We remove all terms that act on orbital 1
 +print("================ PartialOperator  {1} exclude =============")
 +print(PartialOperator(opp,{1},"exclude"))
 +
 +-- We exclude all terms that act on orbital 0 and we exclude all terms that act on orbital 2
 +print("================ PartialOperator  {0,2} exclude =============")
 +print(PartialOperator(opp,{0,2},"exclude"))
 +
 +-- We only keep the terms that keep the occupation of orbital 1 conserved
 +print("================ PartialOperator  {1} conserve =============")
 +print(PartialOperator(opp,{1},"conserve"))
 +
 +-- We only keep the terms that keep the occupation of orbital 0 conserved and that keep
 +-- the occupation of orbital 2 conserved
 +print("================ PartialOperator  {0,2} conserve =============")
 +print(PartialOperator(opp,{0,2},"conserve"))
 +
 +-- We only keep those terms that keep the sum of the occupation of orbital 0 and 2 conserved
 +print("================ PartialOperator  {{0,2}} conserve =============")
 +print(PartialOperator(opp,{{0,2}},"conserve"))
 +</code>
 +
 +==== Result ====
 +<file Quanty_Output>
 +================ opp =============
 +
 +Operator: Operator
 +QComplex         =          0 (Real==0 or Complex==1 or Mixed==2)
 +MaxLength        =          4 (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)
 +|  1.00000000000000E+00
 +
 +Operator of Length   1
 +QComplex      =          0 (Real==0 or Complex==1)
 +N             =          6 (number of operators of length   1)
 +C  0 |  1.00000000000000E+00
 +C  1 |  1.00000000000000E+00
 +C  2 |  1.00000000000000E+00
 +A  0 |  4.00000000000000E+00
 +A  1 |  4.00000000000000E+00
 +A  2 |  4.00000000000000E+00
 +
 +Operator of Length   2
 +QComplex      =          0 (Real==0 or Complex==1)
 +N             =          9 (number of operators of length   2)
 +C  0 A  0 |  4.00000000000000E+00
 +C  1 A  0 |  4.00000000000000E+00
 +C  2 A  0 |  4.00000000000000E+00
 +C  0 A  1 |  4.00000000000000E+00
 +C  1 A  1 |  4.00000000000000E+00
 +C  2 A  1 |  4.00000000000000E+00
 +C  0 A  2 |  4.00000000000000E+00
 +C  1 A  2 |  4.00000000000000E+00
 +C  2 A  2 |  4.00000000000000E+00
 +
 +Operator of Length   3
 +QComplex      =          0 (Real==0 or Complex==1)
 +N             =          9 (number of operators of length   3)
 +C  0 A  1 A  0 |  0.00000000000000E+00
 +C  0 A  2 A  0 |  0.00000000000000E+00
 +C  1 A  1 A  0 |  0.00000000000000E+00
 +C  1 A  2 A  0 |  0.00000000000000E+00
 +C  2 A  1 A  0 |  0.00000000000000E+00
 +C  2 A  2 A  0 |  0.00000000000000E+00
 +C  0 A  2 A  1 |  0.00000000000000E+00
 +C  1 A  2 A  1 |  0.00000000000000E+00
 +C  2 A  2 A  1 |  0.00000000000000E+00
 +
 +Operator of Length   4
 +QComplex      =          0 (Real==0 or Complex==1)
 +N             =          9 (number of operators of length   4)
 +C  1 C  0 A  1 A  0 |  0.00000000000000E+00
 +C  2 C  0 A  1 A  0 |  0.00000000000000E+00
 +C  1 C  0 A  2 A  0 |  0.00000000000000E+00
 +C  2 C  0 A  2 A  0 |  0.00000000000000E+00
 +C  2 C  1 A  1 A  0 |  0.00000000000000E+00
 +C  2 C  1 A  2 A  0 |  0.00000000000000E+00
 +C  1 C  0 A  2 A  1 |  0.00000000000000E+00
 +C  2 C  0 A  2 A  1 |  0.00000000000000E+00
 +C  2 C  1 A  2 A  1 |  0.00000000000000E+00
 +
 +
 +================ PartialOperator  {1} include =============
 +
 +Operator: 
