Subversion Repositories wimsdev

/*    Copyright (C) 1998-2003 XIAO, Gang of Universite de Nice - Sophia Antipolis

 *

 *  This program is free software; you can redistribute it and/or modify

 *  it under the terms of the GNU General Public License as published by

 *  the Free Software Foundation; either version 2 of the License, or

 *  (at your option) any later version.

 *

 *  This program 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 General Public License for more details.

 *

 *  You should have received a copy of the GNU General Public License

 *  along with this program; if not, write to the Free Software

 *  Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.

 */

/* subroutines for texmath */

#include "wims.h"

/* Careful! increasing this number risks stack overflow. */

#define MAX_FACTORS 256

enum {

    type_integer, type_numeric, type_var,

      type_poly, type_transcend

};

typedef struct afactor{

    char *beg, *end;

    int type, side;

} afactor;

char texmathbuf[MAX_LINELEN+1];

char *find_term_end(char *p);

void t_onestring(char *p);

void t_oneterm(char *p, int num);

void t_onefactor(struct afactor *p, int num);

/* never used or defined ?? */

void n_onestring(char *p);

void n_oneterm(char *p, int num);

void n_onefactor(struct afactor *p, int num);

/* */

void texmath(char *p);

/* print to texmathbuf */

void tprint(char *s,...)

{

    va_list vp;

    char buf[MAX_LINELEN+1];

    va_start(vp,s); vsnprintf(buf,sizeof(buf),s,vp); va_end(vp);

    if(strlen(buf)+strlen(texmathbuf)>=MAX_LINELEN)

      user_error("cmd_output_too_long");

    strcat(texmathbuf,buf);

}

/* transforms sum(n,n=1..infinity) , product(n/(n+1),n=1..infinity). */

void _tex_sums(char *p, char *name, int type)

{

    char *p1,*p2,*p3;

    p1=find_item_end(p); if(*p1) *(p1++)=0;

    p2=find_item_end(p1); p3=strparstr(p1,"=");

    if(p3<p2) p2=p3;

    if(*p2) *(p2++)=0;

    p3=find_item_end(p2);

    if(*p3) *(p3++)=0;

    tprint("\\%s ",name);

    if(type) {

      if(*p2) {

        tprint("_{"); t_onestring(p2); tprint("}");

      }

    }

    else if(*p1) {

      tprint("_{%s",p1);

      if(*p2) { tprint("="); t_onestring(p2); }

      tprint("}");

    }

    if(*p3) {

      tprint("^{"); t_onestring(p3); tprint("}");

    }

    strip_trailing_spaces(p); if(find_term_end(p)<p+strlen(p)) {

      tprint("\\left("); t_onestring(p); tprint("\\right)");

    }

    else t_onestring(p);

    if(type && *p1) {

      strip_trailing_spaces(p1); tprint("\\,\\textrm{d}"); // case of the integrale

      if(find_term_end(p1)<p1+strlen(p1)) {

        tprint("\\left("); t_onestring(p1); tprint("\\right)");

      }

      else t_onestring(p1);

