version 1.107, 2005/12/11 05:27:30 |
version 1.112, 2005/12/18 01:57:21 |
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* DEVELOPER SHALL HAVE NO LIABILITY IN CONNECTION WITH THE USE, |
* DEVELOPER SHALL HAVE NO LIABILITY IN CONNECTION WITH THE USE, |
* PERFORMANCE OR NON-PERFORMANCE OF THE SOFTWARE. |
* PERFORMANCE OR NON-PERFORMANCE OF THE SOFTWARE. |
* |
* |
* $OpenXM: OpenXM_contrib2/asir2000/builtin/strobj.c,v 1.106 2005/12/10 14:14:15 noro Exp $ |
* $OpenXM: OpenXM_contrib2/asir2000/builtin/strobj.c,v 1.111 2005/12/18 01:44:16 noro Exp $ |
*/ |
*/ |
#include "ca.h" |
#include "ca.h" |
#include "parse.h" |
#include "parse.h" |
Line 76 struct TeXSymbol { |
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Line 76 struct TeXSymbol { |
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#define IS_BINARYPWR(f) (((f)->id==I_BOP) &&(OPNAME(f)=='^')) |
#define IS_BINARYPWR(f) (((f)->id==I_BOP) &&(OPNAME(f)=='^')) |
#define IS_NARYADD(f) (((f)->id==I_NARYOP) &&(OPNAME(f)=='+')) |
#define IS_NARYADD(f) (((f)->id==I_NARYOP) &&(OPNAME(f)=='+')) |
#define IS_NARYMUL(f) (((f)->id==I_NARYOP) &&(OPNAME(f)=='*')) |
#define IS_NARYMUL(f) (((f)->id==I_NARYOP) &&(OPNAME(f)=='*')) |
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#define IS_MUL(f) (((f)->id==I_NARYOP||(f)->id==I_BOP) &&(OPNAME(f)=='*')) |
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extern char *parse_strp; |
extern char *parse_strp; |
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Line 92 void Pquotetotex(); |
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Line 93 void Pquotetotex(); |
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void Pquotetotex_env(); |
void Pquotetotex_env(); |
void Pflatten_quote(); |
void Pflatten_quote(); |
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void Pqt_is_integer(),Pqt_is_rational(),Pqt_is_number(); |
void Pqt_is_integer(),Pqt_is_rational(),Pqt_is_number(),Pqt_is_coef(); |
void Pqt_is_dependent(),Pqt_is_function(); |
void Pqt_is_dependent(),Pqt_is_function(),Pqt_is_var(); |
void Pqt_set_ord(); |
void Pqt_set_ord(),Pqt_set_coef(),Pqt_set_weight(); |
void Pqt_normalize(); |
void Pqt_normalize(); |
void Pnqt_comp(); |
void Pnqt_comp(),Pnqt_weight(); |
void Pnqt_match(); |
void Pnqt_match(); |
void Pnqt_match_rewrite(); |
void Pnqt_match_rewrite(); |
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Line 127 FNODE partial_eval(FNODE), fnode_to_nary(FNODE), fnode |
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Line 128 FNODE partial_eval(FNODE), fnode_to_nary(FNODE), fnode |
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FNODE nfnode_add(FNODE a1,FNODE a2,int expand); |
FNODE nfnode_add(FNODE a1,FNODE a2,int expand); |
FNODE nfnode_mul(FNODE a1,FNODE a2,int expand); |
FNODE nfnode_mul(FNODE a1,FNODE a2,int expand); |
FNODE nfnode_pwr(FNODE a1,FNODE a2,int expand); |
FNODE nfnode_pwr(FNODE a1,FNODE a2,int expand); |
FNODE nfnode_mul_coef(Num c,FNODE f,int expand); |
FNODE nfnode_mul_coef(Obj c,FNODE f,int expand); |
FNODE fnode_expand_pwr(FNODE f,int n,int expand); |
FNODE fnode_expand_pwr(FNODE f,int n,int expand); |
FNODE to_narymul(FNODE f); |
FNODE to_narymul(FNODE f); |
FNODE to_naryadd(FNODE f); |
FNODE to_naryadd(FNODE f); |
FNODE fnode_node_to_nary(ARF op,NODE n); |
FNODE fnode_node_to_nary(ARF op,NODE n); |
void fnode_base_exp(FNODE f,FNODE *bp,FNODE *ep); |
void fnode_base_exp(FNODE f,FNODE *bp,FNODE *ep); |
void fnode_coef_body(FNODE f,Num *cp,FNODE *bp); |
void fnode_coef_body(FNODE f,Obj *cp,FNODE *bp); |
FNODE nfnode_match_rewrite(FNODE f,FNODE p,FNODE c,FNODE a,int mode); |
FNODE nfnode_match_rewrite(FNODE f,FNODE p,FNODE c,FNODE a,int mode); |
FNODE fnode_apply(FNODE f,FNODE (*func)(),int expand); |
FNODE fnode_apply(FNODE f,FNODE (*func)(),int expand); |
FNODE fnode_normalize(FNODE f,int expand); |
FNODE fnode_normalize(FNODE f,int expand); |
Line 155 struct ftab str_tab[] = { |
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Line 156 struct ftab str_tab[] = { |
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{"string_to_tb",Pstring_to_tb,1}, |
{"string_to_tb",Pstring_to_tb,1}, |
{"get_quote_id",Pget_quote_id,1}, |
{"get_quote_id",Pget_quote_id,1}, |
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{"qt_is_var",Pqt_is_var,1}, |
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{"qt_is_coef",Pqt_is_coef,1}, |
{"qt_is_number",Pqt_is_number,1}, |
{"qt_is_number",Pqt_is_number,1}, |
{"qt_is_rational",Pqt_is_rational,1}, |
{"qt_is_rational",Pqt_is_rational,1}, |
{"qt_is_integer",Pqt_is_integer,1}, |
{"qt_is_integer",Pqt_is_integer,1}, |
{"qt_is_function",Pqt_is_function,1}, |
{"qt_is_function",Pqt_is_function,1}, |
{"qt_is_dependent",Pqt_is_dependent,2}, |
{"qt_is_dependent",Pqt_is_dependent,2}, |
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{"qt_set_coef",Pqt_set_coef,-1}, |
{"qt_set_ord",Pqt_set_ord,-1}, |
{"qt_set_ord",Pqt_set_ord,-1}, |
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{"qt_set_weight",Pqt_set_weight,-1}, |
{"qt_normalize",Pqt_normalize,-2}, |
{"qt_normalize",Pqt_normalize,-2}, |
{"qt_match",Pqt_match,2}, |
{"qt_match",Pqt_match,2}, |
{"nqt_match_rewrite",Pnqt_match_rewrite,3}, |
{"nqt_match_rewrite",Pnqt_match_rewrite,3}, |
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{"nqt_weight",Pnqt_weight,1}, |
{"nqt_comp",Pnqt_comp,2}, |
{"nqt_comp",Pnqt_comp,2}, |
{"nqt_match",Pnqt_match,-3}, |
{"nqt_match",Pnqt_match,-3}, |
{"qt_to_nbp",Pqt_to_nbp,1}, |
{"qt_to_nbp",Pqt_to_nbp,1}, |
Line 607 void Pqt_to_bin(NODE arg,QUOTE *rp) |
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Line 613 void Pqt_to_bin(NODE arg,QUOTE *rp) |
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MKQUOTE(*rp,f); |
