=================================================================== RCS file: /home/cvs/OpenXM_contrib2/asir2000/builtin/strobj.c,v retrieving revision 1.94 retrieving revision 1.124 diff -u -p -r1.94 -r1.124 --- OpenXM_contrib2/asir2000/builtin/strobj.c 2005/11/02 10:02:32 1.94 +++ OpenXM_contrib2/asir2000/builtin/strobj.c 2015/08/14 13:51:54 1.124 @@ -45,7 +45,7 @@ * DEVELOPER SHALL HAVE NO LIABILITY IN CONNECTION WITH THE USE, * PERFORMANCE OR NON-PERFORMANCE OF THE SOFTWARE. * - * $OpenXM: OpenXM_contrib2/asir2000/builtin/strobj.c,v 1.93 2005/11/02 09:39:10 noro Exp $ + * $OpenXM: OpenXM_contrib2/asir2000/builtin/strobj.c,v 1.123 2015/08/06 10:01:52 fujimoto Exp $ */ #include "ca.h" #include "parse.h" @@ -60,7 +60,7 @@ extern jmp_buf environnement; #if defined(__GNUC__) #define INLINE inline -#elif defined(VISUAL) +#elif defined(VISUAL) || defined(__MINGW32__) #define INLINE __inline #else #define INLINE @@ -76,6 +76,7 @@ struct TeXSymbol { #define IS_BINARYPWR(f) (((f)->id==I_BOP) &&(OPNAME(f)=='^')) #define IS_NARYADD(f) (((f)->id==I_NARYOP) &&(OPNAME(f)=='+')) #define IS_NARYMUL(f) (((f)->id==I_NARYOP) &&(OPNAME(f)=='*')) +#define IS_MUL(f) (((f)->id==I_NARYOP||(f)->id==I_BOP) &&(OPNAME(f)=='*')) extern char *parse_strp; @@ -92,15 +93,26 @@ void Pquotetotex(); void Pquotetotex_env(); void Pflatten_quote(); -void Pquote_is_integer(),Pquote_is_rational(),Pquote_is_number(); -void Pquote_is_dependent(),Pquote_is_function(); -void Pquote_normalize(); -void Pquote_normalize_comp(); -void Pquote_normalize_match(); +void Pqt_is_integer(),Pqt_is_rational(),Pqt_is_number(),Pqt_is_coef(); +void Pqt_is_dependent(),Pqt_is_function(),Pqt_is_var(); +void Pqt_set_ord(),Pqt_set_coef(),Pqt_set_weight(); +void Pqt_normalize(); +void Pnqt_comp(),Pnqt_weight(); +void Pnqt_match(); +void Pnqt_match_rewrite(); +void Pqt_to_nbp(); +void Pshuffle_mul(), Pharmonic_mul(); +void Pnbp_hm(), Pnbp_ht(), Pnbp_hc(), Pnbp_rest(); +void Pnbp_tm(), Pnbp_tt(), Pnbp_tc(), Pnbp_trest(); +void Pnbm_deg(), Pnbm_index(); +void Pnbm_hp_rest(); +void Pnbm_hxky(), Pnbm_xky_rest(); +void Pnbm_hv(), Pnbm_tv(), Pnbm_rest(),Pnbm_trest(); + void Pquote_to_funargs(),Pfunargs_to_quote(),Pget_function_name(); -void Pquote_match(),Pget_quote_id(),Pquote_match_rewrite(); -void Pquote_to_nary(),Pquote_to_bin(); +void Pqt_match(),Pget_quote_id(); +void Pqt_to_nary(),Pqt_to_bin(); void fnode_do_assign(NODE arg); void do_assign(NODE arg); void fnodetotex_tb(FNODE f,TB tb); @@ -112,7 +124,22 @@ void tb_to_string(TB tb,STRING *rp); void fnodenodetotex_tb(NODE n,TB tb); void fargstotex_tb(char *opname,FNODE f,TB tb); int top_is_minus(FNODE f); -int quote_match(Obj f,Obj pat,NODE *rp); +int qt_match(Obj f,Obj pat,NODE *rp); +FNODE partial_eval(FNODE), fnode_to_nary(FNODE), fnode_to_bin(FNODE,int); +FNODE nfnode_add(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_mul_coef(Obj c,FNODE f,int expand); +FNODE fnode_expand_pwr(FNODE f,int n,int expand); +FNODE to_narymul(FNODE f); +FNODE to_naryadd(FNODE f); +FNODE fnode_node_to_nary(ARF op,NODE n); +void fnode_base_exp(FNODE f,FNODE *bp,FNODE *ep); +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 fnode_apply(FNODE f,FNODE (*func)(),int expand); +FNODE fnode_normalize(FNODE f,int expand); +FNODE rewrite_fnode(FNODE f,NODE arg,int qarg); struct ftab str_tab[] = { {"sprintf",Psprintf,-99999999}, @@ -130,25 +157,54 @@ struct ftab