www.pudn.com > calc.rar > roots.h

 
#ifndef __ROOTS_H__ 
#define __ROOTS_H__ 
#include "integer.h" 
#include "stack.h" 
 
 
 
typedef struct _Interval { 
  MPR *left; 
  MPR *right; 
} *Interval; 
 
/* Returns a newly created Interval if there is enough memory.   
 * Returns NULL on error. 
 */ 
Interval createInterval(MPR* left, MPR *right); 
 
/* Frees an interval previously created with createInterval  
 * Undefined behaviour occurs if 'intvl' this is not true.  
 */  
void freeInterval(Interval intvl); 
 
/* 
 * Calculates an upperbound on the positve roots of the supplied polynomial 
 * using Cauchy's Rule. See Akritas, Elements of Computer Algebra. 
 */ 
MPR *CAUCHY(POLYI P); 
 
/* Using a bisection method this finds the integer part root of the 
 * supplied polynomial in the supplied _OPEN_ interval.  This function is 
 * only guaranteed to return the correct value if the interval 
 * supplied contains exactly one root, and this root does not fall at the 
 * end points. */ 
MPI *rootInIntervalI(POLYI P, MPI *LEFT, MPI *RIGHT); 
/* Using a bisection method this finds the integer part root of the 
 * supplied polynomial in the supplied _OPEN_ interval.  This function is 
 * only guaranteed to return the correct value if the interval 
 * supplied contains exactly one root, and this root does not fall at the 
 * end points. */ 
MPI *rootInIntervalR(POLYI P, MPR *LEFT, MPR *RIGHT); 
 
 
/* A wrapper function that takes a single polynomial as its argument. 
 * (Handled by parser).  Returns open rational intervals that are 
 * guaranteed to enclose the real roots of the supplied polynomial. 
 */ 
void STURM_W(Stack s); 
 
/* Finds the continued fraction expansion of all real roots of the supplied 
 * polynomial using Lagrange's method and methods first presented in a paper 
 * by Cantor, Galyean and Zimmer called A Continued Fraction Algorithm for 
 * Real Algebraic Number  
 */ 
void ROOTEXPANSION(Stack s); 
 
 
#endif