...n Hessenberg determinants. Continuants The determinant of a tridiagonal matrix is called a continuant. Continuants are intimately connected to continued fractions, from which they get their name (see =-=[3]-=-). We will denote the determinant fi fi fi fi fi fi fi fi fi fi fi fi fi d 0 (1) d 1 (1) 0 \Delta \Delta \Delta 0 d \Gamma1 (1) d 0 (2) d 1 (2) . . . . . . 0 d \Gamma1 (2) d 0 (3) . . . 0 . . . . . . ...

... i. Other shortcuts like omitting double specication of overlapping corner elements are also possible (refer to the online help pages or [5] for details). Examples ? with(FRAMEFORMS): ? Arrow(n,[ [row=-=[1]-=-,a], [col[1],[2..n,b]], ? [diag,[2..n,1]] ],print,check); Matrix : 2 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 4 a a a o o o a b 1 0 0 0 0 0 b 0 1 0 0 0 0 o 0 0 o 0 0 0 o 0 0 0 o 0 0 o 0 0 0 0 o 0 b 0 0 0 0 0 1 3...

...tries. Matrices of this class will be called frameforms. Motivation Geometric predicates such as the in-sphere testsdo d + 2 points of IR d lie on a common sphere ?smay be written in determinant form =-=[1]-=-. Consider the following example in [1]: We have a conguration of d + 2 points in IR d , two distinct points s = (s; : : : ; s) and t = (t; : : : ; t) from the main diagonal and one point t i = t i \D...

...Maple packages that automatically derive the determinant formula for specied matrices of these classes. Introduction Determinants have a long history in mathematics and arise in numerous applications =-=[2]-=-. Here we are not interested in the value of a determinant of xed integer order but rather in the determinant formula of a specially structured matrix of symbolic dimension n. It is assumed that a cer...