MKQUOTE(*rp,f); |
} |
} |
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void Pqt_is_var(NODE arg,Q *rp) |
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{ |
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QUOTE q; |
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int ret; |
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q = (QUOTE)ARG0(arg); |
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asir_assert(q,O_QUOTE,"qt_is_var"); |
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ret = fnode_is_var(BDY(q)); |
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STOQ(ret,*rp); |
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} |
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void Pqt_is_coef(NODE arg,Q *rp) |
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{ |
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QUOTE q; |
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int ret; |
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q = (QUOTE)ARG0(arg); |
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asir_assert(q,O_QUOTE,"qt_is_coef"); |
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ret = fnode_is_coef(BDY(q)); |
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STOQ(ret,*rp); |
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} |
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void Pqt_is_number(NODE arg,Q *rp) |
void Pqt_is_number(NODE arg,Q *rp) |
{ |
{ |
QUOTE q; |
QUOTE q; |
Line 1404 void Pget_function_name(NODE arg,STRING *rp) |
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Line 1432 void Pget_function_name(NODE arg,STRING *rp) |
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} |
} |
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FNODE strip_paren(FNODE); |
FNODE strip_paren(FNODE); |
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void objtotex_tb(Obj obj,TB tb); |
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void fnodetotex_tb(FNODE f,TB tb) |
void fnodetotex_tb(FNODE f,TB tb) |
{ |
{ |
Line 1412 void fnodetotex_tb(FNODE f,TB tb) |
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Line 1441 void fnodetotex_tb(FNODE f,TB tb) |
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char *opname,*vname_conv,*prefix_conv; |
char *opname,*vname_conv,*prefix_conv; |
Obj obj; |
Obj obj; |
int i,len,allzero,elen,elen2,si; |
int i,len,allzero,elen,elen2,si; |
C cplx; |
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char *r; |
char *r; |
FNODE fi,f2,f1; |
FNODE fi,f2,f1; |
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Line 1480 void fnodetotex_tb(FNODE f,TB tb) |
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Line 1508 void fnodetotex_tb(FNODE f,TB tb) |
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write_tb("}",tb); |
write_tb("}",tb); |
break; |
break; |
case '^': |
case '^': |
fnodetotex_tb((FNODE)FA1(f),tb); |
f1 = (FNODE)FA1(f); |
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if ( fnode_is_var(f1) ) |
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fnodetotex_tb(f1,tb); |
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else { |
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write_tb("(",tb); |
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fnodetotex_tb(f1,tb); |
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write_tb(")",tb); |
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} |
write_tb("^{",tb); |
write_tb("^{",tb); |
fnodetotex_tb(strip_paren((FNODE)FA2(f)),tb); |
fnodetotex_tb(strip_paren((FNODE)FA2(f)),tb); |
write_tb("} ",tb); |
write_tb("} ",tb); |
Line 1497 void fnodetotex_tb(FNODE f,TB tb) |
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Line 1532 void fnodetotex_tb(FNODE f,TB tb) |
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break; |
break; |
case I_NARYOP: |
case I_NARYOP: |
args = (NODE)FA1(f); |
args = (NODE)FA1(f); |
write_tb("(",tb); |
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switch ( OPNAME(f) ) { |
switch ( OPNAME(f) ) { |
case '+': |
case '+': |
fnodetotex_tb((FNODE)BDY(args),tb); |
fnodetotex_tb((FNODE)BDY(args),tb); |
for ( args = NEXT(args); args; args = NEXT(args) ) { |
for ( args = NEXT(args); args; args = NEXT(args) ) { |
write_tb("+",tb); |
write_tb("+",tb); |
fnodetotex_tb((FNODE)BDY(args),tb); |
f1 = (FNODE)BDY(args); |
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if ( fnode_is_var(f1) || IS_MUL(f1) ) |
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fnodetotex_tb(f1,tb); |
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else { |
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write_tb("(",tb); |
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fnodetotex_tb(f1,tb); |
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write_tb(")",tb); |
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} |
} |
} |
break; |
break; |
case '*': |
case '*': |
f1 = (FNODE)BDY(args); |
f1 = (FNODE)BDY(args); |
if ( f1->id == I_FORMULA && MUNIQ(FA0(f1)) ) |
if ( f1->id == I_FORMULA && MUNIQ(FA0(f1)) ) { |
write_tb("-",tb); |
write_tb("- ",tb); args = NEXT(args); |
else |
} |
fnodetotex_tb(f1,tb); |
for ( ; args; args = NEXT(args) ) { |
write_tb(" ",tb); |
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for ( args = NEXT(args); args; args = NEXT(args) ) { |
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/* XXX special care for DP */ |
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f2 = (FNODE)BDY(args); |
f2 = (FNODE)BDY(args); |
if ( f2->id == I_EV ) { |
if ( fnode_is_var(f2) || IS_BINARYPWR(f2) ) |
n = (NODE)FA0(f2); |
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for ( i = 0; n; n = NEXT(n), i++ ) { |
