adic 0.5.1

Arithmetic and rootfinding for p-adic numbers
Documentation 
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
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230

use num::traits::Pow;

use crate::num_adic::test_util::{e, u, qe, qu};


// PowAdic

#[test]
fn add_adic_power() {

    assert_eq!(apow!(u::two(), 2), apow!(u::one(), 2) + apow!(u::one(), 2));
    assert_eq!(apow!(u::five(), 2), apow!(u::two(), 2) + apow!(u::three(), 2));
    assert_eq!(apow!(u::twenty_five(), 2), apow!(u::ten(), 2) + apow!(u::fifteen(), 2));
    assert_eq!(apow!(qu::two(), 2), apow!(qu::one(), 2) + apow!(qu::one(), 2));
    assert_eq!(apow!(qu::five(), 2), apow!(qu::two(), 2) + apow!(qu::three(), 2));
    assert_eq!(apow!(qu::three_fifth(), 2), apow!(qu::one_fifth(), 2) + apow!(qu::two_fifth(), 2));

    assert_eq!(apow!(e::neg_two(), 2), apow!(e::neg_one(), 2) + apow!(e::neg_one(), 2));
    assert_eq!(apow!(qe::neg_five(), 2), apow!(qe::neg_two(), 2) + apow!(qe::neg_three(), 2));
    assert_eq!(apow!(e::zero(), 2), apow!(e::two(), 2) + apow!(e::neg_two(), 2));

    assert_eq!(apow!(e::two(), 5), apow!(e::one(), 5) + apow!(e::one(), 5));
    assert_eq!(apow!(qe::pos_3_5(), 2), apow!(qe::pos_1_5(), 2) + apow!(qe::pos_2_5(), 2));
    assert_eq!(apow!(e::two(), 2), apow!(e::neg_5_6(), 2) + apow!(e::pos_17_6(), 2));

}

#[test]
fn neg_adic_power() {

    assert_eq!(apow!(e::neg_one(), 2), -apow!(e::one(), 2));
    assert_eq!(apow!(e::zero(), 2), -apow!(e::zero(), 2));
    assert_eq!(apow!(e::neg_five(), 2), -apow!(e::five(), 2));
    assert_eq!(apow!(e::neg_twenty_five(), 2), -apow!(e::twenty_five(), 2));
    assert_eq!(apow!(qe::neg_one_fifth(), 2), -apow!(qe::one_fifth(), 2));

    assert_eq!(apow!(e::neg_five(), 2), -apow!(e::five(), 2));
    assert_eq!(apow!(e::neg_1_6(), 2), -apow!(e::pos_1_6(), 2));
    assert_eq!(apow!(e::neg_5_6(), 2), -apow!(e::pos_5_6(), 2));
    assert_eq!(apow!(qe::neg_1_120(), 2), -apow!(qe::pos_1_120(), 2));

}

#[test]
fn sub_adic_power() {

    assert_eq!(apow!(e::one(), 2), apow!(e::two(), 2) - apow!(e::one(), 2));
    assert_eq!(apow!(e::zero(), 2), apow!(e::one(), 2) - apow!(e::one(), 2));
    assert_eq!(apow!(e::neg_one(), 2), apow!(e::one(), 2) - apow!(e::two(), 2));
    assert_eq!(apow!(e::neg_five(), 2), apow!(e::one(), 2) - apow!(e::six(), 2));
    assert_eq!(apow!(qe::four_fifth(), 2), apow!(qe::one(), 2) - apow!(qe::one_fifth(), 2));
    assert_eq!(apow!(qe::neg_one_fifth(), 2), apow!(qe::three_fifth(), 2) - apow!(qe::four_fifth(), 2));

    assert_eq!(apow!(e::one(), 2), apow!(e::three(), 2) - apow!(e::two(), 2));
    assert_eq!(apow!(e::zero(), 2), apow!(e::four(), 2) - apow!(e::four(), 2));
    assert_eq!(apow!(e::six(), 2), apow!(e::one(), 2) - apow!(e::neg_five(), 2));
    assert_eq!(apow!(qe::neg_1_31(), 2), apow!(qe::pos_30_31(), 2) - apow!(qe::one(), 2));

