Z.J.HUANG,J.S.DENG.Y.Y.FENG AND F.L.CHEN raBkMI -Ei(m+((m-a)n+1). t盆bad民oare恤mndr以rn-ins nd the mmlr时 e fll a 6a明=∑∑i=1 e((1),ht m6j1+a+1. 会会宫(r -言空三(0》- -宫区人x -宫以)》a10 Z.J. HUANG, J.S. DENG, Y.Y. FENG AND F.L. CHEN Theorem 3.2. Let M be the coefficient matrix of the global in-line conformality condition MZ = 0, suppose m 2α + 1, n 2β + 1, then rankM = Ei h(m + 1)(n − β) + Ei v(m − α)(n + 1), where Ei h and Ei v are the number of horizontal in-lines and the number of vertical in-lines, respectively. Proof. According to the property of M, we only need to show M is row full rank. Suppose the form of the vertex cofactor ci(x, y) ∈ Pm−α−1,n−β−1 be ci(x, y) = m−α−1 j=0 n−  β−1 k=0 ci jkxjyk, i = 1,...,V. For a horizontal in-line conformality condition(Equation (11)), let Ci k = (ci 0,k, ci 1,k,...,ci m−α−1,k) T , k = 0, 1,...,n − β − 1 Ci = (Ci 0, Ci 1,...,Ci n−β−1) T , Ck = (Ci0 k , Ci1 k ,...,Ciκ k ) T , C = (Ci0 , Ci1 ,...,Ciκ ) T . Given t(t = 0, 1,...,κ) and k(k = 0, 1,...,n − β − 1), let Am,α(xit )Cit k = (b0, b1,...,bm)T , where for j = 0,...,m, bj = m− α−1 l=0 aj,lc it l,k = min(j,m −α−1) l=max(0,j−α−1) α + 1 j − l  xα+1−(j−l) it c it l,k, since 0 l m − α − 1, and aj,l is nonzero when l j l + α + 1. Then we have κ t=0 cit (x, y)(x − xit ) α+1 = κ t=0 m− α−1 j=0 n−  β−1 k=0 c it jkxjyk(x − xit ) α+1 = κ t=0 m− α−1 j=0 n−  β−1 k=0 α  +1 l=0 α + 1 l  (−xit ) α+1−l c it jkxj+l yk = n−  β−1 k=0 ykκ t=0 m− α−1 j=0 α  +1 l=0 α + 1 l  (−xit ) α+1−l c it jkxj+l = n−  β−1 k=0 ykκ t=0 m j=0 min(j,m −α−1) l=max(0,j−α−1) α + 1 j − l  (−xit ) α+1−(j−l) c it l,kxj = n−  β−1 k=0 yk κ t=0 Am,α(−xit )Cit k  · X = n−  β−1 k=0 yk Am,α(−xi0 ) Am,α(−xi1 ) ... Am,α(−xiκ )  Ck  · X,