#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 obj 18 19 \$1.inlet a; #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 18 199 \$1.outlet ab-ba; #X obj 127 199 \$1.outlet ab+ba; #X obj 93 19 \$1.inlet b; #X obj 80 74 \$1.swap; #X obj 80 98 \$1.do \$2; #X obj 18 74 \$1.do \$2; #X obj 18 121 \$1.taa; #X obj 18 38 \$1.taa; #X obj 18 180 \$1.do -; #X obj 127 180 \$1.do +; #X connect 6 0 19 0; #X connect 14 0 15 1; #X connect 14 0 17 1; #X connect 15 0 16 0; #X connect 15 1 16 1; #X connect 16 0 20 1; #X connect 16 0 21 0; #X connect 17 0 18 0; #X connect 18 0 20 0; #X connect 18 1 21 1; #X connect 19 0 17 0; #X connect 19 1 15 0; #X connect 20 0 12 0; #X connect 21 0 13 0;