 +QComplex         =          0 (Real==0 or Complex==1 or Mixed==2)
 +MaxLength        =          4 (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   1
 +QComplex      =          0 (Real==0 or Complex==1)
 +N             =          2 (number of operators of length   1)
 +C  1 |  1.00000000000000E+00
 +A  1 |  4.00000000000000E+00
 +
 +Operator of Length   2
 +QComplex      =          0 (Real==0 or Complex==1)
 +N             =          5 (number of operators of length   2)
 +C  1 A  0 |  4.00000000000000E+00
 +C  0 A  1 |  4.00000000000000E+00
 +C  1 A  1 |  4.00000000000000E+00
 +C  2 A  1 |  4.00000000000000E+00
 +C  1 A  2 |  4.00000000000000E+00
 +
 +Operator of Length   3
 +QComplex      =          0 (Real==0 or Complex==1)
 +N             =          7 (number of operators of length   3)
 +C  0 A  1 A  0 |  0.00000000000000E+00
 +C  1 A  1 A  0 |  0.00000000000000E+00
 +C  1 A  2 A  0 |  0.00000000000000E+00
 +C  2 A  1 A  0 |  0.00000000000000E+00
 +C  0 A  2 A  1 |  0.00000000000000E+00
 +C  1 A  2 A  1 |  0.00000000000000E+00
 +C  2 A  2 A  1 |  0.00000000000000E+00
 +
 +Operator of Length   4
 +QComplex      =          0 (Real==0 or Complex==1)
 +N             =          8 (number of operators of length   4)
 +C  1 C  0 A  1 A  0 |  0.00000000000000E+00
 +C  2 C  0 A  1 A  0 |  0.00000000000000E+00
 +C  1 C  0 A  2 A  0 |  0.00000000000000E+00
 +C  2 C  1 A  1 A  0 |  0.00000000000000E+00
 +C  2 C  1 A  2 A  0 |  0.00000000000000E+00
 +C  1 C  0 A  2 A  1 |  0.00000000000000E+00
 +C  2 C  0 A  2 A  1 |  0.00000000000000E+00
 +C  2 C  1 A  2 A  1 |  0.00000000000000E+00
 +
 +
 +================ PartialOperator  {0,2} include =============
 +
 +Operator: 
 +QComplex         =          0 (Real==0 or Complex==1 or Mixed==2)
 +MaxLength        =          4 (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   1
 +QComplex      =          0 (Real==0 or Complex==1)
 +N             =          4 (number of operators of length   1)
 +C  0 |  1.00000000000000E+00
 +C  2 |  1.00000000000000E+00
 +A  0 |  4.00000000000000E+00
 +A  2 |  4.00000000000000E+00
 +
 +Operator of Length   2
 +QComplex      =          0 (Real==0 or Complex==1)
 +N             =          8 (number of operators of length   2)
 +C  0 A  0 |  4.00000000000000E+00
 +C  1 A  0 |  4.00000000000000E+00
 +C  2 A  0 |  4.00000000000000E+00
 +C  0 A  1 |  4.00000000000000E+00
 +C  2 A  1 |  4.00000000000000E+00
 +C  0 A  2 |  4.00000000000000E+00
 +C  1 A  2 |  4.00000000000000E+00
 +C  2 A  2 |  4.00000000000000E+00
 +
 +Operator of Length   3
 +QComplex      =          0 (Real==0 or Complex==1)
 +N             =          9 (number of operators of length   3)
 +C  0 A  1 A  0 |  0.00000000000000E+00
 +C  0 A  2 A  0 |  0.00000000000000E+00
 +C  1 A  1 A  0 |  0.00000000000000E+00
 +C  1 A  2 A  0 |  0.00000000000000E+00
 +C  2 A  1 A  0 |  0.00000000000000E+00
 +C  2 A  2 A  0 |  0.00000000000000E+00
 +C  0 A  2 A  1 |  0.00000000000000E+00
 +C  1 A  2 A  1 |  0.00000000000000E+00
 +C  2 A  2 A  1 |  0.00000000000000E+00
 +
 +Operator of Length   4
 +QComplex      =          0 (Real==0 or Complex==1)
 +N             =          9 (number of operators of length   4)
 +C  1 C  0 A  1 A  0 |  0.00000000000000E+00
 +C  2 C  0 A  1 A  0 |  0.00000000000000E+00
