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POLY.PAS
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Pascal/Delphi Source File
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1980-01-01
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11KB
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395 lines
(***********************************************************)
(* PROGRAM Poly which will serve as a main program for *)
(* various operations on polynomials. Several of these *)
(* are currently implemented as stubs. *)
(* by PRB 2/91 *)
(***********************************************************)
PROGRAM Poly(Input,Output);
TYPE ExpType = 0..Maxint;
TermPtr = ^TermType;
TermType = RECORD
Coef: Integer;
Exp: ExpType;
Next: TermPtr;
END;
VAR Poly1,Poly2,Sum,Prod,Sub,Deriv,Mon,
Work,Temp,MonPoly1,MonPoly2,p1,q1,p2,q2: TermPtr;
(***********************************************************)
(* Auxilliary procedure for spacing output *)
(***********************************************************)
PROCEDURE PrintBlankLines(N:Integer);
VAR I: Integer;
BEGIN
FOR I:= 1 TO N DO Writeln;
END;
(*********************************************************)
(* Creates a term with given coefficient and exponent *)
(*********************************************************)
PROCEDURE MakeTerm(Coef:Integer; Exp:ExpType);
BEGIN
END;
(********************************************************)
(* Pre: The monomial has been created *)
(* Post: The monomial is written to the screen *)
(********************************************************)
PROCEDURE WriteMon(Mon:TermPtr);
BEGIN
IF (Mon = nil) THEN Writeln(' 0');
IF (Mon^.coef>0) THEN (* WRITE SIGN *)
Write('+')
ELSE
Write(' - ');
WITH Mon^ DO
IF Exp = 0 THEN (* WRITE TERM *)
Write(Abs(Coef):1)
ELSE
IF Exp = 1 THEN
Write(Abs(Coef):1,'*X')
ELSE
Write(Abs(Coef):1,'*X^',Exp:1);
Writeln;
END;
(*********************************************************)
(* Pre: The polynomial has been created *)
(* Post: The polynomial is written to the screen *)
(*********************************************************)
PROCEDURE WritePoly(Poly:TermPtr);
VAR P: TermPtr;
BEGIN
P:=Poly^.Next;
IF (P = nil) THEN Writeln(' 0');
WHILE (P<> NIL) DO
BEGIN
IF (P^.Coef>0) THEN (* Write sign *)
Write(' + ')
ELSE
Write(' - ');
WITH P^ DO
IF Exp = 0 THEN (* Write term *)
Write(Abs(Coef):1)
ELSE
IF Exp = 1 THEN
Write(Abs(Coef):1,'*X')
ELSE
Write(Abs(Coef):1,'*X^',Exp:1);
P:= P^.Next;
END; (** WHILE **)
Writeln;
END;
(***********************************************************)
(* Pre: Zero Poly must exist. *)
(* Post: The user has supplied the coefficients *)
(* for a polynomial. *)
(***********************************************************)
PROCEDURE ReadPoly(VAR Poly: TermPtr);
VAR P: TermPtr;
Coef: Integer;
Exp: ExpType;
BEGIN
Writeln;
Writeln('Enter the coefficients and Exps of the polynomial');
Writeln('in descending order. To exit, enter a zero coeficient.');
Writeln('Coef, Exp');
Readln(Coef,Exp);
P:= Poly;
WHILE Coef<>0 DO
BEGIN
New(P^.Next);
P:= P^.Next;
P^.Coef:= Coef;
