1% Test of algebraic number package.
2
3defpoly sqrt2**2-2;
4
51/(sqrt2+1);
6
7(x**2+2*sqrt2*x+2)/(x+sqrt2);
8
9on gcd;
10
11(x**3+(sqrt2-2)*x**2-(2*sqrt2+3)*x-3*sqrt2)/(x**2-2);
12
13off gcd;
14
15sqrt(x**2-2*sqrt2*x*y+2*y**2);
16
17off arnum;  %to start a new algebraic extension.
18
19
20defpoly cbrt5**3-5;
21
22on rationalize;
23
241/(x-cbrt5);
25
26off rationalize;
27
28off arnum;  %to start a new algebraic extension.
29
30
31%The following examples are taken from P.S. Wang Math. Comp. 30,
32%    134,(1976),p.324.
33
34on factor;
35
36defpoly i**2+1=0;
37
38w0 := x**2+1;
39
40w1 := x**4-1;
41
42w2 := x**4+(i+2)*x**3+(2*i+5)*x**2+(2*i+6)*x+6;
43
44w3 := (2*i+3)*x**4+(3*i-2)*x**3-2*(i+1)*x**2+i*x-1;
45
46off arnum;
47
48
49defpoly a**2-5;
50
51w4 := x**2+x-1;
52
53off arnum;
54
55
56defpoly a**2+a+2;
57
58w5 := x**4+3*x**2+4;
59
60off arnum;
61
62
63defpoly a**3+2=0;
64
65w6:=64*x**6-4;
66
67off arnum;
68
69
70defpoly a**4+a**3+a**2+a+1=0;
71
72w7:=16*x**4+8*x**3+4*x**2+2*x+1;
73
74off arnum, factor;
75
76
77defpoly sqrt5**2-5,cbrt3**3-3;
78
79cbrt3**3;
80
81sqrt5**2;
82
83cbrt3;
84
85sqrt5;
86
87sqrt(x**2+2*(sqrt5-cbrt3)*x+5-2*sqrt5*cbrt3+cbrt3**2);
88
89on rationalize;
90
911/(x+sqrt5-cbrt3);
92
93off arnum, rationalize;
94
95
96split_field(x**3+2);
97
98for each j in ws product (x-j);
99
100split_field(x**3+4*x**2+x-1);
101
102for each j in ws product (x-j);
103
104split_field(x**3-3*x+7);
105
106for each j in ws product (x-j);
107
108split_field(x**3+4*x**2+x-1);
109
110for each j in ws product (x-j);
111
112split_field(x**3-x**2-x-1);
113
114for each j in ws product (x-j);
115
116% A longer example.
117
118off arnum;
119
120defpoly a**6+3*a**5+6*a**4+a**3-3*a**2+12*a+16;
121
122factorize(x**3-3);
123
124end;
125