```(* ----------------------------------------------------------------------------
* \$Id: MASQ.mi,v 1.3 1992/10/15 16:28:14 kredel Exp \$
* ----------------------------------------------------------------------------
* This file is part of MAS.
* ----------------------------------------------------------------------------
* Copyright (c) 1989 - 1992 Universitaet Passau
* ----------------------------------------------------------------------------
* \$Log: MASQ.mi,v \$
* Revision 1.3  1992/10/15  16:28:14  kredel
* Changed rcsid variable
*
* Revision 1.2  1992/09/28  18:34:55  kredel
* Updated revision string.
*
* Revision 1.1  1992/09/28  17:29:13  kredel
* Initial revision
*
* ----------------------------------------------------------------------------
*)

IMPLEMENTATION MODULE MASQ;

(* MAS Quaternion Number Implementation Module. *)

(* Import lists and declarations. *)

FROM MASBIOS IMPORT SWRITE, CWRITE, CREADB, MASORD, BKSP, BLINES;

FROM MASSTOR IMPORT LIST, ADV, COMP, FIRST, SIL;

FROM MASERR IMPORT severe, ERROR;

FROM SACLIST IMPORT OWRITE, SECOND, THIRD, FOURTH, FIRST4, LIST4, COMP4,
AWRITE, EQUAL;

FROM SACRN IMPORT RNSUM, RNPROD, RNCOMP, RNNEG, RNDIF,

FROM MASRN IMPORT RNDWR, RNDRD, RNONE;

CONST rcsidi = "\$Id: MASQ.mi,v 1.3 1992/10/15 16:28:14 kredel Exp \$";

(* Representation of a + i b + j c + k d, with a, b, c, d rational numbers,
is

0   if a=0 and b=0 and c=0 and d=0
(a,b,c,d)   else   *)

PROCEDURE QABS(R: LIST): LIST;
(*Quaternion number absolute value.  R is a quaternion number.  S is the
absolute value of R, a rational number. *)
VAR   S, r, i, j, k: LIST;
BEGIN
(*1*) IF R = 0 THEN S:=R; RETURN(S) END;
(*2*) FIRST4(R,r,i,j,k);
S:=RNSUM(RNPROD(r,r),RNPROD(i,i));
S:=RNSUM(S,RNPROD(j,j)); S:=RNSUM(S,RNPROD(k,k));
RETURN(S);
(*4*) END QABS;

PROCEDURE QCON(R: LIST): LIST;
(*Quaternion number conjugate.  R is a quaternion number. S is the
quaternion conjugate of R. *)
VAR   S, r, i, j, k: LIST;
BEGIN
(*1*) IF R = 0 THEN RETURN(0) END;
(*2*) FIRST4(R,r,i,j,k);
S:=COMP4(r,RNNEG(i),RNNEG(j),RNNEG(k),SIL);
RETURN(S);
(*4*) END QCON;

PROCEDURE QCOMP(R,S: LIST): LIST;
(*Quaternion number comparison.  R and S are quaternion numbers.
