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/* M. Beeson, for MathXpert.
Reverse trig operators.
Original date 2.10.97
Last modified 2.27.98
2.9.05 added include graphstr.h, mpdoc.h
3.14.23  changed theta to t to avoid "illegal character encoding"
5.13.24 more reasons in display math, and others just in $.
*/

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

#include "globals.h"
#include "ops.h"
#include "trig.h"
#include "match.h"
#include "order.h"
#include "cancel.h"
#include "simpsums.h"  /* collect */
#include "checkarg.h"  /* needed by automode.h */
#include "graphstr.h"
#include "mpdoc.h"
#include "automode.h"  /* get_intflag */
#include "mstring.h"     /* mstring */
#include "deval.h"
#include "symbols.h"
#include "pvalaux.h"   /* content_factor */
#include "mathmode.h"    /* get_mathmode   */
#include "calc.h"      /* polyvalop      */
#include "errbuf.h"
#include "autosimp.h"  /* set_pathtail, SetShowStepOperation */


/*______________________________________________________________________*/
int sinsumrev(term t, term arg, term *next, char *reason)
/* sin u cos v + cos u sin v = sin(u+v)      */
{ term lhs,rhs,a[2],temp;
  int err;
  lhs = sum(product(sin1(var0),cos1(var1)),product(cos1(var0),sin1(var1)));
  rhs = sin1(sum(var0,var1));
  err = match(t,lhs,rhs,a,&temp);   /* instantiate a[0],a[1], and *next */
  if(err)
     { destroy_term(lhs);
       destroy_term(rhs);
       return 1;
     }
  polyval(temp,next);  /* this is important so that e.g. x + pi/6 - (x-pi/6)
                          becomes 2x.  Preops checks for a non-sum in the
                          arg of the answer. */
  strcpy(reason, "$$sin u cos v + cos u sin v=sin(u+v)$$");
  HIGHLIGHT(*next);
  return 0;
}
/*______________________________________________________________________*/
int sindifrev(term t, term arg, term *next, char *reason)
/* sin u cos v - cos u sin v = sin(u-v)      */
{ term lhs,rhs,a[2],temp;
  int err;
  lhs = sum(product(sin1(var0),cos1(var1)),tnegate(product(cos1(var0),sin1(var1))));
  rhs = sin1(sum(var0,tnegate(var1)));
  err = match(t,lhs,rhs,a,&temp);   /* instantiate a[0],a[1], and *next */
  if(err)
     { destroy_term(lhs);
       destroy_term(rhs);
       return 1;
     }
  polyval(temp,next);
  strcpy(reason, "$$sin u cos v -cos u sin v=sin(u-v)$$");
  HIGHLIGHT(*next);
  return 0;
}


