```(* ----------------------------------------------------------------------------
* \$Id: RRUADOM.md,v 1.1 1994/03/11 15:21:51 pesch Exp \$
* ----------------------------------------------------------------------------
* This file is part of MAS.
* ----------------------------------------------------------------------------
* Copyright (c) 1993 Universitaet Passau
* ----------------------------------------------------------------------------
* \$Log: RRUADOM.md,v \$
* Revision 1.1  1994/03/11  15:21:51  pesch
* Counting real roots of multivariate polynomials, Diplomarbeit F. Lippold
*
* ----------------------------------------------------------------------------
*)

(* Real Root Univariate Arbitrary Domain Definition Module *)

(* Import lists and declarations. *)

FROM MASSTOR IMPORT LIST;

CONST rcsid = "\$Id: RRUADOM.md,v 1.1 1994/03/11 15:21:51 pesch Exp \$";
CONST copyright = "Copyright (c) 1993 Universitaet Passau";

PROCEDURE RRUADPOLTOVEC(D,g,d: LIST): LIST;
(* Real root univariate arbitrary domain polynomial to vector.
g is an univariate polynomial of domain D with degree less than d.
If a(i) is the coefficient of X**i in g then the list (a(d-1),...,a(0))
is returned. *)

PROCEDURE RRUADSTRCONST(D,f,h: LIST): LIST;
(* Real root univariate arbitrary domain structure constants.
f and h are univariate polynomials of domain D.
f is monic with degree p > 0. A matrix beta with entries beta[i,j]
from D for 0 le i le p-1 and 0 le j le 3*p-3 is created, such that
h * X**j = beta[0,j]+beta[1,j]*X+...+beta[p-1,j]X**(p-1) modulo f.
beta is represented columnwise. *)

(* Real root univariate arbitrary domain quadratic form.
beta is the set of structure constants as computed by RRUADSTRCONST.
Let s(k) = tr(M(h)*M(X**k))=beta[0,k]+beta[1,k+1]+...+beta[p-1,k+p-1].
The matrix Q=(q(i,j)) with q(i,j) = s(i+j-2) is computed. *)

PROCEDURE RRUADCOUNT(D,f,H,v,tf: LIST): LIST;
(* Real root univariate arbirary domain count.
f is a monic univariate polynomial of domain D with degree p > 0.
H is a list of univariate polynomials of length s. v is a vector of signs
with length not greater than s. tf is the trace flag.
ZNL is a list of pairs (z,n) with n is an element of {-1,0,+1}**s and z > 0
is the number of real zeroes of f wrt the sign condition n for the elements
of H. ZNL is sorted wrt the invers lexicographical order of the n. If there
does not exist any real zero or a zero satisfiing the sign condition v,
then the empty list is returned. *)