Solving systems with determinants

Using these procedures it is possible to design the equation
evaluation procedure that are used in the general solving procedure of
`ALIAS` as described in 2.3.4.3. Assume for example that
you have to evaluate the
expression

where

INTERVAL_MATRIX A(6,6),B(6,6); A=Compute_A(V) //compute A for the interval value of x,y B=Compute_B(V) //compute B for the interval value of x,y W(1)=(V(1)+Medium_Determinant(A))*V(2)+2*(V(2)+Medium_Determinant(B));You must be however careful when using this procedure in a denominator as the presence of 0 in the interval evaluation of the determinant is not checked, which will lead to an error when computing the interval evaluation of an equation (see section 2.1.1.3).

Note that the `MakeF` procedure of the `ALIAS`-Maple package
is able to produce efficient code for an equation file even if
unexpanded determinants are present in the equation.

There are also procedures to compute the derivatives of a determinant
Note that the `MakeJ` procedure of the `ALIAS`-Maple package
is able to produce a procedure compatible with the requirements of the
gradient procedure required by the library (see
section 2.4.2.2) even if determinants are
present in the equation.

There are also procedures to compute the
second order derivatives of a determinant
Note that the `MakeH` procedure of the `ALIAS`-Maple package
is able to produce a procedure compatible with the requirements of the
hessian procedure required by the library (see section 2.5.2.1)
even if determinants are
present in the equation.