t-charge.c

/* This file is part of the MAYLIB libray.
   Copyright 2007-2018 Patrick Pelissier

This Library is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation; either version 3 of the License, or (at your
option) any later version.

This Library 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 Lesser General Public
License for more details.

You should have received a copy of the GNU Lesser General Public License
along with th Library; see the file COPYING.LESSER.txt.
If not, write to the Free Software Foundation, Inc.,
51 Franklin St, Fifth Floor, Boston,
MA 02110-1301, USA. */

#include <stdio.h>
#include <stdlib.h>
#include <sys/types.h>
#include <sys/resource.h>
#include <sys/time.h>

#include "may.h"

static int verbose = 2;


static int
cputime (void)
{
#ifndef MAY_WANT_THREAD
  struct rusage rus;

  getrusage (0, &rus);
  return rus.ru_utime.tv_sec * 1000 + rus.ru_utime.tv_usec / 1000;
#else
  struct timeval tv;
  gettimeofday (&tv, NULL);
  return tv.tv_sec * 1000 + tv.tv_usec / 1000;
#endif
}

int
test_construct (void)
{
  may_mark ();
  if (verbose >= 2) {
    printf ("Construct (3*(a*x+b*y+c*z) with a=1/2, b=2/3 and c=4/5...");
    fflush (stdout);
  }

  int t0 = 0;
  unsigned long long m0, m;
  may_t a = may_set_si_ui (1,2);
  may_t b = may_set_si_ui (2,3);
  may_t c = may_set_si_ui (4,5);
  may_t x = may_set_str ("x");
  may_t y = may_set_str ("y");
  may_t z = may_set_str ("z");
  may_t three = may_set_ui (3);

  for (m0 = 300000; t0 < 50 ; m0*=2) {
    t0 = cputime ();
    may_mark ();
    for (m= 0; m < m0; m++) {
      may_t temp[3];
      temp[0] = may_mul_c (a, x);
      temp[1] = may_mul_c (b, y);
      temp[2] = may_mul_c (c, z);
      temp[0] = may_add_vc (3, temp);
      temp[0] = may_mul_c (three, temp[0]);
      may_eval (temp[0]);
    }
    may_keep (NULL);
    t0 = cputime () - t0;
  }

  if (verbose >= 2)
    printf ("%2.5fms [%Ld execs/sec]\n", ((double)t0)/(m0/2), 1000*(m0/2)/t0);

  may_keep (NULL);
  return t0/(m0/2);
}

int
test_eval (long n)
{
  may_t *base = malloc (n*sizeof (long));
  may_t x;
  long i;
  int  t0, t1, m0, m1, m;
  char buffer[100];
  may_mark_t mark;

  may_mark (mark);

  if (verbose >= 2) {
    printf ("eval (sum ai*ai*ai) - quite different - N=%ld...", n);
    fflush (stdout);
  }

  for (i = 0; i < n ; i++) {
    sprintf (buffer, "a%d*a%d*a%d", rand(), rand (), rand());
    base[i] = may_parse_str (buffer);
  }

  if (verbose >= 2) {
    printf ("...");
    fflush (stdout);
  }

  for (m0 = t0 = 1; m0 < 10000 && t0 < 10 ; m0++) {
    t0 = cputime ();
    for (m = 0; m < m0; m++) {
      x = may_add_vc (n, base);
      x = may_eval (x);
    }
    t0 = cputime () - t0;
  }

  if (verbose >= 2)
    printf ("%2.2fms\n", ((double) t0)/(m0-1));

  may_compact (mark, NULL);

  if (verbose >= 2) {
    printf ("eval (sum ai*ai*ai) -  quite similar  - N=%ld...", n);
    fflush (stdout);
  }

  for (i = 0; i < n ; i++) {
    sprintf (buffer, "a%d*a%d*a%d", rand() % 5, rand () % 5, rand()) % 5;
    base[i] = may_parse_str (buffer);
  }

  if (verbose >= 2) {
    printf ("...");
    fflush (stdout);
  }

  for (m1 = t1 = 1; m1 < 10000 && t1 < 10 ; m1++) {
    t1 = cputime ();
    for (m = 0; m < m1; m++) {
      x = may_add_vc (n, base);
      x = may_eval (x);
    }
    t1 = cputime () - t1;
  }

  if (verbose >= 2)
    printf ("%2.2fms\n", ((double)t1)/(m1-1));

  may_compact (mark, NULL);
  free (base);

  return t0/(m0-1)+t1/(m1-1);
}

/* Test add many numericals and a 'x' */
int
test_addnum (int n)
{
  int t0;
  may_t s;
  may_mark ();

  if (verbose >= 2) {
    printf ("eval(sum(i,i=0..%d)+x+sum(i,i=0..%d))...", n, n);
    fflush (stdout);
  }
  t0 = cputime ();

  s = may_set_ui (0);
  for (int i = 0; i < n; i++)
    s = may_addinc_c (s, may_set_ui (i));
  s = may_addinc_c (s, may_set_str ("x"));
  for (int i = 0; i < n; i++)
    s = may_addinc_c (s, may_set_ui (i));
  s = may_eval (s);

  t0 = cputime () - t0;
  if (verbose >= 2)
    printf ("%dms\n", t0);

  may_keep (NULL);
  return t0;
}

/* Test small expand with many variables, replace and evaluator */
int
test_expand (int n)
{
  may_t ai, a0, sum, s2;
  char tmp[10];
  int t0, i;

  may_mark ();
  if (verbose >= 2) {
    printf ("expand ((a0+...a%d)^2), replace a0, reeval...", n);
    fflush (stdout);
  }

  t0 = cputime ();

  sum = s2 = may_set_ui (0);
  for (i = 0; i < n; i++) {
    sprintf (tmp, "a%d", i);
    ai = may_set_str (tmp);
    sum = may_addinc_c (sum, ai);
    if (i >= 2)
      s2 = may_addinc_c (s2, ai);
    if (i == 0)
      a0 = ai;
  }
  sum = may_sqr_c (sum);
  sum = may_eval (sum);
  sum = may_expand (sum);

  if (verbose >= 3) {
    printf ("%dms...", cputime ()-t0);
    fflush (stdout);
  }

  s2  = may_eval (may_neg_c (s2));
  sum = may_replace (sum, a0, s2);

  if (verbose >= 3) {
    printf ("%dms...", cputime ()-t0);
    fflush (stdout);
  }

  sum = may_expand (sum);

  t0 = cputime () - t0;
  if (verbose >= 2)
    printf ("%dms\n", t0);

  may_keep (NULL);
  return t0;
}


/* Test multivariate polynomial */
int
test_expand2 (int n, int d)
{
  may_t x, sum;
  char buffer[10];
  int i, t0;
  may_mark_t mark;

  may_mark (mark);
  if (verbose >= 2) {
    printf ("expand ((x0+...x%d+1)^%d*(1+(x0+...x%d+1)^%d))...",
            n-1, d, n-1, d);
    fflush (stdout);
  }
  t0 = cputime ();

  /* DO IT */
  sum = may_set_ui (1);
  for (i =0; i < n; i++) {
    sprintf (buffer, "x%d", i);
    x = may_set_str (buffer);
    sum = may_addinc_c (sum, x);
  }
  sum = may_pow_c (sum, may_set_ui (d));
  sum = may_eval (sum);
  sum = may_expand (sum);
  x   = may_add (sum, may_set_ui (1));
  sum = may_mul (sum, x);
  sum = may_compact (mark, sum);

  if (verbose >= 3) {
    printf ("%dms...", cputime () - t0);
    fflush (stdout);
  }

  sum = may_expand (sum);
  t0 = cputime() - t0;

  /* End */
  if (verbose >= 2)
    printf ("%dms\n", t0);
  may_compact (mark, NULL);

  return t0;
}

int
test_expand3 (int d)
{
  may_t sum;
  char buffer[100];
  int t0;

  may_mark ();
  sprintf (buffer, "(x+y^400000000000+z)^%d*(1+x+y+z^-1)^%d", d, d);

  if (verbose >= 2) {
    printf ("expand (%s)...", buffer);
    fflush (stdout);
  }
  sum = may_parse_str (buffer);
  t0 = cputime ();
  sum = may_expand (sum);
  t0 = cputime() - t0;

  /* End */
  if (verbose >= 2)
    printf ("%dms\n", t0);
  may_keep (NULL);
  return t0;
}

int
test_expand4 (int d)
{
  char buffer1[100];
  char buffer2[100];
  int t0;

  may_mark ();
  sprintf (buffer1, "(1+x)^%d*(1+y)^%d", d, d);
  sprintf (buffer2, "(1-x)^%d*(2-y)^%d", d, d);

  if (verbose >= 2) {
    printf ("expand (expand(%s) * expand(%s))...", buffer1, buffer2);
    fflush (stdout);
  }

  may_t a = may_expand (may_parse_str (buffer1));
  may_t b = may_expand (may_parse_str (buffer2));

  t0 = cputime ();
  may_expand (may_mul (a, b));
  t0 = cputime() - t0;

  /* End */
  if (verbose >= 2)
    printf ("%dms\n", t0);
  may_keep (NULL);
  return t0;
}

int
test_expand5 (int d)
{
  char buffer[100];
  int t0;

  may_mark ();
  sprintf (buffer, "(a+b+c+d+e+f+g+h)^%d", d);

  if (verbose >= 2) {
    printf ("expand (expand(%s) * expand(%s))...", buffer, buffer);
    fflush (stdout);
  }

  may_t a = may_expand (may_parse_str (buffer));
  may_t b = may_expand (may_parse_str (buffer));

  t0 = cputime ();
  may_expand (may_mul (a, b));
  t0 = cputime() - t0;

  /* End */
  if (verbose >= 2)
    printf ("%dms\n", t0);
  may_keep (NULL);
  return t0;
}

int
test_expand6 (int n)
{
  int t0;

  may_mark ();

  if (verbose >= 2) {
    printf ("expand ((1+x+...+x^%d)*(1+2*x+x^2+...+x^%d))...", n-1, n-1);
    fflush (stdout);
  }

  t0 = cputime ();

  may_t s = may_set_ui (0);
  may_t x = may_set_str ("x");
  for (int i = 0; i < n; i++)
    s = may_addinc_c (s, may_pow_si_c (x, i));
  s = may_eval (s);
  may_t s2 = may_add (s, x);
  s = may_mul (s, s2);
  s = may_compact (s);
  s = may_expand (s);
  t0 = cputime() - t0;

  /* End */
  if (verbose >= 2)
    printf ("%dms\n", t0);
  may_keep (NULL);
  return t0;
}

/* Test univariate multiply */
int
test_univariate_multiply (int a, int b, int n)
{
  char Buffer[100];
  may_t x;
  int t0;

  /* Begin */
  may_mark ();
  sprintf (Buffer, "(%d+x)^%d*(%d+x)^%d", a, n, b, n);
  x = may_parse_str (Buffer);
  if (verbose >= 2) {
    printf ("expand ((%d+x)^%d*(%d+x)^%d)...", a, n, b, n);
    fflush (stdout);
  }

  /* DO IT */
  t0 = cputime ();
  x = may_expand (x);
  t0 = cputime() - t0;

  /* End */
  if (verbose >= 2)
    printf ("%dms\n", t0);
  may_keep (NULL);
  return t0;
}

/* Test expand ((1+sqrt(5)) ^N */
int
test_power_field (int n)
{
  char Buffer[100];
  may_t x;
  int t0;

  /* Begin */
  may_mark ();
  sprintf (Buffer, "(1+sqrt(5))^%d", n);
  x = may_parse_str (Buffer);
  if (verbose >= 2) {
    printf ("expand (%s)...", Buffer);
    fflush (stdout);
  }

  /* DO IT */
  t0 = cputime ();
  x = may_expand (x);
  t0 = cputime() - t0;