    }

}

/* integration, sum and product */

void tex_int(char *p) {  _tex_sums(p,"int",1); }

void tex_sum(char *p) {  _tex_sums(p,"sum",0); }

void tex_prod(char *p) { _tex_sums(p,"prod",0);}

struct tmathfn tmathfn[]={

      {"Arg",      1,  "\\rm{Arg}",      "\\right)"},

      {"Int",      2,  "","",        tex_int},

      {"Prod",     2,  "","",        tex_prod},

      {"Sum",      2,  "","",        tex_sum},

      {"abs",      0,  "\\left|",      "\\right|"},

      {"acos",     1,  "\\rm{arccos}",  "\\right)"},

      {"acosh",    1,  "\\rm{Argch}",      "\\right)"},

      {"arg",      1,  "\\rm{Arg}",      "\\right)"},

      {"asin",     1,  "\\rm{arcsin}",  "\\right)"},

      {"asinh",    1,  "\\rm{Argsh}",      "\\right)"},

      {"atan",     1,  "\\rm{arctg}",      "\\right)"},

      {"atanh",    1,  "\\rm{Argth}",      "\\right)"},

      {"ch",       1,  "\\rm{ch}",      "\\right)"},

      {"conj",     0,  "\\overline{",      "}"},

      {"conjugate",0,  "\\overline{",      "}"},

      {"cos",      1,  "\\cos",      "\\right)"},

      {"cosh",     1,  "\\rm{ch}",      "\\right)"},

      {"cot",      1,  "\\rm{ctg}",      "\\right)"},

      {"cotan",    1,  "\\rm{ctg}",      "\\right)"},

      {"cotanh",   1,  "\\rm{cth}",      "\\right)"},

      {"csc",      1,  "\\rm{csc}",      "\\right)"},

      {"ctg",      1,  "\\rm{ctg}",      "\\right)"},

      {"cth",      1,  "\\rm{cth}",      "\\right)"},

      {"det",      1,  "\\rm{det}",      "\\right)"},

      {"erf",      1,  "\\rm{erf}",      "\\right)"},

      {"exp",      1,  "\\exp",      "\\right)"},

      {"int",      2,  "","",        tex_int},

      {"integrate",2,  "","",        tex_int},

      {"lg",       1,  "\\rm{lg}",      "\\right)"},

      {"ln",       1,  "\\ln",        "\\right)"},

      {"log",      1,  "\\log",      "\\right)"},

      {"prod",     2,  "","",        tex_prod},

      {"product",  2,  "","",        tex_prod},

      {"sec",      1,  "\\rm{sec}",      "\\right)"},

      {"sgn",      1,  "\\rm{sgn}",      "\\right)"},

      {"sh",       1,  "\\rm{sh}",      "\\right)"},

      {"sign",     1,  "\\rm{sign}",      "\\right)"},

      {"sin",      1,  "\\sin",      "\\right)"},

      {"sinh",     1,  "\\rm{sh}",      "\\right)"},

      {"sqrt",     0,  "\\sqrt{",      "}"},

      {"sum",      2,  "","",        tex_sum},

      {"tan",      1,  "\\tan",      "\\right)"},

      {"tanh",     1,  "\\rm{th}",      "\\right)"},

      {"tg",       1,  "\\rm{tg}",      "\\right)"},

      {"th",       1,  "\\rm{th}",      "\\right)"}

};

int tmathfn_no=(sizeof(tmathfn)/sizeof(tmathfn[0]));

struct tmathvar tmathvar[]={

      {"CC",      "\\mathbb{C}"},

      {"Delta",   "\\Delta"},

      {"Gamma",   "\\Gamma"},

      {"Inf",     "\\infty"},

      {"Lambda",  "\\Lambda"},

      {"NN",      "\\mathbb{N}"},

      {"Omega",   "\\Omega"},

      {"PI",      "\\pi"},

      {"Phi",     "\\Phi"},

      {"Pi",      "\\Pi"},

      {"Psi",     "\\Psi"},

      {"QQ",      "\\mathbb{Q}"},

      {"RR",      "\\mathbb{R}"},

      {"Sigma",   "\\Sigma"},

      {"Theta",   "\\Theta"},

      {"Upsilon", "\\Upsilon"},

      {"Xi",      "\\Xi"},

      {"ZZ",      "\\mathbb{Z}"},

      {"aleph",   "\\aleph"},

      {"alpha",   "\\alpha"},

      {"beta",   "\\beta"},

      {"chi",    "\\chi"},

      {"delta",  "\\delta"},

      {"epsilon","\\epsilon"},

      {"eta",    "\\eta"},

      {"gamma",  "\\gamma"},

      {"inf",    "\\infty"},

      {"infinity","\\infty"},

      {"infty",  "\\infty"},

      {"iota",   "\\iota"},

      {"kappa",  "\\kappa"},

      {"lambda", "\\lambda"},

      {"mu",     "\\mu"},

      {"neq",    "\\neq"},

      {"nu",     "\\nu"},

      {"omega",  "\\omega"},

      {"phi",    "\\phi"},

      {"pi",     "\\pi"},

      {"psi",    "\\psi"},

      {"rho",    "\\rho"},

      {"sigma",  "\\sigma"},

      {"tau",    "\\tau"},

      {"theta",  "\\theta"},

      {"xi",     "\\xi"},

      {"zeta",   "\\zeta"}

};

int tmathvar_no=(sizeof(tmathvar)/sizeof(tmathvar[0]));

/* find the end of an additive term. */

char *find_term_end(char *p)

{

    char *pp;

    pp=p;

    if(*pp==',' || *pp==';' || *pp=='=' || *pp=='<') pp++;

    while(*pp=='+' || *pp=='-' || *pp=='=' || *pp=='>') pp++;

    for(;*pp;pp++) {

      switch(*pp) {

        case '(': pp=find_matching(pp+1,')'); goto loopend;

        case '[': pp=find_matching(pp+1,']'); goto loopend;