/*______________________________________________________________________*/
int cossumrev(term t, term arg, term *next, char *reason)
/* cos u cos v - sin u sin v = cos(u+v)      */
{ term lhs,rhs,a[2],temp;
  int err;
  lhs = sum(product(cos1(var0),cos1(var1)),tnegate(product(sin1(var0),sin1(var1))));
  rhs = cos1(sum(var0,var1));
  err = match(t,lhs,rhs,a,&temp);   /* instantiate a[0],a[1], and *next */
  if(err)
     { destroy_term(lhs);
       destroy_term(rhs);
       return 1;
     }
  polyval(temp,next);
  strcpy(reason, "$$cos u cos v - sin u sin v=cos(u+v)$$");
  HIGHLIGHT(*next);
  return 0;
}
/*______________________________________________________________________*/
int cosdifrev(term t, term arg, term *next, char *reason)
/* cos u cos v + sin u sin v = cos(u-v)      */
{ term lhs,rhs,a[2],temp;
  int err;
  lhs = sum(product(cos1(var0),cos1(var1)),product(sin1(var0),sin1(var1)));
  rhs = cos1(sum(var0,tnegate(var1)));
  err = match(t,lhs,rhs,a,&temp);   /* instantiate a[0],a[1], and *next */
  if(err)
     { destroy_term(lhs);
       destroy_term(rhs);
       return 1;
     }
  polyval(temp,next);
  strcpy(reason, "$$cos u cos v + sin u sin v=cos(u-v)$$");
  HIGHLIGHT(*next);
  return 0;
}
/*______________________________________________________________________*/
int tansumrev(term t, term arg, term *next, char *reason)
/* (tan u+tan v)/(1-tan u tan v) = tan(u+v)  */
{ term num,denom,a,b,c,u,v;
  if(!FRACTION(t))
     return 1;
  num = ARG(0,t);
  denom = ARG(1,t);
  if(FUNCTOR(num) != '+' || FUNCTOR(denom) != '+' ||
     ARITY(num) != 2 || ARITY(denom) != 2
    )
     return 1;
  if(!ONE(ARG(0,denom)) || !NEGATIVE(ARG(1,denom)))
     return 1;
  a = ARG(0,num);
  b = ARG(1,num);
  c = ARG(0,ARG(1,denom));
  if(FUNCTOR(a) != TAN || FUNCTOR(b) != TAN ||
     FUNCTOR(c) != '*' || ARITY(c) != 2
    )
     return 1;
  u = ARG(0,a);
  v = ARG(0,b);
  if(
      (equals(a,ARG(0,c)) && equals(b,ARG(1,c))) ||
      (equals(a,ARG(1,c)) && equals(b,ARG(0,c)))
    )
      { *next = tan1(sum(u,v));
        HIGHLIGHT(*next);
        strcpy(reason,"$$(tan u+tan v)/(1-tan u tan v) =    tan(u+v)$$");
        return 0;
      }
  return 1;
}
/*______________________________________________________________________*/
int tandifrev(term t, term arg, term *next, char *reason)
/* (tan u-tan v)/(1+tan u tan v) = tan(u-v)  */
{ term num,denom,a,b,c,u,v;
  if(!FRACTION(t))
     return 1;
  num = ARG(0,t);
  denom = ARG(1,t);
  if(FUNCTOR(num) != '+' || FUNCTOR(denom) != '+' ||
     ARITY(num) != 2 || ARITY(denom) != 2
    )
     return 1;
  if(FUNCTOR(ARG(0,num)) != TAN || !NEGATIVE(ARG(1,num)) ||
     FUNCTOR(ARG(0,ARG(1,num))) != TAN
    )
     return 1;
  u = ARG(0,ARG(0,num));
  v = ARG(0,ARG(0,ARG(1,num)));
  if(ONE(ARG(0,denom)))
     c = ARG(1,denom);
  else if(ONE(ARG(1,denom)))
     c = ARG(0,denom);
  else
     return 1;
  if(FUNCTOR(c) != '*' || ARITY(c) != 2)
     return 1;
  a = ARG(0,c);
  b = ARG(1,c);
  if(
     (equals(a,ARG(0,num)) && equals(b,ARG(0,ARG(1,num)))) ||
     (equals(b,ARG(0,num)) && equals(a,ARG(0,ARG(1,num))))
    )
     { *next = tan1(sum(u,tnegate(v)));
       HIGHLIGHT(*next);
       strcpy(reason, "$$(tan u-tan v)/ (1+tan u tan v) =    tan(u-v)$$");
       return 0;
     }
  return 1;
}
/*______________________________________________________________________*/
int cotsumrev(term t, term arg, term *next, char *reason)
/* (cot u cot v-1)/(cot u+cot v) = cot(u+v)  */
{ term num,denom,a,b,c,u,v;
  if(!FRACTION(t))
     return 1;
  num = ARG(0,t);
  denom = ARG(1,t);
  if(FUNCTOR(num) != '+' || FUNCTOR(denom) != '+' ||
     ARITY(num) != 2 || ARITY(denom) != 2 ||
     !NEGATIVE(ARG(1,num)) || !ONE(ARG(0,ARG(1,num))) ||
     FUNCTOR(ARG(0,num)) != '*' || ARITY(ARG(0,num)) != 2
    )
     return 1;
  a = ARG(0,denom);
  b = ARG(1,denom);
  if(FUNCTOR(a) != COT || FUNCTOR(b) != COT)
     return 1;
  u = ARG(0,a);
  v = ARG(0,b);
  c = ARG(0,num);
  if(
     (equals(a,ARG(0,c)) && equals(b,ARG(1,c))) ||
     (equals(b,ARG(0,c)) && equals(a,ARG(1,c)))
    )
     { *next = cot1(sum(u,v));
       HIGHLIGHT(*next);
       strcpy(reason,"$$(cot u cot v-1)/(cot u+cot v) = cot(u+v)$$");
       return 0;
     }
  return 1;
}
/*______________________________________________________________________*/
int cotdifrev(term t, term arg, term *next, char *reason)
/* (1+cot u cot v)/(cot v-cot u) = cot(u-v)  */
{ term num,denom, u,v,a,b,c;
  if(!FRACTION(t))
     return 1;
  num = ARG(0,t);
  denom = ARG(1,t);
  if(FUNCTOR(num) != '+' || FUNCTOR(denom) != '+' ||
     ARITY(num) != 2 || ARITY(denom) != 2 ||
     !NEGATIVE(ARG(1,denom))
    )
     return 1;
  a = ARG(0,denom);
  b = ARG(0,ARG(1,denom));
  if(FUNCTOR(a) != COT || FUNCTOR(b) != COT)
     return 1;
  u = ARG(0,a);
  v = ARG(0,b);
  if(ONE(ARG(0,num)))
     c = ARG(1,num);
  else if(ONE(ARG(1,num)))
     c = ARG(0,num);
  else
     return 1;
  if(FUNCTOR(c) != '*' || ARITY(c) != 2)
     return 1;
  if(
     (equals(ARG(0,c),a) && equals(ARG(1,c),b)) ||
     (equals(ARG(0,c),b) && equals(ARG(1,c),a))
    )
     { *next = cot1(sum(u,tnegate(v)));
       HIGHLIGHT(*next);
       strcpy(reason,"$$(1+cot u cot v)/(cot v-cot u) = cot(u-v)$$");
       return 0;
     }
  return 1;
}
/*______________________________________________________________________*/
int tanhalf1rev(term t, term arg, term *next, char *reason)
/* (sin t)/(1+cos t) = tan(t/2) */
{ term num,denom,u,a,b;
  if(!FRACTION(t))
     return 1;
  num = ARG(0,t);
  denom = ARG(1,t);
  if(FUNCTOR(num) != SIN)
     return 1;
  u = ARG(0,num);
  if(FUNCTOR(denom) != '+' || ARITY(denom) != 2)
     return 1;
  a = ARG(0,denom);
  b = ARG(1,denom);
  if(
     (ONE(a) && FUNCTOR(b) == COS && equals(ARG(0,b),u)) ||
     (ONE(b) && FUNCTOR(a) == COS && equals(ARG(0,a),u))
    )
     { *next = tan1(make_fraction(u,two));
       HIGHLIGHT(*next);
       strcpy(reason,"$$(sin t)/(1+cos t) =  tan(t/2)$$");
       return 0;
     }
  return 1;
}
/*______________________________________________________________________*/
int tanhalf2rev(term t, term arg, term *next, char *reason)
/* (1-cos t)/sin t = tan(t/2) */
{ term num,denom,u,b;
  if(!FRACTION(t))
     return 1;
  num = ARG(0,t);
  denom = ARG(1,t);
  if(FUNCTOR(denom) != SIN)
     return 1;
  u = ARG(0,denom);
  if(FUNCTOR(num) != '+' || ARITY(num) != 2 ||
     !ONE(ARG(0,num)) || !NEGATIVE(ARG(1,num)))
     return 1;
  b = ARG(0,ARG(1,num));
  if(FUNCTOR(b) != COS || !equals(ARG(0,b),u))
     return 1;
  *next = tan1(make_fraction(u,two));
  HIGHLIGHT(*next);
  strcpy(reason,"$$(1-cos t)/sin t =    tan(t/2)$$");
  return 0;
}

