-
Notifications
You must be signed in to change notification settings - Fork 1
/
symbolize.h
143 lines (135 loc) · 9.23 KB
/
symbolize.h
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
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
#ifndef symbolize
#define symbolize
#include <string>
#include <vector>
#include <sstream> //计算输出长度
#include <iostream>//输出几个提醒
#include <algorithm>
using namespace std;
class monomial;
class polynomial;
class fraction;
class monomial //单项式类
{
public:
double coefficient=1; //数字系数
string expression; //字母表达式
public:
monomial() { coefficient = 1; expression.clear(); }
monomial(double x) :coefficient(x) { expression.clear(); }
monomial (string const &expression);
monomial (double coefficient, string const &expression) :coefficient(coefficient), expression(expression) {};
monomial (monomial const &m) :coefficient(m.coefficient), expression(m.expression) {};
void arrange(void); //将表达式按字母升序排列
bool isZero(void) const { return (tools::isZero(coefficient)); }
monomial getCoeff(char var) const; //获取其中某个字母的系数
vector<char> getVar(void) const; //获取单项式中所含字母
monomial *split(void) const; //将单项式中指数小于零的项拆分
monomial changeSign(void) const{ monomial result(*this); result.coefficient *= -1; return result; } //改变单项式符号,用于处理减法
polynomial operator + (monomial const &m2) const; //重载单项式互加
monomial operator * (monomial const &m2) const; //重载单项式互乘，未重载与系数相乘
monomial operator / (monomial const &m2) const; //重载单项式互除
bool operator ==(monomial const &m2) const; //重载单项式比较
friend ostream &operator <<(ostream &output, monomial const &m); //重载单项式输出
/*单项式多项式混合运算*/
friend polynomial operator +(monomial const &m, polynomial const &p); //重载单项式加多项式
friend polynomial operator +(polynomial const &p, monomial const &m);
friend polynomial operator *(monomial const &m, polynomial const &p); //重载单项式乘多项式
friend polynomial operator *(polynomial const &p, monomial const &m);
friend fraction operator /(monomial const &m, polynomial const &p); //重载单项式除以多项式
friend fraction operator /(polynomial const &p, monomial const &m); //重载多项式除以单项式
friend fraction operator +(monomial const &m, fraction const &f); //重载单项式加分式
friend fraction operator +(fraction const &f, monomial const &m);
friend fraction operator *(monomial const &m, fraction const &f); //重载单项式加分式
friend fraction operator *(fraction const &f, monomial const &m);
friend fraction operator /(monomial const &m, fraction const &f); //重载单项式除以分式
friend fraction operator /(fraction const &f, monomial const &m); //重载分式除以单项式
};
monomial nextValue(int &step, vector<char> const & Coeff, vector<char> const & Const, vector<double> const & value); //创造一项可能的因式
class polynomial : public monomial //多项式类,公有继承单项式类作为公因式
{
public:
int termNumber = 0;
vector<monomial> terms;
public:
polynomial() { coefficient = 1; }
polynomial(string const &expression); //从字符串构造多项式
polynomial(monomial const &m) { coefficient = 1; termNumber = 1; terms.push_back(m); } //从单项式构造多项式,项数为1
polynomial(monomial &coefficient, int termNumber, vector<monomial> &terms) :monomial(coefficient), termNumber(termNumber), terms(terms) {}; //考虑如何设置系数缺省值为1
bool isZero(void) const;
bool isNegative(void) const; //确认多项式是否"小于零"
void orderBy(char a); //按字符a降幂排序
int getLength(void) const; //获取输出后字符串的长度
char getMainTerm(void) const; //获取幂次最高的字母
int getCoeff(void) const; //获取多项式的公系数
int factorPower(polynomial const &factor) const; //获取某多项式因子在另一多项式中的次数
polynomial getConst(char var) const; //获取对某字母而言的常数项
polynomial getCoeff(char var, int power) const; //获取对某字母而言最高次幂的系数项
vector<char> getVar(void) const; //获取多项式中所含字母
polynomial changeSign(void) const;
vector<polynomial> factorize(char var) const; //递归地分解因式
polynomial extraction(void) const; //提取公因式
polynomial expansion(void) const; //多项式展开
bool tryDivide(polynomial const &p);//若整除则除并返回true，否则不改变且返回false
polynomial DivideWithRemainder(polynomial const ÷r); //带余除法，返回余式
