#N canvas 394 81 620 407 10;
#X obj 18 84 \$1;
#X obj 18 210 -;
#X obj 68 115 \$1;
#X obj 68 96 f;
#X obj 18 19 inlet a;
#X obj 84 32 inlet b;
#X text 75 134 ba;
#X text 33 103 ab;
#X obj 18 38 t a b a;
#X text 218 15 commutativity rule for operator \$1 is: a \$1 b = b
\$1 a;
#X text 218 32 which is also a \$1 b - b \$1 a = 0;
#X text 218 48 the commutator is a \$1 b - b \$1 a;
#X obj 18 229 outlet ab-ba;
#X text 189 112 when \$1 = + this is also known as a "group commutator"
;
#X text 189 132 when \$1 = * this is also known as a "ring commutator"
;
#X text 190 153 however \, this thing i call commutator is more general
;
#X text 189 172 see commutative-test.pd;
#X obj 106 229 outlet ab+ba;
#X obj 18 141 t a a;
#X obj 106 210 +;
#X text 106 247 anticommutator;
#X text 19 247 commutator;
#X connect 0 0 18 0;
#X connect 1 0 12 0;
#X connect 2 0 1 1;
#X connect 2 0 19 0;
#X connect 3 0 2 0;
#X connect 4 0 8 0;
#X connect 5 0 3 1;
#X connect 5 0 0 1;
#X connect 8 0 0 0;
#X connect 8 1 3 0;
#X connect 8 2 2 1;
#X connect 18 0 1 0;
#X connect 18 1 19 1;
#X connect 19 0 17 0;