/* 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];
user_error("cmd_output_too_long");
}
/* 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("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;
}
}
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;
}
}
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;
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;}
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
}
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(" {");
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(" \\over "); /* 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;
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);
pe
=find_mathvar_end
(p
); while(*pe
&& strchr("'\"!",*pe
)!=NULL
) pe
++;
if(*pe=='(') {
p=pe;
/* search in list of math functions*/
i=search_list(tmathfn, tmathfn_no, sizeof(tmathfn[0]), fbuf);
if(i>=0) {
switch(tmathfn[i].expind) {
case 0: {
tprint(" %s",tmathfn[i].left);
rp=tmathfn[i].right; break;
}
case 1: {
tprint(" %s",tmathfn[i].left);
pe=find_matching(pe+1,')')+1;
if(*pe
&& strchr("^'\"!",*pe
)!=NULL
) {
t_exponential(pe); *pe=0;
}
tprint(" \\left("); rp=tmathfn[i].right;
break;
}
case 2: { /* routine */
p++;pe=find_matching(p,rp2); *pe=0;
tmathfn[i].routine(p);
pe++; goto expon;
}
default: rp=""; break;
}
}
else {
putvar(fbuf);
rp="\\right) "; tprint(" \\left(");
}
rp2=')'; goto paren;
}
else {
putvar(fbuf);
if(*pe=='_') {
char *ptt, buff[256];
tprint("_"); pe++;
if(*pe=='(') {
ptt=find_matching(pe+1,')'); if(ptt) ptt++;
}
else {
if(*pe=='{') {
ptt=find_matching(pe+1,'}'); if(ptt) ptt++;
}
else ptt=find_mathvar_end(pe);
}
if(ptt==NULL || ptt-pe>128) goto expon;
memmove(buff
,pe
,ptt
-pe
); buff
[ptt
-pe
]=0; pe
=ptt
;
strip_enclosing_par(buff);
tprint("{%s}",buff);
}
}
}
/* exponential */
expon
: if(*pe
&& strchr("^'\"!",*pe
)!=NULL
) t_exponential
(pe
);
}
void t_onestring(char *p)
{
char termbuf[MAX_LINELEN+1];
char *pp, *pe;
int i;
for(pp=p,i=0;*pp;pp=pe,i++) {
pe=find_term_end(pp);
memmove(termbuf
,pp
,pe
-pp
); termbuf
[pe
-pp
]=0;
t_oneterm(termbuf,i);
}
}
/* replace \pmatrix{ } by latex syntax \begin{pmatrix} .. \end{pmatrix} */
void _replace_matrix ( char *p , char *s_mat1, char *s_mat2 )
{
char pbuf[MAX_LINELEN];
while ( (p
= strstr(p
,s_mat1
)) ){
char *p2
= find_matching
(p
+strlen(s_mat1
),'}');
long len
= p2
-p
-strlen(s_mat1
);
if (!p2) { module_error("unmatched_parentheses"); return; }
p2 ++ ;
string_modify(p, p, p2, "\\begin{%s}%s\\end{%s}",s_mat2,pbuf,s_mat2);
}
}
/* translate raw math expression into TeX source */
void texmath(char *p)
{
char *pp;
_replace_matrix (p,"\\matrix{","matrix");
_replace_matrix (p,"\\pmatrix{","pmatrix");
if(strpbrk(p
,"{}\\")!=NULL
) return;
if(pp
>p
&& !isspace(*(pp
-1))) continue;
string_modify(p,pp,pp+2,"*neq*");
}
/* remove spaces */
for(pp=p; *pp; pp++) {
if(isspace(*pp
)) {ovlstrcpy
(pp
,pp
+1); pp
--;}
}
/* replace ** by ^ see __replace_badchar(p,"**", "^");*/
*pp='^'; ovlstrcpy(pp+1,pp+2);
}
if(check_parentheses(p,1)!=0) module_error("unmatched_parentheses");
texmathbuf[0]=0; t_onestring(p);
singlespace(texmathbuf);strip_trailing_spaces(texmathbuf);
mystrncpy(p,texmathbuf,MAX_LINELEN);
}