str_tab[] = { {"string_to_tb",Pstring_to_tb,1}, {"get_quote_id",Pget_quote_id,1}, - {"quote_is_number",Pquote_is_number,1}, - {"quote_is_rational",Pquote_is_rational,1}, - {"quote_is_integer",Pquote_is_integer,1}, - {"quote_is_function",Pquote_is_function,1}, - {"quote_is_dependent",Pquote_is_dependent,2}, + {"qt_is_var",Pqt_is_var,1}, + {"qt_is_coef",Pqt_is_coef,1}, + {"qt_is_number",Pqt_is_number,1}, + {"qt_is_rational",Pqt_is_rational,1}, + {"qt_is_integer",Pqt_is_integer,1}, + {"qt_is_function",Pqt_is_function,1}, + {"qt_is_dependent",Pqt_is_dependent,2}, - {"quote_normalize",Pquote_normalize,-2}, - {"quote_normalize_comp",Pquote_normalize_comp,2}, + {"qt_set_coef",Pqt_set_coef,-1}, + {"qt_set_ord",Pqt_set_ord,-1}, + {"qt_set_weight",Pqt_set_weight,-1}, + {"qt_normalize",Pqt_normalize,-2}, + {"qt_match",Pqt_match,2}, + {"nqt_match_rewrite",Pnqt_match_rewrite,3}, - {"quote_to_nary",Pquote_to_nary,1}, - {"quote_to_bin",Pquote_to_bin,2}, + {"nqt_weight",Pnqt_weight,1}, + {"nqt_comp",Pnqt_comp,2}, + {"nqt_match",Pnqt_match,-3}, + {"qt_to_nbp",Pqt_to_nbp,1}, + {"shuffle_mul",Pshuffle_mul,2}, + {"harmonic_mul",Pharmonic_mul,2}, + + {"nbp_hm", Pnbp_hm,1}, + {"nbp_ht", Pnbp_ht,1}, + {"nbp_hc", Pnbp_hc,1}, + {"nbp_rest", Pnbp_rest,1}, + {"nbp_tm", Pnbp_tm,1}, + {"nbp_tt", Pnbp_tt,1}, + {"nbp_tc", Pnbp_tc,1}, + {"nbp_trest", Pnbp_trest,1}, + {"nbm_deg", Pnbm_deg,1}, + {"nbm_index", Pnbm_index,1}, + {"nbm_hxky", Pnbm_hxky,1}, + {"nbm_xky_rest", Pnbm_xky_rest,1}, + {"nbm_hp_rest", Pnbm_hp_rest,1}, + {"nbm_hv", Pnbm_hv,1}, + {"nbm_tv", Pnbm_tv,1}, + {"nbm_rest", Pnbm_rest,1}, + {"nbm_trest", Pnbm_trest,1}, + + {"qt_to_nary",Pqt_to_nary,1}, + {"qt_to_bin",Pqt_to_bin,2}, + {"quotetotex_tb",Pquotetotex_tb,2}, {"quotetotex",Pquotetotex,1}, {"quotetotex_env",Pquotetotex_env,-99999999}, {"flatten_quote",Pflatten_quote,-2}, {"quote_to_funargs",Pquote_to_funargs,1}, - {"quote_match",Pquote_match,2}, - {"quote_normalize_match",Pquote_normalize_match,2}, - {"quote_match_rewrite",Pquote_match_rewrite,-4}, {"funargs_to_quote",Pfunargs_to_quote,1}, {"get_function_name",Pget_function_name,1}, {0,0,0}, @@ -414,7 +470,7 @@ int register_conv_func(Obj arg) if ( !arg ) { convfunc = 0; return 1; - } else if ( OID(arg) == O_P && (int)(VR((P)arg))->attr == V_SR ) { + } else if ( OID(arg) == O_P && (long)(VR((P)arg))->attr == V_SR ) { convfunc = (FUNC)(VR((P)arg)->priv); /* f must be a function which takes single argument */ return 1; @@ -546,9 +602,7 @@ void Pwrite_to_tb(NODE arg,Q *rp) *rp = 0; } -FNODE partial_eval(FNODE), fnode_to_nary(FNODE), fnode_to_bin(FNODE,int); - -void Pquote_to_nary(NODE arg,QUOTE *rp) +void Pqt_to_nary(NODE arg,QUOTE *rp) { FNODE f; @@ -556,7 +610,7 @@ void Pquote_to_nary(NODE arg,QUOTE *rp) MKQUOTE(*rp,f); } -void Pquote_to_bin(NODE arg,QUOTE *rp) +void Pqt_to_bin(NODE arg,QUOTE *rp) { FNODE f; int direction; @@ -567,46 +621,68 @@ void Pquote_to_bin(NODE arg,QUOTE *rp) MKQUOTE(*rp,f); } -void Pquote_is_number(NODE arg,Q *rp) +void Pqt_is_var(NODE arg,Q *rp) { QUOTE q; int ret; q = (QUOTE)ARG0(arg); - asir_assert(q,O_QUOTE,"quote_is_number"); + asir_assert(q,O_QUOTE,"qt_is_var"); + ret = fnode_is_var(BDY(q)); + STOQ(ret,*rp); +} + +void Pqt_is_coef(NODE arg,Q *rp) +{ + QUOTE q; + int ret; + + q = (QUOTE)ARG0(arg); + asir_assert(q,O_QUOTE,"qt_is_coef"); + ret = fnode_is_coef(BDY(q)); + STOQ(ret,*rp); +} + +void Pqt_is_number(NODE arg,Q *rp) +{ + QUOTE q; + int ret; + + q = (QUOTE)ARG0(arg); + asir_assert(q,O_QUOTE,"qt_is_number"); ret = fnode_is_number(BDY(q)); STOQ(ret,*rp); } -void Pquote_is_rational(NODE arg,Q *rp) +void Pqt_is_rational(NODE arg,Q *rp) { QUOTE q; int ret; q = (QUOTE)ARG0(arg); - asir_assert(q,O_QUOTE,"quote_is_rational"); + asir_assert(q,O_QUOTE,"qt_is_rational"); ret = fnode_is_rational(BDY(q)); STOQ(ret,*rp); } -void Pquote_is_integer(NODE arg,Q *rp) +void Pqt_is_integer(NODE arg,Q *rp) { QUOTE q; int ret; q = (QUOTE)ARG0(arg); - asir_assert(q,O_QUOTE,"quote_is_integer"); + asir_assert(q,O_QUOTE,"qt_is_integer"); ret = fnode_is_integer(BDY(q)); STOQ(ret,*rp); } -void Pquote_is_function(NODE arg,Q *rp) +void Pqt_is_function(NODE arg,Q *rp) { QUOTE