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/* M. Beeson, for Mathpert
ratsimp simplifies a rational function, if possible eliminating
common zeroes of num and denom.  This is used before calculating
singularities.

Original date 1.30.97
Last modified 1.29.98
1.16.05 removed include debug.h
8.8.24 replaced math.h with sincos.h
*/

#include <assert.h>
#include <string.h>
#include <math.h>

#include "globals.h"
#include "pvalaux.h"
#include "deval.h"
#include "order.h"
#include "cancel.h"
#include "probtype.h"
#include "prover.h"
#include "polynoms.h"
#include "mpmem.h"
#include "simpsums.h"
#include "binomial.h"
#include "trig.h"
#include "ratsimp.h"
#include "factor.h"
#include "polyquo.h"

void ratsimp(term t, term *ans)
/* simplify rational function t, eliminating common zeroes of num and
denom if possible, but this is not guaranteed.
*/
{ term u,v,num,denom,w;
  POLYnomial p,q;
  term x = get_eigenvariable();
  int err,err2;
  void  *savenode = heapmax();
  int savegcdflag = get_polyvalgcdflag();
  int savefunctionflag = get_polyvalfunctionflag();
  int savecomdenomflag = get_polyvalcomdenomflag();
  int savefactorflag = get_polyvalfactorflag();
  int savenegexpflag = get_polyvalnegexpflag();
  int savefractexpflag = get_polyvalfractexpflag();
  int savelogflag = get_polyvallogflag();
  int savefactorflag2 = get_polyvalfactorflag2();
  err = polyval(t,&u);
  /* This will perform cancellations, etc., before we try polyquo */
  if(!err)
     { save_and_reset(u,savenode,&t);
       savenode = heapmax();  /* because now t is above the old savenode */
     }
  if(grat(t,x))
     { err = make_polyquo(t,x,&p,&q);
       if(!err)
          { u = make_fraction(poly_term(p,x),poly_term(q,x));
            save_and_reset(u,savenode,ans);
            return;
          }
     }
  reset_heap(savenode);  /* after make_polyquo */
  set_polyvalfactorflag(1);
  set_polyvalfactorflag2(0x100);  /* factor all sums */
  set_polyvalgcdflag(1);
  set_polyvalcomdenomflag(1);
  set_polyvalfractexpflag(1);
  set_polyvalnegexpflag(-1);  /* eliminate negative exponents */
  set_polyvallogflag(2);
  set_polyvalfunctionflag(1);
  copy(t,&w);
  clear_already(&w);
  polyval(w,&u);
  /* destroy_term(w) is permissible but superfluous
     in view of save_and_reset coming soon. */
  set_polyvalnegexpflag(savenegexpflag);
  set_polyvalgcdflag(savegcdflag);
  set_polyvalfactorflag(savefactorflag);
  set_polyvalfunctionflag(savefunctionflag);
  set_polyvalcomdenomflag(savecomdenomflag);
  set_polyvalfractexpflag(savefractexpflag);
  set_polyvalfactorflag2(savefactorflag2);
  set_polyvallogflag(savelogflag);
  save_and_reset(u,savenode,&t);
  if(FRACTION(t))
     { num = ARG(0,t);
       denom = ARG(1,t);
       if(mvpoly2(num))
          { err = purefactor(num,&u);
            if(err)
               u = num;
          }
       else
          { err = 1;
            u = num;
          }
       if(mvpoly2(denom))
          { err2 = purefactor(denom,&v);
            if(err2)
               v = denom;
          }
       else
          { err2 = 1;
            v = denom;
          }
       if(err && err2)
          { *ans = t;
            return;
          }
       ratsimp(make_fraction(u,v),ans);
     }
  *ans = t;
}