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fi = (FNODE)BDY(n); |
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if ( fi->id != I_FORMULA || FA0(fi) ) |
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break; |
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} |
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if ( n ) |
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fnodetotex_tb(f2,tb); |
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} else |
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fnodetotex_tb(f2,tb); |
fnodetotex_tb(f2,tb); |
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else { |
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write_tb("(",tb); |
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fnodetotex_tb(f2,tb); |
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write_tb(")",tb); |
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} |
} |
} |
break; |
break; |
default: |
default: |
error("invalid nary op"); |
error("invalid nary op"); |
break; |
break; |
} |
} |
write_tb(")",tb); |
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break; |
break; |
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case I_COP: |
case I_COP: |
Line 1758 void fnodetotex_tb(FNODE f,TB tb) |
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Line 1791 void fnodetotex_tb(FNODE f,TB tb) |
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/* internal object */ |
/* internal object */ |
case I_FORMULA: |
case I_FORMULA: |
obj = (Obj)FA0(f); |
objtotex_tb((Obj)FA0(f),tb); |
if ( !obj ) |
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write_tb("0",tb); |
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else if ( OID(obj) == O_N && NID(obj) == N_C ) { |
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cplx = (C)obj; |
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write_tb("(",tb); |
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if ( cplx->r ) { |
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r = objtostr((Obj)cplx->r); write_tb(r,tb); |
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} |
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if ( cplx->i ) { |
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if ( cplx->r && compnum(0,cplx->i,0) > 0 ) { |
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write_tb("+",tb); |
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if ( !UNIQ(cplx->i) ) { |
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r = objtostr((Obj)cplx->i); write_tb(r,tb); |
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} |
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} else if ( MUNIQ(cplx->i) ) |
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write_tb("-",tb); |
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else if ( !UNIQ(cplx->i) ) { |
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r = objtostr((Obj)cplx->i); write_tb(r,tb); |
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} |
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write_tb("\\sqrt{-1}",tb); |
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} |
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write_tb(")",tb); |
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} else if ( OID(obj) == O_P ) |
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write_tb(conv_rule(VR((P)obj)->name),tb); |
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else |
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write_tb(objtostr(obj),tb); |
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break; |
break; |
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/* program variable */ |
/* program variable */ |
Line 1800 void fnodetotex_tb(FNODE f,TB tb) |
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Line 1807 void fnodetotex_tb(FNODE f,TB tb) |
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} |
} |
} |
} |
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void objtotex_tb(Obj obj,TB tb) |
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{ |
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C cplx; |
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char *r; |
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P t; |
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DCP dc; |
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char *v; |
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if ( !obj ) { |
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write_tb("0",tb); |
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return; |
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} |
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switch ( OID(obj) ) { |
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case O_N: |
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switch ( NID(obj) ) { |
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case N_C: |
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cplx = (C)obj; |
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write_tb("(",tb); |
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if ( cplx->r ) { |
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r = objtostr((Obj)cplx->r); write_tb(r,tb); |
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} |
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if ( cplx->i ) { |
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if ( cplx->r && compnum(0,cplx->i,0) > 0 ) { |
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write_tb("+",tb); |
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if ( !UNIQ(cplx->i) ) { |
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r = objtostr((Obj)cplx->i); write_tb(r,tb); |