 +C  1 C  0 A  2 A  0 |  0.00000000000000E+00
 +C  2 C  0 A  2 A  0 |  0.00000000000000E+00
 +C  2 C  1 A  1 A  0 |  0.00000000000000E+00
 +C  2 C  1 A  2 A  0 |  0.00000000000000E+00
 +C  1 C  0 A  2 A  1 |  0.00000000000000E+00
 +C  2 C  0 A  2 A  1 |  0.00000000000000E+00
 +C  2 C  1 A  2 A  1 |  0.00000000000000E+00
 +
 +
 +================ PartialOperator  {1} exclude =============
 +
 +Operator: 
 +QComplex         =          0 (Real==0 or Complex==1 or Mixed==2)
 +MaxLength        =          4 (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)
 +|  1.00000000000000E+00
 +
 +Operator of Length   1
 +QComplex      =          0 (Real==0 or Complex==1)
 +N             =          4 (number of operators of length   1)
 +C  0 |  1.00000000000000E+00
 +C  2 |  1.00000000000000E+00
 +A  0 |  4.00000000000000E+00
 +A  2 |  4.00000000000000E+00
 +
 +Operator of Length   2
 +QComplex      =          0 (Real==0 or Complex==1)
 +N             =          4 (number of operators of length   2)
 +C  0 A  0 |  4.00000000000000E+00
 +C  2 A  0 |  4.00000000000000E+00
 +C  0 A  2 |  4.00000000000000E+00
 +C  2 A  2 |  4.00000000000000E+00
 +
 +Operator of Length   3
 +QComplex      =          0 (Real==0 or Complex==1)
 +N             =          2 (number of operators of length   3)
 +C  0 A  2 A  0 |  0.00000000000000E+00
 +C  2 A  2 A  0 |  0.00000000000000E+00
 +
 +Operator of Length   4
 +QComplex      =          0 (Real==0 or Complex==1)
 +N             =          1 (number of operators of length   4)
 +C  2 C  0 A  2 A  0 |  0.00000000000000E+00
 +
 +
 +================ PartialOperator  {0,2} exclude =============
 +
 +Operator: 
 +QComplex         =          0 (Real==0 or Complex==1 or Mixed==2)
 +MaxLength        =          4 (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)
 +|  1.00000000000000E+00
 +
 +Operator of Length   1
 +QComplex      =          0 (Real==0 or Complex==1)
 +N             =          2 (number of operators of length   1)
 +C  1 |  1.00000000000000E+00
 +A  1 |  4.00000000000000E+00
 +
 +Operator of Length   2
 +QComplex      =          0 (Real==0 or Complex==1)
 +N             =          1 (number of operators of length   2)
 +C  1 A  1 |  4.00000000000000E+00
 +
 +
 +================ PartialOperator  {1} conserve =============
 +
 +Operator: 
 +QComplex         =          0 (Real==0 or Complex==1 or Mixed==2)
 +MaxLength        =          4 (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)
 +|  1.00000000000000E+00
 +
 +Operator of Length   1
 +QComplex      =          0 (Real==0 or Complex==1)
 +N             =          4 (number of operators of length   1)
 +C  0 |  1.00000000000000E+00
 +C  2 |  1.00000000000000E+00
 +A  0 |  4.00000000000000E+00
 +A  2 |  4.00000000000000E+00
 +
 +Operator of Length   2
 +QComplex      =          0 (Real==0 or Complex==1)
 +N             =          5 (number of operators of length   2)
 +C  0 A  0 |  4.00000000000000E+00
 +C  2 A  0 |  4.00000000000000E+00
 +C  1 A  1 |  4.00000000000000E+00
 +C  0 A  2 |  4.00000000000000E+00
 +C  2 A  2 |  4.00000000000000E+00
 +
 +Operator of Length   3
 +QComplex      =          0 (Real==0 or Complex==1)
 +N             =          4 (number of operators of length   3)
 +C  0 A  2 A  0 |  0.00000000000000E+00
 +C  1 A  1 A  0 |  0.00000000000000E+00
