1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
|
// file: kfloatpoly.h
// update: 10/04/02
#ifndef _KFLOATPOLY_H
#define _KFLOATPOLY_H
#include <cassert>
#include <cmath>
#include <cstdlib>
#include <iostream>
#include "bigrational.h"
using namespace std;
class K_FLOATPOLY
{
// A class for representing polynomials with bigrational coefficients
unsigned long num_vars; // Number of variables
long* deg; // Max. degree in each variable
unsigned long num_coeffs; // Number of coefficients (terms)
double* coeffs;
// primitives
long* index_to_powers(const unsigned long i) const;
// For an index, i, return the powers, p, of the term
// to which the i-th coefficient belongs to.
unsigned long powers_to_index(const long* const p) const;
// Return the index of the term of the powers p.
int reduce_deg();
// arithmetic
K_FLOATPOLY add(const K_FLOATPOLY&) const;
K_FLOATPOLY sub(const K_FLOATPOLY&) const;
K_FLOATPOLY mul(const K_FLOATPOLY&) const;
K_FLOATPOLY mul(const double) const;
K_FLOATPOLY neg() const;
// stream
ostream& output(ostream&) const;
public:
// constructors, assignment and destructor
K_FLOATPOLY();
K_FLOATPOLY(const unsigned long, const long* const);
K_FLOATPOLY(const unsigned long, const long* const, const double* const);
K_FLOATPOLY(const K_FLOATPOLY&);
K_FLOATPOLY& operator =(const K_FLOATPOLY&);
~K_FLOATPOLY();
// stream
friend ostream& operator <<(ostream&, const K_FLOATPOLY&);
// arithmetic
friend K_FLOATPOLY operator +(const K_FLOATPOLY&, const K_FLOATPOLY&);
friend K_FLOATPOLY operator -(const K_FLOATPOLY&, const K_FLOATPOLY&);
friend K_FLOATPOLY operator *(const K_FLOATPOLY&, const K_FLOATPOLY&);
friend K_FLOATPOLY operator *(const K_FLOATPOLY&, const double);
friend K_FLOATPOLY operator *(const double, const K_FLOATPOLY&);
friend K_FLOATPOLY operator -(const K_FLOATPOLY&);
// others
K_FLOATPOLY derivative(const unsigned long) const;
K_FLOATPOLY subst_first_var(const double) const;
double evaluate(const double* const) const;
K_FLOATPOLY subst_val(const unsigned long, const double) const;
K_FLOATPOLY subst_expr(const unsigned long, const K_FLOATPOLY&) const;
K_FLOATPOLY subst_expr(const unsigned long,
const K_FLOATPOLY&, const K_FLOATPOLY&) const;
// other univariate functions
// unsigned long gen_fp_roots(const double l,
// const doubld h,
// double*& X) const
// PROVIDED *this is a univariate polynomial,
// compute roots X of *this in [l, h] by using only FP arithmetic.
unsigned long gen_fp_roots(const double, const double, double*&) const;
};
#endif
|
