IntegerRing/IntegerRing.cpp at master · MikeWarren2014/IntegerRing · GitHub

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
144
145
146
147
148
149
150
151
152
153
154
155
156
#include "IntegerRing.h"
#include "IntegerGroup.h"
#include "Operators.h"

#include <iostream>

IntegerRing::Element::Element()
	: IntegerGroup::GroupElement()
{

}

IntegerRing::IntegerRing(int n)
	: IntegerGroup::IntegerGroup(n)
{

}

IntegerRing::Element::Element(int m, IntegerGroup * g)
	: IntegerGroup::GroupElement(m, g)
{

}

IntegerRing::Element::Element(const IntegerGroup::GroupElement& el)
	: IntegerGroup::GroupElement(el)
{

}

IntegerRing::Element IntegerRing::Element::operator+(int x)
{
	return (IntegerRing::Element)(((IntegerGroup::GroupElement)(*this)) * x);
}

IntegerRing::Element IntegerRing::Element::operator+(const IntegerRing::Element& b)
{
	// IntegerRing is simply Abelian group under addition
	// thus, we treat the elements like group elements first, multiply under that group, and cast to ring elements
	return (IntegerRing::Element)(((IntegerGroup::GroupElement)(*this)) * ((IntegerGroup::GroupElement)b));
}

IntegerRing::Element operator+(int x, const IntegerRing::Element& el)
{
	return (const_cast <IntegerRing::Element&>(el) + x);
}

IntegerRing::Element IntegerRing::Element::operator-()
{
	return IntegerRing::Element(-this->m, this->group);
}

IntegerRing::Element IntegerRing::Element::operator-(int x)
{
	return ((*this) - IntegerRing::Element(x, this->group));
}

IntegerRing::Element IntegerRing::Element::operator-(const IntegerRing::Element& b)
{
	int val;
	// if this has a group
	if (this->group)
	{
		// compute (this->m - b.m) % this->group->size()
		val = (this->m - b.m) % this->group->size();
		// if that value is negative, add this->group->size() to it
		if (val < 0) val = this->group->size() + val;
	}
	// otherwise, val is simply the integer difference of this->m,b.m
	else val = this->m - b.m;
	// return element with this value
	return Element(val, this->group);
}


IntegerRing::Element operator-(int x, const IntegerRing::Element& el)
{
	//return (x + -(const_cast<IntegerRing::Element>(el)));
	return IntegerRing::Element(x - el.m, el.group);
}

IntegerRing::Element IntegerRing::Element::operator*(int x)
{
	return ((*this) * IntegerRing::Element(x, this->group));
}

IntegerRing::Element IntegerRing::Element::operator*(const IntegerRing::Element& b)
{
	if (this->group)
		return IntegerRing::Element((this->m * b.m) % this->group->size(), this->group);
	return IntegerRing::Element(this->m * b.m, this->group);
}

IntegerRing::Element operator*(int x, const IntegerRing::Element& el)
{
	return (const_cast<IntegerRing::Element&>(el) * x);
}

IntegerRing::Element IntegerRing::Element::operator+=(const IntegerRing::Element& b)
{
	return ((*this) = (*this) + b);
}

IntegerRing::Element IntegerRing::Element::operator-=(const IntegerRing::Element& b)
{
	return ((*this) = (*this) - b);
}

IntegerRing::Element IntegerRing::Element::operator*=(const IntegerRing::Element& b)
{
	return ((*this) = (*this) * b);
}

IntegerRing::Element IntegerRing::identity(Operators op)
{
	// if op is ADDITIVE
	if (op == ADDITIVE)
		// return what the base version of this method would return
		return (IntegerRing::Element)(((IntegerGroup)(*this)).identity());
	// multiplicative identity requested, and it is 1
	return (IntegerRing::Element)this->elements[0];
}

IntegerRing::Element IntegerRing::inverse(int x)
{
	// make sure x in (0, this->n) . If not, either throw exception or return 0
	if ((x <= 0) || (x >= this->n)) throw IntegerRing::Element(0, this);
	// Extended Euclidean Algorithm
	int t = 0,
		r = this->n,
		newT = 1,
		newR = x;
	while (newR != 0)
	{
		int quotient = r / newR,
			tCopy = t,
			rCopy = r,
			newTCopy = newT,
			newRCopy = newR;
		t = newT;
		newT = tCopy - quotient * newTCopy;
		r = newR;
		newR = rCopy - quotient * newRCopy;
	}
	if (r > 1)
	{
		throw IntegerRing::Element(0, this);
	}
	if (t < 0) t = t + this->n;
	return IntegerRing::Element(t, this);
}

IntegerRing::Element IntegerRing::inverse(const IntegerRing::Element& el)
{
	return this->inverse(el.val());
}