/*     case '{': pp=find_matching(pp+1,'}'); goto loopend;*/

        case 0:

        case '<':

        case '>':

        case ',':

        case ';':

        case '=':

        case ')':

        case ']':

        case '}':

        case '-':

        case '+': return pp;

        case '*':

        case '/':

        case '^': {

          while(*(pp+1)=='+' || *(pp+1)=='-') pp++;

          goto loopend;

        }

      }

      if(isalnum(*pp) || *pp=='.') {

        pp=find_mathvar_end(pp); pp--; continue;

      }

      continue;

      loopend:

      if(pp==NULL) module_error("unmatched_parentheses");

    }

    return pp;

}

/* find the end of an multiplicative factor. */

char *find_factor_end(char *p)

{

    char *pp;

    pp=p; if(*pp==',' || *pp==';' || *pp=='=') pp++;

    while(*pp=='+' || *pp=='-' || *pp=='*' || *pp=='/') pp++;

    for(;*pp;pp++) {

      switch(*pp) {

        case '(': pp=find_matching(pp+1,')'); goto loopend;

        case '[': pp=find_matching(pp+1,']'); goto loopend;

/*    case '{': pp=find_matching(pp+1,'}'); goto loopend;*/

        case 0:

        case '<':

        case '>':

        case ',':

        case ';':

        case '=':

        case ')':

        case ']':

        case '}':

        case '+':

        case '-':

        case '*':

        case '/': return pp;

        case '^': {

          while(*(pp+1)=='+' || *(pp+1)=='-') pp++;

          goto loopend;

        }

      }

      if(isalnum(*pp) || *pp=='.') {

        pp=find_mathvar_end(pp); pp--; continue;

      }

      continue;

      loopend:

      if(pp==NULL) module_error("unmatched_parentheses");

    }

    return pp;

}

    /* returns the number of terms */

int term_cnt(char *p)

{

    char *pe, *pp;

    int i;

    pe=p+strlen(p);

    for(i=0,pp=p;pp<pe;pp=find_term_end(pp),i++);

    return i;

}

/* Print a number: transform 4E+05 in 4 \times 10^{5} and  4E-05 in 4 \times 10^{-5}

suppress multiple + or 0 ; see rawmath.c

*/

void putnumber(char *p)

 {

     char *sgn = "", *pp = strpbrk(p,"Ee");

     if (pp == NULL) { tprint("%s",p); return; }

     *pp++ = 0;

     if (*pp == '-') { sgn = "-"; pp++; }

     while (*pp == '0' || *pp == '+') pp++;

     tprint("%s \\times 10^{%s%s}", p, sgn, pp);

 }

/* Print a variable name ; transform abc475 in abc_475 */

void putvar(char *p)

{

    char vbuf[1024];

    char *pp, *p2;

    int i;

    vbuf[0]=0;

    if(*(p+1)==0) {tprint("%c",*p); return;}

    for(pp=p;isalpha(*pp);pp++);

    if(myisdigit(*pp)) {

    for(p2=pp+1;myisdigit(*p2);p2++);

    if(*p2==0) {/* subscript */

        mystrncpy(vbuf,pp,sizeof(vbuf));*pp=0;

    }

    }

    i=search_list(tmathvar, tmathvar_no, sizeof(tmathvar[0]), p);

    if(i>=0) tprint("%s ",tmathvar[i].tex);

    else tprint("%s ",p);

    if(vbuf[0]) {

    if(vbuf[1]==0) tprint("_%c ",vbuf[0]);

    else tprint("_{%s} ",vbuf);

    }

}

/* sort according to type */

int fsort(const void *p1, const void *p2)

{

  struct afactor *t1, *t2;

  int i1,i2;

  t1=*(struct afactor **) p1; t2=*(struct afactor **) p2;

  i1=t1->type; i2=t2->type;

  if(i1>type_var) i1=type_var;

  if(i2>type_var) i2=type_var;

  return i1-i2;

}

void t_oneterm(char *p, int num)

{

  int sign, fcnt, s, i, dentype, rel;

  char *pp, *pe, *pt;

  struct afactor factors[MAX_FACTORS];

  struct afactor *numerator[MAX_FACTORS],

    *denominator[MAX_FACTORS],

    *neutral[MAX_FACTORS];

  int numcnt,dencnt,neucnt;

/* interpret some arrows */

  rel=0;

  switch(*p) {

    case '<': {

      rel++; p++; if(*p!='=') {tprint(" < "); break;} // <

      do p++; while(*p=='=');

      if(*p!='>') {tprint("\\le ");break;} // <= , <===

      else {tprint("\\iff ");p++; break;} // <==>

    }

    case '>': {

      rel++; p++; if(*p!='=') {tprint(" > "); rel=1; break;} // >

      while(*p=='=') p++;

        tprint("\\ge "); // >=

        break;

