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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 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;
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