# Extract procedure

We consider the differential system of full rank of the form

A1y' + A0y = 0

where A1, A0 are square matrices and y is unknown vector, some components of which are selected (are of more interest to us then the other ones). The leading matrix A1 may be singular (i.e. the initial system may be a differential-algebraic system). The Extract procedure builds a new normal differential system

' = Aỹ

for the part of unknowns y. If some selected unknowns are not the part of then additionally Extract procedure builds an algebraic system of special form where every equation is an expression of some selected unknown that is not the part of the only via the selected unknowns from .

## Calling Sequence

Extract(A1, A0, ns, R)

## Parameters

A1 - leading matrix of the system;

A0 - trailing matrix of the system;

ns - set of positive integers - indices of the selected unknowns

R - Ore algebra chosen by OreTools:-SetOreRing function.

## Result

The output is [A, ns1, T, ns2], where A is the matrix of the normal differential system and ns1 is the set of pairs, the first element of each is the index out of ns and the second one is the index of the same undetermined function in the normal differential system; T is a matrix of the algebraic system and ns2 is the set of pairs, the first element of each is the index out of ns and the second one is the number of algebraic equation (row of T) to determine the selected unknown with index from the first element.

# Source

extract.mpl - the Maple code of the procedure

extr_sample.pdf - the pdf copy of Maple session with example