P^.Exp:= Exp;
Writeln('Coef, Exp');
Readln(Coef, Exp);
END;
P^.Next:= nil;
END;
(******************************************************)
(* Pre: Poly1, Poly2, exist *)
(* Post: The user suplied the monomial *)
(******************************************************)
PROCEDURE ReadMon(VAR Mon:TermPtr);
VAR M : TermPtr;
coef : Integer;
Exp : Exptype;
BEGIN
Writeln;
Writeln('Enter the coefficient and Exp of the monomial');
Writeln('Coef, Exp');
Readln(Coef,Exp);
New(M);
M := Mon;
M^.Coef := Coef;
M^.Exp := Exp;
M^.Next := nil;
END;
(******************************************************)
(* Pre: Poly1, Poly2, and Sum exist. *)
(* Post: Sum has been formed from Poly1, Poly2 *)
(******************************************************)
PROCEDURE AddPolys(Poly1,Poly2:TermPtr; VAR Sum:TermPtr);
VAR P1,P2,S: TermPtr;
Sumcoef: Integer;
BEGIN (* Initialize *)
P1:= Poly1^.Next;
P2:= Poly2^.Next;
S:= Sum;
WHILE (P1<>nil) AND (P2<>nil) DO
BEGIN
IF P1^.Exp = P2^.Exp THEN
BEGIN (* Add Like terms *)
Sumcoef:= P1^.coef + P2^.coef;
IF (Sumcoef<>0) THEN
BEGIN
New(S^.Next);
S:= S^.Next;
S^.coef:= Sumcoef;
S^.Exp:= P1^.Exp;
END;
P1:= P1^.Next;
P2:= P2^.Next;
END
ELSE
BEGIN (* Lone term cases *)
new(S^.Next); (* copy a single term to sum *)
S:= S^.Next;
IF P1^.Exp > P2^.Exp THEN
BEGIN
S^:= P1^;
P1:= P1^.Next;
END
ELSE
BEGIN
S^:= P2^;
P2:= P2^.Next;
END;
END;
END;
WHILE (P1<>nil) DO (* Append any remaining *)
BEGIN (* terms to sum *)
New(S^.Next);
S:= S^.Next;
S^:= P1^;
P1:= P1^.Next;
END;
WHILE (P2<>nil) DO
BEGIN
New(S^.Next);
S:= S^.Next;
S^:= P2^;
P2:= P2^.Next;
END;
END;
(***************************************************************)
(* Pre: Poly1, Poly2 and Sum exist. *)
(* Post: Sum has been formed from Poly1, Poly2 *)
(***************************************************************)
(* Subtract Procedure *)
PROCEDURE SubPolys(Poly1,Poly2:TermPtr; VAR Sub:TermPtr);
VAR P1,P2,Sb: TermPtr;
Sumcoef: Integer;
BEGIN (* Initialize *)
P1:= Poly1^.Next;
P2:= Poly2^.Next;
Sb:= Sub;
WHILE (P1<>nil) AND (P2<>nil) DO
BEGIN
IF P1^.Exp = P2^.Exp THEN
BEGIN (* Subtract Like terms *)
Sumcoef:= P1^.coef - P2^.coef;
IF (Sumcoef<>0) THEN
BEGIN
New(Sb^.Next);
Sb:= Sb^.Next;
Sb^.coef:= Sumcoef;
Sb^.Exp:= P1^.Exp;
END;
P1:= P1^.Next;
P2:= P2^.Next;
END
ELSE
BEGIN (* Lone term cases *)
new(Sb^.Next); (* copy a single term to sub *)
Sb:= Sb^.Next;
IF P1^.Exp > P2^.Exp THEN
BEGIN
Sb^:= P1^;
P1:= P1^.Next;
END
ELSE
BEGIN
P2:= P2^.Next;
END;
END;
END;
WHILE (P1<>nil) DO (* Append any remaining *)
BEGIN (* terms to sub *)
New(Sb^.Next);
Sb:= Sb^.Next;
Sb^:= P1^;
P1:= P1^.Next;
END;
WHILE (P2<>nil) DO
BEGIN
New(Sb^.Next);
Sb:= Sb^.Next;
Sb^:= P2^;
P2:= P2^.Next;
END;
END;
(***********************************************************)
(* Multiplies monomial and a polynomial. The product is *)
(* pointed to by Prod1 and Prod2. *)
(***********************************************************)
PROCEDURE MultMon(Poly1,Poly2,Mon : TermPtr; VAR MonPoly1,MonPoly2 : TermPtr);
VAR P1,P2,Prod1,Prod2:TermPtr;
Prodcoef : Integer;
BEGIN
P1 := Poly1^.Next;
