## Blow-up substitutions

In this post, we introduce a type of substitutions to be used in our normalization algorithm: let $X$ and $Y$ be two single indeterminates. Definition For $\lambda \in \RR$, we let $\bl_\lambda:\Ps{R}{X,Y} \into \Ps{R}{X,Y}$ be the blow-up substitution defined by $$\bl_\lambda(X):= X \quad\text{and}\quad \bl_\lambda(Y):= X(\lambda+Y).$$ We also let $\bl_\infty:\Ps{R}{X,Y} \into \Ps{R}{X,Y}$ be the blow-up substitution…