    }

    case '-': {

      for(pp=p;*pp=='-';pp++);

      if(*pp!='>') break;

      rel++; tprint("\\to "); p=++pp; //->

      break;

    }

    case '=': {

        rel++; for(pp=p;*pp=='=';pp++);

        if(*pp!='>') break;

        tprint("\\Rightarrow "); p=++pp; // =>

        break;

    }

  }

  if(*p==',' || *p==';' || *p=='=') {tprint("%c",*p); p++; num=0;}

    sign=1; while(*p=='+' || *p=='-') {

      if(*p=='-') sign*=-1;

      p++;

  }

  for(fcnt=0, pp=p; fcnt<MAX_FACTORS && *pp; fcnt++, pp=pe) {

    s=1;

    while(*pp=='*' || *pp=='/') {

      if(*pp=='/') s=-1;

      pp++;

    }

    factors[fcnt].side=s;

    while(*pp=='+' || *pp=='-') {

      if(*pp=='-') sign*=-1;

      pp++;

    }

    pe=find_factor_end(pp); if(pe<=pp) break;

    factors[fcnt].beg=pp; factors[fcnt].end=pe;

    if(pe-pp==1 && *pp=='1') fcnt--;

    if(*pp=='(') {

      char *pt, *pe2, buf[MAX_LINELEN+1];

      int ss;

      pp++; pt=find_matching(pp,')');

      if(pt>=pe-1) {

        memmove(buf,pp,pt-pp); buf[pt-pp]=0;

        i=term_cnt(buf);

        if(i==1) { /* remove parentheses */

          for(;pp<pt && fcnt<MAX_FACTORS;pp=pe2,fcnt++) {

            ss=s;

            while(*pp=='*' || *pp=='/') {

              if(*pp=='/') ss=-s;

              pp++;

            }

            factors[fcnt].side=ss;

            while(*pp=='+' || *pp=='-') {

              if(*pp=='-') sign*=-1;

              pp++;

            }

            pe2=find_factor_end(pp);

            if(pe2<=pp) goto bailout;

            factors[fcnt].beg=pp; factors[fcnt].end=pe2;

            if(pe2-pp==1 && *pp=='1') fcnt--;

          }

          fcnt--;

        }

      }

    }

  }

  bailout:

/* decide if the factor is of type numeric, integer, poly, transcend or variable

*  (see priorities)

*/

  for(i=0;i<fcnt;i++) {

    pp=factors[i].beg; pe=factors[i].end;

    if(myisdigit(*pp) || *pp=='.') {

      for(pt=pp;pt<pe && myisdigit(*pt);pt++);

      if(pt<pe) factors[i].type=type_numeric; // digits with a point

      else factors[i].type=type_integer;  // digits without point

      continue;

    }

    if(*pp=='(') {

      factors[i].type=type_poly; continue; //there exists a parenthesis

    }

    pt=strchr(pp,'(');

    if(pt!=NULL && pt<pe) factors[i].type=type_transcend; //??

    else factors[i].type=type_var;  // variable in other cases

  }

  dentype=-1;

  for(i=0;i<fcnt;i++) if(factors[i].side<0 && factors[i].type>dentype)

    dentype=factors[i].type; // denominator type will be compared to the type of the factors

  dencnt=numcnt=neucnt=0;

  for(i=0;i<fcnt;i++) {

    if(factors[i].type>dentype) neutral[neucnt++]=factors+i;

    else {

      if(factors[i].side>0) numerator[numcnt++]=factors+i;

      else denominator[dencnt++]=factors+i;

    }

  }

  if(dencnt>0) qsort(denominator,dencnt,sizeof(denominator[0]),fsort);

  if(numcnt>0) qsort(numerator,numcnt,sizeof(numerator[0]),fsort);

  if(neucnt>0) qsort(neutral,neucnt,sizeof(neutral[0]),fsort);

  if(sign>0 && num>0 && rel==0) tprint(" +");

  if(sign<0) tprint(" -");

  if(fcnt<1) tprint("1 "); // no factors why 1 - don't remove the 1 if [1,2;3,4], the 1 is useful?

  if(dencnt>0) {

    tprint(" {\\frac{");

    if(numcnt==0) tprint(" 1"); // no numerator ? will write {1 over denominator}

    else {/* numerator */

      if(numcnt==1 && *numerator[0]->beg=='(' &&

          find_matching(numerator[0]->beg+1,')')==(numerator[0]->end)-1) {

        *(numerator[0]->end-1)=0;

        t_onestring(numerator[0]->beg+1);