}

#[test]
fn mul_adic_power() {

    assert_eq!(apow!(u::two(), 2), apow!(u::two(), 2) * apow!(u::one(), 2));
    assert_eq!(apow!(u::one(), 2), apow!(u::one(), 2) * apow!(u::one(), 2));
    assert_eq!(apow!(qu::one_twenty_fifth(), 2), apow!(qu::one_fifth(), 2) * apow!(qu::one_fifth(), 2));

    assert_eq!(apow!(e::one(), 2), apow!(e::neg_one(), 2) * apow!(e::neg_one(), 2));
    assert_eq!(apow!(e::six(), 2), apow!(e::neg_two(), 2) * apow!(e::neg_three(), 2));
    assert_eq!(apow!(e::neg_twenty_five(), 2), apow!(e::five(), 2) * apow!(e::neg_five(), 2));
    assert_eq!(apow!(e::zero(), 2), apow!(e::two(), 2) * apow!(e::zero(), 2));
    assert_eq!(apow!(e::zero(), 2), apow!(e::neg_two(), 2) * apow!(e::zero(), 2));
    assert_eq!(apow!(qe::one_twenty_fifth(), 2), apow!(qe::one_fifth(), 2) * apow!(qe::one_fifth(), 2));

    assert_eq!(apow!(e::neg_one(), 2), apow!(e::neg_1_24(), 2) * apow!(e::four(), 2) * apow!(e::six(), 2));
    assert_eq!(apow!(qe::neg_1_120(), 2), apow!(qe::neg_1_24(), 2) * apow!(qe::pos_1_5(), 2));
    assert_eq!(apow!(qe::pos_25_16(), 2), apow!(qe::twenty_five(), 2) * apow!(qe::pos_1_16(), 2));

}

#[test]
fn pow_adic_power() {

    assert_eq!(apow!(u::zero(), 2), apow!(u::zero(), 2).pow(2));
    assert_eq!(apow!(u::one(), 2), apow!(u::zero(), 2).pow(0));
    assert_eq!(apow!(u::one(), 2), apow!(u::one(), 2).pow(3));
    assert_eq!(apow!(u::four(), 2), apow!(u::two(), 2).pow(2));
    assert_eq!(apow!(u::eight(), 2), apow!(u::two(), 2).pow(3));
    assert_eq!(apow!(u::twenty_five(), 2), apow!(u::five(), 2).pow(2));
    assert_eq!(apow!(qu::one_twenty_fifth(), 2), apow!(qu::one_fifth(), 2).pow(2));

    assert_eq!(apow!(e::one(), 2), apow!(e::neg_two(), 2).pow(0));
    assert_eq!(apow!(e::neg_one(), 2), apow!(e::neg_one(), 2).pow(1));
    assert_eq!(apow!(e::one(), 2), apow!(e::neg_one(), 2).pow(2));
    assert_eq!(apow!(e::four(), 2), apow!(e::neg_two(), 2).pow(2));
    assert_eq!(apow!(qe::one_twenty_fifth(), 2), apow!(qe::one_fifth(), 2).pow(2));

    assert_eq!(apow!(e::pos_1_16(), 2), apow!(e::neg_1_4(), 2).pow(2));
    assert_eq!(apow!(e::neg_1_64(), 2), apow!(e::neg_1_4(), 2).pow(3));
    assert_eq!(apow!(qe::pos_1_25(), 2), apow!(qe::neg_1_5(), 2).pow(2));
    assert_eq!(apow!(qe::pos_1_25(), 2), apow!(qe::pos_1_5(), 2).pow(2));

