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#N canvas 394 81 620 407 10;
#X text 90 114 ba;
#X text 33 93 ab;
#X text 220 113 however \, this thing i call commutator is more general
;
#X text 219 132 see commutative-test.pd;
#X text 127 217 anticommutator;
#X text 19 217 commutator;
#X text 218 15 Say operator \$2 is *. Then the commutativity rule is:
;
#X text 218 32 a*b=b*a which is also a*b-b*a = 0;
#X text 218 48 the commutator is a*b - b*a;
#X text 219 72 when \$2=+ this is also known as a "group commutator"
;
#X text 219 92 when \$2=* this is also known as a "ring commutator"
;
#X obj 18 19 inlet.\$1 a;
#X obj 93 19 inlet.\$1 b;
#X obj 18 38 taa.\$1;
#X obj 18 74 op2.\$1 \$2;
#X obj 80 98 op2.\$1 \$2;
#X obj 80 74 swap.\$1;
#X obj 18 180 op2.\$1 -;
#X obj 127 180 op2.\$1 +;
#X obj 18 199 outlet.\$1 ab-ba;
#X obj 127 199 outlet.\$1 ab+ba;
#X obj 18 121 taa.\$1;
#X connect 11 0 13 0;
#X connect 12 0 14 1;
#X connect 12 0 16 1;
#X connect 13 0 14 0;
#X connect 13 1 16 0;
#X connect 14 0 21 0;
#X connect 15 0 17 1;
#X connect 15 0 18 0;
#X connect 16 0 15 0;
#X connect 16 1 15 1;
#X connect 17 0 19 0;
#X connect 18 0 20 0;
#X connect 21 0 17 0;
#X connect 21 1 18 1;
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