        *(numerator[0]->end-1)=')';

      }

      else for(i=0; i<numcnt; i++) {t_onefactor(numerator[i],i);

      if(i<numcnt-1) tprint(" ");} /* add space between factors */

    }

    tprint(" }{ ");      /* Now denominator */

    if(dencnt==1 && *denominator[0]->beg=='(' &&

      find_matching(denominator[0]->beg+1,')')==(denominator[0]->end)-1) {

       *(denominator[0]->end-1)=0;

       t_onestring(denominator[0]->beg+1);

       *(denominator[0]->end-1)=')';

    }

    else for(i=0;i<dencnt;i++) {t_onefactor(denominator[i],i);

    if(i<dencnt-1) tprint(" ");} /* add space between factors */

    tprint("}} ");

  }

  for(i=0;i<neucnt;i++) {t_onefactor(neutral[i],i+dencnt);

  if(i<neucnt-1) tprint(" ");} /* add space between factors */

}

/* put exponential */

void t_exponential(char *pp)

{

  char *pe, *pt;

  int t=0;

  while(*pp && strchr("!'\"",*pp)!=NULL) {

    tprint("%c",*pp); pp++;

  }

  if(*pp=='^') pp++; else return;

  if(*pp=='(') {

    pe=find_matching(pp+1,')');

    if(*(pe+1)==0) {

      pp++;*pe=0;

      for(pt=pp;*pt && (isalnum(*pt) || *pt=='.');pt++);

      if(*pt==0) t=1;

    }

  }

  if(strlen(pp)==1 && t==0) tprint("^%s ",pp);

  else {

    tprint(" ^{"); if(t) tprint("(");

    t_onestring(pp);

    if(t) tprint(")");

    tprint("} ");

  }

}

void t_onefactor(struct afactor *fb, int num)

{

  char *p, *pe, lp, *rp, rp2, rpbuf[128];

  char fbuf[MAX_LINELEN+1], pbuf[MAX_LINELEN+1];

  int i;

  memmove(pbuf,fb->beg,fb->end-fb->beg);

  pbuf[fb->end-fb->beg]=0;

  if(num>0 && (myisdigit(pbuf[0]) || pbuf[0]=='.'))

    tprint("\\times ");

  rp2=')'; p=pbuf;

  if(strchr("({[",*p)!=NULL) {

  lp=*p; switch(lp) {

    case '(': rp2=')';  break;

    case '[': { /* verify for matrices */

      char *pt;

      pe=find_matching(p+1,']');

      for(pt=p+1;pt<pe;pt++) {

        switch(*pt) {

          case '(': pt=find_matching(pt+1,')'); break;

          case '[': pt=find_matching(pt+1,']'); break;

          case '{': pt=find_matching(pt+1,'}'); break;

          case '|': pt=find_matching(pt+1,'|'); break;

          case ',':

          case ';': goto out;

        }

      }

      out: if(*pt==';' || *pt==',') { /* is matrix of the form [ 1,2;5,6] */

        char mbuf[MAX_LINELEN+1];

        char *pp, *pt;

        p++; if(*pe) *pe++=0;

        tprint(" \\begin{pmatrix}");

        for(pp=p,i=0;*pp;pp=pt,i++) {

          pt=find_term_end(pp);

          memmove(mbuf,pp,pt-pp); mbuf[pt-pp]=0;

          t_oneterm(mbuf,i);

          if(*pt==',') {

            tprint(" &"); pt++; i=-1;

          }

          if(*pt==';') {

            tprint("\\cr "); pt++; i=-1;

          }

        }

        tprint(" \\end{pmatrix}"); goto expon;

      }

      rp2=']'; break;

    }

    case '{': { /* protected */

      pe=find_matching(p+1,'}');

      *pe=0;tprint(" %s} ",p);

      goto expon;

    }

  }

  tprint(" \\left%c",lp);

  snprintf(rpbuf,sizeof(rpbuf),"\\right%c ",rp2); rp=rpbuf;

  paren: p++;pe=find_matching(p,rp2); *pe=0;

  t_onestring(p); tprint(rp); pe++; goto expon;

  }

  pe=find_mathvar_end(p); while(*pe && strchr("'\"!",*pe)!=NULL) pe++;

  memmove(fbuf,p,pe-p); fbuf[pe-p]=0;

  if(myisdigit(*p) || *p=='.') putnumber(fbuf);