(* DIP Rational Function Definition Module. *)

DEFINITION MODULE DIPRF;


FROM MASSTOR IMPORT LIST;


PROCEDURE IFWRIT(R,V: LIST); 
(*Integral function write.
R is an integral function.  R is the variable list.
R is written in the output stream. *)


PROCEDURE RFDEN(R: LIST): LIST; 
(*Rational function denominator.  R is a rational function.
BL is the denominator of R, a positive integral polynomial
in RL variables. *)


PROCEDURE RFDIF(R,S: LIST): LIST; 
(*Rational function difference.  R and S are rational functions.
T=R-S.*)


PROCEDURE RFEXP(A,NL: LIST): LIST; 
(*Rational function exponentiation.  A is a rational function,
NL is a non-negative beta-integer.  B=A**NL.*)


PROCEDURE RFFIP(RL,A: LIST): LIST; 
(*Rational function from integral polynomial. A is an integral
polynomial in RL variables. R is the rational function A/1.*)


PROCEDURE RFINV(R: LIST): LIST; 
(*Rational function inverse. R is a non-zero rational
function. S=1/R.*)


PROCEDURE RFNEG(R: LIST): LIST; 
(*Rational function negative. R is a rational function. S=-R.*)


PROCEDURE RFNOV(R: LIST): LIST; 
(*Rational function number of variables. R is a rational
function. RL is the number of variables of the numerator
and denumerator of R. *)


PROCEDURE RFNUM(R: LIST): LIST; 
(*Rational function numerator.  R is a rational function.
AL is the numerator of R, an integral polynomial. *)


PROCEDURE RFONE(R: LIST): LIST; 
(*Rational function one.  R is a rational function.  SL=1 if R=1,
SL=0 else. *)


PROCEDURE RFPROD(R,S: LIST): LIST; 
(*Rational function product.  R and S are rational functions.
T=R*S.*)


PROCEDURE RFQ(R,S: LIST): LIST; 
(*Rational function quotient. R and S are rational functions,
S non-zero. T=R/S.*)


PROCEDURE RFREAD(V: LIST): LIST; 
(*Rational function read. The rational function R is read
from the input stream. V is the variable list. any preceding
blanks are skipped.*)


PROCEDURE RFRED(RL,A,B: LIST): LIST; 
(*Rational function reduction to lowest terms.  A and B are
integral polynomials in RL variables, B non-zero. R is the
rational function A/B in canonical form.*)


PROCEDURE RFSIGN(R: LIST): LIST; 
(*Rational function sign.  R is a rational function.  SL=sign(R).*)


PROCEDURE RFSUM(R,S: LIST): LIST; 
(*Rational function sum.  R and S are rational functions.  T=R+S.*)


PROCEDURE RFWRIT(R,V: LIST); 
(*Rational function write.
R is a rational function.  V is the variable list.
R is written in the output stream. *)


END DIPRF.