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} |
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} else if ( MUNIQ(cplx->i) ) |
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write_tb("-",tb); |
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else if ( !UNIQ(cplx->i) ) { |
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r = objtostr((Obj)cplx->i); write_tb(r,tb); |
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} |
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write_tb("\\sqrt{-1}",tb); |
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} |
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write_tb(")",tb); |
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break; |
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default: |
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write_tb(objtostr(obj),tb); |
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break; |
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} |
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break; |
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case O_P: |
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v = conv_rule(VR((P)obj)->name); |
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for ( dc = DC((P)obj); dc; dc = NEXT(dc) ) { |
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if ( !DEG(dc) ) |
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objtotex_tb((Obj)COEF(dc),tb); |
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else { |
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if ( NUM(COEF(dc)) && UNIQ((Q)COEF(dc)) ) |
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; |
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else if ( NUM(COEF(dc)) && MUNIQ((Q)COEF(dc)) ) |
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write_tb("-",tb); |
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else if ( NUM(COEF(dc)) || !NEXT(DC(COEF(dc)))) |
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objtotex_tb((Obj)COEF(dc),tb); |
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else { |
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write_tb("(",tb); objtotex_tb((Obj)COEF(dc),tb); |
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write_tb(")",tb); |
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} |
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write_tb(v,tb); |
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if ( cmpq(DEG(dc),ONE) ) { |
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write_tb("^",tb); |
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if ( INT(DEG(dc)) && SGN(DEG(dc))>0 ) { |
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write_tb("{",tb); |
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objtotex_tb((Obj)DEG(dc),tb); |
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write_tb("}",tb); |
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} else { |
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write_tb("{",tb); objtotex_tb((Obj)DEG(dc),tb); |
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write_tb("}",tb); |
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} |
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} |
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} |
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if ( NEXT(dc) ) { |
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t = COEF(NEXT(dc)); |
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if ( !DEG(NEXT(dc)) ) { |
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if ( NUM(t) ) { |
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if ( !mmono(t) ) write_tb("+",tb); |
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} else { |
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if ( !mmono(COEF(DC(t))) ) write_tb("+",tb); |
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} |
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} else { |
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if ( !mmono(t) ) write_tb("+",tb); |
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} |
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} |
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} |
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break; |
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case O_R: |
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write_tb("\\frac{",tb); |
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objtotex_tb((Obj)NM((R)obj),tb); |
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write_tb("}{",tb); |
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objtotex_tb((Obj)DN((R)obj),tb); |
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write_tb("}",tb); |
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break; |
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default: |
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write_tb(objtostr(obj),tb); |
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break; |
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} |
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} |
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char *objtostr(Obj obj) |
char *objtostr(Obj obj) |
{ |
{ |
int len; |
int len; |
Line 1915 int top_is_minus(FNODE f) |
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Line 2019 int top_is_minus(FNODE f) |
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case O_N: |
case O_N: |
return mmono((P)obj); |
return mmono((P)obj); |
case O_P: |
case O_P: |
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#if 0 |
/* must be a variable */ |
/* must be a variable */ |
opname = conv_rule(VR((P)obj)->name); |
