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some code simplification
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@JohnCremona
JohnCremona committed May 1, 2024
1 parent 4d03e00 commit e5b44c7
Showing 1 changed file with 34 additions and 120 deletions.
154 changes: 34 additions & 120 deletions libsrc/curvered.cc
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Original file line number Diff line number Diff line change
Expand Up @@ -60,38 +60,37 @@ ostream& operator<<(ostream& os, const Kodaira_code& c)
bigint root(const bigint& aa, int e, const bigint & p)
// the e'th root of aa, mod p
{
bigint i, ans, temp; int found=0;
const bigint& a = mod(aa, p);
for (i = 1; (! found); ++i)
{ans = i;
if (e==2) temp = ans*ans - a;
else temp = ans*ans*ans - a;
found = div(p, temp); }
// bigint ans;
// int found = 0;
// bigint a = aa % p;
// for ( ans = 1; (ans<=p) && (! found); ++ans)
// found = div(p, pow(ans,e) - a); //N.B. pow(0,p) causes problems.
return ans;
bigint a = aa%p, r, b, xe(e);
if (is_zero(a)) return a;
if (e==2)
{
sqrt_mod_p(r, a, p);
return r;
}
for (r = 1; r<p; ++r)
{
power_mod(b, r, xe, p);
if (b==a) return r;
}
return bigint(0);
}

// test if quadratic aX^2 + bX + c = 0 (mod p) has roots
int rootsexist(const bigint& aa, const bigint& bb, const bigint& cc, const bigint& p)
{
if (even(p)) return is_zero((aa*bb*cc)%p);
const bigint& a = aa % p;
if (is_zero(a)) return 1;
const bigint& b = bb % p;
const bigint& c = cc % p;
const bigint& temp = (a*b*c)%p;
if (even(p)) return sign(temp)==0;
if (sign(a)==0) return 1;
const bigint& d = b*b - 4*a*c;
return legendre(d, p) >= 0; //ie true if legendre(d,p)=0,1
if (is_zero(c)) return 1;
return legendre(b*b - 4*a*c, p) >= 0; //ie true if legendre(d,p)=0,1
}

//monic version
int rootsexist(const bigint& bb, const bigint& cc, const bigint& p)
{
static bigint one; one=1;
static const bigint one(1);
return rootsexist(one,bb,cc,p);
}

Expand Down Expand Up @@ -354,8 +353,8 @@ bigint local_Tamagawa_exponent(CurveRed& c, const bigint& p)

bigint global_Tamagawa_exponent(const CurveRed& c, int real_too)
{
const bigint one = BIGINT(1);
const bigint two = BIGINT(2);
static const bigint one(1);
static const bigint two(2);
bigint ans = ((real_too && (c.conncomp==2))? two: one);

for( const auto& ri : c.reduct_array)
Expand Down Expand Up @@ -389,29 +388,25 @@ vector<long> tamagawa_primes(const CurveRed& C, int real_too)
int getord_p_discr(const CurveRed& c, const bigint& p)
{
auto ri = c.reduct_array.find(p);
if(ri==c.reduct_array.end()) return 0;
return (ri->second).ord_p_discr;
return (ri==c.reduct_array.end()? 0 : (ri->second).ord_p_discr);
}

int getord_p_N(const CurveRed& c, const bigint& p)
{
auto ri = c.reduct_array.find(p);
if(ri==c.reduct_array.end()) return 0;
return (ri->second).ord_p_N;
return (ri==c.reduct_array.end()? 0 : (ri->second).ord_p_N);
}

int getord_p_j_denom(const CurveRed& c, const bigint& p)
{
auto ri = c.reduct_array.find(p);
if(ri==c.reduct_array.end()) return 0;
return (ri->second).ord_p_j_denom;
return (ri==c.reduct_array.end()? 0 : (ri->second).ord_p_j_denom);
}

int getc_p(const CurveRed& c, const bigint& p)
{
auto ri = c.reduct_array.find(p);
if(ri==c.reduct_array.end()) return 1;
return (ri->second).c_p;
return (ri==c.reduct_array.end()? : (ri->second).c_p);
}

vector<bigint> all_cp(const CurveRed& c)
Expand Down Expand Up @@ -444,8 +439,7 @@ bigint global_Tamagawa_number(CurveRed& c, int real_too)
Kodaira_code getKodaira_code(const CurveRed& c, const bigint& p)
{
auto ri = c.reduct_array.find(p);
if(ri==c.reduct_array.end()) return Kodaira_code();
return (ri->second).Kcode;
return (ri==c.reduct_array.end()? Kodaira_code() : (ri->second).Kcode);
}

void CurveRed::output(ostream& os) const
Expand Down Expand Up @@ -533,30 +527,20 @@ int kro_3(long x); // kronecker(x,3)

void CurveRed::setLocalRootNumber2()
{
static const bigint two = BIGINT(2);
static const bigint two(2);
auto ri = reduct_array.find(two);
if(ri==reduct_array.end()) return;
Reduction_type& info = ri->second;
int kod = PariKodairaCode(info.Kcode);
int n2 = neron(2,kod);