q; int ret; q = (QUOTE)ARG0(arg); - asir_assert(q,O_QUOTE,"quote_is_function"); + asir_assert(q,O_QUOTE,"qt_is_function"); if ( q->id == I_FUNC || q->id == I_IFUNC ) ret = 1; else @@ -614,7 +690,7 @@ void Pquote_is_function(NODE arg,Q *rp) STOQ(ret,*rp); } -void Pquote_is_dependent(NODE arg,Q *rp) +void Pqt_is_dependent(NODE arg,Q *rp) { P x; QUOTE q,v; @@ -623,8 +699,8 @@ void Pquote_is_dependent(NODE arg,Q *rp) q = (QUOTE)ARG0(arg); v = (QUOTE)ARG1(arg); - asir_assert(q,O_QUOTE,"quote_is_dependent"); - asir_assert(v,O_QUOTE,"quote_is_dependent"); + asir_assert(q,O_QUOTE,"qt_is_dependent"); + asir_assert(v,O_QUOTE,"qt_is_dependent"); x = (P)eval(BDY(v)); if ( !x || OID(x) != O_P ) *rp = 0; @@ -634,7 +710,7 @@ void Pquote_is_dependent(NODE arg,Q *rp) } -void Pquote_match(NODE arg,Q *rp) +void Pqt_match(NODE arg,Q *rp) { FNODE f,g; Obj obj; @@ -642,14 +718,8 @@ void Pquote_match(NODE arg,Q *rp) NODE r; int ret; -#if 0 - g = partial_eval(BDY(((QUOTE)ARG0(arg)))); - MKQUOTE(q,g); - ret = quote_match((Obj)q,(Obj)ARG1(arg),&r); -#else obj = (Obj)ARG0(arg); - ret = quote_match(obj,(Obj)ARG1(arg),&r); -#endif + ret = qt_match(obj,(Obj)ARG1(arg),&r); if ( ret ) { do_assign(r); *rp = ONE; @@ -657,16 +727,18 @@ void Pquote_match(NODE arg,Q *rp) *rp = 0; } -void Pquote_normalize_match(NODE arg,Q *rp) +void Pnqt_match(NODE arg,Q *rp) { QUOTE fq,pq; FNODE f,p; int ret; + Q mode; NODE r; - fq = (QUOTE)ARG0(arg); Pquote_normalize(mknode(2,fq,0),&fq); f = (FNODE)BDY(fq); - pq = (QUOTE)ARG1(arg); Pquote_normalize(mknode(2,pq,0),&pq); p = (FNODE)BDY(pq); - ret = fnode_normalize_match(f,p,&r); + mode = argc(arg)==3 ? (Q)ARG2(arg) : 0; + fq = (QUOTE)ARG0(arg); Pqt_normalize(mknode(2,fq,mode),&fq); f = (FNODE)BDY(fq); + pq = (QUOTE)ARG1(arg); Pqt_normalize(mknode(2,pq,mode),&pq); p = (FNODE)BDY(pq); + ret = nfnode_match(f,p,&r); if ( ret ) { fnode_do_assign(r); *rp = ONE; @@ -674,47 +746,98 @@ void Pquote_normalize_match(NODE arg,Q *rp) *rp = 0; } -FNODE rewrite_fnode(FNODE,NODE); +void Pnqt_match_rewrite(NODE arg,Obj *rp) +{ + FNODE f,p,c,a,r; + Obj obj,pat,cond,action; + NODE rule; + QUOTE q; + Q mode; + int m; -extern Obj VOIDobj; + obj = (Obj)ARG0(arg); + rule = BDY((LIST)ARG1(arg)); + mode = (Q)ARG2(arg); + if ( length(rule) == 2 ) { + pat = ARG0(rule); + cond = (Obj)ONE; + action = (Obj)ARG1(rule); + } else { + pat = ARG0(rule); + cond = ARG1(rule); + action = (Obj)ARG2(rule); + } + Pqt_normalize(mknode(2,obj,mode),&q); f = (FNODE)BDY(q); + Pqt_normalize(mknode(2,pat,mode),&q); p = (FNODE)BDY(q); + Pqt_normalize(mknode(2,action,mode),&q); + a = (FNODE)BDY(q); + if ( OID(cond) == O_QUOTE ) c = BDY((QUOTE)cond); + else c = mkfnode(1,I_FORMULA,ONE); -void Pquote_match_rewrite(NODE arg,Obj *rp) + m = QTOS(mode); + r = nfnode_match_rewrite(f,p,c,a,m); + if ( r ) { + MKQUOTE(q,r); + *rp = (Obj)q; + } else + *rp = obj; +} + +/* f is NARYOP => do submatch */ + +#define PV_ANY 99999999 + +FNODE nfnode_match_rewrite(FNODE f,FNODE p,FNODE c,FNODE a,int mode) { - FNODE f,g,h,c,value; - Obj obj; + ARF op; + NODE arg,h0,t,h,valuen; + NODE r,s0,s,pair; + FNODE any,pany,head,tail,a1,a2; QUOTE q; - NODE r,t,s,s0,pair; - int ret,ind,ac; + int ret; + FNODE value; + int ind; - obj = (Obj)ARG0(arg); - ret = quote_match(obj,(Obj)ARG1(arg),&r); - if ( ret ) { - for ( t = r, s0 = 0; t; t = NEXT(t) ) { - NEXTNODE(s0,s); - pair = BDY((LIST)BDY(t)); - ind = (int)FA0((FNODE)BDY((QUOTE)BDY(pair))); - value = BDY((QUOTE)(BDY(NEXT(pair)))); - BDY(s) = mknode(2,ind,value); - } - if ( s0 ) NEXT(s) = 0; - switch ( ac = argc(arg) ) { - case 3: - h = rewrite_fnode(BDY((QUOTE)ARG2(arg)),s0); - MKQUOTE(q,h); *rp = (Obj)q; + if ( f->id == I_NARYOP ) { + op = (ARF)FA0(f); + arg = (NODE)FA1(f); + pany = 0; + for ( h0 = 0, t = arg; t; t = NEXT(t) ) { + tail = fnode_node_to_nary(op,t); + ret = nfnode_match(tail,p,&r) && eval(rewrite_fnode(c,r,1)); + if ( ret ) break; + + /* append a variable to the pattern */ + if ( !pany ) { + any = mkfnode(1,I_PVAR,PV_ANY); + pany = mkfnode(3,I_BOP,op,p,any); + pany = fnode_normalize(pany,mode); + } + ret = nfnode_match(tail,pany,&r) && eval(rewrite_fnode(c,r,1)); + if ( ret ) { + a = fnode_normalize(mkfnode(3,I_BOP,op,a,any),mode); break; - case 4: - c = rewrite_fnode(BDY((QUOTE)ARG2(arg)),s0); - if ( eval(c) ) { - h = rewrite_fnode(BDY((QUOTE)ARG3(arg)),s0); - MKQUOTE(q,h); *rp = (Obj)q; - } else - *rp = VOIDobj; - break; - default: - error("quote_match_rewrite : invalid argument"); + } + + NEXTNODE(h0,h); + BDY(h) = BDY(t); } + if ( t ) { + if ( h0 ) NEXT(h) = 0; + head = fnode_node_to_nary(op,h0); + a = fnode_normalize(mkfnode(3,I_BOP,op,head,a),mode); + ret = 1; + } else + ret = 0; } else - *rp = VOIDobj; + ret = nfnode_match(f,p,&r) && eval(rewrite_fnode(c,r,1)); + + if ( ret ) { + a1 = rewrite_fnode(a,r,0); + a2 = partial_eval(a1); + return fnode_normalize(a2,mode); + } else + return 0; } void do_assign(NODE arg) @@ -726,7 +849,7 @@ void do_assign(NODE arg) for ( t = arg; t; t = NEXT(t) ) { pair = BDY((LIST)BDY(t)); - pv = (int)FA0((FNODE)BDY((QUOTE)BDY(pair))); + pv = (long)FA0((FNODE)BDY((QUOTE)BDY(pair))); value = (QUOTE)(BDY(NEXT(pair))); ASSPV(pv,value); } @@ -740,12 +863,18 @@ void fnode_do_assign(NODE arg) int pv; FNODE f; QUOTE value; + QUOTEARG qa; for ( t = arg; t; t = NEXT(t) ) { pair = (NODE)BDY(t); pv = (int)BDY(pair); f = (FNODE)(BDY(NEXT(pair))); - MKQUOTE(value,f); + if ( f->id == I_FUNC_HEAD ) { + /* XXX : I_FUNC_HEAD is a dummy id to pass FUNC */ + MKQUOTEARG(qa,A_func,FA0(f)); + value = (QUOTE)qa; + } else + MKQUOTE(value,f); ASSPV(pv,value); } } @@ -785,14 +914,14 @@ int merge_matching_node(NODE n,NODE a,NODE *rp) return 1; } -int quote_match_node(NODE f,NODE pat,NODE *rp) { +int qt_match_node(NODE f,NODE pat,NODE *rp) { NODE r,a,tf,tp,r1; int ret; if ( length(f) != length(pat) ) return 0; r = 0; for ( tf = f, tp = pat; tf; tf = NEXT(tf), tp = NEXT(tp) ) { - ret = quote_match((Obj)BDY(tf),(Obj)BDY(tp),&a); + ret = qt_match((Obj)BDY(tf),(Obj)BDY(tp),&a); if ( !ret ) return 0; ret = merge_matching_node(r,a,&r1); if ( !ret ) return 0; @@ -804,7 +933,7 @@ int quote_match_node(NODE f,NODE pat,NODE *rp) { /* f = [a,b,c,...] pat = [X,Y,...] rpat matches the rest of f */ -int quote_match_cons(NODE f,NODE pat,Obj rpat,NODE *rp) { +int qt_match_cons(NODE f,NODE pat,Obj rpat,NODE *rp) { QUOTE q; Q id; FNODE fn; @@ -816,7 +945,7 @@ int quote_match_cons(NODE f,NODE pat,Obj rpat,NODE *rp if ( length(f) < length(pat) ) return 0; r = 0; for ( tf = f, tp = pat; tp; tf = NEXT(tf), tp = NEXT(tp) ) { - ret = quote_match((Obj)BDY(tf),(Obj)BDY(tp),&a); + ret = qt_match((Obj)BDY(tf),(Obj)BDY(tp),&a); if ( !ret ) return 0; ret = merge_matching_node(r,a,&r1); if ( !ret ) return 0; @@ -828,7 +957,7 @@ int quote_match_cons(NODE f,NODE pat,Obj rpat,NODE *rp MKLIST(alist,a); arg = mknode(1,alist); Pfunargs_to_quote(arg,&q); - ret = quote_match((Obj)q,rpat,&a); + ret = qt_match((Obj)q,rpat,&a); if ( !ret ) return 0; ret = merge_matching_node(r,a,&r1); if ( !ret ) return 0; @@ -847,7 +976,7 @@ void get_quote_id_arg(QUOTE f,int *id,NODE *r) /* *rp : [[quote(A),quote(1)],...] */ -int quote_match(Obj f, Obj pat, NODE *rp) +int qt_match(Obj f, Obj pat, NODE *rp) { NODE tf,tp,head,body; NODE parg,farg,r; @@ -866,7 +995,7 @@ int quote_match(Obj f, Obj pat, NODE *rp) return 0; else if ( OID(pat) == O_LIST ) { if ( OID(f) == O_LIST ) - return quote_match_node(BDY((LIST)f),BDY((LIST)pat),rp); + return qt_match_node(BDY((LIST)f),BDY((LIST)pat),rp); else return 0; } else if ( OID(pat) == O_QUOTE ) { @@ -893,10 +1022,10 @@ int