  /* End */
  if (verbose >= 2)
    printf ("%dms\n", t0);
  may_keep (NULL);
  return t0;
}

int
test_pow_multivariate (int n)
{
  char Buffer[100];
  may_t x;
  int t0;

  /* Begin */
  may_mark ();
  sprintf (Buffer, "(1+x+y)^%d", n);
  x = may_parse_str (Buffer);
  if (verbose >= 2) {
    printf ("expand (%s)...", Buffer);
    fflush (stdout);
  }

  /* DO IT */
  t0 = cputime ();
  x = may_expand (x);
  t0 = cputime() - t0;

  /* End */
  if (verbose >= 2)
    printf ("%dms\n", t0);
  may_keep (NULL);
  return t0;
}



/* Test evaluator and fast replace */
static may_t identity (may_t x) { return x; }
static may_t (*tfunc[]) (may_t) = {&identity};
static const char* tname[] = {"f"};

int
test_critical (int n)
{
  may_t x, s;
  int i, t0;

  may_mark ();
  if (verbose >= 2) {
    printf ("eval(x+f(x)+f(f(x))+...+f(%d)(x)), subs f to id...", n);
    fflush (stdout);
  }

  t0 = cputime ();
  x = may_set_str ("x");
  s = may_set_ui (0);

  for (i=0; i < n; i++) {
    s = may_addinc_c (s, x);
    x = may_func_c ("f", x);
  }
  s = may_eval (s);

  if (verbose >= 3) {
    printf ("%dms...", cputime () - t0);
    fflush (stdout);
  }

  s = may_subs_c (s, n+1,1, tname, (void*) tfunc);
  s = may_eval (s);

  t0 = cputime () - t0;
  if (verbose >= 2)
    printf ("%dms\n", t0);

  may_keep (NULL);
  return t0;
}

int
test_sum_x (int n)
{
  int t0;
  may_t s, x;
  may_mark ();

  if (verbose >= 2) {
    printf ("eval(sum(i*x^i, n=0..%d)...", n);
    fflush (stdout);
  }
  t0 = cputime ();
  s = may_set_ui (0);
  x = may_set_str ("x");
  for (int i = 0; i < n; i++)
    s = may_addinc_c (s, may_mul_c (may_set_ui (i), may_pow_c (x, may_set_ui (i))));
  s = may_eval (s);

  t0 = cputime () - t0;
  if (verbose >= 2)
    printf ("%dms\n", t0);

  may_keep (NULL);
  return t0;
}

int
test_sin_pi6 (int n)
{
  int t0;
  may_t s, pi6;
  may_mark ();

  if (verbose >= 2) {
    printf ("eval(sum(sin(n*PI/6), n=0..%d)...", n);
    fflush (stdout);
  }
  t0 = cputime ();
  s = may_set_ui (0);
  pi6 = may_div (may_set_str ("PI"), may_set_ui (6));
  for (int i = 0; i < n; i++)
    s = may_addinc_c (s, may_sin_c (may_mul_c (may_set_ui (i), pi6)));
  s = may_eval (s);

  t0 = cputime () - t0;
  if (verbose >= 2)
    printf ("%dms\n", t0);

  may_keep (NULL);
  return t0;
}

int
test_complex (int n)
{
  int t0;
  may_mark ();
  if (verbose >= 2) {
    printf ("eval((2+3*I/4)^%d)...", n);
    fflush (stdout);
  }
  t0 = cputime ();
  may_eval (may_pow_c (may_set_cx (may_set_ui (2), may_set_si_ui (3,4)), may_set_si (n)));
  t0 = cputime () - t0;
  if (verbose >= 2)
    printf ("%dms\n", t0);

  may_keep (NULL);
  return t0;
}

int
test_evalf (int p)
{
  int t0;
  may_mark ();
  if (verbose >= 2) {
    printf ("evalf(sin(1+PI)^2+3^sqrt(1+PI^2)) to %d bits...", p);
    fflush (stdout);
  }
  may_t e = may_parse_str ("sin(1+PI)^2+3^sqrt(1+PI^2)");
  may_kernel_prec (p);
  t0 = cputime ();
  may_evalf (e);
  t0 = cputime () - t0;
  may_kernel_prec (113);
  if (verbose >= 2)
    printf ("%dms\n", t0);

  may_keep (NULL);
  return t0;
}


/* DIVIDE */
int
test_divide (const char *buffer1, const char *buffer2, const char *var)
{
  int t0;
  may_t q, r, a, b, v;

  may_mark ();

  /* Input */
  a = may_expand (may_parse_str (buffer1));
  b = may_expand (may_parse_str (buffer2));
  v = may_parse_str (var);

  if (verbose >= 2) {
    printf ("divide ( %s , %s, %s)...", buffer1, buffer2, var);
    fflush (stdout);
  }
  t0 = cputime ();

  /* Do it */
  may_div_qr (&q, &r, a, b, v);

  /* End */
  t0 = cputime() - t0;
  if (verbose >= 2)
    printf ("%dms\n", t0);
  may_keep (NULL);
  return t0;
}

/* GCD (((i+1)*Sum(ai))^d,((-i*Sum(ai)+1)^d) */
int
test_gcd (const char *buffer1, const char *buffer2)
{
  may_t tab[2];
  int t0;
  char buf2print1[50];
  char buf2print2[50];
  int do_expand;

  /* BEGIN */
  may_mark ();
  tab[0] =  may_parse_str (buffer1);
  tab[1] =  may_parse_str (buffer2);
  if (may_nan_p (tab[0]) || may_nan_p (tab[1]))
    abort ();

  do_expand = may_get_name (tab[0]) != may_sum_name || may_get_name (tab[1]) != may_sum_name;

  strncpy (buf2print1, buffer1, sizeof buf2print1);
  buf2print1[sizeof buf2print1 - 3] = '.';
  buf2print1[sizeof buf2print1 - 2] = '.';
  buf2print1[sizeof buf2print1 - 1] = 0;
  strncpy (buf2print2, buffer2, sizeof buf2print2);
  buf2print2[sizeof buf2print2 - 3] = '.';
  buf2print2[sizeof buf2print2 - 2] = '.';
  buf2print2[sizeof buf2print2 - 1] = 0;

  if (verbose >= 2) {
    printf ("       gcd ( %s , %s )...", buf2print1, buf2print2);
    fflush (stdout);
  }

  /* DO IT */
  t0 = cputime ();
  may_gcd (2, tab);
  t0  = cputime () - t0;

  /* END */
  if (verbose >= 2)
    printf ("%dms\n", t0);
  may_compact (NULL);

  /* BEGIN */
  if (do_expand == 0)
    return t0;

  tab[0] = may_expand (may_parse_str (buffer1));
  tab[1] = may_expand (may_parse_str (buffer2));
  if (verbose >= 2) {
    printf ("expand+gcd ( %s , %s )...", buf2print1, buf2print2);
    fflush (stdout);
  }

  /* DO IT */
  t0 = cputime ();
  may_gcd (2, tab);
  t0  = cputime () - t0;

  /* END */
  if (verbose >= 2)
    printf ("%dms\n", t0);
  may_keep (NULL);
  return t0;
}

static may_t
sum_y_i (int start, int end, int v)
{
  may_t s;
  may_mark ();
  s = may_set_ui (0);
  for (int i = start ; i <= end; i++) {
    char buffer[100];
    sprintf (buffer, "y%d", i);
    may_t y = may_set_str (buffer);
    s = may_addinc_c (s, may_pow_si_c (y, v));
  }
  return may_keep (may_eval (s));
}

static may_t
mul_y_i (int start, int end, int v)
{
  may_t s;
  may_mark ();
  s = may_set_ui (1);
  may_t vy = may_set_si (v);
  for (int i = start ; i <= end; i++) {
    char buffer[100];
    sprintf (buffer, "y%d", i);
    may_t y = may_set_str (buffer);
    s = may_mul_c (s, may_add_c (y, vy));
  }
  return may_keep (may_eval (s));
}

/* From 'Evaluation of the Heuristic Polynomial GCD' by Fateman */
int
test_gcd2 (int n1, int n2, int n3, int n4, int n5, int n6, int n7, int n8, int n9, int n10)
{
  int t0 = 0, t;
  may_mark ();

  may_t d, f, g, x, y, z, y1, x_2, y1_2, tab[2];
  x    = may_set_str ("x");
  y    = may_set_str ("y");
  z    = may_set_str ("z");
  y1   = may_set_str ("y1");
  x_2  = may_mul (x, x);
  y1_2 = may_mul (y1, y1);

  /* F = (x   + sum(y[i],i=1..n) + 1) * (x + sum(y[i],i=1..n)+2)
     G = (x^2 + sum(y[i]^2,i=1..n) + 1) * (-3*y[1]*x^2+y[1]^2-1) */
  f = may_mul_c (may_add_vac (x, sum_y_i (1, n1, 1), may_set_ui (1), NULL),
                 may_add_vac (x, sum_y_i (1, n1, 1), may_set_ui (2), NULL));
  g = may_mul_c (may_add_vac (x_2, sum_y_i (1, n1, 2), may_set_ui (1), NULL),
                 may_add_vac (may_mul_vac (may_set_si(-3), y1, x_2, NULL), y1_2, may_set_si (-1), NULL));
  tab[0] = may_expand (may_eval (f));
  tab[1] = may_expand (may_eval (g));
  if (verbose >= 2) {
    printf ("GCDFT1: gcd = 1 (n=%d)...", n1);
    fflush (stdout);
  }
  t = cputime ();
  may_gcd (2, tab);
  t  = cputime () - t;
  if (verbose >= 2)
    printf ("%dms\n", t);
  t0 += t;

  /* D = (x + sum(y[i],i=1,n)+1) ^2
     F = D* (x- sum(y[i],i=1,n)-2) ^2
     G = D* (x+ sum(y[i],i=1,n)+2) ^2 */
  d = may_pow_si_c (may_add_vac (x, sum_y_i (1, n2, 1), may_set_ui (1), NULL), 2);
  f = may_pow_si_c (may_sub_c (x, may_add_c (sum_y_i (1, n2, 1), may_set_ui (2))), 2);
  g = may_pow_si_c (may_add_vac (x, sum_y_i (1, n2, 1), may_set_ui (2), NULL), 2);
  tab[0] = may_expand (may_eval (may_mul_c (d, f)));
  tab[1] = may_expand (may_eval (may_mul_c (d, g)));
  if (verbose >= 2) {
    printf ("GCDFT2: gcd of linearly dense quartic inputs with quadratic GCDs (n=%d)...", n2);
    fflush (stdout);
  }
  t = cputime ();
  may_gcd (2, tab);
  t  = cputime () - t;
  if (verbose >= 2)
    printf ("%dms\n", t);
  t0 += t;

  /* D = x^(n+1) + sum (y[i]^(n+1),i=1..n) + 1
     F = D* (x^(n+1) + sum (y[i]^(n+1),i=1..n) - 2)
     G = D* (x^(n+1) + sum (y[i]^(n+1),i=1..n) + 2) */
  d = may_add_vac (may_pow_si_c (x, n3+1), sum_y_i (1, n3, n3+1), may_set_ui (1), NULL);
  f = may_add_vac (may_pow_si_c (x, n3+1), sum_y_i (1, n3, n3+1), may_set_si (-2), NULL);
  g = may_add_vac (may_pow_si_c (x, n3+1), sum_y_i (1, n3, n3+1), may_set_si (+2), NULL);
  tab[0] = may_expand (may_eval (may_mul_c (d, f)));
  tab[1] = may_expand (may_eval (may_mul_c (d, g)));
  if (verbose >= 2) {
    printf ("GCDFT3: gcd of sparse inputs where degree // to #vars (n=%d)...", n3);
    fflush (stdout);
  }
  t = cputime ();
  may_gcd (2, tab);
  t  = cputime () - t;
  if (verbose >= 2)
    printf ("%dms\n", t);
  t0 += t;

