Symmetric system 2 Yin-Yang system 2

Symmetric system 3

Symmetric system 4^a

$+\times +=+$

$+\times +=-$

$+\times +=-$

$-\times -=-$

$-\times -=+$

$-\times -=+$

$+\times -=$ Not allowed, needed?

$+\times -=\pm$

$+\times -=$ Not allowed, needed?

$-\times +=$ Not allowed, needed?

$-\times +=\pm$

$-\times +=$ Not allowed, needed?

$\sqrt{+}=+$

$\sqrt{+}=-$

$\sqrt{+}=-$

$\sqrt{-}=-$

$\sqrt{-}=+$

$\sqrt{-}=+$

Numerical examples

$2\times 2=4$

$2\times 2=-4$

$2\times 2=-4$

$-2\times -2=-4$

$-2\times -2=4$

$-2\times -2=4$

$2\times -2=$ Not allowed

$2\times -2=\pm 4$

$2\times -2=$ Not allowed

$-2\times 2=$ Not allowed

$-2\times 2=\pm 4$

$-2\times 2=$ Not allowed

$\sqrt{4}=2$

$\sqrt{4}=-2$

$\sqrt{4}=-2$

$\sqrt{-4}=-2$

$\sqrt{-4}=2$

$\sqrt{-4}=2$

$\sqrt{\pm 4}=$ Not allowed

$\sqrt{\pm 4}=\sqrt{2}\sqrt{-2}$

$\sqrt{\pm 4}=$ Not allowed

Addition and subtraction identical for all systems, as there is no sign dominance.

$2+2=4$

$2+2=4$

$2+2=4$

$-2+2=0$

$-2+2=0$

$-2+2=0$

$2-2=0$

$2-2=0$

$2-2=0$

$-2-2=-4$

$-2-2=-4$

$-2-2=-4$