opname = conv_rule(VR((P)obj)->name); |
return opname[0]=='-'; |
return opname[0]=='-'; |
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#else |
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return mmono((P)obj); |
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#endif |
default: |
default: |
/* ??? */ |
/* ??? */ |
len = estimate_length(CO,obj); |
len = estimate_length(CO,obj); |
Line 2141 VL reordvars(VL vl0,NODE head) |
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Line 2249 VL reordvars(VL vl0,NODE head) |
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return vl; |
return vl; |
} |
} |
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VL qt_current_ord; |
struct wtab { |
LIST qt_current_ord_obj; |
V v; |
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int w; |
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}; |
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struct wtab *qt_weight_tab; |
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VL qt_current_ord, qt_current_coef; |
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LIST qt_current_ord_obj,qt_current_coef_obj,qt_current_weight_obj; |
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LIST qt_current_weight_obj; |
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void Pqt_set_ord(NODE arg,LIST *rp) |
void Pqt_set_ord(NODE arg,LIST *rp) |
{ |
{ |
NODE r0,r; |
NODE r0,r; |
Line 2152 void Pqt_set_ord(NODE arg,LIST *rp) |
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Line 2267 void Pqt_set_ord(NODE arg,LIST *rp) |
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if ( !argc(arg) ) |
if ( !argc(arg) ) |
*rp = qt_current_ord_obj; |
*rp = qt_current_ord_obj; |
else { |
else if ( !ARG0(arg) ) { |
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qt_current_ord_obj = 0; |
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qt_current_ord = 0; |
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} else { |
qt_current_ord = reordvars(CO,BDY((LIST)ARG0(arg))); |
qt_current_ord = reordvars(CO,BDY((LIST)ARG0(arg))); |
for ( r0 = 0, vl = qt_current_ord; vl; vl = NEXT(vl) ) { |
for ( r0 = 0, vl = qt_current_ord; vl; vl = NEXT(vl) ) { |
NEXTNODE(r0,r); MKV(vl->v,v); BDY(r) = v; |
NEXTNODE(r0,r); MKV(vl->v,v); BDY(r) = v; |
Line 2163 void Pqt_set_ord(NODE arg,LIST *rp) |
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Line 2281 void Pqt_set_ord(NODE arg,LIST *rp) |
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} |
} |
} |
} |
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void Pqt_set_weight(NODE arg,LIST *rp) |
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{ |
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NODE n,pair; |
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int l,i; |
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struct wtab *tab; |
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if ( !argc(arg) ) |
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*rp = qt_current_weight_obj; |
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else if ( !ARG0(arg) ) { |
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qt_current_weight_obj = 0; |
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qt_weight_tab = 0; |
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} else { |
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n = BDY((LIST)ARG0(arg)); |
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l = length(n); |
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tab = qt_weight_tab = (struct wtab *)MALLOC((l+1)*sizeof(struct wtab)); |
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for ( i = 0; i < l; i++, n = NEXT(n) ) { |
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pair = BDY((LIST)BDY(n)); |
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tab[i].v = VR((P)ARG0(pair)); |
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tab[i].w = QTOS((Q)ARG1(pair)); |
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} |
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tab[i].v = 0; |
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qt_current_weight_obj = (LIST)ARG0(arg); |
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*rp = qt_current_weight_obj; |
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} |
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} |
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void Pqt_set_coef(NODE arg,LIST *rp) |
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{ |
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NODE r0,r,n; |
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VL vl0,vl; |
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P v; |
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if ( !argc(arg) ) |
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*rp = qt_current_coef_obj; |
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else if ( !ARG0(arg) ) { |
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qt_current_coef_obj = 0; |
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qt_current_coef = 0; |
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} else { |
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n = BDY((LIST)ARG0(arg)); |
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for ( vl0 = 0, r0 = 0; n; n = NEXT(n) ) { |
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NEXTNODE(r0,r); |
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NEXTVL(vl0,vl); |
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vl->v = VR((P)BDY(n)); |
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MKV(vl->v,v); BDY(r) = v; |
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} |