  /* D = x^(n+1) + sum (y[i]^n,i=1..n) + 1
     F = D* (x^(n+1) + sum (y[i]^(n+1),i=1..n) - 2)
     G = D* (x^(n+1) + sum (y[i]^(n+1),i=1..n) + 2) */
  d = may_add_vac (may_pow_si_c (x, n4+1), sum_y_i (1, n4, n4), may_set_ui (1), NULL);
  f = may_add_vac (may_pow_si_c (x, n4+1), sum_y_i (1, n4, n4+1), may_set_si (-2), NULL);
  g = may_add_vac (may_pow_si_c (x, n4+1), sum_y_i (1, n4, n4+1), may_set_si (+2), NULL);
  tab[0] = may_expand (may_eval (may_mul_c (d, f)));
  tab[1] = may_expand (may_eval (may_mul_c (d, g)));
  if (verbose >= 2) {
    printf ("GCDFT4: gcd of sparse inputs where degree // to #vars (second) (n=%d)...", n4);
    fflush (stdout);
  }
  t = cputime ();
  may_gcd (2, tab);
  t  = cputime () - t;
  if (verbose >= 2)
    printf ("%dms\n", t);
  t0 += t;

  /* D = y1^2*x^2 + sum( y[i]^2,i=2..n) + 1
     F = D* (x^2-y1^2+sum(y[i]^2,i=2..n) -1)
     G = D* (y1*x+sum(y[i],i=2..n)+ 2)^2 */
  d = may_add_vac (may_mul_c (y1_2, x_2), sum_y_i (2,n5,2), may_set_ui (1), NULL);
  f = may_sub_c (may_add_c (x_2, sum_y_i (2,n5,2)), may_add_c (y1_2, may_set_ui (1)));
  g = may_add_vac (may_mul_c (y1, x), sum_y_i (2,n5,1),may_set_ui (2), NULL);
  g = may_pow_si_c (g, 2);
  tab[0] = may_expand (may_eval (may_mul_c (d, f)));
  tab[1] = may_expand (may_eval (may_mul_c (d, g)));
  if (verbose >= 2) {
    printf ("GCDFT5: gcd quadratic non-monic with other quadratic factors (n=%d)...", n5);
    fflush (stdout);
  }
  t = cputime ();
  may_gcd (2, tab);
  t  = cputime () - t;
  if (verbose >= 2)
    printf ("%dms\n", t);
  t0 += t;

  /* D= (x+1) * product (y[i]+1, i=1..n)-3
     F=D* ((x-2)*product (y[i]-2, i=1..n)+3)
     G=D* ((x+2)*product (y[i]+2, i=1..n)-3) */
  d = may_add_c (may_mul_c (may_add_c (x, may_set_ui (1)), mul_y_i (1, n6, 1)), may_set_si (-3));
  f = may_add_c (may_mul_c (may_add_c (x, may_set_si (-2)), mul_y_i (1, n6, -2)), may_set_si (3));
  g = may_add_c (may_mul_c (may_add_c (x, may_set_si (2)), mul_y_i (1, n6, 2)), may_set_si (-3));
  tab[0] = may_expand (may_eval (may_mul_c (f, d)));
  tab[1] = may_expand (may_eval (may_mul_c (g, d)));
  if (verbose >= 2) {
    printf ("GCDFT7: gcd completly dense non-monic quadratic inputs (n=%d)...", n6);
    fflush (stdout);
  }
  t = cputime ();
  may_gcd (2, tab);
  t  = cputime () - t;
  if (verbose >= 2)
    printf ("%dms\n", t);
  t0 += t;

  /* D= x * product (y[i], i=1..n)-1
     F=D* (x*product (y[i], i=1..n)+3)
     G=D* (x*product (y[i], i=1..n)-3) */
  d = may_add_c (may_mul_c (x, mul_y_i (1, n7, 0)), may_set_si (-1));
  f = may_add_c (may_mul_c (x, mul_y_i (1, n7, 0)), may_set_si (3));
  g = may_add_c (may_mul_c (x, mul_y_i (1, n7, 0)), may_set_si (-3));
  tab[0] = may_expand (may_eval (may_mul_c (f, d)));
  tab[1] = may_expand (may_eval (may_mul_c (g, d)));
  if (verbose >= 2) {
    printf ("GCDFT8: gcd sparse non-monic quadratic inputs with linear gcds (n=%d)...", n7);
    fflush (stdout);
  }
  t = cputime ();
  may_gcd (2, tab);
  t  = cputime () - t;
  if (verbose >= 2)
    printf ("%dms\n", t);
  t0 += t;

  /* D = x^n*y*(z-1)
     F=D* (x^n+y^(n+1)*z^n+1)
     G=D* (x^(n+1)+y^n*z^(n+1)-7) */
  d = may_mul_vac (may_pow_si_c (x, n8), y, may_add_c (z, may_set_si (-1)), NULL);
  f = may_add_vac (may_pow_si_c (x, n8), may_mul_c (may_pow_si_c (y, n8+1), may_pow_si_c (z, n8)), may_set_si (1), NULL);
  g = may_add_vac (may_pow_si_c (x, n8+1), may_mul_c (may_pow_si_c (y, n8), may_pow_si_c (z, n8+1)), may_set_si (-7), NULL);
  tab[0] = may_expand (may_eval (may_mul_c (f, d)));
  tab[1] = may_expand (may_eval (may_mul_c (g, d)));
  if (verbose >= 2) {
    printf ("GCDFT9: trivariate inputs with increasing degrees (n=%d)...", n8);
    fflush (stdout);
  }
  t = cputime ();
  may_gcd (2, tab);
  t  = cputime () - t;
  if (verbose >= 2)
    printf ("%dms\n", t);
  t0 += t;

  /* F = (x-y*z+1)^n9*(x-y+3*z)^n9
     G = (x-y*z+1)^n9*(x-y+3*z)^n10 */
  f = may_parse_str ("x-y*z+1");
  g = may_parse_str ("x-y+3*z");
  tab[0] = may_expand (may_eval (may_mul_c (may_pow_si_c (f, n9), may_pow_si_c (g, n9))));
  tab[1] = may_expand (may_eval (may_mul_c (may_pow_si_c (f, n9), may_pow_si_c (g, n10))));
  if (verbose >= 2) {
    printf ("GCDFT10: trivariate polynomials whose GCD has common factors with cofactors (j=%d,k=%d)...", n9, n10);
    fflush (stdout);
  }
  t = cputime ();
  may_gcd (2, tab);
  t  = cputime () - t;
  if (verbose >= 2)
    printf ("%dms\n", t);
  t0 += t;

  may_keep (NULL);
  return t0;
}

int
test_diff (const char *buffer)
{
  may_mark ();
  if (verbose >= 2) {
    printf ("diff ( %s , x)...", buffer);
    fflush (stdout);
  }
  int m0, t0;
  may_t x = may_set_str ("x");
  may_t e = may_parse_str (buffer);

  for (m0 = t0 = 1; t0 < 100 ; m0*=2) {
    may_mark ();
    t0 = cputime ();
    for (int m = 0; m < m0; m++)
      may_diff (e, x);
    t0 = cputime () - t0;
    may_keep (NULL);
  }

  if (verbose >= 2)
    printf ("%2.5fms\n", ((double)t0)/(2*m0));
  may_keep (NULL);
  return t0/(2*m0);
}


/* Function f(z)=sqrt(1/3)*z^2 + i/3 */
static may_t f_1_3, sqrt_1_3;
static may_t
f_c (may_t z)
{
  may_t y;
  y = may_mul_c (sqrt_1_3, may_sqr_c (z));
  y = may_add_c (y, f_1_3);
  return may_expand (may_eval (y));
}

int
test_R1 (int n)
{
  may_mark ();
  if (verbose >= 2) {
    printf ("R1: f(f(...) with f(z)=sqrt(1/3)*z^2 + i/3 and n=%d...", n);
    fflush (stdout);
  }
  int i, t = cputime();

  f_1_3    = may_set_si_ui(1, 3);
  sqrt_1_3 = may_sqrt (f_1_3);
  f_1_3    = may_set_cx (may_set_ui (0), f_1_3);

  may_t z = may_set_cx (may_set_ui(0), may_set_si_ui (1, 2));
  for (i = 0; i < n ;i++)
    z = may_func_c ("f", z);
  const char *vartab[] = {"f"};
  const void *valuetab[] = { (void*) &f_c};
  z = may_subs_c (z, 1, 1, vartab, valuetab);
  z = may_real (may_eval (z));

  t = cputime () - t;
  if (verbose >= 2)
    printf ("%dms\n", t);
  may_keep (NULL);
  return t;
}

static may_t
hermite( int n, may_t y)
{
  if (n == 1) return may_mul (y, may_set_ui (2));
  if (n == 0) return may_set_ui (1);
  may_t z = may_sub_c (may_mul_c (may_mul_c (may_set_ui (2), y), hermite (n-1, y)),
                       may_mul_c (may_set_ui (2*(n-1)), hermite (n-2, y)));
  return may_expand (may_eval (z));
}

int
test_R2 (int n)
{
  may_mark ();
  if (verbose >= 2) {
    printf ("R2: hermite(%d,y)...", n);
    fflush (stdout);
  }
  int t = cputime();
  hermite(n, may_set_str ("y"));
  t = cputime () - t;
  if (verbose >= 2)
    printf ("%dms\n", t);
  may_keep (NULL);
  return t;
}

int
test_R6 (int n)
{
  may_mark ();
  if (verbose >= 2) {
    printf ("R6: sum(((x+sin(i))/x+(x-sin(i))/x) for n=%d...", n);
    fflush (stdout);
  }
  int i, t = cputime();

  may_t x = may_set_str ("x"), s = may_set_ui (0);
  for (i = 0; i < n ; i++) {
    may_t sini = may_sin_c (may_set_ui (i));
    s = may_addinc_c (s, may_div_c (may_add_c (x, sini), x));
    s = may_addinc_c (s, may_div_c (may_sub_c (x, sini), x));
  }
  s = may_eval (s);
  s = may_rationalize (s);

  t = cputime () - t;
  if (verbose >= 2)
    printf ("%dms\n", t);
  may_keep (NULL);
  return t;
}

int
test_R7 (int n)
{
  may_mark ();
  if (verbose >= 2) {
    printf ("R7: %d random float eval of x^24+34*x^12+45*x^3+9*x^18 +34*x^10+ 32*x^21...", n);
    fflush (stdout);
  }
  may_kernel_prec (53);
  int i, t = cputime();

  may_t w = may_parse_str ("x^24+34*x^12+45*x^3+9*x^18 +34*x^10+ 32*x^21");
  may_t x_str = may_set_str ("x"), x_val;
  for (i = 0; i < n; i++) {
    x_val = may_set_d (((double) rand()) / RAND_MAX);
    may_replace (w, x_str, x_val);
  }

  t = cputime () - t;
  may_kernel_prec (113);
  if (verbose >= 2)
    printf ("%dms\n", t);
  may_keep (NULL);
  return t;
}

static may_t
right (may_t (*f) (may_t), may_t a, may_t b, int n)
{
  may_t deltax = may_div (may_sub (b, a), may_set_ui (n));
  may_t c = a;
  may_t est = may_set_ui (0);
  int i;

  for (i = 0; i < n ; i++) {
    c = may_addinc_c (c, deltax);
    est = may_addinc_c (est, may_eval ((*f) (c)));
  }

  return may_eval (may_mul_c (est, deltax));
}


int
test_R8 (int n)
{
  may_mark ();
  if (verbose >= 2) {
    printf ("R8:right(x^2,0,5,%d) ...", n);
    fflush (stdout);
  }
  int t = cputime();
  may_t w = right (may_sqr_c, may_set_ui (0), may_set_ui (5), n);
  t = cputime () - t;
  if (verbose >= 2)
    printf ("%dms\n", t);
  may_keep (NULL);
  return t;
}

