-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathSymbolicOctonion.cpp
158 lines (126 loc) · 5.98 KB
/
SymbolicOctonion.cpp
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
157
158
#include "SymbolicOctonion.h"
void SymbolicOctonion::operator=(const SymbolicOctonion &inSymbolicOctonion){
this->e0 = inSymbolicOctonion.e0;
this->e1 = inSymbolicOctonion.e1;
this->e2 = inSymbolicOctonion.e2;
this->e3 = inSymbolicOctonion.e3;
this->e4 = inSymbolicOctonion.e4;
this->e5 = inSymbolicOctonion.e5;
this->e6 = inSymbolicOctonion.e6;
this->e7 = inSymbolicOctonion.e7;
}
void SymbolicOctonion::operator+=(const SymbolicOctonion &inSymbolicOctonion){
this->e0 = this->e0 + inSymbolicOctonion.e0;
this->e1 = this->e1 + inSymbolicOctonion.e1;
this->e2 = this->e2 + inSymbolicOctonion.e2;
this->e3 = this->e3 + inSymbolicOctonion.e3;
this->e4 = this->e4 + inSymbolicOctonion.e4;
this->e5 = this->e5 + inSymbolicOctonion.e5;
this->e6 = this->e6 + inSymbolicOctonion.e6;
this->e7 = this->e7 + inSymbolicOctonion.e7;
}
void SymbolicOctonion::operator-=(const SymbolicOctonion &inSymbolicOctonion){
this->e0 = this->e0 - inSymbolicOctonion.e0;
this->e1 = this->e1 - inSymbolicOctonion.e1;
this->e2 = this->e2 - inSymbolicOctonion.e2;
this->e3 = this->e3 - inSymbolicOctonion.e3;
this->e4 = this->e4 - inSymbolicOctonion.e4;
this->e5 = this->e5 - inSymbolicOctonion.e5;
this->e6 = this->e6 - inSymbolicOctonion.e6;
this->e7 = this->e7 - inSymbolicOctonion.e7;
}
void SymbolicOctonion::operator*=(const SymbolicOctonion &inOct){
PolynomialFraction e0New = e0*inOct.e0 - e1*inOct.e1 - e2*inOct.e2 - e3*inOct.e3 - e4*inOct.e4 - e5*inOct.e5 - e6*inOct.e6 - e7*inOct.e7;
PolynomialFraction e1New = e0*inOct.e1 + e1*inOct.e0 + e2*inOct.e4 + e3*inOct.e7 - e4*inOct.e2 + e5*inOct.e6 - e6*inOct.e5 - e7*inOct.e3;
PolynomialFraction e2New = e0*inOct.e2 - e1*inOct.e4 + e2*inOct.e0 + e3*inOct.e5 + e4*inOct.e1 - e5*inOct.e3 + e6*inOct.e7 - e7*inOct.e6;
PolynomialFraction e3New = e0*inOct.e3 - e1*inOct.e7 - e2*inOct.e5 + e3*inOct.e0 + e4*inOct.e6 + e5*inOct.e2 - e6*inOct.e4 + e7*inOct.e1;
PolynomialFraction e4New = e0*inOct.e4 + e1*inOct.e2 - e2*inOct.e1 - e3*inOct.e6 + e4*inOct.e0 + e5*inOct.e7 + e6*inOct.e3 - e7*inOct.e5;
PolynomialFraction e5New = e0*inOct.e5 - e1*inOct.e6 + e2*inOct.e3 - e3*inOct.e2 - e4*inOct.e7 + e5*inOct.e0 + e6*inOct.e1 + e7*inOct.e4;
PolynomialFraction e6New = e0*inOct.e6 + e1*inOct.e5 - e2*inOct.e7 + e3*inOct.e4 - e4*inOct.e3 - e5*inOct.e1 + e6*inOct.e0 + e7*inOct.e2;
PolynomialFraction e7New = e0*inOct.e7 + e1*inOct.e3 + e2*inOct.e6 - e3*inOct.e1 + e4*inOct.e5 - e5*inOct.e4 - e6*inOct.e2 + e7*inOct.e0;
e0 = e0New;
e1 = e1New;
e2 = e2New;
e3 = e3New;
e4 = e4New;
e5 = e5New;
e6 = e6New;
e7 = e7New;
}
SymbolicOctonion SymbolicOctonion::operator+(const SymbolicOctonion &inSymbolicOctonion) const
{
SymbolicOctonion tmp(*this);
tmp+=inSymbolicOctonion;
return tmp;
}
SymbolicOctonion SymbolicOctonion::operator-(const SymbolicOctonion &inSymbolicOctonion) const