quote_match(Obj f, Obj pat, NODE *rp) tp = BDY((LIST)BDY(parg)); if ( pid == I_LIST ) - return quote_match_node(tf,tp,rp); + return qt_match_node(tf,tp,rp); else { rpat = (Obj)BDY(NEXT(parg)); - return quote_match_cons(tf,tp,rpat,rp); + return qt_match_cons(tf,tp,rpat,rp); } case I_PVAR: @@ -912,7 +1041,7 @@ int quote_match(Obj f, Obj pat, NODE *rp) if ( id == I_FUNC ) { r = mknode(2,BDY(parg),BDY(farg)); MKLIST(l,r); head = mknode(1,l); - ret = quote_match(BDY(NEXT(farg)), + ret = qt_match(BDY(NEXT(farg)), BDY(NEXT(parg)),&body); if ( !ret ) return 0; else return merge_matching_node(head,body,rp); @@ -940,7 +1069,7 @@ int quote_match(Obj f, Obj pat, NODE *rp) get_quote_id_arg((QUOTE)pat,&pid,&parg); get_quote_id_arg((QUOTE)f,&id,&farg); if ( compqa(CO,BDY(farg),BDY(parg)) ) return 0; - return quote_match_node(NEXT(farg),NEXT(parg),rp); + return qt_match_node(NEXT(farg),NEXT(parg),rp); default: if ( OID(f) != O_QUOTE ) return 0; @@ -948,7 +1077,7 @@ int quote_match(Obj f, Obj pat, NODE *rp) if ( id != pid ) return 0; get_quote_id_arg((QUOTE)pat,&pid,&parg); get_quote_id_arg((QUOTE)f,&id,&farg); - return quote_match_node(farg,parg,rp); + return qt_match_node(farg,parg,rp); } } } @@ -1159,6 +1288,7 @@ NODE arg; Obj *rp; { FNODE fnode; + SNODE snode; char *cmd; #if defined(PARI) void recover(int); @@ -1172,8 +1302,13 @@ Obj *rp; # endif #endif cmd = BDY((STRING)ARG0(arg)); +#if 0 exprparse_create_var(0,cmd,&fnode); *rp = eval(fnode); +#else + exprparse_create_var(0,cmd,&snode); + *rp = evalstat(snode); +#endif } void Prtostr(arg,rp) @@ -1195,6 +1330,7 @@ NODE arg; P *rp; { char *p; + FUNC f; p = BDY((STRING)ARG0(arg)); #if 0 @@ -1208,7 +1344,11 @@ P *rp; makevar(p,rp); } #else - makevar(p,rp); + gen_searchf_searchonly(p,&f); + if ( f ) + makesrvar(f,rp); + else + makevar(p,rp); #endif } @@ -1296,21 +1436,27 @@ char *symbol_name(char *name) void Pget_function_name(NODE arg,STRING *rp) { - QUOTEARG qa; - ARF f; - char *opname; + QUOTEARG qa; - qa = (QUOTEARG)BDY(arg); - if ( !qa || OID(qa) != O_QUOTEARG || qa->type != A_arf ) + qa = (QUOTEARG)BDY(arg); + if ( !qa || OID(qa) != O_QUOTEARG ) { + *rp = 0; return; + } + switch ( qa->type ) { + case A_arf: + MKSTR(*rp,((ARF)BDY(qa))->name); + break; + case A_func: + MKSTR(*rp,((FUNC)BDY(qa))->name); + break; + default: *rp = 0; - else { - f = (ARF)BDY(qa); - opname = f->name; - MKSTR(*rp,opname); - } + break; + } } FNODE strip_paren(FNODE); +void objtotex_tb(Obj obj,TB tb); void fnodetotex_tb(FNODE f,TB tb) { @@ -1319,7 +1465,6 @@ void fnodetotex_tb(FNODE f,TB tb) char *opname,*vname_conv,*prefix_conv; Obj obj; int i,len,allzero,elen,elen2,si; - C cplx; char *r; FNODE fi,f2,f1; @@ -1387,7 +1532,14 @@ void fnodetotex_tb(FNODE f,TB tb) write_tb("}",tb); break; case '^': - fnodetotex_tb((FNODE)FA1(f),tb); + f1 = (FNODE)FA1(f); + if ( fnode_is_var(f1) ) + fnodetotex_tb(f1,tb); + else { + write_tb("(",tb); + fnodetotex_tb(f1,tb); + write_tb(")",tb); + } write_tb("^{",tb); fnodetotex_tb(strip_paren((FNODE)FA2(f)),tb); write_tb("} ",tb); @@ -1404,43 +1556,41 @@ void fnodetotex_tb(FNODE f,TB tb) break; case I_NARYOP: args = (NODE)FA1(f); - write_tb("(",tb); switch ( OPNAME(f) ) { case '+': fnodetotex_tb((FNODE)BDY(args),tb); for ( args = NEXT(args); args; args = NEXT(args) ) { write_tb("+",tb); - fnodetotex_tb((FNODE)BDY(args),tb); + f1 = (FNODE)BDY(args); + /* if ( fnode_is_var(f1) || IS_MUL(f1) ) + fnodetotex_tb(f1,tb); + else */ { + write_tb("(",tb); + fnodetotex_tb(f1,tb); + write_tb(")",tb); + } } break; case '*': f1 = (FNODE)BDY(args); - if ( f1->id == I_FORMULA && MUNIQ(FA0(f1)) ) - write_tb("-",tb); - else - fnodetotex_tb(f1,tb); - write_tb(" ",tb); - for ( args = NEXT(args); args; args = NEXT(args) ) { - /* XXX special care for DP */ + if ( f1->id == I_FORMULA && MUNIQ(FA0(f1)) ) { + write_tb("- ",tb); args = NEXT(args); + } + for ( ; args; args = NEXT(args) ) { f2 = (FNODE)BDY(args); - if ( f2->id == I_EV ) { - n = (NODE)FA0(f2); - for ( i = 0; n; n = NEXT(n), i++ ) { - fi = (FNODE)BDY(n); - if ( fi->id != I_FORMULA || FA0(fi) ) - break; - } - if ( n ) - fnodetotex_tb(f2,tb); - } else + if ( fnode_is_var(f2) || IS_BINARYPWR(f2) ) fnodetotex_tb(f2,tb); + else { + write_tb("(",tb); + fnodetotex_tb(f2,tb); + write_tb(")",tb); + } } break; default: error("invalid nary op"); break; } - write_tb(")",tb); break; case I_COP: @@ -1665,33 +1815,7 @@ void fnodetotex_tb(FNODE f,TB tb) /* internal object */ case I_FORMULA: - obj = (Obj)FA0(f); - if ( !obj ) - write_tb("0",tb); - else if ( OID(obj) == O_N && NID(obj) == N_C ) { - cplx = (C)obj; - write_tb("(",tb); - if ( cplx->r ) { - r = objtostr((Obj)cplx->r); write_tb(r,tb); - } - if ( cplx->i ) { - if ( cplx->r && compnum(0,cplx->i,0) > 0 ) { - write_tb("+",tb); - if ( !UNIQ(cplx->i) ) { - r = objtostr((Obj)cplx->i); write_tb(r,tb); - } - } else if ( MUNIQ(cplx->i) ) - write_tb("-",tb); - else if ( !UNIQ(cplx->i) ) { - r = objtostr((Obj)cplx->i); write_tb(r,tb); - } - write_tb("\\sqrt{-1}",tb); - } - write_tb(")",tb); - } else if ( OID(obj) == O_P ) - write_tb(conv_rule(VR((P)obj)->name),tb); - else - write_tb(objtostr(obj),tb); + objtotex_tb((Obj)FA0(f),tb); break; /* program variable */ @@ -1707,6 +1831,103 @@ void fnodetotex_tb(FNODE f,TB tb) } } +void objtotex_tb(Obj obj,TB tb) +{ + C cplx; + char *r; + P t; + DCP dc; + char *v; + + if ( !obj ) { + write_tb("0",tb); + return; + } + switch ( OID(obj) ) { + case O_N: + switch ( NID(obj) ) { + case N_C: + cplx = (C)obj; + write_tb("(",tb); + if ( cplx->r ) { + r = objtostr((Obj)cplx->r); write_tb(r,tb); + } + if ( cplx->i ) { + if ( cplx->r && compnum(0,cplx->i,0) > 0 ) { + write_tb("+",tb); + if ( !UNIQ(cplx->i) ) { + r = objtostr((Obj)cplx->i); write_tb(r,tb); + } + } else if ( MUNIQ(cplx->i) ) + write_tb("-",tb); + else if ( !UNIQ(cplx->i) ) { + r = objtostr((Obj)cplx->i); write_tb(r,tb); + } + write_tb("\\sqrt{-1}",tb); + } + write_tb(")",tb); + break; + default: + write_tb(objtostr(obj),tb); + break; + } + break; + case O_P: + v = conv_rule(VR((P)obj)->name); + for ( dc = DC((P)obj); dc; dc = NEXT(dc) ) { + if ( !DEG(dc) ) + objtotex_tb((Obj)COEF(dc),tb); + else { + if ( NUM(COEF(dc)) && UNIQ((Q)COEF(dc)) ) + ; + else if ( NUM(COEF(dc)) && MUNIQ((Q)COEF(dc)) ) + write_tb("-",tb); + else if ( NUM(COEF(dc)) || !NEXT(DC(COEF(dc)))) + objtotex_tb((Obj)COEF(dc),tb); + else { + write_tb("(",tb); objtotex_tb((Obj)COEF(dc),tb); + write_tb(")",tb); + } + write_tb(v,tb); + if ( cmpq(DEG(dc),ONE) ) { + write_tb("^",tb); + if ( INT(DEG(dc)) && SGN(DEG(dc))>0 ) { + write_tb("{",tb); + objtotex_tb((Obj)DEG(dc),tb); + write_tb("}",tb); + } else { + write_tb("{",tb); objtotex_tb((Obj)DEG(dc),tb); + write_tb("}",tb); + } + } + } + if ( NEXT(dc) ) { + t = COEF(NEXT(dc)); + if ( !DEG(NEXT(dc)) ) { + if ( NUM(t) ) { + if ( !mmono(t) ) write_tb("+",tb); + } else { + if ( !mmono(COEF(DC(t))) ) write_tb("+",tb); + } + } else { + if ( !mmono(t) ) write_tb("+",tb); + } + } + } + break; + case O_R: + write_tb("\\frac{",tb); + objtotex_tb((Obj)NM((R)obj),tb); + write_tb("}{",tb); + objtotex_tb((Obj)DN((R)obj),tb); + write_tb("}",tb); + break; + default: + write_tb(objtostr(obj),tb); + break; + } +} + char *objtostr(Obj obj) { int len; @@ -1822,9 +2043,13 @@ int top_is_minus(FNODE f) case O_N: return mmono((P)obj); case O_P: +#if 0 /* must be a variable */ opname = conv_rule(VR((P)obj)->name); return opname[0]=='-'; +#else + return mmono((P)obj); +#endif default: /* ??? */ len = estimate_length(CO,obj); @@ -2015,53 +2240,581 @@ void Pfunargs_to_quote(NODE arg,QUOTE *rp) MKQUOTE(*rp,f); } -FNODE fnode_apply(FNODE f,FNODE (*func)(),int expand); -FNODE fnode_normalize(FNODE f,int expand); +VL reordvars(VL vl0,NODE head) +{ + VL vl,svl,tvl; + int i,j; + NODE n; + P t; + V *va; + V v; -void Pquote_normalize(NODE arg,QUOTE *rp) + for ( vl = 0, i = 0, n = head; n; n = NEXT(n), i++ ) { + NEXTVL(vl,tvl); + if ( !