}


// MAdic

mod c {

    #![allow(dead_code)]
    #![allow(unreachable_pub)]
    use crate::{num_adic::MAdic, EAdic};

    type MEAdic = MAdic<EAdic>;

    pub fn zero() -> MEAdic { MAdic::from_i32(10, 0).unwrap() }
    pub fn one() -> MEAdic { MAdic::from_i32(10, 1).unwrap() }
    pub fn two() -> MEAdic { MAdic::from_i32(10, 2).unwrap() }
    pub fn three() -> MEAdic { MAdic::from_i32(10, 3).unwrap() }
    pub fn four() -> MEAdic { MAdic::from_i32(10, 4).unwrap() }
    pub fn five() -> MEAdic { MAdic::from_i32(10, 5).unwrap() }
    pub fn six() -> MEAdic { MAdic::from_i32(10, 6).unwrap() }
    pub fn seven() -> MEAdic { MAdic::from_i32(10, 7).unwrap() }
    pub fn eight() -> MEAdic { MAdic::from_i32(10, 8).unwrap() }
    pub fn nine() -> MEAdic { MAdic::from_i32(10, 9).unwrap() }
    pub fn ten() -> MEAdic { MAdic::from_i32(10, 10).unwrap() }
    pub fn twenty() -> MEAdic { MAdic::from_i32(10, 20).unwrap() }
    pub fn neg_one() -> MEAdic { MAdic::from_i32(10, -1).unwrap() }
    pub fn neg_two() -> MEAdic { MAdic::from_i32(10, -2).unwrap() }
    pub fn neg_three() -> MEAdic { MAdic::from_i32(10, -3).unwrap() }
    pub fn neg_five() -> MEAdic { MAdic::from_i32(10, -5).unwrap() }
    pub fn neg_ten() -> MEAdic { MAdic::from_i32(10, -10).unwrap() }

    pub fn pure_2_one() -> MEAdic { MAdic::from_pure_p_adic(10, eadic!(2, [1])).unwrap() }
    pub fn pure_2_two() -> MEAdic { MAdic::from_pure_p_adic(10, eadic!(2, [0, 1])).unwrap() }
    pub fn pure_2_three() -> MEAdic { MAdic::from_pure_p_adic(10, eadic!(2, [1, 1])).unwrap() }
    pub fn pure_2_four() -> MEAdic { MAdic::from_pure_p_adic(10, eadic!(2, [0, 0, 1])).unwrap() }
    pub fn pure_2_five() -> MEAdic { MAdic::from_pure_p_adic(10, eadic!(2, [1, 0, 1])).unwrap() }
    pub fn pure_2_ten() -> MEAdic { MAdic::from_pure_p_adic(10, eadic!(2, [0, 1, 0, 1])).unwrap() }
    pub fn pure_2_neg_one() -> MEAdic { MAdic::from_pure_p_adic(10, eadic_neg!(2, [])).unwrap() }
    pub fn pure_2_neg_five() -> MEAdic { MAdic::from_pure_p_adic(10, eadic_neg!(2, [1, 1, 0])).unwrap() }
    pub fn pure_2_neg_ten() -> MEAdic { MAdic::from_pure_p_adic(10, eadic_neg!(2, [0, 1, 1, 0])).unwrap() }

    pub fn pure_5_one() -> MEAdic { MAdic::from_pure_p_adic(10, eadic!(5, [1])).unwrap() }
    pub fn pure_5_two() -> MEAdic { MAdic::from_pure_p_adic(10, eadic!(5, [2])).unwrap() }
    pub fn pure_5_three() -> MEAdic { MAdic::from_pure_p_adic(10, eadic!(5, [3])).unwrap() }
    pub fn pure_5_four() -> MEAdic { MAdic::from_pure_p_adic(10, eadic!(5, [4])).unwrap() }
    pub fn pure_5_five() -> MEAdic { MAdic::from_pure_p_adic(10, eadic!(5, [0, 1])).unwrap() }
    pub fn pure_5_ten() -> MEAdic { MAdic::from_pure_p_adic(10, eadic!(5, [0, 2])).unwrap() }
    pub fn pure_5_neg_one() -> MEAdic { MAdic::from_pure_p_adic(10, eadic_neg!(5, [])).unwrap() }
    pub fn pure_5_neg_five() -> MEAdic { MAdic::from_pure_p_adic(10, eadic_neg!(5, [0, 4])).unwrap() }
    pub fn pure_5_neg_ten() -> MEAdic { MAdic::from_pure_p_adic(10, eadic_neg!(5, [0, 3])).unwrap() }