int
test_S2 (int n)
{
  may_mark ();
  if (verbose >= 2) {
    printf ("S2:expand((x^sin(x) + y^cos(y) - z^(x+y))^%d) ...", n);
    fflush (stdout);
  }
  int t = cputime();

  may_t w = may_parse_str ("x^sin(x) + y^cos(y) - z^(x+y)");
  w = may_pow (w, may_set_ui (n));
  w = may_expand (w);

  t = cputime () - t;
  if (verbose >= 2)
    printf ("%dms\n", t);
  may_keep (NULL);
  return t;
}

int
test_S3 (int n)
{
  may_mark ();
  if (verbose >= 2) {
    printf ("S3:diff(expand((x^y + y^z + z^x)^%d,x) ...", n);
    fflush (stdout);
  }
  int t = cputime();

  may_t w = may_parse_str ("x^y + y^z - z^x");
  w = may_pow (w, may_set_ui (n));
  w = may_expand (w);
  w = may_diff (w, may_set_str ("x"));

  t = cputime () - t;
  if (verbose >= 2)
    printf ("%dms\n", t);
  may_keep (NULL);
  return t;
}

int
test_S4 (int n)
{
  may_mark ();
  if (verbose >= 2) {
    printf ("S4:series(sin(x)*cos(x),x=0,%d) ...", n);
    fflush (stdout);
  }
  int t = cputime();

  may_t w = may_parse_str ("sin(x)*cos(x)"), x = may_set_str ("x");
  w = may_series (w, x, n);

  t = cputime () - t;
  if (verbose >= 2)
    printf ("%dms\n", t);
  may_keep (NULL);
  return t;
}

int
test_series_tan (int n)
{
  may_mark ();
  if (verbose >= 2) {
    printf ("series(tan(2+x),x=0,%d) ...", n);
    fflush (stdout);
  }
  int t = cputime();

  may_t w = may_parse_str ("tan(2+x)"), x = may_set_str ("x");
  w = may_series (w, x, n);

  t = cputime () - t;
  if (verbose >= 2)
    printf ("%dms\n", t);
  may_keep (NULL);
  return t;
}

int
test_sum_rationalize (int n)
{
  may_mark ();
  if (verbose >= 2) {
    printf ("Rationalize sum((i*y*t^i)/(y+i*t)^i),i=1..%d ...", n);
    fflush (stdout);
  }
  int t1 = cputime();

  may_t s = may_set_ui(0);
  may_t y = may_set_str ("y");
  may_t t = may_set_str ("t");

  for (int i = 1; i <= n; i++) {
    may_t ii = may_set_ui (i);
    s = may_addinc_c (s, may_div_c (may_mul_vac (ii, y, may_pow_c (t, ii), NULL),
                                 may_pow_c  (may_add_c (y, may_mul_c (ii, t)), ii)));
  }
  s = may_eval (s);
  s = may_rationalize (s);

  t1 = cputime () - t1;
  if (verbose >= 2)
    printf ("%dms\n", t1);
  may_keep (NULL);
  return t1;
}

int
test_sum_rationalize2 (int n)
{
  may_mark ();
  if (verbose >= 2) {
    printf ("Rationalize sum((i*y*t^i)/(y+abs(5-i)*t)^i),i=1..%d ...", n);
    fflush (stdout);
  }
  int t1 = cputime();

  may_t s = may_set_ui(0);
  may_t y = may_set_str ("y");
  may_t t = may_set_str ("t");

  for (int i = 1; i <= n; i++) {
    may_t ii = may_set_ui (i);
    s = may_addinc_c (s, may_div_c (may_mul_vac (ii, y, may_pow_c (t, ii), NULL),
                                 may_pow_c  (may_add_c (y, may_mul_c (may_set_ui (abs(5-i)), t)), ii)));
  }
  s = may_eval (s);
  s = may_rationalize (s);

  t1 = cputime () - t1;
  if (verbose >= 2)
    printf ("%dms\n", t1);
  may_keep (NULL);
  return t1;
}

int
test_rationalize (int n)
{
  may_mark ();
  if (verbose >= 2) {
    printf ("Rationalize nested expression %d ...", n);
    fflush (stdout);
  }