(t = (P)BDY(n)) || (OID(t) != O_P) ) + error("reordvars : invalid argument"); + VR(tvl) = VR(t); + } + va = (V *)ALLOCA(i*sizeof(V)); + for ( j = 0, svl = vl; j < i; j++, svl = NEXT(svl) ) + va[j] = VR(svl); + for ( svl = vl0; svl; svl = NEXT(svl) ) { + v = VR(svl); + for ( j = 0; j < i; j++ ) + if ( v == va[j] ) + break; + if ( j == i ) { + NEXTVL(vl,tvl); + VR(tvl) = v; + } + } + if ( vl ) + NEXT(tvl) = 0; + return vl; +} + +struct wtab { + V v; + int w; +}; + +struct wtab *qt_weight_tab; +VL qt_current_ord, qt_current_coef; +LIST qt_current_ord_obj,qt_current_coef_obj,qt_current_weight_obj; +LIST qt_current_weight_obj; + +void Pqt_set_ord(NODE arg,LIST *rp) { + NODE r0,r; + VL vl; + P v; + + if ( !argc(arg) ) + *rp = qt_current_ord_obj; + else if ( !ARG0(arg) ) { + qt_current_ord_obj = 0; + qt_current_ord = 0; + } else { + qt_current_ord = reordvars(CO,BDY((LIST)ARG0(arg))); + for ( r0 = 0, vl = qt_current_ord; vl; vl = NEXT(vl) ) { + NEXTNODE(r0,r); MKV(vl->v,v); BDY(r) = v; + } + if ( r0 ) NEXT(r) = 0; + MKLIST(*rp,r0); + qt_current_ord_obj = *rp; + } +} + +void Pqt_set_weight(NODE arg,LIST *rp) +{ + NODE n,pair; + int l,i; + struct wtab *tab; + + if ( !argc(arg) ) + *rp = qt_current_weight_obj; + else if ( !ARG0(arg) ) { + qt_current_weight_obj = 0; + qt_weight_tab = 0; + } else { + n = BDY((LIST)ARG0(arg)); + l = length(n); + tab = qt_weight_tab = (struct wtab *)MALLOC((l+1)*sizeof(struct wtab)); + for ( i = 0; i < l; i++, n = NEXT(n) ) { + pair = BDY((LIST)BDY(n)); + tab[i].v = VR((P)ARG0(pair)); + tab[i].w = QTOS((Q)ARG1(pair)); + } + tab[i].v = 0; + qt_current_weight_obj = (LIST)ARG0(arg); + *rp = qt_current_weight_obj; + } +} + +void Pqt_set_coef(NODE arg,LIST *rp) +{ + NODE r0,r,n; + VL vl0,vl; + P v; + + if ( !argc(arg) ) + *rp = qt_current_coef_obj; + else if ( !ARG0(arg) ) { + qt_current_coef_obj = 0; + qt_current_coef = 0; + } else { + n = BDY((LIST)ARG0(arg)); + for ( vl0 = 0, r0 = 0; n; n = NEXT(n) ) { + NEXTNODE(r0,r); + NEXTVL(vl0,vl); + vl->v = VR((P)BDY(n)); + MKV(vl->v,v); BDY(r) = v; + } + if ( r0 ) NEXT(r) = 0; + if ( vl0 ) NEXT(vl) = 0; + qt_current_coef = vl0; + MKLIST(*rp,r0); + qt_current_coef_obj = *rp; + } +} + +void Pqt_normalize(NODE arg,QUOTE *rp) +{ QUOTE q,r; FNODE f; int expand,ac; ac = argc(arg); - if ( !ac ) error("quote_normalize : invalid argument"); + if ( !ac ) error("qt_normalize : invalid argument"); q = (QUOTE)ARG0(arg); - expand = ac==2 && ARG1(arg); - if ( !q || OID(q) != O_QUOTE ) { + if ( ac == 2 ) + expand = QTOS((Q)ARG1(arg)); + if ( !q || OID(q) != O_QUOTE ) *rp = q; - return; - } else if ( q->normalized && (q->expanded || !expand) ) - *rp = q; else { f = fnode_normalize(BDY(q),expand); MKQUOTE(r,f); - r->normalized = 1; - if ( expand ) r->expanded = 1; *rp = r; } } -void Pquote_normalize_comp(NODE arg,Q *rp) +NBP fnode_to_nbp(FNODE f); + +void Pqt_to_nbp(NODE arg,NBP *rp) { + QUOTE q; + FNODE f; + + q = (QUOTE)ARG0(arg); f = (FNODE)BDY(q); + f = fnode_normalize(f,0); + *rp = fnode_to_nbp(f); +} + +void Pshuffle_mul(NODE arg,NBP *rp) +{ + NBP p1,p2; + + p1 = (NBP)ARG0(arg); + p2 = (NBP)ARG1(arg); + shuffle_mulnbp(CO,p1,p2,rp); +} + +void Pharmonic_mul(NODE arg,NBP *rp) +{ + NBP p1,p2; + + p1 = (NBP)ARG0(arg); + p2 = (NBP)ARG1(arg); + harmonic_mulnbp(CO,p1,p2,rp); +} + +void Pnbp_hm(NODE arg, NBP *rp) +{ + NBP p; + NODE n; + NBM m; + + p = (NBP)ARG0(arg); + if ( !p ) *rp = 0; + else { + m = (NBM)BDY(BDY(p)); + MKNODE(n,m,0); + MKNBP(*rp,n); + } +} + +void