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if ( r0 ) NEXT(r) = 0; |
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if ( vl0 ) NEXT(vl) = 0; |
|
qt_current_coef = vl0; |
|
MKLIST(*rp,r0); |
|
qt_current_coef_obj = *rp; |
|
} |
|
} |
|
|
void Pqt_normalize(NODE arg,QUOTE *rp) |
void Pqt_normalize(NODE arg,QUOTE *rp) |
{ |
{ |
QUOTE q,r; |
QUOTE q,r; |
Line 2414 NBP fnode_to_nbp(FNODE f) |
|
Line 2585 NBP fnode_to_nbp(FNODE f) |
|
} |
} |
} |
} |
|
|
|
void Pnqt_weight(NODE arg,Q *rp) |
|
{ |
|
QUOTE q; |
|
FNODE f; |
|
int w; |
|
|
|
q = (QUOTE)ARG0(arg); f = (FNODE)BDY(q); |
|
f = fnode_normalize(f,0); |
|
w = nfnode_weight(qt_weight_tab,f); |
|
STOQ(w,*rp); |
|
} |
|
|
void Pnqt_comp(NODE arg,Q *rp) |
void Pnqt_comp(NODE arg,Q *rp) |
{ |
{ |
QUOTE q1,q2; |
QUOTE q1,q2; |
Line 2428 void Pnqt_comp(NODE arg,Q *rp) |
|
Line 2611 void Pnqt_comp(NODE arg,Q *rp) |
|
STOQ(r,*rp); |
STOQ(r,*rp); |
} |
} |
|
|
INLINE int fnode_is_number(FNODE f) |
int fnode_is_var(FNODE f) |
{ |
{ |
Obj obj; |
Obj obj; |
|
VL vl,t,s; |
|
DCP dc; |
|
|
|
if ( fnode_is_coef(f) ) return 0; |
switch ( f->id ) { |
switch ( f->id ) { |
|
case I_PAREN: |
|
return fnode_is_var(FA0(f)); |
|
|
|
case I_FORMULA: |
|
obj = FA0(f); |
|
if ( obj && OID(obj) == O_P ) { |
|
dc = DC((P)obj); |
|
if ( !cmpq(DEG(dc),ONE) && !NEXT(dc) |
|
&& !arf_comp(CO,(Obj)COEF(dc),(Obj)ONE) ) return 1; |
|
else return 0; |
|
} else return 0; |
|
|
|
default: |
|
return 0; |
|
} |
|
} |
|
|
|
int fnode_is_coef(FNODE f) |
|
{ |
|
Obj obj; |
|
VL vl,t,s; |
|
|
|
switch ( f->id ) { |
case I_MINUS: case I_PAREN: |
case I_MINUS: case I_PAREN: |
|
return fnode_is_coef(FA0(f)); |
|
|
|
case I_FORMULA: |
|
obj = FA0(f); |
|
if ( !obj ) return 1; |
|
else if ( OID(obj) == O_QUOTE ) |
|
return fnode_is_coef(BDY((QUOTE)obj)); |
|
else if ( NUM(obj) ) return 1; |
|
else if ( OID(obj) == O_P || OID(obj) == O_R) { |
|
get_vars_recursive(obj,&vl); |
|
for ( t = vl; t; t = NEXT(t) ) { |
|
if ( t->v->attr == (pointer)V_PF ) continue; |
|
for ( s = qt_current_coef; s; s = NEXT(s) ) |
|
if ( t->v == s->v ) break; |
|
if ( !s ) |
|
return 0; |
|
} |
|
return 1; |
|
} else return 0; |
|
|
|
case I_BOP: |
|
return fnode_is_coef(FA1(f)) && fnode_is_coef(FA2(f)); |
|
|
|
default: |
|
return 0; |
|
} |
|
} |
|
|
|
int fnode_is_number(FNODE f) |
|
{ |
|
Obj obj; |
|
|
|
switch ( f->id ) { |
|
case I_MINUS: case I_PAREN: |
return fnode_is_number(FA0(f)); |
return fnode_is_number(FA0(f)); |
|
|
case I_FORMULA: |
case I_FORMULA: |
Line 2588 FNODE fnode_normalize(FNODE f,int expand) |
|
Line 2831 FNODE fnode_normalize(FNODE f,int expand) |
|
break; |
break; |
|
|
case I_MINUS: |
case I_MINUS: |
r = nfnode_mul_coef((Num)q, |
r = nfnode_mul_coef((Obj)q, |
fnode_normalize(FA0(f),expand),expand); |
fnode_normalize(FA0(f),expand),expand); |
break; |
break; |
|
|
Line 2601 FNODE fnode_normalize(FNODE f,int expand) |
|
Line 2844 FNODE fnode_normalize(FNODE f,int expand) |
|
r = nfnode_add(a1,a2,expand); |
r = nfnode_add(a1,a2,expand); |
break; |
break; |
case '-': |
case '-': |
a2 = nfnode_mul_coef((Num)q,a2,expand); |
a2 = nfnode_mul_coef((Obj)q,a2,expand); |
r = nfnode_add(a1,a2,expand); |
r = nfnode_add(a1,a2,expand); |
break; |
break; |
case '*': |
case '*': |
Line 2688 FNODE nfnode_add(FNODE f1,FNODE f2,int expand) |
|
Line 2931 FNODE nfnode_add(FNODE f1,FNODE f2,int expand) |
|
NODE n1,n2,r0,r; |
NODE n1,n2,r0,r; |
FNODE b1,b2; |
FNODE b1,b2; |
int s; |
int s; |
Num c1,c2,c; |
Obj c1,c2,c; |
|
|
if ( IS_ZERO(f1) ) return f2; |
if ( IS_ZERO(f1) ) return f2; |
else if ( IS_ZERO(f2) ) return f1; |
else if ( IS_ZERO(f2) ) return f1; |
Line 2702 FNODE nfnode_add(FNODE f1,FNODE f2,int expand) |
|
Line 2945 FNODE nfnode_add(FNODE f1,FNODE f2,int expand) |
|
} else if ( s < 0 ) { |
} else if ( s < 0 ) { |
NEXTNODE(r0,r); BDY(r) = BDY(n2); n2 = NEXT(n2); |
NEXTNODE(r0,r); BDY(r) = BDY(n2); n2 = NEXT(n2); |
} else { |
} else { |
addnum(0,c1,c2,&c); |
arf_add(CO,c1,c2,&c); |
if ( c ) { |
if ( c ) { |
NEXTNODE(r0,r); BDY(r) = nfnode_mul_coef(c,b1,expand); |
NEXTNODE(r0,r); BDY(r) = nfnode_mul_coef(c,b1,expand); |
} |
} |
Line 2738 FNODE nfnode_mul(FNODE f1,FNODE f2,int expand) |
|
Line 2981 FNODE nfnode_mul(FNODE f1,FNODE f2,int expand) |
|
FNODE b1,b2,e1,e2,cc,t,t1; |
FNODE b1,b2,e1,e2,cc,t,t1; |
FNODE *m; |
FNODE *m; |
int s; |
int s; |
Num c1,c2,c,e; |
Obj c1,c2,c,e; |
int l1,l,i,j; |
int l1,l,i,j; |
|
|
if ( IS_ZERO(f1) || IS_ZERO(f2) ) return mkfnode(1,I_FORMULA,0); |
if ( IS_ZERO(f1) || IS_ZERO(f2) ) return mkfnode(1,I_FORMULA,0); |
else if ( fnode_is_number(f1) ) |
else if ( fnode_is_coef(f1) ) |
return nfnode_mul_coef((Num)eval(f1),f2,expand); |
return nfnode_mul_coef((Obj)eval(f1),f2,expand); |
else if ( fnode_is_number(f2) ) |
else if ( fnode_is_coef(f2) ) |
return nfnode_mul_coef((Num)eval(f2),f1,expand); |
return nfnode_mul_coef((Obj)eval(f2),f1,expand); |
|
|
if ( expand && IS_NARYADD(f1) ) { |
if ( expand && IS_NARYADD(f1) ) { |
t = mkfnode(1,I_FORMULA,0); |
t = mkfnode(1,I_FORMULA,0); |
Line 2765 FNODE nfnode_mul(FNODE f1,FNODE f2,int expand) |
|
Line 3008 FNODE nfnode_mul(FNODE f1,FNODE f2,int expand) |
|
} |
} |
|
|
fnode_coef_body(f1,&c1,&b1); fnode_coef_body(f2,&c2,&b2); |
fnode_coef_body(f1,&c1,&b1); fnode_coef_body(f2,&c2,&b2); |
mulnum(0,c1,c2,&c); |
arf_mul(CO,c1,c2,&c); |
if ( !c ) return mkfnode(1,I_FORMULA,0); |
if ( !c ) return mkfnode(1,I_FORMULA,0); |
|
|
|
|
Line 2779 FNODE nfnode_mul(FNODE f1,FNODE f2,int expand) |
|
Line 3022 FNODE nfnode_mul(FNODE f1,FNODE f2,int expand) |
|
else { |
else { |
fnode_base_exp(m[i-1],&b1,&e1); fnode_base_exp(BDY(r),&b2,&e2); |
fnode_base_exp(m[i-1],&b1,&e1); fnode_base_exp(BDY(r),&b2,&e2); |
if ( compfnode(b1,b2) ) break; |
if ( compfnode(b1,b2) ) break; |
