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scratchpad7

v7	v8
108	108
109	109
110		Also note, that the indexing of the temperatures is commutative, and that all of the diagonal temperature terms will have two contributions. One from $\alpha ~~\pm i \pm j$ and one from $\alpha \pm j \pm i~~$. We can rewrite
	110	Also note, that the indexing of the temperatures is commutative, and that all of the diagonal temperature terms will have two contributions. One from $\alpha_{\pm i \pm j}$ and one from $\alpha_{\pm j \pm i}$. We can rewrite
111	111
112	112	$\displaystyle \sum_{\pm i, \pm j,i \ne j} \alpha_{\pm i, \pm j} T^{\lambda+1}_{\pm \hat{i} \pm \hat{j}} = \sum_{\pm i, \pm j,i < j} \left ( \alpha_{\pm i, \pm j} + \alpha_{\pm j, \pm i} \right ) T^{\lambda+1}_{\pm \hat{i} \pm \hat{j}} = \sum_{\pm i, \pm j,i < j} \alpha*_{\pm i, \pm j}T^{\lambda+1}_{\pm \hat{i} \pm \hat{j}}$