polynomial substitution(char var, polynomial value) const; //代入并消除同类项
polynomial operator +(polynomial const &p2) const; //重载多项式互加
polynomial operator *(polynomial const &p2) const; //重载多项式互乘
fraction operator /(polynomial const &p2) const; //重载多项式互除
bool operator ==(polynomial const &p2) const; //重载多项式比较
/*单项式多项式混合运算*/
friend polynomial operator +(monomial const &m, polynomial const &p); //重载多项式加单项式
friend polynomial operator +(polynomial const &p, monomial const &m);
friend polynomial operator *(monomial const &m, polynomial const &p); //重载多项式乘单项式
friend polynomial operator *(polynomial const &p, monomial const &m);
friend fraction operator /(monomial const &m, polynomial const &p); //重载单项式除以多项式
friend fraction operator /(polynomial const &p, monomial const &m); //重载多项式除以单项式
friend fraction operator +(polynomial const &p, fraction const &f); //重载多项式加分式
friend fraction operator +(fraction const &f, polynomial const &p);
friend fraction operator *(polynomial const &p, fraction const &f); //重载多项式加分式
friend fraction operator *(fraction const &f, polynomial const &p);
friend fraction operator /(polynomial const &p, fraction const &f); //重载多项式除以分式
friend fraction operator /(fraction const &f, polynomial const &p); //重载分式除以多项式
friend ostream &operator <<(ostream &output, polynomial const &p);
};
polynomial createTerm(char var, monomial &value, vector<int> &power); //创造提取公因式中的一项(x的值为单项式)
polynomial createTerm(char var, fraction &value, vector<int> &power); //创造提取公因式中的一项(x的值为分式)，替换下面这个
polynomial createTerm(char var, polynomial const Coeff, int coeffPower, polynomial const Const, int constpower); //创造提取公因式中的一项
vector<int> nextPower(vector<char> &vars, int *powers, vector<int> *factors,int step); //获取下一个因式中可能的幂次组合(单项式因子)
vector<int>nextPower(vector<polynomial> &terms, polynomial &Const, polynomial &Coeff); //获取下一个因式中可能的幂次组合(多项式因子)
class fraction : public polynomial //分式类，公有继承多项式类作为整式部分
{
public:
polynomial numerator;
polynomial denominator=monomial(1);
public:
fraction() { termNumber = 1; terms.push_back(monomial("1")); }
fraction(monomial const &m); //从单项式构造分式,分母为1
fraction(polynomial const &p); //从多项式构造分式,分母为1
fraction(fraction const &f) :polynomial(f), numerator(f.numerator), denominator(f.denominator) {};
fraction (fraction &integrate, fraction &numerator, fraction &denominator) : polynomial(integrate), numerator(numerator), denominator(denominator) {};
fraction changeSign(void) const;
bool isZero(void) const{ return numerator.isZero(); }
bool isDigit(void) const; //判断分式是否为数字
double toDigit(void) const; //将是纯数的分式转化为double
fraction trySimplify(void); //调整幂次为正，约去公因子
friend fraction myPow(fraction const &f, int power); //求幂运算，用于计算"^"操作符
fraction operator +(fraction const &f2) const; //重载分式互加
fraction operator *(fraction const &f2) const; //重载分式互乘
fraction operator /(fraction const &f2) const; //重载分式互除
friend ostream &operator <<(ostream &output, fraction const &f); //重载分式输出
friend fraction operator +(monomial const &m, fraction const &f); //重载单项式加分式
friend fraction operator +(fraction const &f, monomial const &m);
friend fraction operator *(monomial const &m, fraction const &f); //重载单项式加分式
friend fraction operator *(fraction const &f, monomial const &m);
friend fraction operator /(monomial const &m, fraction const &f); //重载单项式除以分式
friend fraction operator /(fraction const &f, monomial const &m); //重载分式除以单项式
friend fraction operator +(polynomial const &p, fraction const &f); //重载多项式加分式
friend fraction operator +(fraction const &f, polynomial const &p);
friend fraction operator *(polynomial const &p, fraction const &f); //重载多项式加分式
friend fraction operator *(fraction const &f, polynomial const &p);
friend fraction operator /(polynomial const &p, fraction const &f); //重载多项式除以分式
friend fraction operator /(fraction const &f, polynomial const &p); //重载分式除以多项式
};
void output(fraction ** const Matrix, int row, int column); //用于debug的输出
#endif // !symbolize