TriangularMatrixOperations(R, Row, Col, M)

intclos.spad line 1 [edit on github]

• R : IntegralDomain
• Row : FiniteLinearAggregate(R)
• Col : FiniteLinearAggregate(R)
• M : MatrixCategory(R, Row, Col)

This package provides functions that compute "fraction-free" inverses of upper and lower triangular matrices over a integral domain. By "fraction-free inverses" 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). Thus, it is not necessary to pass to the quotient field in any of our computations.

LowTriBddDenomInv : (M, R) -> M

LowTriBddDenomInv(B, d) returns M, where B is a non-singular lower triangular matrix and d is an element of R such that M = d * inv(B) has entries in R.

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 M = d * inv(B) has entries in R.