#ifdef DEBUG_ESIGN
cout<<"\nIn LocalRootNumber2(), n2 = "<<n2<<"..."<<endl;
#endif

bigint mu,mv; long u,v; int v4,v6;

if (is_zero(c4)) {v4=12; u=0;}
else {mu=c4; v4=divide_out(mu,two); u = posmod(mu,64);}
#ifdef DEBUG_ESIGN
cout<<"c4="<<c4<<", v4="<<v4<<", u="<<u<<endl;
#endif

if (is_zero(c6)) {v6=12; v=0;}
else {mv=c6; v6=divide_out(mv,two); v = posmod(mv,64);}
#ifdef DEBUG_ESIGN
cout<<"c6="<<c6<<", v6="<<v6<<", v="<<v<<endl;
#endif

if (kod > 4)
{
Expand Down Expand Up @@ -730,16 +714,13 @@ void CurveRed::setLocalRootNumber2()

void CurveRed::setLocalRootNumber3()
{
static const bigint three = BIGINT(3);
static const bigint three(3);
auto ri = reduct_array.find(three);
if(ri==reduct_array.end()) return;
Reduction_type& info = ri->second;
int kod = PariKodairaCode(info.Kcode);
int n2 = neron(3,kod);

#ifdef DEBUG_ESIGN
cout<<"\nIn LocalRootNumber3()..."<<endl;
#endif
bigint mu,mv; long u,v; int v4;

if (is_zero(c4)) {
Expand All @@ -752,10 +733,6 @@ void CurveRed::setLocalRootNumber3()
u = posmod(mu,81);
}

#ifdef DEBUG_ESIGN
cout<<"c4="<<c4<<", v4="<<v4<<", u="<<u<<endl;
#endif

if (is_zero(c6)) {
v=0;
}
Expand All @@ -765,25 +742,11 @@ void CurveRed::setLocalRootNumber3()
v = posmod(mv,81);
}

#ifdef DEBUG_ESIGN
cout<<"c6="<<c6<<", v6="<<v6<<", v="<<v<<endl;
#endif

bigint tmp = discr;
divide_out(tmp,three);
long d1=posmod(tmp,81);

#ifdef DEBUG_ESIGN
cout<<"d1="<<d1<<endl;
#endif

long r6 = posmod(v,9);
long K4=kro_3(u), K6=kro_3(v);
#ifdef DEBUG_ESIGN
cout<<"r6="<<r6<<endl;
cout<<"K4="<<K4<<endl;
cout<<"K6="<<K6<<endl;
#endif

if (kod > 4)
{
Expand Down Expand Up @@ -900,89 +863,40 @@ void CurveRed::setLocalRootNumber(const bigint& p)

int kro(const bigint& d, const bigint& n)
{
#ifdef DEBUG_ESIGN
cout<<"kro("<<d<<","<<n<<") returns "<<flush;
#endif
int ans = kronecker(d,n);
#ifdef DEBUG_ESIGN
cout<<ans<<endl;
#endif
return ans;
return kronecker(d,n);
}

int kro(const bigint& d, long n)
{
#ifdef DEBUG_ESIGN
cout<<"kro("<<d<<","<<n<<") returns "<<flush;
#endif
int ans = kronecker(d,n);
#ifdef DEBUG_ESIGN
cout<<ans<<endl;
#endif
return ans;
return kronecker(d,n);
}

int kro(long d, long n)
{
#ifdef DEBUG_ESIGN
cout<<"kro("<<d<<","<<n<<") returns "<<flush;
#endif
int ans = kronecker(d,n);
#ifdef DEBUG_ESIGN
cout<<ans<<endl;
#endif
return ans;
return kronecker(d,n);
}

int kro_m1(long x) // kronecker(-1,x) with x>0 odd
{
static const int kro_m1_tab[4] = {0,1,0,-1};
#ifdef DEBUG_ESIGN
if (!((x>0)&&(odd(x))))
{
cout<<"kro_m1() called with x="<<x<<endl;
return 0;
}
#endif
return kro_m1_tab[x&3];
}

int kro_p2(long x) // kronecker(2,x) with x>0 odd
{
static const int kro_p2_tab[8] = {0,1,0,-1,0,-1,0,1};
#ifdef DEBUG_ESIGN
if (!((x>0)&&(odd(x))))
{
cout<<"kro_p2() called with x="<<x<<endl;
return 0;
}
#endif
return kro_p2_tab[x&7];
}

int kro_m2(long x) // kronecker(-2,x) with x>0 odd
{
static const int kro_m2_tab[8] = {0,1,0,1,0,-1,0,-1};
#ifdef DEBUG_ESIGN
if (!((x>0)&&(odd(x))))
{
cout<<"kro_m2() called with x="<<x<<endl;
return 0;
}
#endif
return kro_m2_tab[x&7];
}

int kro_3(long x) // kronecker(x,3)
{
static const int kro_3_tab[3] = {0,1,-1};
#ifdef DEBUG_ESIGN
if (!(x>0))
{
cout<<"kro_3() called with x="<<x<<endl;
return 0;
}
#endif
return kro_3_tab[x%3];
}

Expand Down Expand Up @@ -1109,10 +1023,10 @@ int CurveRed::neron(long p, int kod)

bigint Trace_Frob(CurveRed& c, const bigint& p)
{
const bigint zero=BIGINT(0);
const bigint one=BIGINT(1);
const bigint two=BIGINT(2);
const bigint three=BIGINT(3);
static const bigint zero(0);
static const bigint one(1);
static const bigint two(2);
static const bigint three(3);
// cout<<"Trace_Frob at "<<p<<endl;

int f = getord_p_N(c,p);
Expand Down

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