q ∑ i =1 α$_{i}$ = ¯ α. S =    1 0 0 0 1 0 1 1 − 1    When ¯ G ( y ) exists for some a and some matrix S , the matrix S can always be chosen such that 0 ≤ α$_{1}$ ≤ ... ≤ α$_{q}$ ≤ ¯ α. Definition 4.1. A q × p matrix of polynomials G ( y ) satisfies the ”conti- nuity of lower degree ranks property” (CLDR) if for some non-singular q × q matrix S and for some α = ( α$_{1}$, ..., α$_{q}$ ) such that q ∑ i =1 α$_{i}$ = ¯ α , 0 ≤ α$_{1}$ ≤ ... ≤ α$_{q}$ ≤ ¯ α, (15) provides a rank q matrix of polynomials ¯ G ( y ) . Essentially, the CLDR property holds if for some S the transformed SG ( y ) is such that the stabilizing rate ¯ a for the determinant is shared be- tween the rows of the matrix SG ( y ) according to (15), and the limit matrix is non-singular. The matrix ¯ G ( y ) depends upon the choice of the matrix S . Indeed in Example 4.1 ¯ α = 4 but it is clear that for S = I Lemma 4.1 does not hold. This is a consequence of the fact that there is a linear dependence between the degree one polynomial terms in the rows of the matrix. However setting 18