}

#[test]
fn add_adic_composite() {

    assert_eq!(c::two(), c::one() + c::one());
    assert_eq!(c::five(), c::two() + c::three());
    assert_eq!(c::seven(), c::three() + c::four());
    assert_eq!(c::ten(), c::two() + c::eight());

    assert_eq!(c::pure_2_five(), c::pure_2_two() + c::pure_2_three());
    assert_eq!(c::pure_5_five(), c::pure_5_two() + c::pure_5_three());
    assert_eq!(c::five(), c::pure_2_five() + c::pure_5_five());

}

#[test]
fn neg_adic_composite() {

    assert_eq!(c::neg_one(), -c::one());
    assert_eq!(c::zero(), -c::zero());
    assert_eq!(c::neg_five(), -c::five());
    assert_eq!(c::neg_ten(), -c::ten());

    assert_eq!(c::pure_2_neg_ten(), -c::pure_2_ten());
    assert_eq!(c::pure_5_neg_ten(), -c::pure_5_ten());
    assert_eq!(c::pure_5_neg_ten(), -c::pure_5_ten());
    assert_eq!(c::pure_5_five() + c::pure_2_neg_one(), -(c::pure_5_neg_five() + c::pure_2_one()));

}

#[test]
fn sub_adic_composite() {

    assert_eq!(c::one(), c::two() - c::one());
    assert_eq!(c::zero(), c::three() - c::three());
    assert_eq!(c::neg_one(), c::one() - c::two());
    assert_eq!(c::neg_ten(), c::neg_five() - c::five());
    assert_eq!(c::five(), c::neg_five() - c::neg_ten());

    assert_eq!(c::ten(), c::pure_2_ten() - c::pure_5_neg_ten());
    assert_eq!(c::pure_2_five(), c::five() - c::pure_5_five());
    assert_eq!(c::pure_5_five(), c::five() - c::pure_2_five());

}

#[test]
fn mul_adic_composite() {

    assert_eq!(c::six(), c::two() * c::three());
    assert_eq!(c::neg_ten(), c::five() * c::neg_two());
    assert_eq!(c::seven(), c::seven() * c::one());
    assert_eq!(c::zero(), c::neg_two() * c::zero());

    assert_eq!(c::pure_2_ten(), c::pure_2_two() * c::pure_2_five());
    assert_eq!(c::pure_5_ten(), c::pure_5_two() * c::pure_5_five());
    assert_eq!(c::zero(), c::pure_2_two() * c::pure_5_five());

}

#[test]
fn pow_adic_composite() {

    assert_eq!(c::eight(), c::two().pow(3));
    assert_eq!(c::seven(), c::seven().pow(1));
    assert_eq!(c::one(), c::two().pow(0));
    assert_eq!(c::zero(), c::zero().pow(3));
    assert_eq!(c::one(), c::zero().pow(0));

    assert_eq!(c::pure_2_four(), c::pure_2_two().pow(2));
    assert_eq!(c::pure_5_four(), c::pure_5_two().pow(2));
    assert_eq!(c::pure_2_two(), c::pure_2_two().pow(1));
    assert_eq!(c::pure_5_two(), c::pure_5_two().pow(1));
    assert_eq!(c::one(), c::pure_2_two().pow(0));
    assert_eq!(c::one(), c::pure_5_two().pow(0));

}