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
|
// mptest.cc -- test program for marith functions
//////////////////////////////////////////////////////////////////////////
//
// Copyright 1990-2012 John Cremona
//
// This file is part of the eclib package.
//
// eclib is free software; you can redistribute it and/or modify it
// under the terms of the GNU General Public License as published by the
// Free Software Foundation; either version 2 of the License, or (at your
// option) any later version.
//
// eclib is distributed in the hope that it will be useful, but WITHOUT
// ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
// FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
// for more details.
//
// You should have received a copy of the GNU General Public License
// along with eclib; if not, write to the Free Software Foundation,
// Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA
//
//////////////////////////////////////////////////////////////////////////
//
#include <eclib/marith.h>
#define MAXPRIME 1000000
int main()
{
initprimes("PRIMES",1);
cout<<"long prime factors of 420:\n";
vector<long> lplist = pdivs(420);
cout<<lplist<<endl;
cout<<" with posdivs (long version)\n";
vector<long> lqlist = posdivs(420, lplist);
cout<<lqlist<<endl;
bigint num; num=420;
vector<bigint> a(3);
a[0]=10; a[1]=20; a[2]=30;
vector<bigint> b = a;
cout << "Elements of a are: " << a[0]<<"\t"<<a[1]<<"\t"<<a[2]<<endl;
cout << "Elements of b are: " << b[0]<<"\t"<<b[1]<<"\t"<<b[2]<<endl;
cout << "a = " << a << endl << "end of output of a" << endl;
cout << "b = " << b << endl << "end of output of b" << endl;
b=a;
cout<<"After b=a, b = " << endl << b << endl;
cout<<"bigint versions of divisor functions:\n\n";
cout<<"bigint prime factors of 420:\n";
vector<bigint> iplist = pdivs(num);
cout<<iplist<<endl;
cout<<" with posdivs (bigint version) \n";
vector<bigint> iqlist = posdivs(num, iplist);
cout<<iqlist<<endl;
cout<<"and alldivs (bigint version) \n";
//deliberately reuse space
iqlist = alldivs(num, iplist);
cout<<iqlist<<endl;
cout<<"making a copy of iqlist\n";
iplist=iqlist;
cout<<" reuse iqlist for sqdivs\n";
iqlist = sqdivs(num);
cout<<"iqlist (should be sqdivs) "<<iqlist<<endl;
cout<<"iplist (should be alldivs) "<<iplist<<endl;
cout<<"making an vector<bigint> of iplist (alldivs)\n";
vector<bigint> irary(iplist);
cout<<"stream output: "<<irary<<endl;
cout<<"irary(7) is "<<irary[7]<<"\tirary[3] is "<<irary[3]<<endl;
cout<<"testing find function\n";
vector<bigint>::iterator vi;
vi = find(irary.begin(),irary.end(),35);
if(vi==irary.end()) cout<<"35 is not there\n";
else cout<<"35 is there: "<<*vi<<" is item number "<<(vi-irary.begin())<<endl;
vi = find(irary.begin(),irary.end(),13);
if(vi==irary.end()) cout<<"13 is not there\n";
else cout<<"13 is there: "<<*vi<<" is item number "<<(vi-irary.begin())<<endl;
cout<<"\n\nTest of sqrt and isqrt\n";
bigint astop; astop=999;
bigint aaa,roota; int res;
while (cout << "\nEnter a positive bigint a (999 to stop): ", cin >> aaa, aaa!=astop)
{
res = sign(aaa);
cout << "a = " << aaa << ", sign(a) = " << res << "\n";
roota = sqrt(aaa);
cout << "a = " << aaa << ", sqrt(a) = " << roota << " (rounded down)\n";
res = isqrt(aaa,roota);
if(res) cout << "a is a square with exact square root " << roota << "\n";
else cout << "a is not a square\n";
}
cout<<"\n\nTest of sqrt mod p\n";
bigint bb,p,r;
while(cout << "Enter a prime p: ", cin>>p, cout<<p<<endl, is_positive(p))
{
int nbad=0; long x;
for(x=1; x<100; x++)
{
bb=x;
if(legendre(bb,p)==1)
{
bb%=p; if(bb<0) bb+=p;
sqrt_mod_p(r,bb,p);
cout << "sqrt("<<x<<" mod p) = " << r << "\t";
if(div(p,(r*r-x))) cout << "---OK\n";
else {cout << "---WRONG\n"; nbad++;}
}
else
{
cout << x<< " is not a quadratic residue mod p!\n";
}
}
if(nbad==0) cout << "First 100 OK"<<endl;
else cout << nbad << " wrong ones out of first 100"<<endl;
}
bigint m;
while (cout << "\nEnter a bigint m (0 to stop): ", cin >> m, sign(m)!=0)
{
cout << "m = " << m << endl;
vector<bigint> plist=pdivs(m);
cout << "m has " << plist.size() << " prime divisors: " << plist << endl;
cout << "with exponents: ";
for(vector<bigint>::const_iterator pr = plist.begin(); pr!=plist.end(); pr++)
cout << *pr <<":"<<val(*pr,m) << "\t";
cout<<endl;
vector<bigint> dlist=alldivs(m,plist);
cout << "m has " << dlist.size() << " divisors: " << dlist << endl;
dlist = posdivs(m,plist);
cout << "m has " << dlist.size()
<< " positive divisors: " << dlist << endl;
dlist = sqdivs(m,plist);
cout << "m has " << dlist.size()
<< " positive divisors whose square divides m: " << dlist << endl;
dlist = sqfreedivs(m,plist);
cout << "m has " << dlist.size()
<< " positive square-free divisors: " << dlist << endl;
}
cout<<endl;
} // end of main
|