  may_t w = may_parse_str ("1/(7+x)^2+1/(6+x)^2-((1/((5+x)*(6+x))+1/((3+x)*(4+x))+1/((7+x)*(6+x))+1/((7+x)*(8+x))-(1/((5+x)*(3+x))+1/((4+x)*(2+x))+1/((3+x)*(1+x))+1/((6+x)*(4+x))+1/((7+x)*(5+x)))*(1/((7+x)*(4+x))+1/((5+x)*(8+x))+1/((3+x)*(6+x))+1/((1+x)*(4+x))+1/((5+x)*(2+x)))/(1/(1+x)^2+1/(3+x)^2+1/(5+x)^2+1/(2+x)^2+1/(4+x)^2)+1/((5+x)*(4+x))-(1/((3+x)*(2+x))+1/((5+x)*(6+x))-(1/((5+x)*(3+x))+1/((4+x)*(2+x))+1/((3+x)*(1+x))+1/((6+x)*(4+x))+1/((7+x)*(5+x)))*(1/((3+x)*(2+x))+1/((5+x)*(6+x))+1/((3+x)*(4+x))+1/((1+x)*(2+x))+1/((5+x)*(4+x)))/(1/(1+x)^2+1/(3+x)^2+1/(5+x)^2+1/(2+x)^2+1/(4+x)^2)+1/((3+x)*(4+x))+1/((7+x)*(6+x))+1/((5+x)*(4+x)))*(1/((5+x)*(3+x))+1/((4+x)*(2+x))+1/((6+x)*(4+x))-(1/((3+x)*(2+x))+1/((5+x)*(6+x))+1/((3+x)*(4+x))+1/((1+x)*(2+x))+1/((5+x)*(4+x)))*(1/((7+x)*(4+x))+1/((5+x)*(8+x))+1/((3+x)*(6+x))+1/((1+x)*(4+x))+1/((5+x)*(2+x)))/(1/(1+x)^2+1/(3+x)^2+1/(5+x)^2+1/(2+x)^2+1/(4+x)^2)+1/((7+x)*(5+x))+1/((8+x)*(6+x)))/(1/(6+x)^2+1/(3+x)^2+1/(5+x)^2-(1/((3+x)*(2+x))+1/((5+x)*(6+x))+1/((3+x)*(4+x))+1/((1+x)*(2+x))+1/((5+x)*(4+x)))^2/(1/(1+x)^2+1/(3+x)^2+1/(5+x)^2+1/(2+x)^2+1/(4+x)^2)+1/(2+x)^2+1/(4+x)^2))*(1/((5+x)*(3+x))+1/((9+x)*(7+x))+1/((6+x)*(4+x))+1/((7+x)*(5+x))-(1/((3+x)*(2+x))+1/((5+x)*(6+x))-(1/((5+x)*(3+x))+1/((4+x)*(2+x))+1/((3+x)*(1+x))+1/((6+x)*(4+x))+1/((7+x)*(5+x)))*(1/((3+x)*(2+x))+1/((5+x)*(6+x))+1/((3+x)*(4+x))+1/((1+x)*(2+x))+1/((5+x)*(4+x)))/(1/(1+x)^2+1/(3+x)^2+1/(5+x)^2+1/(2+x)^2+1/(4+x)^2)+1/((3+x)*(4+x))+1/((7+x)*(6+x))+1/((5+x)*(4+x)))*(1/((7+x)*(4+x))+1/((5+x)*(8+x))+1/((3+x)*(6+x))+1/((9+x)*(6+x))-(1/((3+x)*(2+x))+1/((5+x)*(6+x))+1/((3+x)*(4+x))+1/((1+x)*(2+x))+1/((5+x)*(4+x)))*(1/((5+x)*(1+x))+1/((7+x)*(3+x))+1/((6+x)*(2+x))+1/((8+x)*(4+x))+1/((9+x)*(5+x)))/(1/(1+x)^2+1/(3+x)^2+1/(5+x)^2+1/(2+x)^2+1/(4+x)^2)+1/((5+x)*(2+x)))/(1/(6+x)^2+1/(3+x)^2+1/(5+x)^2-(1/((3+x)*(2+x))+1/((5+x)*(6+x))+1/((3+x)*(4+x))+1/((1+x)*(2+x))+1/((5+x)*(4+x)))^2/(1/(1+x)^2+1/(3+x)^2+1/(5+x)^2+1/(2+x)^2+1/(4+x)^2)+1/(2+x)^2+1/(4+x)^2)-(1/((5+x)*(3+x))+1/((4+x)*(2+x))+1/((3+x)*(1+x))+1/((6+x)*(4+x))+1/((7+x)*(5+x)))*(1/((5+x)*(1+x))+1/((7+x)*(3+x))+1/((6+x)*(2+x))+1/((8+x)*(4+x))+1/((9+x)*(5+x)))/(1/(1+x)^2+1/(3+x)^2+1/(5+x)^2+1/(2+x)^2+1/(4+x)^2)+1/((8+x)*(6+x)))/(1/(7+x)^2+1/(6+x)^2+1/(3+x)^2+1/(5+x)^2-(1/((3+x)*(2+x))+1/((5+x)*(6+x))-(1/((5+x)*(3+x))+1/((4+x)*(2+x))+1/((3+x)*(1+x))+1/((6+x)*(4+x))+1/((7+x)*(5+x)))*(1/((3+x)*(2+x))+1/((5+x)*(6+x))+1/((3+x)*(4+x))+1/((1+x)*(2+x))+1/((5+x)*(4+x)))/(1/(1+x)^2+1/(3+x)^2+1/(5+x)^2+1/(2+x)^2+1/(4+x)^2)+1/((3+x)*(4+x))+1/((7+x)*(6+x))+1/((5+x)*(4+x)))^2/(1/(6+x)^2+1/(3+x)^2+1/(5+x)^2-(1/((3+x)*(2+x))+1/((5+x)*(6+x))+1/((3+x)*(4+x))+1/((1+x)*(2+x))+1/((5+x)*(4+x)))^2/(1/(1+x)^2+1/(3+x)^2+1/(5+x)^2+1/(2+x)^2+1/(4+x)^2)+1/(2+x)^2+1/(4+x)^2)-(1/((5+x)*(3+x))+1/((4+x)*(2+x))+1/((3+x)*(1+x))+1/((6+x)*(4+x))+1/((7+x)*(5+x)))^2/(1/(1+x)^2+1/(3+x)^2+1/(5+x)^2+1/(2+x)^2+1/(4+x)^2)+1/(4+x)^2)+(1/((7+x)*(4+x))+1/((5+x)*(8+x))+1/((3+x)*(6+x))+1/((1+x)*(4+x))+1/((5+x)*(2+x)))*(1/((5+x)*(1+x))+1/((7+x)*(3+x))+1/((6+x)*(2+x))+1/((8+x)*(4+x))+1/((9+x)*(5+x)))/(1/(1+x)^2+1/(3+x)^2+1/(5+x)^2+1/(2+x)^2+1/(4+x)^2)-1/((5+x)*(6+x))+(1/((7+x)*(4+x))+1/((5+x)*(8+x))+1/((3+x)*(6+x))+1/((9+x)*(6+x))-(1/((3+x)*(2+x))+1/((5+x)*(6+x))+1/((3+x)*(4+x))+1/((1+x)*(2+x))+1/((5+x)*(4+x)))*(1/((5+x)*(1+x))+1/((7+x)*(3+x))+1/((6+x)*(2+x))+1/((8+x)*(4+x))+1/((9+x)*(5+x)))/(1/(1+x)^2+1/(3+x)^2+1/(5+x)^2+1/(2+x)^2+1/(4+x)^2)+1/((5+x)*(2+x)))*(1/((5+x)*(3+x))+1/((4+x)*(2+x))+1/((6+x)*(4+x))-(1/((3+x)*(2+x))+1/((5+x)*(6+x))+1/((3+x)*(4+x))+1/((1+x)*(2+x))+1/((5+x)*(4+x)))*(1/((7+x)*(4+x))+1/((5+x)*(8+x))+1/((3+x)*(6+x))+1/((1+x)*(4+x))+1/((5+x)*(2+x)))/(1/(1+x)^2+1/(3+x)^2+1/(5+x)^2+1/(2+x)^2+1/(4+x)^2)+1/((7+x)*(5+x))+1/((8+x)*(6+x)))/(1/(6+x)^2+1/(3+x)^2+1/(5+x)^2-(1/((3+x)*(2+x))+1/((5+x)*(6+x))+1/((3+x)*(4+x))+1/((1+x)*(2+x))+1/((5+x)*(4+x)))^2/(1/(1+x)^2+1/(3+x)^2+1/(5+x)^2+1/(2+x)^2+1/(4+x)^2)+1/(2+x)^2+1/(4+x)^2)-1/((7+x)*(6+x))-1/((7+x)*(8+x))-1/((9+x)*(8+x))-1/((5+x)*(4+x)))^2/(1/(7+x)^2-(1/((5+x)*(6+x))+1/((3+x)*(4+x))+1/((7+x)*(6+x))+1/((7+x)*(8+x))-(1/((5+x)*(3+x))+1/((4+x)*(2+x))+1/((3+x)*(1+x))+1/((6+x)*(4+x))+1/((7+x)*(5+x)))*(1/((7+x)*(4+x))+1/((5+x)*(8+x))+1/((3+x)*(6+x))+1/((1+x)*(4+x))+1/((5+x)*(2+x)))/(1/(1+x)^2+1/(3+x)^2+1/(5+x)^2+1/(2+x)^2+1/(4+x)^2)+1/((5+x)*(4+x))-(1/((3+x)*(2+x))+1/((5+x)*(6+x))-(1/((5+x)*(3+x))+1/((4+x)*(2+x))+1/((3+x)*(1+x))+1/((6+x)*(4+x))+1/((7+x)*(5+x)))*(1/((3+x)*(2+x))+1/((5+x)*(6+x))+1/((3+x)*(4+x))+1/((1+x)*(2+x))+1/((5+x)*(4+x)))/(1/(1+x)^2+1/(3+x)^2+1/(5+x)^2+1/(2+x)^2+1/(4+x)^2)+1/((3+x)*(4+x))+1/((7+x)*(6+x))+1/((5+x)*(4+x)))*(1/((5+x)*(3+x))+1/((4+x)*(2+x))+1/((6+x)*(4+x))-(1/((3+x)*(2+x))+1/((5+x)*(6+x))+1/((3+x)*(4+x))+1/((1+x)*(2+x))+1/((5+x)*(4+x)))*(1/((7+x)*(4+x))+1/((5+x)*(8+x))+1/((3+x)*(6+x))+1/((1+x)*(4+x))+1/((5+x)*(2+x)))/(1/(1+x)^2+1/(3+x)^2+1/(5+x)^2+1/(2+x)^2+1/(4+x)^2)+1/((7+x)*(5+x))+1/((8+x)*(6+x)))/(1/(6+x)^2+1/(3+x)^2+1/(5+x)^2-(1/((3+x)*(2+x))+1/((5+x)*(6+x))+1/((3+x)*(4+x))+1/((1+x)*(2+x))+1/((5+x)*(4+x)))^2/(1/(1+x)^2+1/(3+x)^2+1/(5+x)^2+1/(2+x)^2+1/(4+x)^2)+1/(2+x)^2+1/(4+x)^2))^2/(1/(7+x)^2+1/(6+x)^2+1/(3+x)^2+1/(5+x)^2-(1/((3+x)*(2+x))+1/((5+x)*(6+x))-(1/((5+x)*(3+x))+1/((4+x)*(2+x))+1/((3+x)*(1+x))+1/((6+x)*(4+x))+1/((7+x)*(5+x)))*(1/((3+x)*(2+x))+1/((5+x)*(6+x))+1/((3+x)*(4+x))+1/((1+x)*(2+x))+1/((5+x)*(4+x)))/(1/(1+x)^2+1/(3+x)^2+1/(5+x)^2+1/(2+x)^2+1/(4+x)^2)+1/((3+x)*(4+x))+1/((7+x)*(6+x))+1/((5+x)*(4+x)))^2/(1/(6+x)^2+1/(3+x)^2+1/(5+x)^2-(1/((3+x)*(2+x))+1/((5+x)*(6+x))+1/((3+x)*(4+x))+1/((1+x)*(2+x))+1/((5+x)*(4+x)))^2/(1/(1+x)^2+1/(3+x)^2+1/(5+x)^2+1/(2+x)^2+1/(4+x)^2)+1/(2+x)^2+1/(4+x)^2)-(1/((5+x)*(3+x))+1/((4+x)*(2+x))+1/((3+x)*(1+x))+1/((6+x)*(4+x))+1/((7+x)*(5+x)))^2/(1/(1+x)^2+1/(3+x)^2+1/(5+x)^2+1/(2+x)^2+1/(4+x)^2)+1/(4+x)^2)+1/(6+x)^2+1/(8+x)^2-(1/((5+x)*(3+x))+1/((4+x)*(2+x))+1/((6+x)*(4+x))-(1/((3+x)*(2+x))+1/((5+x)*(6+x))+1/((3+x)*(4+x))+1/((1+x)*(2+x))+1/((5+x)*(4+x)))*(1/((7+x)*(4+x))+1/((5+x)*(8+x))+1/((3+x)*(6+x))+1/((1+x)*(4+x))+1/((5+x)*(2+x)))/(1/(1+x)^2+1/(3+x)^2+1/(5+x)^2+1/(2+x)^2+1/(4+x)^2)+1/((7+x)*(5+x))+1/((8+x)*(6+x)))^2/(1/(6+x)^2+1/(3+x)^2+1/(5+x)^2-(1/((3+x)*(2+x))+1/((5+x)*(6+x))+1/((3+x)*(4+x))+1/((1+x)*(2+x))+1/((5+x)*(4+x)))^2/(1/(1+x)^2+1/(3+x)^2+1/(5+x)^2+1/(2+x)^2+1/(4+x)^2)+1/(2+x)^2+1/(4+x)^2)+1/(5+x)^2-(1/((7+x)*(4+x))+1/((5+x)*(8+x))+1/((3+x)*(6+x))+1/((1+x)*(4+x))+1/((5+x)*(2+x)))^2/(1/(1+x)^2+1/(3+x)^2+1/(5+x)^2+1/(2+x)^2+1/(4+x)^2)+1/(4+x)^2)+1/(8+x)^2-(1/((7+x)*(4+x))+1/((5+x)*(8+x))+1/((3+x)*(6+x))+1/((9+x)*(6+x))-(1/((3+x)*(2+x))+1/((5+x)*(6+x))+1/((3+x)*(4+x))+1/((1+x)*(2+x))+1/((5+x)*(4+x)))*(1/((5+x)*(1+x))+1/((7+x)*(3+x))+1/((6+x)*(2+x))+1/((8+x)*(4+x))+1/((9+x)*(5+x)))/(1/(1+x)^2+1/(3+x)^2+1/(5+x)^2+1/(2+x)^2+1/(4+x)^2)+1/((5+x)*(2+x)))^2/(1/(6+x)^2+1/(3+x)^2+1/(5+x)^2-(1/((3+x)*(2+x))+1/((5+x)*(6+x))+1/((3+x)*(4+x))+1/((1+x)*(2+x))+1/((5+x)*(4+x)))^2/(1/(1+x)^2+1/(3+x)^2+1/(5+x)^2+1/(2+x)^2+1/(4+x)^2)+1/(2+x)^2+1/(4+x)^2)+1/(5+x)^2-(1/((5+x)*(1+x))+1/((7+x)*(3+x))+1/((6+x)*(2+x))+1/((8+x)*(4+x))+1/((9+x)*(5+x)))^2/(1/(1+x)^2+1/(3+x)^2+1/(5+x)^2+1/(2+x)^2+1/(4+x)^2)-(1/((5+x)*(3+x))+1/((9+x)*(7+x))+1/((6+x)*(4+x))+1/((7+x)*(5+x))-(1/((3+x)*(2+x))+1/((5+x)*(6+x))-(1/((5+x)*(3+x))+1/((4+x)*(2+x))+1/((3+x)*(1+x))+1/((6+x)*(4+x))+1/((7+x)*(5+x)))*(1/((3+x)*(2+x))+1/((5+x)*(6+x))+1/((3+x)*(4+x))+1/((1+x)*(2+x))+1/((5+x)*(4+x)))/(1/(1+x)^2+1/(3+x)^2+1/(5+x)^2+1/(2+x)^2+1/(4+x)^2)+1/((3+x)*(4+x))+1/((7+x)*(6+x))+1/((5+x)*(4+x)))*(1/((7+x)*(4+x))+1/((5+x)*(8+x))+1/((3+x)*(6+x))+1/((9+x)*(6+x))-(1/((3+x)*(2+x))+1/((5+x)*(6+x))+1/((3+x)*(4+x))+1/((1+x)*(2+x))+1/((5+x)*(4+x)))*(1/((5+x)*(1+x))+1/((7+x)*(3+x))+1/((6+x)*(2+x))+1/((8+x)*(4+x))+1/((9+x)*(5+x)))/(1/(1+x)^2+1/(3+x)^2+1/(5+x)^2+1/(2+x)^2+1/(4+x)^2)+1/((5+x)*(2+x)))/(1/(6+x)^2+1/(3+x)^2+1/(5+x)^2-(1/((3+x)*(2+x))+1/((5+x)*(6+x))+1/((3+x)*(4+x))+1/((1+x)*(2+x))+1/((5+x)*(4+x)))^2/(1/(1+x)^2+1/(3+x)^2+1/(5+x)^2+1/(2+x)^2+1/(4+x)^2)+1/(2+x)^2+1/(4+x)^2)-(1/((5+x)*(3+x))+1/((4+x)*(2+x))+1/((3+x)*(1+x))+1/((6+x)*(4+x))+1/((7+x)*(5+x)))*(1/((5+x)*(1+x))+1/((7+x)*(3+x))+1/((6+x)*(2+x))+1/((8+x)*(4+x))+1/((9+x)*(5+x)))/(1/(1+x)^2+1/(3+x)^2+1/(5+x)^2+1/(2+x)^2+1/(4+x)^2)+1/((8+x)*(6+x)))^2/(1/(7+x)^2+1/(6+x)^2+1/(3+x)^2+1/(5+x)^2-(1/((3+x)*(2+x))+1/((5+x)*(6+x))-(1/((5+x)*(3+x))+1/((4+x)*(2+x))+1/((3+x)*(1+x))+1/((6+x)*(4+x))+1/((7+x)*(5+x)))*(1/((3+x)*(2+x))+1/((5+x)*(6+x))+1/((3+x)*(4+x))+1/((1+x)*(2+x))+1/((5+x)*(4+x)))/(1/(1+x)^2+1/(3+x)^2+1/(5+x)^2+1/(2+x)^2+1/(4+x)^2)+1/((3+x)*(4+x))+1/((7+x)*(6+x))+1/((5+x)*(4+x)))^2/(1/(6+x)^2+1/(3+x)^2+1/(5+x)^2-(1/((3+x)*(2+x))+1/((5+x)*(6+x))+1/((3+x)*(4+x))+1/((1+x)*(2+x))+1/((5+x)*(4+x)))^2/(1/(1+x)^2+1/(3+x)^2+1/(5+x)^2+1/(2+x)^2+1/(4+x)^2)+1/(2+x)^2+1/(4+x)^2)-(1/((5+x)*(3+x))+1/((4+x)*(2+x))+1/((3+x)*(1+x))+1/((6+x)*(4+x))+1/((7+x)*(5+x)))^2/(1/(1+x)^2+1/(3+x)^2+1/(5+x)^2+1/(2+x)^2+1/(4+x)^2)+1/(4+x)^2)+1/(9+x)^2");
  int t = cputime();
  w = may_rationalize (w);

  t = cputime () - t;
  if (verbose >= 2)
    printf ("%dms\n", t);
  may_keep (NULL);
  return t;
}



