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    $\begingroup$ You should be able to do Attributes[CirclePlus]=Flat, and then your first definition should do the trick $\endgroup$ Commented Oct 19, 2022 at 18:49
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    $\begingroup$ Why not use CircleMinus instead? It already has left grouping. $\endgroup$ Commented Oct 19, 2022 at 21:58
  • $\begingroup$ @CarlWoll That's strange. Why should CircleMinus be automatically left-associative but CirclePlus not? Who made that choice and why? Is it just to make it more consistent with Subtract, which is non-associative and therefore requires a choice or left or right associativity by default? $\endgroup$ Commented Oct 19, 2022 at 22:10
  • $\begingroup$ @ Lukas Lang Now I try ``` Clear[CircleDot, CirclePlus, CircleMinus, CircleTimes]; a_[CirclePlus]b_ := a + b^2; Attributes[CirclePlus] = Flat; ``` But it gave ``` CirclePlus[a]+(CirclePlus[b]+CirclePlus[c]^2)^2 ``` $\endgroup$ Commented Oct 19, 2022 at 22:57
  • $\begingroup$ @CarlWoll Yes, the CircleMinus works. However I need to define more than two different operators. So I need to fix it $\endgroup$ Commented Oct 19, 2022 at 23:05