addnum(0,eval(e1),eval(e2),&e); |
arf_add(CO,eval(e1),eval(e2),&e); |
if ( !e ) i--; |
if ( !e ) i--; |
else if ( UNIQ(e) ) |
else if ( UNIQ(e) ) |
m[i-1] = b1; |
m[i-1] = b1; |
Line 2799 FNODE nfnode_mul(FNODE f1,FNODE f2,int expand) |
|
Line 3042 FNODE nfnode_mul(FNODE f1,FNODE f2,int expand) |
|
FNODE nfnode_pwr(FNODE f1,FNODE f2,int expand) |
FNODE nfnode_pwr(FNODE f1,FNODE f2,int expand) |
{ |
{ |
FNODE b,b1,e1,e,cc,r,mf2,mone,inv; |
FNODE b,b1,e1,e,cc,r,mf2,mone,inv; |
Num c,c1,nf2; |
Obj c,c1; |
|
Num nf2; |
int ee; |
int ee; |
NODE arg,n,t0,t1; |
NODE arg,n,t0,t1; |
Q q; |
Q q; |
|
|
if ( IS_ZERO(f2) ) return mkfnode(1,I_FORMULA,ONE); |
if ( IS_ZERO(f2) ) return mkfnode(1,I_FORMULA,ONE); |
else if ( IS_ZERO(f1) ) return mkfnode(1,I_FORMULA,0); |
else if ( IS_ZERO(f1) ) return mkfnode(1,I_FORMULA,0); |
else if ( fnode_is_number(f1) ) { |
else if ( fnode_is_coef(f1) ) { |
if ( fnode_is_integer(f2) ) { |
if ( fnode_is_integer(f2) ) { |
if ( fnode_is_one(f2) ) return f1; |
if ( fnode_is_one(f2) ) return f1; |
else { |
else { |
pwrnum(0,(Num)eval(f1),(Num)eval(f2),&c); |
arf_pwr(CO,eval(f1),(Obj)eval(f2),&c); |
return mkfnode(1,I_FORMULA,c); |
return mkfnode(1,I_FORMULA,c); |
} |
} |
} else |
} else { |
|
f1 = mkfnode(1,I_FORMULA,eval(f1)); |
return mkfnode(3,I_BOP,pwrfs,f1,f2); |
return mkfnode(3,I_BOP,pwrfs,f1,f2); |
|
} |
} else if ( IS_BINARYPWR(f1) ) { |
} else if ( IS_BINARYPWR(f1) ) { |
b1 = FA1(f1); e1 = FA2(f1); |
b1 = FA1(f1); e1 = FA2(f1); |
e = nfnode_mul(e1,f2,expand); |
e = nfnode_mul(e1,f2,expand); |
Line 2826 FNODE nfnode_pwr(FNODE f1,FNODE f2,int expand) |
|
Line 3072 FNODE nfnode_pwr(FNODE f1,FNODE f2,int expand) |
|
&& fnode_is_integer(f2) ) { |
&& fnode_is_integer(f2) ) { |
fnode_coef_body(f1,&c1,&b1); |
fnode_coef_body(f1,&c1,&b1); |
nf2 = (Num)eval(f2); |
nf2 = (Num)eval(f2); |
pwrnum(0,(Num)c1,nf2,&c); |
arf_pwr(CO,c1,(Obj)nf2,&c); |
ee = QTOS((Q)nf2); |
ee = QTOS((Q)nf2); |
cc = mkfnode(1,I_FORMULA,c); |
cc = mkfnode(1,I_FORMULA,c); |
if ( fnode_is_nonnegative_integer(f2) ) |
if ( fnode_is_nonnegative_integer(f2) ) |
Line 2918 FNODE to_narymul(FNODE f) |
|
Line 3164 FNODE to_narymul(FNODE f) |
|
return r; |
return r; |
} |
} |
|
|
FNODE nfnode_mul_coef(Num c,FNODE f,int expand) |
FNODE nfnode_mul_coef(Obj c,FNODE f,int expand) |
{ |
{ |
FNODE b1,cc; |
FNODE b1,cc; |
Num c1,c2; |
Obj c1,c2; |
NODE n,r,r0; |
NODE n,r,r0; |
|
|
if ( !c ) |
if ( !c ) |
return mkfnode(I_FORMULA,0); |
return mkfnode(I_FORMULA,0); |
else { |
else { |
fnode_coef_body(f,&c1,&b1); |
fnode_coef_body(f,&c1,&b1); |
mulnum(0,c,c1,&c2); |
arf_mul(CO,c,c1,&c2); |
if ( UNIQ(c2) ) return b1; |
if ( UNIQ(c2) ) return b1; |
else { |
else { |
cc = mkfnode(1,I_FORMULA,c2); |
cc = mkfnode(1,I_FORMULA,c2); |
Line 2953 FNODE nfnode_mul_coef(Num c,FNODE f,int expand) |
|
Line 3199 FNODE nfnode_mul_coef(Num c,FNODE f,int expand) |
|
} |
} |
} |
} |
|
|
void fnode_coef_body(FNODE f,Num *cp,FNODE *bp) |
void fnode_coef_body(FNODE f,Obj *cp,FNODE *bp) |
{ |
{ |
FNODE c; |
FNODE c; |
|
|
if ( fnode_is_number(f) ) { |
if ( fnode_is_coef(f) ) { |
*cp = eval(f); *bp = mkfnode(1,I_FORMULA,ONE); |
*cp = (Obj)eval(f); *bp = mkfnode(1,I_FORMULA,ONE); |
} else if ( IS_NARYMUL(f) ) { |
} else if ( IS_NARYMUL(f) ) { |
c=(FNODE)BDY((NODE)FA1(f)); |
c=(FNODE)BDY((NODE)FA1(f)); |
if ( fnode_is_number(c) ) { |
if ( fnode_is_coef(c) ) { |
*cp = eval(c); |
*cp = (Obj)eval(c); |
*bp = fnode_node_to_nary(mulfs,NEXT((NODE)FA1(f))); |
*bp = fnode_node_to_nary(mulfs,NEXT((NODE)FA1(f))); |
} else { |
} else { |
*cp = (Num)ONE; *bp = f; |
*cp = (Obj)ONE; *bp = f; |
} |
} |
} else { |
} else { |
*cp = (Num)ONE; *bp = f; |
*cp = (Obj)ONE; *bp = f; |
} |
} |
} |
} |
|
|
int nfnode_comp_pwr(FNODE f1,FNODE f2); |
int nfnode_weight(struct wtab *tab,FNODE f) |
|
{ |
|
NODE n; |
|
int w,w1; |
|
int i; |
|
Q a2; |
|
V v; |
|
|
|
switch ( f->id ) { |
|
case I_FORMULA: |
|
if ( fnode_is_coef(f) ) return 0; |
|
else if ( fnode_is_var(f) ) { |
|
if ( !tab ) return 1; |
|
v = VR((P)FA0(f)); |
|
for ( i = 0; tab[i].v; i++ ) |
|
if ( v == tab[i].v ) return tab[i].w; |
|
return 1; |
|
} else return 0; |
|
|
|
/* XXX */ |
|
case I_PVAR: return 1; |
|
/* XXX */ |
|
case I_FUNC: I_FUNC: I_FUNC_QARG: |
|
/* w(f) = 1 */ |
|
/* w(f(a1,...,an)=w(a1)+...+w(an) */ |
|
n = FA0((FNODE)FA1(f)); |
|
for ( w = 0; n; n = NEXT(n) ) |
|
w += nfnode_weight(tab,BDY(n)); |
|
return w; |
|
case I_NARYOP: |
|
n = (NODE)FA1(f); |
|
if ( IS_NARYADD(f) ) |
|
for ( w = nfnode_weight(tab,BDY(n)), |
|
n = NEXT(n); n; n = NEXT(n) ) { |
|
w1 = nfnode_weight(tab,BDY(n)); |
|
w = MAX(w,w1); |
|
} |
|
else |
|
for ( w = 0; n; n = NEXT(n) ) |
|
w += nfnode_weight(tab,BDY(n)); |
|
return w; |
|
case I_BOP: |
|
/* must be binary power */ |
|
/* XXX w(2^x)=0 ? */ |
|
if ( fnode_is_rational(FA2(f)) ) { |
|
a2 = (Q)eval(FA2(f)); |
|
w = QTOS(a2); |
|
} else |
|
w = nfnode_weight(tab,FA2(f)); |
|
return nfnode_weight(tab,FA1(f))*w; |
|
default: |
|
error("nfnode_weight : not_implemented"); |
|
} |
|
} |
|
|
int nfnode_comp(FNODE f1,FNODE f2) |
int nfnode_comp(FNODE f1,FNODE f2) |
{ |
{ |
|
int w1,w2; |
|
|
|
if ( qt_weight_tab ) { |
|
w1 = nfnode_weight(qt_weight_tab,f1); |
|
w2 = nfnode_weight(qt_weight_tab,f2); |
|
if ( w1 > w2 ) return 1; |
|
if ( w1 < w2 ) return -1; |
|
} |
|
return nfnode_comp_lex(f1,f2); |
|
} |
|
|
|
int nfnode_comp_lex(FNODE f1,FNODE f2) |
|
{ |
NODE n1,n2; |
NODE n1,n2; |
int r,i1,i2,ret; |
int r,i1,i2,ret; |
char *nm1,*nm2; |
char *nm1,*nm2; |
FNODE b1,b2,e1,e2,g,a1,a2,fn1,fn2; |
FNODE b1,b2,e1,e2,g,a1,a2,fn1,fn2; |
Num ee,ee1,c1,c2; |
Num ee,ee1; |
|
Obj c1,c2; |
|
int w1,w2; |
|
|
if ( IS_NARYADD(f1) || IS_NARYADD(f2) ) { |
if ( IS_NARYADD(f1) || IS_NARYADD(f2) ) { |