t=0 if R=S, t=1 else. *)
VAR   t: LIST;
BEGIN
(*1*) t:=EQUAL(R,S);
IF t = 1 THEN t:=0 ELSE t:=1 END;
RETURN(t);
(*4*) END QCOMP;

PROCEDURE QDIF(R,S: LIST): LIST;
(*Quaternion number difference.  R and S are quaternion numbers.  T=R-S. *)
VAR   T, r1, i1, j1, k1, r2, i2, j2, k2: LIST;
BEGIN
(*1*) IF R = 0 THEN T:=QNEG(S); RETURN(T) END;
IF S = 0 THEN T:=R; RETURN(T) END;
(*2*) FIRST4(R,r1,i1,j1,k1); FIRST4(S,r2,i2,j2,k2);
r1:=RNDIF(r1,r2); i1:=RNDIF(i1,i2);
j1:=RNDIF(j1,j2); k1:=RNDIF(k1,k2);
IF (r1 = 0) AND (i1 = 0) AND (j1 = 0) AND (k1 = 0) THEN RETURN(0) END;
T:=COMP4(r1,i1,j1,k1,SIL);
RETURN(T);
(*4*) END QDIF;

from the input stream.  Any preceding blanks are skipped. *)
VAR   R, r, i, j, k, c: LIST;
BEGIN
(*1*) r:=RNDRD(); i:=0;
IF c = MASORD("i") THEN i:=RNDRD(); ELSE BKSP END;
IF c = MASORD("j") THEN j:=RNDRD(); ELSE BKSP END;
IF c = MASORD("k") THEN k:=RNDRD(); ELSE BKSP END;
IF (r = 0) AND (i = 0) AND (j = 0) AND (k = 0) THEN RETURN(0) END;
R:=COMP4(r,i,j,k,SIL);
RETURN(R);

PROCEDURE QDWRITE(R,NL: LIST);
(*Quaternion number decimal write.  R is a quaternion number.  n is a
non-negative integer.  R is approximated by a decimal fraction D with
n decimal digits following the decimal point and D is written in the
output stream.  The inaccuracy of the approximation is at most
(1/2)*10**-n. *)
VAR   r, i, j, k: LIST;
BEGIN
(*1*) IF R = 0 THEN AWRITE(R); RETURN END;
(*2*) FIRST4(R,r,i,j,k);
RNDWR(r,NL);
IF i <> 0 THEN SWRITE(" i "); RNDWR(i,NL) END;
IF j <> 0 THEN SWRITE(" j "); RNDWR(j,NL) END;
IF k <> 0 THEN SWRITE(" k "); RNDWR(k,NL) END;
(*4*) END QDWRITE;

PROCEDURE QEXP(A,NL: LIST): LIST;
(*Quaternion number exponentiation.  A is a quaternion number,
n is a non-negative beta-integer.  B=A**n. *)
VAR   B, KL: LIST;
BEGIN
(*1*) (*n less than or equal to 1.*)
IF NL = 0 THEN B:=QINT(1); RETURN(B); END;
IF NL = 1 THEN B:=A; RETURN(B); END;
(*2*) (*recursion.*) KL:=NL DIV 2; B:=QEXP(A,KL); B:=QPROD(B,B);
IF NL > 2*KL THEN B:=QPROD(B,A); END;
RETURN(B);
(*5*) END QEXP;

PROCEDURE QIMi(R: LIST): LIST;
(*Quaternion number imaginary part i.  R is a quaternion number.  b is the
imaginary part i of R, a rational number. *)
BEGIN
(*1*) IF R = 0 THEN RETURN(0) END;
(*2*) RETURN(SECOND(R));
(*4*) END QIMi;

PROCEDURE QIMj(R: LIST): LIST;
(*Quaternion number imaginary part j.  R is a quaternion number.  b is the
imaginary part j of R, a rational number. *)
BEGIN
(*1*) IF R = 0 THEN RETURN(0) END;
(*2*) RETURN(THIRD(R));
(*4*) END QIMj;

PROCEDURE QIMk(R: LIST): LIST;
(*Quaternion number imaginary part k.  R is a quaternion number.  b is the
imaginary part k of R, a rational number. *)
BEGIN
(*1*) IF R = 0 THEN RETURN(0) END;
(*2*) RETURN(FOURTH(R));
(*4*) END QIMk;

PROCEDURE QINT(A: LIST): LIST;
(*Quaternion number from integer.  A is an integer.  R is the quaternion
number with real part A/1 and imaginary part 0. *)
VAR   R: LIST;
BEGIN
(*1*) IF A = 0 THEN R:=A; RETURN(R) END;
(*2*) R:=COMP4(RNINT(A),0,0,0,SIL);
RETURN(R);
(*4*) END QINT;

PROCEDURE QRE(R: LIST): LIST;
(*Quaternion number real part.  R is a quaternion number.  b is the
real part of R, a rational number. *)
BEGIN
(*1*) IF R = 0 THEN RETURN(0) END;
(*2*) RETURN(FIRST(R));
(*4*) END QRE;

PROCEDURE QRN(A: LIST): LIST;
(*Quaternion number from rational number.  A is a rational number.
