sys

-

list of equations; linear functional system

vars

-

list of function variables such as [y1(x), y2(x), ...]; variables to solve for

A

-

Matrix with rational elements

b

-

Vector with rational elements

x

-

independent variable

case

-

name indicating the case of the system; one of 'differential', 'difference', or 'qdifference'

'method'    - either 'quasimodular'  if the quasimodular

              version of the EG-algorithm is invoked or 'ordinary'

              if the ordinary version is invoked

'input'     - either 'lists' for list input type or 'matrices'

              for matrix input type

'case'      - 'differential', 'difference', or 'qdifference'

'order'     - order of the system

'var'       - independent variable

'q_par'     - name of the parameter q in the q-difference case

              extracted from the given system, or it's value in case

              the parameter is a number

'system'    - system in list form

'functions' - functions to be solved for

'fnames'    - names of the functions to be solved for

'shifts'    - shifts of function variables in the difference case

'qshifts'   - q-shifts of function variables in the q-difference case

'mat'       - matrix of the matrix input form

'vec'       - vector of the matrix input form

'matdenom'  - list of denominators of the rows of the

              matrix for the matrix input form

1. At least two arguments must be specified.

2. For the matrix input type:

   (a) the matrix must be square

   (b) the number of arguments is at most four

   (c) if the number of arguments is three, the third

       argument must specify the case of the system

   (d) the second argument must be a name for the

       3-argument case, and a vector for the 4-argument case

   (e) vector and matrix sizes must be the same

   (f) if the number of arguments is four, the third

       argument must be a name specifying the independent

       variable, the fourth argument must specify the

       case of the system

3. For the list input type:

   (a) the number of arguments is two

   (b) the first argument must be a list of equations,

       the second argument must be a list of functions

       to be solved for

   (c) the independent variable must be specified only once

   (d) the system must be linear

   (e) the number of equations must be equal to

       the number of functions to be solved for

4. The functions to be solved for must appear in equations.

5. There exist unknown function names.

6. There exist extra independent variables in the system.

7. The type of the system is not supported.