{
SymbolicOctonion tmp(*this);
tmp+=inSymbolicOctonion;
return tmp;
}
SymbolicOctonion SymbolicOctonion::operator*(const SymbolicOctonion &inSymbolicOctonion) const
{
SymbolicOctonion tmp(*this);
tmp*=inSymbolicOctonion;
return tmp;
}
PolynomialFraction SymbolicOctonion::normSqr(){
return e0*e0+e1*e1+e2*e2+e3*e3+e4*e4+e5*e5+e6*e6+e7*e7;
}
SymbolicOctonion inv(SymbolicOctonion &inSymbolicOctonion){
SymbolicOctonion result;
result.e0 = inSymbolicOctonion.e0/(inSymbolicOctonion.normSqr());
result.e1 = - inSymbolicOctonion.e1/(inSymbolicOctonion.normSqr());
result.e2 = - inSymbolicOctonion.e2/(inSymbolicOctonion.normSqr());
result.e3 = - inSymbolicOctonion.e3/(inSymbolicOctonion.normSqr());
result.e4 = - inSymbolicOctonion.e4/ (inSymbolicOctonion.normSqr());
result.e5 = - inSymbolicOctonion.e5/ (inSymbolicOctonion.normSqr());
result.e6 = - inSymbolicOctonion.e6/ (inSymbolicOctonion.normSqr());
result.e7 = - inSymbolicOctonion.e7/ (inSymbolicOctonion.normSqr());
return result;
}
SymbolicOctonion SymbolicOctonion::operator()(const SymbolicOctonion &inSymbolicOctonion) const {
map <Variable, PolynomialFraction> substitution;
//filling map
substitution[Variable(string("x_0")) ] = inSymbolicOctonion.e0;
substitution[Variable(string("x_1")) ] = inSymbolicOctonion.e1;
substitution[Variable(string("x_2")) ] = inSymbolicOctonion.e2;
substitution[Variable(string("x_3")) ] = inSymbolicOctonion.e3;
substitution[Variable(string("x_4")) ] = inSymbolicOctonion.e4;
substitution[Variable(string("x_5")) ] = inSymbolicOctonion.e5;
substitution[Variable(string("x_6")) ] = inSymbolicOctonion.e6;
substitution[Variable(string("x_7")) ] = inSymbolicOctonion.e7;
SymbolicOctonion result;
result.e0 = e0(substitution);
result.e1 = e1(substitution);
result.e2 = e2(substitution);
result.e3 = e3(substitution);
result.e4 = e4(substitution);
result.e5 = e5(substitution);
result.e6 = e6(substitution);
result.e7 = e7(substitution);
return result;
}
SymbolicOctonion SymbolicOctonion::evaluate(const SymbolicOctonion &inSymbolicOctonion) const {
map <Variable, PolynomialFraction> substitution;
//filling map
substitution[Variable(string("x_0")) ] = inSymbolicOctonion.e0;
substitution[Variable(string("x_1")) ] = inSymbolicOctonion.e1;
substitution[Variable(string("x_2")) ] = inSymbolicOctonion.e2;
substitution[Variable(string("x_3")) ] = inSymbolicOctonion.e3;
substitution[Variable(string("x_4")) ] = inSymbolicOctonion.e4;
substitution[Variable(string("x_5")) ] = inSymbolicOctonion.e5;
substitution[Variable(string("x_6")) ] = inSymbolicOctonion.e6;
substitution[Variable(string("x_7")) ] = inSymbolicOctonion.e7;
SymbolicOctonion result;
result.e0 = e0(substitution);
result.e1 = e1(substitution);
result.e2 = e2(substitution);
result.e3 = e3(substitution);
result.e4 = e4(substitution);
result.e5 = e5(substitution);
result.e6 = e6(substitution);
result.e7 = e7(substitution);
return result;
}