/* First Fermat test.
   On a Pentium 4 1.6 Ghz, Fermat 3.5.6 takes 28.3 secs.
   On a Pentium M 1.7 Ghz, MAY doesn't do it. (200,000,000,000 terms...)
*/
int
test_fermat (void)
{
  may_t s1, s2, s3, s4, res, x, y;
  int t0, t1;

  if (verbose >= 2) {
    printf ("fermat test 1 ...");
    fflush (stdout);
  }

  t0 = cputime ();
  s1 = may_parse_str ("(l2*g*a22^3-l1*g*a12*a21*a22^2-l2*n22*a21*a22^2+l2*n11*a21*a22^2+2*l2*g*a12*a22^2-l1*g*a12*a22^2+l2*g^2*a22^2-l2*n11*n22*a22^2+l2*n11*a22^2+l1*n22*a12*a21^2*a22-l1*n11*a12*a21^2*a22-l2*g*a21^2*a22-l1*g*a12^2*a21*a22-l2*g^2*a12*a21*a22-l1*g^2*a12*a21*a22+l2*n11*n22*a12*a21*a22+l1*n11*n22*a12*a21*a22-2*l2*n22*a12*a21*a22+l1*n22*a12*a21*a22+l2*n11*a12*a21*a22-2*l1*n11*a12*a21*a22-l2*g*a21*a22+l2*g*a12^2*a22-l1*g*a12^2*a22+l2*g^2*a12*a22-l1*g^2*a12*a22-l2*n11*n22*a12*a22+l1*n11*n22*a12*a22+l2*n11*a12*a22-l1*n11*a12*a22+l1*g*a12*a21^3+l1*g^2*a12^2*a21^2-l1*n11*n22*a12^2*a21^2+l1*n22*a12^2*a21^2-l2*g*a12*a21^2+2*l1*g*a12*a21^2-l2*g^2*a12^2*a21+l1*g^2*a12^2*a21+l2*n11*n22*a12^2*a21-l1*n11*n22*a12^2*a21-l2*n22*a12^2*a21+l1*n22*a12^2*a21-l2*g*a12*a21+l1*g*a12*a21)/(l2*g*a12*a21*a22^2-l1*g*a12*a21*a22^2-l2*n22*a21*a22^2+l1*n22*a21*a22^2+l1*l2*g*a12*a22^2-l1*g*a12*a22^2-l1*l2*n22*a22^2+l1*n22*a22^2+l2*n11*a12*a21^2*a22-l1*n11*a12*a21^2*a22-l2*g*a21^2*a22+l1*g*a21^2*a22-l1*l2*g*a12^2*a21*a22+2*l2*g*a12^2*a21*a22-l1*g*a12^2*a21*a22+l1*l2*n22*a12*a21*a22-2*l2*n22*a12*a21*a22+l1*n22*a12*a21*a22+l1*l2*n11*a12*a21*a22+l2*n11*a12*a21*a22-2*l1*n11*a12*a21*a22-l1*l2*g*a21*a22-l2*g*a21*a22+2*l1*g*a21*a22+l1*l2*g*a12^2*a22-l1*g*a12^2*a22-l1*l2*n22*a12*a22+l1*n22*a12*a22+l1*l2*n11*a12*a22-l1*n11*a12*a22-l1*l2*g*a22+l1*g*a22-l1*l2*n11*a12^2*a21^2+l2*n11*a12^2*a21^2+l1*l2*g*a12*a21^2-l2*g*a12*a21^2-l1*l2*g*a12^3*a21+l2*g*a12^3*a21+l1*l2*n22*a12^2*a21-l2*n22*a12^2*a21-l1*l2*n11*a12^2*a21+l2*n11*a12^2*a21+l1*l2*g*a12*a21-l2*g*a12*a21)");
  if (may_nan_p (s1))
    abort ();

 s2 = may_parse_str ("(l2*g*a12*a22^2-l2*n22*a22^2+l2*a22^2-l1*g*a12^2*a21*a22+l1*n22*a12*a21*a22+l2*n11*a12*a21*a22-l2*a12*a21*a22-l1*a12*a21*a22-l2*g*a21*a22+l2*g*a12^2*a22-l1*g*a12^2*a22-l2*n22*a12*a22+l1*n22*a12*a22+l2*a12*a22-l1*a12*a22-l1*n11*a12^2*a21^2+l1*a12^2*a21^2+l1*g*a12*a21^2+l2*n11*a12^2*a21-l1*n11*a12^2*a21-l2*a12^2*a21+l1*a12^2*a21-l2*g*a12*a21+l1*g*a12*a21)/(l2*g*a12*a22^2-g*a12*a22^2-l2*n22*a22^2+n22*a22^2-l1*g*a12^2*a21*a22+g*a12^2*a21*a22+l1*n22*a12*a21*a22-n22*a12*a21*a22+l2*n11*a12*a21*a22-n11*a12*a21*a22-l2*g*a21*a22+g*a21*a22+l2*g*a12^2*a22-g*a12^2*a22-l2*n22*a12*a22+n22*a12*a22+l2*n11*a12*a22-n11*a12*a22-l2*g*a22+g*a22-l1*n11*a12^2*a21^2+n11*a12^2*a21^2+l1*g*a12*a21^2-g*a12*a21^2-l1*g*a12^3*a21+g*a12^3*a21+l1*n22*a12^2*a21-n22*a12^2*a21-l1*n11*a12^2*a21+n11*a12^2*a21+l1*g*a12*a21-g*a12*a21)");
  if (may_nan_p (s2))
    abort ();

  s3 = may_parse_str ("(l2*p21*a22^3-l1*p21*a12*a21*a22^2-l2*p22*a21*a22^2+l2*p11*a21*a22^2+2*l2*p21*a12*a22^2-l1*p21*a12*a22^2-l2*p11*p22*a22^2+l2*p12*p21*a22^2+l2*p11*a22^2+l1*p22*a12*a21^2*a22-l1*p11*a12*a21^2*a22-l2*p12*a21^2*a22-l1*p21*a12^2*a21*a22+l2*p11*p22*a12*a21*a22+l1*p11*p22*a12*a21*a22-2*l2*p22*a12*a21*a22+l1*p22*a12*a21*a22-l2*p12*p21*a12*a21*a22-l1*p12*p21*a12*a21*a22+l2*p11*a12*a21*a22-2*l1*p11*a12*a21*a22-l2*p12*a21*a22+l2*p21*a12^2*a22-l1*p21*a12^2*a22-l2*p11*p22*a12*a22+l1*p11*p22*a12*a22+l2*p12*p21*a12*a22-l1*p12*p21*a12*a22+l2*p11*a12*a22-l1*p11*a12*a22+l1*p12*a12*a21^3-l1*p11*p22*a12^2*a21^2+l1*p22*a12^2*a21^2+l1*p12*p21*a12^2*a21^2-l2*p12*a12*a21^2+2*l1*p12*a12*a21^2+l2*p11*p22*a12^2*a21-l1*p11*p22*a12^2*a21-l2*p22*a12^2*a21+l1*p22*a12^2*a21-l2*p12*p21*a12^2*a21+l1*p12*p21*a12^2*a21-l2*p12*a12*a21+l1*p12*a12*a21)/(l2*p21*a12*a21*a22^2-l1*p21*a12*a21*a22^2-l2*p22*a21*a22^2+l1*p22*a21*a22^2+l1*l2*p21*a12*a22^2-l1*p21*a12*a22^2-l1*l2*p22*a22^2+l1*p22*a22^2+l2*p11*a12*a21^2*a22-l1*p11*a12*a21^2*a22-l2*p12*a21^2*a22+l1*p12*a21^2*a22-l1*l2*p21*a12^2*a21*a22+2*l2*p21*a12^2*a21*a22-l1*p21*a12^2*a21*a22+l1*l2*p22*a12*a21*a22-2*l2*p22*a12*a21*a22+l1*p22*a12*a21*a22+l1*l2*p11*a12*a21*a22+l2*p11*a12*a21*a22-2*l1*p11*a12*a21*a22-l1*l2*p12*a21*a22-l2*p12*a21*a22+2*l1*p12*a21*a22+l1*l2*p21*a12^2*a22-l1*p21*a12^2*a22-l1*l2*p22*a12*a22+l1*p22*a12*a22+l1*l2*p11*a12*a22-l1*p11*a12*a22-l1*l2*p12*a22+l1*p12*a22-l1*l2*p11*a12^2*a21^2+l2*p11*a12^2*a21^2+l1*l2*p12*a12*a21^2-l2*p12*a12*a21^2-l1*l2*p21*a12^3*a21+l2*p21*a12^3*a21+l1*l2*p22*a12^2*a21-l2*p22*a12^2*a21-l1*l2*p11*a12^2*a21+l2*p11*a12^2*a21+l1*l2*p12*a12*a21-l2*p12*a12*a21)");
  if (may_nan_p (s3))
    abort ();

  s4 = may_parse_str ("(l2*p21*a12*a22^2-l2*p22*a22^2+l2*a22^2-l1*p21*a12^2*a21*a22+l1*p22*a12*a21*a22+l2*p11*a12*a21*a22-l2*a12*a21*a22-l1*a12*a21*a22-l2*p12*a21*a22+l2*p21*a12^2*a22-l1*p21*a12^2*a22-l2*p22*a12*a22+l1*p22*a12*a22+l2*a12*a22-l1*a12*a22-l1*p11*a12^2*a21^2+l1*a12^2*a21^2+l1*p12*a12*a21^2+l2*p11*a12^2*a21-l1*p11*a12^2*a21-l2*a12^2*a21+l1*a12^2*a21-l2*p12*a12*a21+l1*p12*a12*a21)/(l2*p21*a12*a22^2-p21*a12*a22^2-l2*p22*a22^2+p22*a22^2-l1*p21*a12^2*a21*a22+p21*a12^2*a21*a22+l1*p22*a12*a21*a22-p22*a12*a21*a22+l2*p11*a12*a21*a22-p11*a12*a21*a22-l2*p12*a21*a22+p12*a21*a22+l2*p21*a12^2*a22-p21*a12^2*a22-l2*p22*a12*a22+p22*a12*a22+l2*p11*a12*a22-p11*a12*a22-l2*p12*a22+p12*a22-l1*p11*a12^2*a21^2+p11*a12^2*a21^2+l1*p12*a12*a21^2-p12*a12*a21^2-l1*p21*a12^3*a21+p21*a12^3*a21+l1*p22*a12^2*a21-p22*a12^2*a21-l1*p11*a12^2*a21+p11*a12^2*a21+l1*p12*a12*a21-p12*a12*a21)");
  if (may_nan_p (s4))
    abort ();

  if (0) {
    s1 = may_parse_str ("n1/d1");
    s2 = may_parse_str ("n2/d2");
    s3 = may_parse_str ("n3/d3");
    s4 = may_parse_str ("n4/d4");
  }
  if (0) {
    s1 = may_parse_str ("(n11+n12)/(d12+d22)");
    s2 = may_parse_str ("(n21+n22)/(d21+d22)");
    s3 = may_parse_str ("(n31+n32)/(d31+d32)");
    s4 = may_parse_str ("(n41+n42)/(d41+d42)");
  }