 +C  2 A  2 A  0 |  0.00000000000000E+00
 +C  1 A  2 A  1 |  0.00000000000000E+00
 +
 +Operator of Length   4
 +QComplex      =          0 (Real==0 or Complex==1)
 +N             =          5 (number of operators of length   4)
 +C  1 C  0 A  1 A  0 |  0.00000000000000E+00
 +C  2 C  0 A  2 A  0 |  0.00000000000000E+00
 +C  2 C  1 A  1 A  0 |  0.00000000000000E+00
 +C  1 C  0 A  2 A  1 |  0.00000000000000E+00
 +C  2 C  1 A  2 A  1 |  0.00000000000000E+00
 +
 +
 +================ PartialOperator  {0,2} conserve =============
 +
 +Operator: 
 +QComplex         =          0 (Real==0 or Complex==1 or Mixed==2)
 +MaxLength        =          4 (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)
 +|  1.00000000000000E+00
 +
 +Operator of Length   1
 +QComplex      =          0 (Real==0 or Complex==1)
 +N             =          2 (number of operators of length   1)
 +C  1 |  1.00000000000000E+00
 +A  1 |  4.00000000000000E+00
 +
 +Operator of Length   2
 +QComplex      =          0 (Real==0 or Complex==1)
 +N             =          3 (number of operators of length   2)
 +C  0 A  0 |  4.00000000000000E+00
 +C  1 A  1 |  4.00000000000000E+00
 +C  2 A  2 |  4.00000000000000E+00
 +
 +Operator of Length   3
 +QComplex      =          0 (Real==0 or Complex==1)
 +N             =          2 (number of operators of length   3)
 +C  0 A  1 A  0 |  0.00000000000000E+00
 +C  2 A  2 A  1 |  0.00000000000000E+00
 +
 +Operator of Length   4
 +QComplex      =          0 (Real==0 or Complex==1)
 +N             =          3 (number of operators of length   4)
 +C  1 C  0 A  1 A  0 |  0.00000000000000E+00
 +C  2 C  0 A  2 A  0 |  0.00000000000000E+00
 +C  2 C  1 A  2 A  1 |  0.00000000000000E+00
 +
 +
 +================ PartialOperator  {{0,2}} conserve =============
 +
 +Operator: 
 +QComplex         =          0 (Real==0 or Complex==1 or Mixed==2)
 +MaxLength        =          4 (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)
 +|  1.00000000000000E+00
 +
 +Operator of Length   1
 +QComplex      =          0 (Real==0 or Complex==1)
 +N             =          2 (number of operators of length   1)
 +C  1 |  1.00000000000000E+00
 +A  1 |  4.00000000000000E+00
 +
 +Operator of Length   2
 +QComplex      =          0 (Real==0 or Complex==1)
 +N             =          5 (number of operators of length   2)
 +C  0 A  0 |  4.00000000000000E+00
 +C  2 A  0 |  4.00000000000000E+00
 +C  1 A  1 |  4.00000000000000E+00
 +C  0 A  2 |  4.00000000000000E+00
 +C  2 A  2 |  4.00000000000000E+00
 +
 +Operator of Length   3
 +QComplex      =          0 (Real==0 or Complex==1)
 +N             =          4 (number of operators of length   3)
 +C  0 A  1 A  0 |  0.00000000000000E+00
 +C  2 A  1 A  0 |  0.00000000000000E+00
 +C  0 A  2 A  1 |  0.00000000000000E+00
 +C  2 A  2 A  1 |  0.00000000000000E+00
 +
 +Operator of Length   4
 +QComplex      =          0 (Real==0 or Complex==1)
 +N             =          5 (number of operators of length   4)
 +C  1 C  0 A  1 A  0 |  0.00000000000000E+00
 +C  2 C  0 A  2 A  0 |  0.00000000000000E+00
 +C  2 C  1 A  1 A  0 |  0.00000000000000E+00
 +C  1 C  0 A  2 A  1 |  0.00000000000000E+00
 +C  2 C  1 A  2 A  1 |  0.00000000000000E+00
 +</file>
 +
 +===== Table of contents =====
 +{{indexmenu>.#1}}
  

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