R is the quaternion number with real part A and imaginary part 0. *)
VAR   R: LIST;
BEGIN
(*1*) IF A = 0 THEN RETURN(0) END;
(*2*) R:=COMP4(A,0,0,0,SIL);
RETURN(R);
(*4*) END QRN;

PROCEDURE QRN4(A, B, C, D: LIST): LIST;
(*Quaternion number from 4-tuple of rational numbers.  A, B, C and D
are rational numbers.  R is the quaternion number with real part A
and imaginary part i B, imaginary part j C, imaginary part k D. *)
VAR   R: LIST;
BEGIN
(*1*) IF (A = 0) AND (B = 0) THEN RETURN(0) END;
(*2*) R:=COMP4(A,B,C,D,SIL);
RETURN(R);
(*4*) END QRN4;

PROCEDURE QINV(R: LIST): LIST;
(*Quaternion number inverse.  R is a non-zero quaternion number.  S R=1. *)
VAR   S, r, i, j, k, a: LIST;
BEGIN
(*1*) IF R = 0 THEN ERROR(severe,"QINV: division by zero."); END;
(*2*) FIRST4(R,r,i,j,k);
a:=RNSUM(RNPROD(r,r),RNPROD(i,i));
a:=RNSUM(a,RNPROD(j,j));
a:=RNSUM(a,RNPROD(k,k));
r:=RNQ(r,a); i:=RNQ(RNNEG(i),a);
j:=RNQ(RNNEG(j),a); k:=RNQ(RNNEG(k),a);
S:=COMP4(r,i,j,k,SIL);
RETURN(S);
(*4*) END QINV;

PROCEDURE QNEG(R: LIST): LIST;
(*Quaternion number negative.  R is a quaternion number.  S=-R. *)
VAR   S, r, i, j, k: LIST;
BEGIN
(*1*) IF R = 0 THEN RETURN(0) END;
(*2*) FIRST4(R,r,i,j,k);
S:=COMP4(RNNEG(r),RNNEG(i),RNNEG(j),RNNEG(k),SIL);
RETURN(S);
(*4*) END QNEG;

PROCEDURE QONE(R: LIST): LIST;
(*Quaternion number one.  R is a quaternion number.  s=1 if R=1,
s=0 else. *)
VAR   r, i, j, k, t: LIST;
BEGIN
(*1*) IF R = 0 THEN RETURN(0) END;
(*2*) FIRST4(R,r,i,j,k);
IF (i <> 0) OR (j <> 0) OR (k <> 0) THEN RETURN(0) END;
t:=RNONE(r);
RETURN(t);
(*4*) END QONE;

PROCEDURE QPROD(R,S: LIST): LIST;
(*Quaternion number product.  R and S are quaternion numbers.  T=R*S. *)
VAR   T, r1, i1, j1, k1, r2, i2, j2, k2, r, i, j, k: LIST;
BEGIN
(*1*) IF (R = 0) OR (S = 0) THEN RETURN(0) END;
(*2*) FIRST4(R,r1,i1,j1,k1); FIRST4(S,r2,i2,j2,k2);
r:=RNDIF(RNPROD(r1,r2),RNPROD(i1,i2));
r:=RNDIF(r,RNPROD(j1,j2)); r:=RNDIF(r,RNPROD(k1,k2));
i:=RNSUM(RNPROD(r1,i2),RNPROD(i1,r2));
i:=RNSUM(i,RNPROD(j1,k2)); i:=RNDIF(i,RNPROD(k1,j2));
j:=RNDIF(RNPROD(r1,j2),RNPROD(i1,k2));
j:=RNSUM(j,RNPROD(j1,r2)); j:=RNSUM(j,RNPROD(k1,i2));
k:=RNSUM(RNPROD(r1,k2),RNPROD(i1,j2));
k:=RNDIF(k,RNPROD(j1,i2)); k:=RNSUM(k,RNPROD(k1,r2));
IF (r = 0) AND (i = 0) AND (j = 0) AND (k = 0) THEN RETURN(0) END;
T:=COMP4(r,i,j,k,SIL);
RETURN(T);
(*4*) END QPROD;

PROCEDURE QQ(R,S: LIST): LIST;
(*Quaternion number quotient.  R and S are quaternion numbers, S non-zero.
