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// Asymptote module implementing rational arithmetic.
int gcd(int m, int n)
{
if(m < n) {
int temp=m;
m=n;
n=temp;
}
while(n != 0) {
int r=m % n;
m=n;
n=r;
}
return m;
}
int lcm(int m, int n)
{
return m#gcd(m,n)*n;
}
struct rational {
int p=0,q=1;
void reduce() {
int d=gcd(p,q);
if(abs(d) > 1) {
p #= d;
q #= d;
}
if(q <= 0) {
if(q == 0) abort("Division by zero");
p=-p;
q=-q;
}
}
void operator init(int p=0, int q=1, bool reduce=true) {
this.p=p;
this.q=q;
if(reduce) reduce();
}
}
rational operator cast(int p) {
return rational(p,false);
}
rational[] operator cast(int[] a) {
return sequence(new rational(int i) {return a[i];},a.length);
}
rational[][] operator cast(int[][] a) {
return sequence(new rational[](int i) {return a[i];},a.length);
}
real operator ecast(rational r) {
return r.p/r.q;
}
rational operator -(rational r)
{
return rational(-r.p,r.q,false);
}
rational operator +(rational r, rational s)
{
return rational(r.p*s.q+s.p*r.q,r.q*s.q);
}
rational operator -(rational r, rational s)
{
return rational(r.p*s.q-s.p*r.q,r.q*s.q);
}
rational operator *(rational r, rational s)
{
return rational(r.p*s.p,r.q*s.q);
}
rational operator /(rational r, rational s)
{
return rational(r.p*s.q,r.q*s.p);
}
bool operator ==(rational r, rational s)
{
return r.p == s.p && r.q == s.q;
}
bool operator !=(rational r, rational s)
{
return r.p != s.p || r.q != s.q;
}
bool operator <(rational r, rational s)
{
return r.p*s.q-s.p*r.q < 0;
}
bool operator >(rational r, rational s)
{
return r.p*s.q-s.p*r.q > 0;
}
bool operator <=(rational r, rational s)
{
return r.p*s.q-s.p*r.q <= 0;
}
bool operator >=(rational r, rational s)
{
return r.p*s.q-s.p*r.q >= 0;
}
bool[] operator ==(rational[] r, rational s)
{
return sequence(new bool(int i) {return r[i] == s;},r.length);
}
bool operator ==(rational[] r, rational[] s)
{
if(r.length != s.length)
abort(" operation attempted on arrays of different lengths: "+
string(r.length)+" != "+string(s.length));
return all(sequence(new bool(int i) {return r[i] == s[i];},r.length));
}
bool operator ==(rational[][] r, rational[][] s)
{
if(r.length != s.length)
abort(" operation attempted on arrays of different lengths: "+
string(r.length)+" != "+string(s.length));
return all(sequence(new bool(int i) {return r[i] == s[i];},r.length));
}
bool[] operator <(rational[] r, rational s)
{
return sequence(new bool(int i) {return r[i] < s;},r.length);
}
bool[] operator >(rational[] r, rational s)
{
return sequence(new bool(int i) {return r[i] > s;},r.length);
}
bool[] operator <=(rational[] r, rational s)
{
return sequence(new bool(int i) {return r[i] <= s;},r.length);
}
bool[] operator >=(rational[] r, rational s)
{
return sequence(new bool(int i) {return r[i] >= s;},r.length);
}
rational min(rational a, rational b)
{
return a <= b ? a : b;
}
rational max(rational a, rational b)
{
return a >= b ? a : b;
}
string string(rational r)
{
return r.q == 1 ? string(r.p) : string(r.p)+"/"+string(r.q);
}
string texstring(rational r)
{
if(r.q == 1) return string(r.p);
string s;
if(r.p < 0) s="-";
return s+"\frac{"+string(abs(r.p))+"}{"+string(r.q)+"}";
}
void write(file fout, string s="", rational r, suffix suffix=none)
{
write(fout,s+string(r),suffix);
}
void write(string s="", rational r, suffix suffix=endl)
{
write(stdout,s,r,suffix);
}
void write(file fout=stdout, string s="", rational[] a, suffix suffix=none)
{
if(s != "")
write(fout,s,endl);
for(int i=0; i < a.length; ++i) {
write(fout,i,none);
write(fout,':\t',a[i],endl);
}
write(fout,suffix);
}
void write(file fout=stdout, string s="", rational[][] a, suffix suffix=none)
{
if(s != "")
write(fout,s);
for(int i=0; i < a.length; ++i) {
rational[] ai=a[i];
for(int j=0; j < ai.length; ++j) {
write(fout,ai[j],tab);
}
write(fout,endl);
}
write(fout,suffix);
}
bool rectangular(rational[][] m)
{
int n=m.length;
if(n > 0) {
int m0=m[0].length;
for(int i=1; i < n; ++i)
if(m[i].length != m0) return false;
}
return true;
}
rational sum(rational[] a)
{
rational sum;
for(rational r:a)
sum += r;
return sum;
}
rational max(rational[] a)
{
rational M=a[0];
for(rational r:a)
M=max(M,r);
return M;
}
rational abs(rational r)
{
return rational(abs(r.p),r.q,false);
}
rational[] operator -(rational[] r)
{
return sequence(new rational(int i) {return -r[i];},r.length);
}
rational[][] rationalidentity(int n)
{
return sequence(new rational[](int i) {return sequence(new rational(int j) {return j == i ? 1 : 0;},n);},n);
}
/*
rational r=rational(1,3)+rational(1,4);
write(r == rational(1,12));
write(r);
real x=r;
write(x);
rational r=3;
write(r);
write(gcd(-8,12));
write(rational(-36,-14));
int[][] a=new int[][] {{1,2},{3,4}};
rational[][] r=a;
write(r);
*/
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