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Such expressions are given by continuants. Sage provides function continuant for computing them - see https://doc.sagemath.org/html/en/reference/rings_standard/sage/arith/misc.html

Such expressions are given by continuants - namely, $p_n(a_0,\dots,a_n)= K_{n+1}(a_0,\dots,a_n)$ and $q_n(a_0,\dots,a_n)= K_n(a_1,\dots,a_n)$ . Sage provides function continuant for computing them - see https://doc.sagemath.org/html/en/reference/rings_standard/sage/arith/misc.html

Such expressions are given by continuants - namely, $p_n(a_0,\dots,a_n)= K_{n+1}(a_0,\dots,a_n)$ and $q_n(a_0,\dots,a_n)= K_n(a_1,\dots,a_n)$ . Sage provides function continuant for computing them - see https://doc.sagemath.org/html/en/reference/rings_standard/sage/arith/misc.html

R.<a> = InfinitePolynomialRing(QQ)
print('p=', continuant( [a[i] for i in (0..5)]) )
print('q=', continuant( [a[i] for i in (1..5)]) )