  res = may_parse_str ("-l1*l2*p11*p22*q1^2*q4^2+l2*p11*p22*q1^2*q4^2+l1*p11*p22*q1^2*q4^2-p11*p22*q1^2*q4^2+l1*l2*p12*p21*q1^2*q4^2-l2*p12*p21*q1^2*q4^2-l1*p12*p21*q1^2*q4^2+p12*p21*q1^2*q4^2+l1*n22*p11*p22*q1*q4^2-n22*p11*p22*q1*q4^2+l2*n11*p11*p22*q1*q4^2-n11*p11*p22*q1*q4^2-l2*p11*p22*q1*q4^2-l1*p11*p22*q1*q4^2+2*p11*p22*q1*q4^2-l1*n22*p12*p21*q1*q4^2+n22*p12*p21*q1*q4^2-l2*n11*p12*p21*q1*q4^2+n11*p12*p21*q1*q4^2+l2*p12*p21*q1*q4^2+l1*p12*p21*q1*q4^2-2*p12*p21*q1*q4^2+g^2*p11*p22*q4^2-n11*n22*p11*p22*q4^2+n22*p11*p22*q4^2+n11*p11*p22*q4^2-p11*p22*q4^2-g^2*p12*p21*q4^2+n11*n22*p12*p21*q4^2-n22*p12*p21*q4^2-n11*p12*p21*q4^2+p12*p21*q4^2+l1*l2*n11*p22*q1*q2*q3*q4-l2*n11*p22*q1*q2*q3*q4-l1*n11*p22*q1*q2*q3*q4+n11*p22*q1*q2*q3*q4-l1*l2*g*p21*q1*q2*q3*q4+l2*g*p21*q1*q2*q3*q4+l1*g*p21*q1*q2*q3*q4-g*p21*q1*q2*q3*q4-l1*l2*g*p12*q1*q2*q3*q4+l2*g*p12*q1*q2*q3*q4+l1*g*p12*q1*q2*q3*q4-g*p12*q1*q2*q3*q4+l1*l2*n22*p11*q1*q2*q3*q4-l2*n22*p11*q1*q2*q3*q4-l1*n22*p11*q1*q2*q3*q4+n22*p11*q1*q2*q3*q4+l1*g^2*p22*q2*q3*q4-g^2*p22*q2*q3*q4-l1*n11*n22*p22*q2*q3*q4+n11*n22*p22*q2*q3*q4+l1*n11*p22*q2*q3*q4-n11*p22*q2*q3*q4-l2*g*p21*q2*q3*q4+g*p21*q2*q3*q4-l1*g*p12*q2*q3*q4+g*p12*q2*q3*q4+l2*g^2*p11*q2*q3*q4-g^2*p11*q2*q3*q4-l2*n11*n22*p11*q2*q3*q4+n11*n22*p11*q2*q3*q4+l2*n22*p11*q2*q3*q4-n22*p11*q2*q3*q4-l1*l2*n11*p22*q1*q3*q4+l1*n11*p22*q1*q3*q4+l1*l2*p22*q1*q3*q4-l1*p22*q1*q3*q4+l1*l2*g*p21*q1*q3*q4-l1*g*p21*q1*q3*q4+l1*l2*g*p12*q1*q3*q4-l2*g*p12*q1*q3*q4-l1*l2*n22*p11*q1*q3*q4+l2*n22*p11*q1*q3*q4+l1*l2*p11*q1*q3*q4-l2*p11*q1*q3*q4-l1*g^2*p22*q3*q4+l1*n11*n22*p22*q3*q4-l1*n22*p22*q3*q4-l1*n11*p22*q3*q4+l1*p22*q3*q4-l2*g^2*p11*q3*q4+l2*n11*n22*p11*q3*q4-l2*n22*p11*q3*q4-l2*n11*p11*q3*q4+l2*p11*q3*q4-l1*n22*p11*p22*q1*q2*q4+n22*p11*p22*q1*q2*q4-l2*n11*p11*p22*q1*q2*q4+n11*p11*p22*q1*q2*q4+l2*n11*p22*q1*q2*q4-n11*p22*q1*q2*q4+l1*n22*p12*p21*q1*q2*q4-n22*p12*p21*q1*q2*q4+l2*n11*p12*p21*q1*q2*q4-n11*p12*p21*q1*q2*q4-l1*g*p21*q1*q2*q4+g*p21*q1*q2*q4-l2*g*p12*q1*q2*q4+g*p12*q1*q2*q4+l1*n22*p11*q1*q2*q4-n22*p11*q1*q2*q4-2*g^2*p11*p22*q2*q4+2*n11*n22*p11*p22*q2*q4-n22*p11*p22*q2*q4-n11*p11*p22*q2*q4+g^2*p22*q2*q4-n11*n22*p22*q2*q4+n11*p22*q2*q4+2*g^2*p12*p21*q2*q4-2*n11*n22*p12*p21*q2*q4+n22*p12*p21*q2*q4+n11*p12*p21*q2*q4-g*p21*q2*q4-g*p12*q2*q4+g^2*p11*q2*q4-n11*n22*p11*q2*q4+n22*p11*q2*q4+2*l1*l2*p11*p22*q1^2*q4-l2*p11*p22*q1^2*q4-l1*p11*p22*q1^2*q4-l1*l2*p22*q1^2*q4+l1*p22*q1^2*q4-2*l1*l2*p12*p21*q1^2*q4+l2*p12*p21*q1^2*q4+l1*p12*p21*q1^2*q4-l1*l2*p11*q1^2*q4+l2*p11*q1^2*q4-l1*n22*p11*p22*q1*q4-l2*n11*p11*p22*q1*q4+l2*p11*p22*q1*q4+l1*p11*p22*q1*q4+l1*n22*p22*q1*q4-l1*p22*q1*q4+l1*n22*p12*p21*q1*q4+l2*n11*p12*p21*q1*q4-l2*p12*p21*q1*q4-l1*p12*p21*q1*q4+l1*g*p21*q1*q4+l2*g*p12*q1*q4+l2*n11*p11*q1*q4-l2*p11*q1*q4+l1*l2*g^2*q2^2*q3^2-l2*g^2*q2^2*q3^2-l1*g^2*q2^2*q3^2+g^2*q2^2*q3^2-l1*l2*n11*n22*q2^2*q3^2+l2*n11*n22*q2^2*q3^2+l1*n11*n22*q2^2*q3^2-n11*n22*q2^2*q3^2-2*l1*l2*g^2*q2*q3^2+l2*g^2*q2*q3^2+l1*g^2*q2*q3^2+2*l1*l2*n11*n22*q2*q3^2-l2*n11*n22*q2*q3^2-l1*n11*n22*q2*q3^2-l1*l2*n22*q2*q3^2+l1*n22*q2*q3^2-l1*l2*n11*q2*q3^2+l2*n11*q2*q3^2+l1*l2*g^2*q3^2-l1*l2*n11*n22*q3^2+l1*l2*n22*q3^2+l1*l2*n11*q3^2-l1*l2*q3^2-l1*g^2*p22*q2^2*q3+g^2*p22*q2^2*q3+l1*n11*n22*p22*q2^2*q3-n11*n22*p22*q2^2*q3-l2*g^2*p11*q2^2*q3+g^2*p11*q2^2*q3+l2*n11*n22*p11*q2^2*q3-n11*n22*p11*q2^2*q3+l2*g^2*q2^2*q3+l1*g^2*q2^2*q3-2*g^2*q2^2*q3-l2*n11*n22*q2^2*q3-l1*n11*n22*q2^2*q3+2*n11*n22*q2^2*q3-l1*l2*n11*p22*q1*q2*q3+l2*n11*p22*q1*q2*q3+l1*l2*g*p21*q1*q2*q3-l2*g*p21*q1*q2*q3+l1*l2*g*p12*q1*q2*q3-l1*g*p12*q1*q2*q3-l1*l2*n22*p11*q1*q2*q3+l1*n22*p11*q1*q2*q3+l1*l2*n22*q1*q2*q3-l1*n22*q1*q2*q3+l1*l2*n11*q1*q2*q3-l2*n11*q1*q2*q3+l1*g^2*p22*q2*q3-l1*n11*n22*p22*q2*q3+l1*n22*p22*q2*q3+l2*g*p21*q2*q3+l1*g*p12*q2*q3+l2*g^2*p11*q2*q3-l2*n11*n22*p11*q2*q3+l2*n11*p11*q2*q3-l2*g^2*q2*q3-l1*g^2*q2*q3+l2*n11*n22*q2*q3+l1*n11*n22*q2*q3-l1*n22*q2*q3-l2*n11*q2*q3+l1*l2*n11*p22*q1*q3-l1*l2*p22*q1*q3-l1*l2*g*p21*q1*q3-l1*l2*g*p12*q1*q3+l1*l2*n22*p11*q1*q3-l1*l2*p11*q1*q3-l1*l2*n22*q1*q3-l1*l2*n11*q1*q3+2*l1*l2*q1*q3+g^2*p11*p22*q2^2-n11*n22*p11*p22*q2^2-g^2*p22*q2^2+n11*n22*p22*q2^2-g^2*p12*p21*q2^2+n11*n22*p12*p21*q2^2-g^2*p11*q2^2+n11*n22*p11*q2^2+g^2*q2^2-n11*n22*q2^2+l1*n22*p11*p22*q1*q2+l2*n11*p11*p22*q1*q2-l1*n22*p22*q1*q2-l2*n11*p22*q1*q2-l1*n22*p12*p21*q1*q2-l2*n11*p12*p21*q1*q2-l1*n22*p11*q1*q2-l2*n11*p11*q1*q2+l1*n22*q1*q2+l2*n11*q1*q2-l1*l2*p11*p22*q1^2+l1*l2*p22*q1^2+l1*l2*p12*p21*q1^2+l1*l2*p11*q1^2-l1*l2*q1^2");
  if (may_nan_p (res))
    abort ();

  if (verbose >= 3) {
    printf ("%dms (parsing)...", cputime () - t0);
    fflush (stdout);
  }

  /* Now replace */
  const char *const name[] = {"q1", "q2", "q3", "q4"};
  const may_t value[] = {s1, s2, s3, s4};
  x = may_subs_c (res, 0, 4, name, (void*) value);
  x = may_eval (x);
  if (verbose >= 3) {
    printf ("%dms (replace+eval)...", cputime () - t0);
    fflush (stdout);
  }

  /* Now expand */
  may_comdenom (&x, &y, x);
  if (verbose >= 3) {
    printf ("%dms (comdenom)...", cputime () - t0);
    fflush (stdout);
  }
  x = may_expand (x);

  t1 = cputime () - t0;
  if (verbose >= 2) {
    printf ("%dms...\n", t1);
    fflush (stdout);
  }
  if (!may_zero_p (x)) {
    printf ("Test failed. Should be 0.\n");
    printf ("x=%s\n\n"
            "y=%s\n\n",
            may_get_string (NULL, 0, x), may_get_string (NULL, 0, y));
    exit (2);
  }

  return t1;
}


/* To be able to dump may_t under GDB */
static void (*const dump)(may_t) = may_dump;

int
main (int argc, const char *argv[])
{
  int t = 0;

  printf ("%s\n", may_get_version ());
  may_kernel_start (0, 0);
  if (argc >= 2)
    verbose = atoi (argv[1]);

  may_kernel_info (stdout, "Start");

  // Test eval
  t += test_construct ();
  t += test_eval (100);
  t += test_eval (1000);
  t += test_eval (10000);
  t += test_eval (100000);
  t += test_eval (1000000);
  t += test_sum_x (20000);
  t += test_critical (5000);
  t += test_addnum (20000);
  t += test_sin_pi6 (20000);
  t += test_complex (1000000);
  t += test_evalf (100000);

  // Test expand
  t += test_expand (500);
  t += test_expand2 (3, 16);
  t += test_expand2 (4, 20);
  t += test_expand3 (20);
  t += test_univariate_multiply (1, 2, 1000);
  t += test_univariate_multiply (17, 42, 600);
  t += test_power_field (65000);
  t += test_pow_multivariate (500);
  t += test_expand4 (50);
  t += test_expand5 (5);
  t += test_expand6 (65536);