P2 := Poly2^.Next;
Prod1 := MonPoly1;
Prod2 := MonPoly2;
While (P1 <> nil) OR (P2 <> nil) DO
BEGIN
IF (P1 <> nil) THEN
BEGIN
Prodcoef := Mon^.coef * P1^.coef;
IF (Prodcoef <> 0) THEN
BEGIN
New(Prod1^.Next);
Prod1 := Prod1^.Next;
Prod1^.coef := Prodcoef;
Prod1^.Exp := P1^.Exp + Mon^.Exp;
END; {IF}
P1 := P1^.Next;
END; { IF }
IF (P2 <> nil) THEN
BEGIN {IF}
Prodcoef := Mon^.coef * P2^.coef;
IF (Prodcoef <> 0) THEN
BEGIN {IF}
New(Prod2^.Next);
Prod2 := Prod2^.Next;
Prod2^.coef := Prodcoef;
Prod2^.Exp := P2^.Exp + Mon^.Exp;
END; {IF }
P2 := P2^.Next;
END;{IF}
END; {WHILE}
END;
(***********************************************************)
(* Multiplies two polynomials pointed to by *)
(* Poly1 and Poly2. The product is pointed *)
(* to by Prod. *)
(***********************************************************)
PROCEDURE MultPolys(VAR Poly1,Poly2,Prod:TermPtr);
VAR P1,P2,hold,H,temp: TermPtr;
Prodcoef,Pexe :integer;
BEGIN {MultPolys}
New(temp);
New(H);
New(hold);
H := hold;
P2 := Poly2^.next;
WHILE P2 <> NIL DO
BEGIN
P1 := Poly1^.next;
WHILE P1 <> NIL DO
BEGIN
Pexe := P1^.exp + P2^.exp; (* add the exponents *)
Prodcoef := P1^.coef * P2^.coef; (* multiply the coeficents *)
temp^.exp := Pexe;
temp^.coef := Prodcoef;
hold^.next := temp;
P1 := P1^.next;
Addpolys(H,Prod,Prod); (* Simplify by adding *)
END;
P2 := P2^.next;
END;
END; {MultPolys}
(***********************************************************)
(* Pre: None. *)
(* Post: All Polynomials have been initialized to zero *)
(***********************************************************)
PROCEDURE Initialize(VAR Poly1,Poly2,Sum,Prod,Deriv,Mon: TermPtr);
BEGIN
New(Poly1);
New(Poly2);
New(Sum);
New(Sub);
New(Prod);
New(Deriv);
New(Mon);
New(MonPoly1);
New(MonPoly2);
Poly1^.Next:= nil;
Poly2^.Next:= nil;
Sum^.Next:= nil;
Sub^.Next:= nil;
Prod^.Next:= nil;
Deriv^.Next:= nil;
Mon^.Next:= nil;
MonPoly1^.Next := nil;
MonPoly2^.Next := nil;
END;
(***********************************************************)
(*************************** MAIN **************************)
BEGIN
Initialize(Poly1,Poly2,Sum,Prod,Deriv,Mon);
(* Describe *)
PrintBlankLines(5);
ReadPoly(Poly1);
Writeln('The first polynomial is:');
WritePoly(Poly1);
Writeln;
ReadPoly(Poly2);
Writeln('The second polynomial is:');
WritePoly(Poly2);
Writeln('Enter Monomial.');
ReadMon(Mon);
Writeln('The Monomial is:');
WriteMon(Mon);
PrintBlankLines(5);
AddPolys(Poly1,Poly2,Sum);
Writeln('The sum of the two Polynomials is:');
Writepoly(Sum);
PrintBlankLines(2);
SubPolys(Poly1,Poly2,Sub);
Writeln('The subtraction of the two Polynomials is:');
Writepoly(Sub);
PrintBlankLines(2);
MultMon(Poly1,Poly2,Mon,MonPoly1,MonPoly2);
Writeln('The Product of the monomial and the polynomial #1 is:');
WritePoly(MonPoly1);
PrintBlankLines(2);
Writeln('The Product of the monomial and the polynomial #2 is:');
WritePoly(MonPoly2);
PrintBlankLines(2);
MultPolys(Poly1,Poly2,Prod);
Writeln('The Product of the two polynomials is:');
WritePoly(Prod);
PrintBlankLines(1);
END.
(********************************************************)
