From functions's declaration:

    UpTriBddDenomInv: (M,R) -> M
      ++ UpTriBddDenomInv(B,d) returns M, where
      ++ B is a non-singular upper triangular matrix and d is an
      ++ element of R such that \spad{M = d * inv(B)} has entries in R.

Here, it's false, but may be use another error message

(1) -> a:=matrix ([[1,2],[0,9]])

(1)

inverse(a)

(2)

)expose TriangularMatrixOperations

   TriangularMatrixOperations is now explicitly exposed in frame 
      initial 
UpTriBddDenomInv(a,9)

(3)

UpTriBddDenomInv(a,7)

   >> Error detected within library code:
   "failed" of mode Union(Integer,"failed") cannot be coerced to mode Integer

a:=matrix ([[1,2],[0,9]])

(4)

a:=transpose(a)

(5)

inverse(a)

(6)

LowTriBddDenomInv(a,9)

(7)

LowTriBddDenomInv(a,7)

   >> Error detected within library code:
   "failed" of mode Union(Integer,"failed") cannot be coerced to mode Integer

From the package:

  ++ This package provides functions that compute "fraction-free"
  ++ inverses of upper and lower triangular matrices over a integral
  ++ domain. By "fraction-free inverse" we mean the following:
  ++ given a matrix B with entries in R and an element d of R such that
  ++ d* inv(B) also has entries in R, we return d * inv(B).

So if you enter B and d such that d * inv(B) does not have entries in R, it is an error. The package is for internal use (that why it is not exposed) where d is always divisible by the determinant of B.

But I don't like computer error. I prefer some mathematical message for example:

d is not an element of R such that \spad{M = d * inv(B)} has entries in R.

Severity: normal => wishlist