f1 = to_naryadd(f1); f2 = to_naryadd(f2); |
f1 = to_naryadd(f1); f2 = to_naryadd(f2); |
n1 = (NODE)FA1(f1); n2 = (NODE)FA1(f2); |
n1 = (NODE)FA1(f1); n2 = (NODE)FA1(f2); |
while ( n1 && n2 ) |
while ( n1 && n2 ) |
if ( r = nfnode_comp(BDY(n1),BDY(n2)) ) return r; |
if ( r = nfnode_comp_lex(BDY(n1),BDY(n2)) ) return r; |
else { |
else { |
n1 = NEXT(n1); n2 = NEXT(n2); |
n1 = NEXT(n1); n2 = NEXT(n2); |
} |
} |
Line 2995 int nfnode_comp(FNODE f1,FNODE f2) |
|
Line 3309 int nfnode_comp(FNODE f1,FNODE f2) |
|
if ( IS_NARYMUL(f1) || IS_NARYMUL(f2) ) { |
if ( IS_NARYMUL(f1) || IS_NARYMUL(f2) ) { |
fnode_coef_body(f1,&c1,&b1); |
fnode_coef_body(f1,&c1,&b1); |
fnode_coef_body(f2,&c2,&b2); |
fnode_coef_body(f2,&c2,&b2); |
if ( !compfnode(b1,b2) ) return compnum(0,c1,c2); |
if ( !compfnode(b1,b2) ) return arf_comp(CO,c1,c2); |
b1 = to_narymul(b1); b2 = to_narymul(b2); |
b1 = to_narymul(b1); b2 = to_narymul(b2); |
n1 = (NODE)FA1(b1); n2 = (NODE)FA1(b2); |
n1 = (NODE)FA1(b1); n2 = (NODE)FA1(b2); |
while ( 1 ) { |
while ( 1 ) { |
Line 3008 int nfnode_comp(FNODE f1,FNODE f2) |
|
Line 3322 int nfnode_comp(FNODE f1,FNODE f2) |
|
fnode_base_exp(BDY(n1),&b1,&e1); |
fnode_base_exp(BDY(n1),&b1,&e1); |
fnode_base_exp(BDY(n2),&b2,&e2); |
fnode_base_exp(BDY(n2),&b2,&e2); |
|
|
if ( r = nfnode_comp(b1,b2) ) { |
if ( r = nfnode_comp_lex(b1,b2) ) { |
if ( r > 0 ) |
if ( r > 0 ) |
return nfnode_comp(e1,mkfnode(1,I_FORMULA,0)); |
return nfnode_comp_lex(e1,mkfnode(1,I_FORMULA,0)); |
else if ( r < 0 ) |
else if ( r < 0 ) |
return nfnode_comp(mkfnode(1,I_FORMULA,0),e2); |
return nfnode_comp_lex(mkfnode(1,I_FORMULA,0),e2); |
} else { |
} else { |
n1 = NEXT(n1); n2 = NEXT(n2); |
n1 = NEXT(n1); n2 = NEXT(n2); |
if ( fnode_is_number(e1) && fnode_is_number(e2) ) { |
if ( fnode_is_number(e1) && fnode_is_number(e2) ) { |
Line 3028 int nfnode_comp(FNODE f1,FNODE f2) |
|
Line 3342 int nfnode_comp(FNODE f1,FNODE f2) |
|
MKNODE(n2,g,n2); |
MKNODE(n2,g,n2); |
} |
} |
} else { |
} else { |
r = nfnode_comp(e1,e2); |
r = nfnode_comp_lex(e1,e2); |
if ( r > 0 ) return 1; |
if ( r > 0 ) return 1; |
else if ( r < 0 ) return -1; |
else if ( r < 0 ) return -1; |
} |
} |
} |
} |
} |
} |
} |
} |
if ( IS_BINARYPWR(f1) || IS_BINARYPWR(f2) ) |
if ( IS_BINARYPWR(f1) || IS_BINARYPWR(f2) ) { |
return nfnode_comp_pwr(f1,f2); |
fnode_base_exp(f1,&b1,&e1); |
|
fnode_base_exp(f2,&b2,&e2); |
|
if ( r = nfnode_comp_lex(b1,b2) ) { |
|
if ( r > 0 ) |
|
return nfnode_comp_lex(e1,mkfnode(1,I_FORMULA,0)); |
|
else if ( r < 0 ) |
|
return nfnode_comp_lex(mkfnode(1,I_FORMULA,0),e2); |
|
} else return nfnode_comp_lex(e1,e2); |
|
} |
|
|
/* now, IDs of f1 and f2 must be I_FORMULA, I_FUNC, I_IFUNC or I_PVAR */ |
/* now, IDs of f1 and f2 must be I_FORMULA, I_FUNC, I_IFUNC or I_PVAR */ |
/* I_IFUNC > I_PVAR > I_FUNC=I_FUNC_QARG > I_FORMULA */ |
/* I_IFUNC > I_PVAR > I_FUNC=I_FUNC_QARG > I_FORMULA */ |
Line 3048 int nfnode_comp(FNODE f1,FNODE f2) |
|
Line 3370 int nfnode_comp(FNODE f1,FNODE f2) |
|
case I_FUNC: case I_IFUNC: case I_PVAR: |
case I_FUNC: case I_IFUNC: case I_PVAR: |
return -1; |
return -1; |
default: |
default: |
error("nfnode_comp : undefined"); |
error("nfnode_comp_lex : undefined"); |
} |
} |
break; |
break; |
case I_FUNC: case I_FUNC_QARG: |
case I_FUNC: case I_FUNC_QARG: |
Line 3066 int nfnode_comp(FNODE f1,FNODE f2) |
|
Line 3388 int nfnode_comp(FNODE f1,FNODE f2) |
|
/* compare args */ |
/* compare args */ |
n1 = FA0((FNODE)FA1(f1)); n2 = FA0((FNODE)FA1(f2)); |
n1 = FA0((FNODE)FA1(f1)); n2 = FA0((FNODE)FA1(f2)); |
while ( n1 && n2 ) |
while ( n1 && n2 ) |
if ( r = nfnode_comp(BDY(n1),BDY(n2)) ) return r; |
if ( r = nfnode_comp_lex(BDY(n1),BDY(n2)) ) return r; |
else { |
else { |
n1 = NEXT(n1); n2 = NEXT(n2); |
n1 = NEXT(n1); n2 = NEXT(n2); |
} |
} |
Line 3074 int nfnode_comp(FNODE f1,FNODE f2) |
|
Line 3396 int nfnode_comp(FNODE f1,FNODE f2) |
|
} |
} |
break; |
break; |
default: |
default: |
error("nfnode_comp : undefined"); |
error("nfnode_comp_lex : undefined"); |
} |
} |
case I_PVAR: |
case I_PVAR: |
switch ( f2->id ) { |
switch ( f2->id ) { |
Line 3088 int nfnode_comp(FNODE f1,FNODE f2) |
|
Line 3410 int nfnode_comp(FNODE f1,FNODE f2) |
|
else if ( i1 < i2 ) return -1; |
else if ( i1 < i2 ) return -1; |
else return 0; |
else return 0; |
default: |
default: |
error("nfnode_comp : undefined"); |
error("nfnode_comp_lex : undefined"); |
} |
} |
break; |
break; |
case I_IFUNC: |
case I_IFUNC: |
Line 3104 int nfnode_comp(FNODE f1,FNODE f2) |
|
Line 3426 int nfnode_comp(FNODE f1,FNODE f2) |
|
/* compare args */ |
/* compare args */ |
n1 = FA0((FNODE)FA1(f1)); n2 = FA0((FNODE)FA1(f2)); |
n1 = FA0((FNODE)FA1(f1)); n2 = FA0((FNODE)FA1(f2)); |
while ( n1 && n2 ) |
while ( n1 && n2 ) |
if ( r = nfnode_comp(BDY(n1),BDY(n2)) ) return r; |
if ( r = nfnode_comp_lex(BDY(n1),BDY(n2)) ) return r; |
else { |
else { |
n1 = NEXT(n1); n2 = NEXT(n2); |
n1 = NEXT(n1); n2 = NEXT(n2); |
} |
} |
Line 3113 int nfnode_comp(FNODE f1,FNODE f2) |
|
Line 3435 int nfnode_comp(FNODE f1,FNODE f2) |
|
break; |
break; |
|
|
default: |
default: |
error("nfnode_comp : undefined"); |
error("nfnode_comp_lex : undefined"); |
} |
} |
break; |
break; |
default: |
default: |
error("nfnode_comp : undefined"); |
error("nfnode_comp_lex : undefined"); |
} |
} |
} |
|
|
|
int nfnode_comp_pwr(FNODE f1,FNODE f2) |
|
{ |
|
FNODE b1,b2,e1,e2; |
|
int r; |
|
|
|
fnode_base_exp(f1,&b1,&e1); |
|
fnode_base_exp(f2,&b2,&e2); |
|
if ( r = nfnode_comp(b1,b2) ) { |
|
if ( r > 0 ) |
|
return nfnode_comp(e1,mkfnode(1,I_FORMULA,0)); |
|
else if ( r < 0 ) |
|
return nfnode_comp(mkfnode(1,I_FORMULA,0),e2); |
|
} else return nfnode_comp(e1,e2); |
|
} |
} |
|
|
NODE append_node(NODE a1,NODE a2) |
NODE append_node(NODE a1,NODE a2) |