  // Test divide
  t += test_divide ("(1+x)^1000+1", "(1-x)^500", "x");
  t += test_divide ("(1+x)^1000+1", "x^3-5*x+17", "x");
  t += test_divide ("(1+x+y^2)^50+1", "(1-x)^25+y", "x");
  t += test_divide ("(1+x+y^2)^25+1", "x^3*y-5*x*y^42+17*y+1", "x");
  t += test_divide ("(1+x+y^2)^50+1", "(1-x)^25+y", "{x,y}");
  t += test_divide ("(1+x+y^2)^25+1", "x^3*y-5*x*y^42+17*y+1", "{x,y}");

  // Test GCD
  t += test_gcd ( "(1+2*x)^200*(x^3+2*x^2+1)", "(1+2*x)^42*(x^3-2*x+42)");
  t += test_gcd ( "(1+2*x)^200*(x^3+2*x^2+1)", "(1+2*x)^42*(x^3-2*x+42)+1");
  t += test_gcd ( "(1+2*x+y)^100*(x^3+2*x^2*y+1)", "(1+2*x+y)^42*(x^3-2*x+42)");
  t += test_gcd ( "(x^2-3*x*y+y^2)^4*(3*x-7*y+2)^5", "(x^2-3*x*y+y^2)^3*(3*x-7*y-2)^6");
  t += test_gcd ( "(7*y*x^2*z^2-3*x*y*z+11*(x+1)*y^2+5*z+1)^4*(3*x-7*y+2*z-3)^6", "(7*y*x^2*z^2-3*x*y*z+11*(x+1)*y^2+5*z+1)^3*(3*x-7*y+2*z+3)^6");
  // t += test_gcd ( "(1+2*x+y)^42*(x^3+2*x^2*y+1)", "(1+2*x+y)^17*(y^3-2*x+42)+1");
  t += test_gcd ( "(x^2-y^2)*(a+b)^10", "(x-y)*(a-c)^10");
  t += test_gcd ("(x-y)^50+a", "(x+y)^50");
  t += test_gcd ("-2107-7967*x+19271*x^50+551*x^49-39300*x^48+23685*x^51-47193*x^61+22470*x^63-11981*x^64+4427*x^65+12796*x^66-11319*x^67-44213*x^68-18278*x^69-8897*x^70-15766*x^71+10258*x^72+13882*x^73-23195*x^74-8704*x^75+4815*x^76-13598*x^77+13217*x^78-16323*x^79-13612*x^80-14833*x^62+25634*x^52+17615*x^54+14299*x^55-19193*x^56-4719*x^57-51084*x^58-14141*x^59+22254*x^60+61350*x^53-7982*x^81-5434*x^82+16274*x^83+7039*x^84+4819*x^85+13739*x^86+7595*x^87+13020*x^88-1874*x^89-11233*x^90-24214*x^91-11353*x^92-2585*x^93+22786*x^94+18677*x^95+16977*x^96+1096*x^97-9941*x^98-5735*x^99-6630*x^100-11236*x^35+21918*x^34-7645*x^33+12569*x^32+44195*x^42+7111*x^41-5940*x^40+8721*x^39+8*x^38+3951*x^37-16955*x^36+8166*x^44+1255*x^43-5677*x^45+2889*x^46-8483*x^47-6954*x^31-21427*x^30-20019*x^29-13763*x^28-8902*x^27-8764*x^26+11613*x^12+1365*x^11-5613*x^10+7489*x^9+3585*x^8-11942*x^15+17166*x^18-12107*x^17-25122*x^16+17961*x^14-3205*x^13+13609*x^20-11190*x^24+3638*x^25+7883*x^23-6332*x^22+511*x^21+31863*x^19-2029*x^4+2383*x^3-4956*x^2+1663*x^7-6356*x^6+4493*x^5",
                 "-2401-3773*x-9484*x^50-4086*x^49-31296*x^48-21634*x^51+18525*x^61-1327*x^63+17211*x^64+6097*x^65+4392*x^66+5639*x^67+26737*x^68+5985*x^69-2186*x^70+3352*x^71+5962*x^72+5413*x^73+15009*x^74+7176*x^75+23806*x^76-860*x^77+16368*x^78+9044*x^79+4566*x^80-7929*x^62-13086*x^52-84580*x^54-17160*x^55-4502*x^56-56940*x^57+5464*x^58-25712*x^59-41935*x^60+2429*x^53+12607*x^81-4635*x^82+1625*x^83+11692*x^84-22514*x^85+14489*x^86+6490*x^87-6581*x^88+5116*x^89-9671*x^90-18639*x^91-1692*x^92-9911*x^93-3458*x^94+2083*x^95-10129*x^96+6425*x^97+986*x^98+1890*x^99+6205*x^100+4746*x^35+14296*x^34+33685*x^33+23430*x^32-20474*x^42+14725*x^41-39167*x^40+11129*x^39+34455*x^38+19625*x^37+6082*x^36+7384*x^44-9814*x^43+11853*x^45-23402*x^46+24318*x^47+10912*x^31+17976*x^30-11869*x^29+11588*x^28+11503*x^27+15005*x^26-11632*x^12-17281*x^11+4819*x^10-17526*x^9+1700*x^8-9352*x^15+5662*x^18-11328*x^17+9618*x^16-3703*x^14+9162*x^13-25581*x^20+13776*x^24-1141*x^25-22249*x^23-3267*x^22-2752*x^21+17790*x^19+13366*x^4-4768*x^3+1366*x^2+2927*x^7+5018*x^6-6514*x^5");
  t += test_gcd 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  t += test_gcd 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  // GCD Mod 181
  may_kernel_intmod (may_set_ui (181));
  printf ("Compute GCD in Z/181Z\n");
  t += test_gcd ( "(1+2*x)^400*(x^3+2*x^2+1)", "(1+2*x)^42*(x^3-2*x+42)");
  t += test_gcd ( "(1+2*x)^400*(x^3+2*x^2+1)", "(1+2*x)^42*(x^3-2*x+42)+1");
  t += test_gcd ( "(1+2*x+y)^100*(x^3+2*x^2*y+1)", "(1+2*x+y)^42*(x^3-2*x+42)");
  t += test_gcd ( "(x^2-3*x*y+y^2)^4*(3*x-7*y+2)^5", "(x^2-3*x*y+y^2)^3*(3*x-7*y-2)^6");
  // t += test_gcd ( "(7*y*x^2*z^2-3*x*y*z+11*(x+1)*y^2+5*z+1)^4*(3*x-7*y+2*z-3)^6", "(7*y*x^2*z^2-3*x*y*z+11*(x+1)*y^2+5*z+1)^3*(3*x-7*y+2*z+3)^6");
  may_kernel_intmod (NULL);

  // GCD Mod 43051
  may_kernel_intmod (may_set_ui (43051));
  printf ("Compute GCD in Z/43051Z\n");
  t += test_gcd ("-936639990+26248623452*x^47-30174373832*x^46-19627087954*x^45+23532819511*x^24-15331409214*x^23-5892518210*x^22-2954269379*x^28-35110566664*x^27-4846605217*x^26-31276301429*x^25-19509035058*x^44+18467021749*x^43+18517327396*x^42-3435911855*x^50-272899085*x^49+1530941050*x^48+4507833875*x+10918084347*x^21+7814495607*x^20+23471621465*x^19-11157075535*x^18-11580405260*x^41-12162845828*x^39+12293848678*x^10-14679334842*x^9+17276957972*x^8+6436149609*x^7-8608995580*x^3-178435747*x^2+21474090980*x^17-3966988360*x^16-1330154020*x^15-13410537172*x^14-31038290506*x^51+17469329915*x^52-15282350857*x^53-11990574398*x^54+4255578378*x^55+2134905268*x^56+38375274669*x^57+9183261708*x^58+23467669465*x^59-5872201799*x^60+44704228721*x^61+27682281779*x^62-17204774085*x^63-7544450778*x^64-319408644*x^65+36034512058*x^66-6744628155*x^67+1363904895*x^68+22219362387*x^69+4275663006*x^70+14038262112*x^71+25591410149*x^72+9385606040*x^73-4745283802*x^74+11598735101*x^75-2508504600*x^76+11912265375*x^77+6624766926*x^78-4828562936*x^79+16636451249*x^80-9654281719*x^81+1913801599*x^82+2030662033*x^83-5474416933*x^84+11196778577*x^85+512268187*x^86-1029159530*x^87+1890708440*x^88+142491112*x^89-1261023993*x^90+3580061526*x^91-967823912*x^92+2292551912*x^93-3890383043*x^94-7104898913*x^95+3692350529*x^96-933592128*x^97+1199649580*x^98-227816977*x^99-12217636980*x^40+26794929142*x^38-41046742100*x^37+8432066353*x^36-6214147095*x^35+741141010*x^100-6270990007*x^34-6863205889*x^33-38388107386*x^32-561107347*x^13-6663332709*x^12+5507703343*x^11+11614165303*x^31-4503859503*x^30+26050790733*x^29+1788729074*x^6+2123912816*x^5-2542140060*x^4",
                 "1882371920-30937311949*x^47+6616907060*x^46-7420079075*x^45-28689993421*x^24+5544486596*x^23+7149046134*x^22+29115114125*x^28-7204610489*x^27-214559874*x^26+3363043648*x^25-6061422988*x^44-85814533599*x^43-5548876327*x^42+20531692560*x^50-23673866858*x^49+1553111326*x^48-7521320830*x-19801882818*x^21+7056872613*x^20-8039690791*x^19+11049483001*x^18+21957440404*x^41+18566882873*x^39-1088265300*x^10+29943249139*x^9+3160532878*x^8+110919258*x^7+1584505491*x^3-2133682609*x^2+11700952246*x^17-12424469513*x^16-426278523*x^15+7561875663*x^14+19494168654*x^51-8174921854*x^52+18073788685*x^53-48441925739*x^54-3850452489*x^55-17753230977*x^56-44973929094*x^57+7332053562*x^58-18246235652*x^59+9980611956*x^60+6961020716*x^61-3323333429*x^62-20693764726*x^63+2577247520*x^64-22463329638*x^65-13528331424*x^66+440594870*x^67+778770195*x^68+24497174109*x^69-11578701274*x^70-217623403*x^71+16461882236*x^72-6001481047*x^73-5750277357*x^74-16262001424*x^75+13760397067*x^76+12678193001*x^77+29675566382*x^78+1889202286*x^79+12672890141*x^80+26252749471*x^81+25061328813*x^82+20393397488*x^83-6344703601*x^84-12986831645*x^85+10287410396*x^86+18964048763*x^87+9141433582*x^88+9742202475*x^89+1800283356*x^90+9411879011*x^91+13562767020*x^92-3883570155*x^93+1190623161*x^94+4638169279*x^95+10385086102*x^96+10263027507*x^97+5186524611*x^98+1309311388*x^99+2485463829*x^40-14414308862*x^38-2750892631*x^37-34230002076*x^36-21558061051*x^35+2789684836*x^100-9973372012*x^34+12038293769*x^33-2280622009*x^32-14841292646*x^13+4463462090*x^12+11039962159*x^11+20714527103*x^31+29530802947*x^30+4813620791*x^29+8841198971*x^6-4237029618*x^5-1135211878*x^4");
  t += test_gcd 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  t += test_gcd 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  may_kernel_intmod (NULL);
  t += test_gcd2 (14, 7, 4, 4, 6, 8, 10, 17, 7, 11);

  t += test_diff ("x/(1+sin(x^(y+x^2)))^2");

  t += test_R1(17);
  t += test_R2(25);
  t += test_R6(100000);
  t += test_R7(100000);
  t += test_R8(100000);
  t += test_S2(500);
  t += test_S3(500);
  t += test_S4(500);
  t += test_series_tan (100);

  // Test rationalize
  t += test_rationalize (1);
  t += test_sum_rationalize (10);
  t += test_sum_rationalize2 (10);

 //t += test_fermat ();

  may_kernel_info (stdout, "End");
  printf ("Total time %dms\n", t);

  may_kernel_end ();
  return 0;
}