/*______________________________________________________________________*/
int cothalf1rev(term t, term arg, term *next, char *reason)
/* (1+cos t)/(sin t) = cot(t/2) */
{ term num,denom,u;
  if(!FRACTION(t))
     return 1;
  num = ARG(0,t);
  denom = ARG(1,t);
  if(FUNCTOR(denom) != SIN)
     return 1;
  u = ARG(0,denom);
  if(FUNCTOR(num) != '+' || ARITY(num) != 2)
     return 1;
  if(
     (ONE(ARG(0,num)) && FUNCTOR(ARG(1,num)) == COS && equals(u,ARG(0,ARG(1,num)))) ||
     (ONE(ARG(1,num)) && FUNCTOR(ARG(0,num)) == COS && equals(u,ARG(0,ARG(0,num))))
    )
     { *next = cot1(make_fraction(u,two));
       HIGHLIGHT(*next);
       strcpy(reason,"$$(1+cos t)/(sin t) =  cot(t/2)$$");
       return 0;
     }
  return 1;
}

/*______________________________________________________________________*/
int cothalf2rev(term t, term arg, term *next, char *reason)
/* sin t/(1-cos t) = cot(t/2) */
{ term num,denom,u,b;
  if(!FRACTION(t))
     return 1;
  num = ARG(0,t);
  denom = ARG(1,t);
  if(FUNCTOR(num) != SIN)
     return 1;
  u = ARG(0,num);
  if(FUNCTOR(denom) != '+' || ARITY(denom) != 2 ||
     !ONE(ARG(0,denom)) || !NEGATIVE(ARG(1,denom))
    )
     return 1;
  b = ARG(0,ARG(1,denom));
  if(FUNCTOR(b) != COS || !equals(ARG(0,b),u))
     return 1;
  *next = cot1(make_fraction(u,two));
  HIGHLIGHT(*next);
  strcpy(reason,"$$sin t/(1-cos t) =    cot(t/2)$$");
  return 0;
}