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/* pI.h */ 
#include "integer.h" 
 
#ifndef __PI_H__ 
#define __PI_H__ 
 
POLYI CREATEPI(); 
/* 
If there is anything in BANKI (the memory bank of TERMI's) then use that, 
otherwise allocate a new one. 
*/ 
 
int DEGREEPI(POLYI Pptr); 
/* 
 * returns the degree of the polynomial Pptr. 
 */ 
 
MPI *LEADPI(POLYI Pptr); 
/* 
 * *Aptr is the  leading coefficient of the polynomial Pptr. 
 */ 
 
void DELETEPI(POLYI Pptr); 
/* 
 * returns back to the system storage dynamically allocated to the linked list 
 * which Pptr points to. 
 */ 
 
void PINSERTPI(int DEG, MPI *COEF, POLYI *Pptr, USI OPT); 
/* 
 * inserts a copy of a single term *Qptr into polynomial *Pptr.  It 
 * has two options that control the insertion in case a term of *Pptr 
 * already has the degree of *Qptr, If OPT = 0, then the term is 
 * replaced; if OPT = 1, then the coefficient of *Qptr is added to 
 * that of the corresponding term of *Pptr.  */ 
 
 
void PURGEPI(POLYI *Pptr); 
/* 
 * gets rid of any zero coefficients in the polynomial Pptr. 
 */ 
 
POLYI COPYPI(POLYI Pptr); 
/* 
 * makes a copy of the polynomial Pptr. 
 */ 
  
void FPRINTPI(FILE *outfile, POLYI Pptr); 
void PRINTPI(POLYI Pptr); 
/* 
 * outputs the terms of the polynomial Pptr. 
 */ 
 
 
 
POLYI SCALARPI(MPI *Cptr, POLYI Pptr); 
/* 
 * multiplying the polynomial Pptr by the MPI *Cptr. 
 */ 
 
 
POLYI ADDPI(POLYI Pptr, POLYI Qptr); 
/* 
 * returns the sum of two polynomials. 
 */ 
 
 
POLYI SUBPI(POLYI Pptr, POLYI Qptr); 
/* 
 * returns the difference Pptr - Qptr of two polynomials. 
 */ 
 
 
POLYI MULTPI(POLYI Pptr, POLYI Qptr); 
/* 
 * returns the product of two polynomials. 
 */ 
 
 
MPI *VALPI(POLYI Pptr, MPI *Cptr); 
/* 
 * Evaluating the polynomial Pptr at the MPI *Cptr. 
 */ 
 
 
POLYI DIVPI(POLYI Fptr, POLYI Gptr); 
/* 
 * Pseudo-division of polynomials: see Knuth, Vol 2, p.407  
 * and H. Flanders, Scientific Pascal, p.510. 
 */ 
 
 
POLYI MODPI(POLYI Fptr, POLYI Gptr); 
/* 
 * Pseudo-division of polynomials: see Knuth, Vol 2, p.407  
 * and H. Flanders, Scientific Pascal, p.510. 
 */ 
 
 
MPI *CONTENTPI(POLYI Pptr); 
/* 
 * *Cptr is the content of the polynomial Pptr. 
 */ 
MPI *CONTENTPI2(POLYI Pptr); 
 
 
POLYI PRIMITIVEPI(POLYI Pptr); 
/* 
 * returns the primitive part of the polynomial Pptr. 
 */ 
 
 
POLYI GCDPI(POLYI Pptr, POLYI Qptr); 
/* 
 * returns the gcd of polynomials Pptr and Qptr. 
 * see Knuth, Vol 2, p.403-408 and H. Flanders, Scientific Pascal, p.510. 
 */ 
 
 
POLYI DERIVPI(POLYI Pptr); 
/* 
 * returns the derivative of a polynomial. 
 */ 
 
 
POLYI *SQUAREFREEPI(POLYI Pptr, USI **D, USI *tptr); 
/* 
 * returns the "squarefree decomposition" of Pptr, a non-constant polynomial: 
 * Pptr = G[0]^D[0]...G[*tpr - 1]^D[*tptr - 1], 
 * where G[i] is squarefree and is the product of the irreducible factors of 
 * multiplicity D[i]. See L. Childs, Introduction to Higher Algebra, p.159. 
 */ 
 
 
POLYI POWERPI(POLYI Pptr, USI n); 
/* 
 * returns Pptr ^ n, where 0 <= n < R0 * R0. 
 */ 
 
 
POLYI ONEPI(); 
/* 
 * returns the constant polynomial 1. 
 */ 
POLYI ZEROPI(); 
 
POLYI CONSTANTPI(MPI *Aptr); 
/* 
 * returns the constant polynomial whose constant term is *Aptr. 
 */ 
 
 
MPI *SUBRESULTANT(POLYI Pptr, POLYI Qptr); 
/* 
 * *Aptr is the resultant of Pptr and Qptr, found using the subresultant 
 * algorithm, p. 130. E. Kaltofen, G. E. Collins etc, Algoritm 4.5. 
 * similar to Knuth, Algorithm C, p. 410. 
 */ 
 
 
MPI *DISCRIMINANTPI(POLYI Pptr); 
/* 
 * *Dptr = Discriminant of Pptr = (1/a[n])*(-1)^{n*(n-1)/2 * Res(Pptr, Pptr'). 
 * See O. Perron, Algebra, Vol 1, p.212. 
 */ 
 
 
MPI *LENGTHSQPI(POLYI Pptr); 
/* 
 * *Cptr is the sum of the squares of the coefficients of Pptr. 
 */ 
 
 
MPI *VAL0PI(POLYI Pptr); 
/* 
 * *Mptr = Pptr(0) 
 */ 
 
/* Returns respectively positive, or negative if the sign of the polynomial  
 * evaluated at the supplied rational number is positive or negative. 
 * Returns zero if polynomial has a root at the supplied rational */ 
int SIGN_AT_R_PI(POLYI P, MPR *R); 
 
/* If P = p(x) then this function returns p(-x) */ 
POLYI P_OF_NEG_X(POLYI P); 
 
/* Returns -1*P(x) */ 
POLYI MINUSPI(POLYI P); 
void P_OF_X_PLUS(POLYI *P, MPI *A); 
 
#endif