## [Reduce-algebra-developers] About unexpected behavior operator sum and commutation rules.

 [Reduce-algebra-developers] About unexpected behavior operator sum and commutation rules. From: abpetrov - 2013-09-16 18:00:39 ```Hi, I wanted calculate some commutators, but I got next unexpectedbehavior of operator sum. The program is below. Aspreliminary note I understand that i <> i1 always. So, I defined anticommuting operators a, ac with corresponding commutation rules. Then I defined commutator com and operator H, after that two rules for ~a and sum - left rule and right rule. After that I tried to calculate commutator com( H, a(i1) ) using rule r1. And I got unexpected result, in which left rule works, but right rule not works. I expectedsome symmetry between left and right. Why is it not true? The program is: off lower\$ on intstr\$ load_package noncom2; operator a,ac; noncom a,a; noncom ac,ac; noncom a,ac; for all i let a(i)*ac(i) = 1 - ac(i)*a(i); for all i,j such that i neq j let a(i)*ac(j) = -ac(j)*a(i); for all i,j such that ordp(i,j) let a(i)*a(j) = -a(j)*a(i); for all i,j such that ordp(i,j) let ac(i)*ac(j) = -ac(j)*ac(i); operator com; for all x,y let com(x,y) = x*y - y*x; r1 := {~a*sum(~k, ~i)=>sum(a*k,i), sum(~k, ~i)*~a =>sum(k*a,i)}; operator H; H := sum( J1*ac(i)*a(i+1), i ); H1 := com( H, a(i1) ); H2 := (H1 where r1); end; Best regards, Petrov Alexander. ```

 [Reduce-algebra-developers] About unexpected behavior operator sum and commutation rules. From: abpetrov - 2013-09-16 18:00:39 ```Hi, I wanted calculate some commutators, but I got next unexpectedbehavior of operator sum. The program is below. Aspreliminary note I understand that i <> i1 always. So, I defined anticommuting operators a, ac with corresponding commutation rules. Then I defined commutator com and operator H, after that two rules for ~a and sum - left rule and right rule. After that I tried to calculate commutator com( H, a(i1) ) using rule r1. And I got unexpected result, in which left rule works, but right rule not works. I expectedsome symmetry between left and right. Why is it not true? The program is: off lower\$ on intstr\$ load_package noncom2; operator a,ac; noncom a,a; noncom ac,ac; noncom a,ac; for all i let a(i)*ac(i) = 1 - ac(i)*a(i); for all i,j such that i neq j let a(i)*ac(j) = -ac(j)*a(i); for all i,j such that ordp(i,j) let a(i)*a(j) = -a(j)*a(i); for all i,j such that ordp(i,j) let ac(i)*ac(j) = -ac(j)*ac(i); operator com; for all x,y let com(x,y) = x*y - y*x; r1 := {~a*sum(~k, ~i)=>sum(a*k,i), sum(~k, ~i)*~a =>sum(k*a,i)}; operator H; H := sum( J1*ac(i)*a(i+1), i ); H1 := com( H, a(i1) ); H2 := (H1 where r1); end; Best regards, Petrov Alexander. ```