(* ---------------------------------------------------------------------------- * $Id: LINALG.md,v 1.1 1994/03/11 15:21:45 pesch Exp $ * ---------------------------------------------------------------------------- * This file is part of MAS. * ---------------------------------------------------------------------------- * Copyright (c) 1993 Universitaet Passau * ---------------------------------------------------------------------------- * $Log: LINALG.md,v $ * Revision 1.1 1994/03/11 15:21:45 pesch * Counting real roots of multivariate polynomials, Diplomarbeit F. Lippold * * ---------------------------------------------------------------------------- *) DEFINITION MODULE LINALG; (* Linear algebra definition module *) FROM MASSTOR IMPORT LIST;CONSTrcsid = "$Id: LINALG.md,v 1.1 1994/03/11 15:21:45 pesch Exp $";CONSTcopyright = "Copyright (c) 1993 Universitaet Passau"; (* Arbitrary domain linear algebra ---------------------------------------- *)PROCEDURE ADUM(D,n: LIST): LIST; (* Arbitrary domain unit matrix. n is an integer. The (n x n) unit matrix of domain D is returned. *)PROCEDURE ADVSPROD(D,A,B: LIST): LIST; (* Arbitrary domain vector scalar product. A and B are vectors of the domain D. The arbitrary domain value C = a1*b1 + ... + an*bn is returned. *)PROCEDURE ADVSVPROD(A,b: LIST): LIST; (* Arbitrary domain vector scalar vector product. A is an arbitrary domain vector and b is a number of the same domain. The arbitrary domain vector C = (a1*b, ..., an*b) is returned. *)PROCEDURE ADVVSUM(A,B: LIST): LIST; (* Arbitrary domain vector vector sum. A and B are arbitrary domain vectors. The arbitrary domain vector C = (a1+b1, ..., an+bn) is returned. *)PROCEDURE ADSMPROD(A,b: LIST): LIST; (* Arbitrary domain scalar and matrix product. A is a arbitrary domain matrix. b is a arbitrary domain number. The arbitrary domain matrix C = A * b is returned. *)PROCEDURE ADMSUM(A,B: LIST): LIST; (* Arbitrary domain matrix sum. A and B are arbitrary domain matrices. The arbitrary domain matrix C = A + B is returned. *)PROCEDURE ADMPROD(D,A,B: LIST): LIST; (* Arbitrary domain matrix product. A and B are matrices of domain D. The matrix C = A * B of domain D is returned, if the number of columns of A is equal to the number of rows of B, otherwise the empty matrix is returned. *)PROCEDURE ADVWRITE(A: LIST); (* Arbitrary domain vector write. A is an arbitrary domain vector. A is written to the output stream. *)PROCEDURE ADMWRITE(A: LIST); (*Arbitrary domain matrix write. A is an arbitrary domain matrix. A is written to the output stream. *)PROCEDURE ADMTRACE(D,A: LIST): LIST; (* Arbitrary domain matrix trace. A is a matrix of domain D. The trace of A is returned. *)PROCEDURE ADMPTRACE(D,A,B: LIST): LIST; (* Arbitrary domain matrix product trace. A and B are matrices of domain D. The trace of A*B is returned. *)PROCEDURE ADCHARPOL(D,Q: LIST): LIST; (* Arbitrary domain characteristic polynomial. Q is a p x p Matrix of domain D. The list al=(a(0),...,a(p)) is created such that a(i) from D is the coefficient of X^(p-i) in det(XE-Q). *)PROCEDURE ADSIG(D,Q: LIST): LIST; (* Arbitrary domain signature. Q is a symmetric p x p Matrix of domain D. The signature of Q ist returned. ADCHARPOL is used. *) (* Integer linear algebra ------------------------------------------------- *)PROCEDURE IMTRACE(A: LIST): LIST; (* Integral matrix trace. A is an integral matrix. The trace of A is returned. *)PROCEDURE IMPTRACE(A,B: LIST): LIST; (* Integral matrix product trace. A and B are integral matrices. The trace of the matrix A*B is returned. *)PROCEDURE ICHARPOL(Q: LIST): LIST; (* Integral matrix characteristic polynomial. Q is an integral p x p Matrix. The list al = (a(0),...,a(p)) of integers is created with a(i) is the coefficient of X^(p-i) in det(XE-Q). *)PROCEDURE ISIG(Q: LIST): LIST; (* Integral matrix signature. Q is a symmetric integral p x p Matrix. The signature of Q ist returned. ICHARPOL is used *)PROCEDURE IMRTPROD(A,B: LIST): LIST; (* Integral matrix right tensor product. A and B are integral matrices. The matrix C is constructed by replacing every entry a(i,j) of A by the matrix a(i,j)*B. *)ENDLINALG. (* -EOF- *)