T=R/S. *)
VAR   T: LIST;
BEGIN
(*1*) T:=QPROD(R,QINV(S));
RETURN(T);
(*4*) END QQ;

PROCEDURE QRAND(NL: LIST): LIST;
(*Quaternion number, random.  n is a positive beta-integer.  Random
rational numbers A and B are generated using RNRAND(n). Then
R is the quaternion number with real part A and imaginary part B. *)
VAR   T, r, i, j, k: LIST;
BEGIN
(*1*) r:=RNRAND(NL); i:=RNRAND(NL); j:=RNRAND(NL); k:=RNRAND(NL);
IF (r = 0) AND (i = 0) AND (j = 0) AND (k = 0) THEN RETURN(0) END;
T:=COMP4(r,i,j,k,SIL);
RETURN(T);
(*4*) END QRAND;

(*Quaternion number read.  The quaternion number R is read from the input
stream.  Any preceding blanks are skipped. *)
VAR   R, r, i, j, k, c: LIST;
BEGIN
IF c = MASORD("i") THEN i:=RNREAD(); ELSE BKSP END;
IF c = MASORD("j") THEN j:=RNREAD(); ELSE BKSP END;
IF c = MASORD("k") THEN k:=RNREAD(); ELSE BKSP END;
IF (r = 0) AND (i = 0) AND (j = 0) AND (k = 0) THEN RETURN(0) END;
R:=COMP4(r,i,j,k,SIL);
RETURN(R);

PROCEDURE QSUM(R,S: LIST): LIST;
(*Quaternion number sum.  R and S are quaternion numbers.  T=R+S. *)
VAR   T, r1, i1, j1, k1, r2, i2, j2, k2: LIST;
BEGIN
(*1*) IF R = 0 THEN T:=S; RETURN(T) END;
IF S = 0 THEN T:=R; RETURN(T) END;
(*2*) FIRST4(R,r1,i1,j1,k1); FIRST4(S,r2,i2,j2,k2);
r1:=RNSUM(r1,r2); i1:=RNSUM(i1,i2);
j1:=RNSUM(j1,j2); k1:=RNSUM(k1,k2);
IF (r1 = 0) AND (i1 = 0) AND (j1 = 0) AND (k1 = 0) THEN RETURN(0) END;
T:=COMP4(r1,i1,j1,k1,SIL);
RETURN(T);
(*4*) END QSUM;

PROCEDURE QNWRITE(R: LIST);
(*Quaternion number write. R is a quaternion number.  R is converted
to decimal and written in the output stream. *)
VAR   r, i, j, k: LIST;
BEGIN
(*1*) IF R = 0 THEN AWRITE(R); RETURN END;
(*2*) FIRST4(R,r,i,j,k);
RNWRIT(r);
IF i <> 0 THEN SWRITE(" i "); RNWRIT(i) END;
IF j <> 0 THEN SWRITE(" j "); RNWRIT(j) END;
IF k <> 0 THEN SWRITE(" k "); RNWRIT(k) END;
(*4*) END QNWRITE;

END MASQ.

(* -EOF- *)
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