Pnbp_ht(NODE arg, NBP *rp) +{ + NBP p; + NODE n; + NBM m,m1; + + p = (NBP)ARG0(arg); + if ( !p ) *rp = 0; + else { + m = (NBM)BDY(BDY(p)); + NEWNBM(m1); + m1->d = m->d; m1->c = (P)ONE; m1->b = m->b; + MKNODE(n,m1,0); + MKNBP(*rp,n); + } +} + +void Pnbp_hc(NODE arg, P *rp) +{ + NBP p; + NBM m; + + p = (NBP)ARG0(arg); + if ( !p ) *rp = 0; + else { + m = (NBM)BDY(BDY(p)); + *rp = m->c; + } +} + +void Pnbp_rest(NODE arg, NBP *rp) +{ + NBP p; + NODE n; + + p = (NBP)ARG0(arg); + if ( !p ) *rp = 0; + else { + n = BDY(p); + if ( !NEXT(n) ) *rp = 0; + else + MKNBP(*rp,NEXT(n)); + } +} + +void Pnbp_tm(NODE arg, NBP *rp) +{ + NBP p; + NODE n; + NBM m; + + p = (NBP)ARG0(arg); + if ( !p ) *rp = 0; + else { + for ( n = BDY(p); NEXT(n); n = NEXT(n) ); + m = (NBM)BDY(n); + MKNODE(n,m,0); + MKNBP(*rp,n); + } +} + +void Pnbp_tt(NODE arg, NBP *rp) +{ + NBP p; + NODE n; + NBM m,m1; + + p = (NBP)ARG0(arg); + if ( !p ) *rp = 0; + else { + for ( n = BDY(p); NEXT(n); n = NEXT(n) ); + m = (NBM)BDY(n); + NEWNBM(m1); + m1->d = m->d; m1->c = (P)ONE; m1->b = m->b; + MKNODE(n,m1,0); + MKNBP(*rp,n); + } +} + +void Pnbp_tc(NODE arg, P *rp) +{ + NBP p; + NBM m; + NODE n; + + p = (NBP)ARG0(arg); + if ( !p ) *rp = 0; + else { + for ( n = BDY(p); NEXT(n); n = NEXT(n) ); + m = (NBM)BDY(n); + *rp = m->c; + } +} + +void Pnbp_trest(NODE arg, NBP *rp) +{ + NBP p; + NODE n,r,r0; + + p = (NBP)ARG0(arg); + if ( !p ) *rp = 0; + else { + n = BDY(p); + for ( r0 = 0; NEXT(n); n = NEXT(n) ) { + NEXTNODE(r0,r); + BDY(r) = (pointer)BDY(n); + } + if ( r0 ) { + NEXT(r) = 0; + MKNBP(*rp,r0); + } else + *rp = 0; + } +} + +void Pnbm_deg(NODE arg, Q *rp) +{ + NBP p; + NBM m; + + p = (NBP)ARG0(arg); + if ( !p ) + STOQ(-1,*rp); + else { + m = (NBM)BDY(BDY(p)); + STOQ(m->d,*rp); + } +} + +void Pnbm_index(NODE arg, Q *rp) +{ + NBP p; + NBM m; + unsigned int *b; + int d,i,r; + + p = (NBP)ARG0(arg); + if ( !p ) + STOQ(0,*rp); + else { + m = (NBM)BDY(BDY(p)); + d = m->d; + if ( d > 32 ) + error("nbm_index : weight too large"); + b = m->b; + for ( r = 0, i = d-2; i > 0; i-- ) + if ( !NBM_GET(b,i) ) r |= (1<<(d-2-i)); + STOQ(r,*rp); + } +} + +void Pnbm_hp_rest(NODE arg, LIST *rp) +{ + NBP p,h,r; + NBM m,m1; + NODE n; + int *b,*b1; + int d,d1,v,i,j,k; + + p = (NBP)ARG0(arg); + if ( !p ) + MKLIST(*rp,0); + else { + m = (NBM)BDY(BDY(p)); + b = m->b; d = m->d; + if ( !d ) + MKLIST(*rp,0); + else { + v = NBM_GET(b,0); + for ( i = 1; i < d; i++ ) + if ( NBM_GET(b,i) != v ) break; + NEWNBM(m1); NEWNBMBDY(m1,i); + b1 = m1->b; m1->d = i; m1->c = (P)ONE; + if ( v ) for ( j = 0; j < i; j++ ) NBM_SET(b1,j); + else for ( j = 0; j < i; j++ ) NBM_CLR(b1,j); + MKNODE(n,m1,0); MKNBP(h,n); + + d1 = d-i; + NEWNBM(m1); NEWNBMBDY(m1,d1); + b1 = m1->b; m1->d = d1; m1->c = (P)ONE; + for ( j = 0, k = i; j < d1; j++, k++ ) + if ( NBM_GET(b,k) ) NBM_SET(b1,j); + else NBM_CLR(b1,j); + MKNODE(n,m1,0); MKNBP(r,n); + n = mknode(2,h,r); + MKLIST(*rp,n); + } + } +} + +void Pnbm_hxky(NODE arg, LIST *rp) +{ + NBP p; + + p = (NBP)ARG0(arg); + if ( !p ) + *rp = 0; + else + separate_xky_nbm((NBM)BDY(BDY(p)),0,rp,0); +} + +void Pnbm_xky_rest(NODE arg,NBP *rp) +{ + NBP p; + + p = (NBP)ARG0(arg); + if ( !p ) + *rp = 0; + else + separate_xky_nbm((NBM)BDY(BDY(p)),0,0,rp); +} + +void Pnbm_hv(NODE arg, NBP *rp) +{ + NBP p; + + p = (NBP)ARG0(arg); + if ( !p ) + *rp = 0; + else + separate_nbm((NBM)BDY(BDY(p)),0,rp,0); +} + +void Pnbm_rest(NODE arg, NBP *rp) +{ + NBP p; + + p = (NBP)ARG0(arg); + if ( !p ) + *rp = 0; + else + separate_nbm((NBM)BDY(BDY(p)),0,0,rp); +} + +void Pnbm_tv(NODE arg, NBP *rp) +{ + NBP p; + + p = (NBP)ARG0(arg); + if ( !p ) + *rp = 0; + else + separate_tail_nbm((NBM)BDY(BDY(p)),0,0,rp); +} + +void Pnbm_trest(NODE arg, NBP *rp) +{ + NBP p; + + p = (NBP)ARG0(arg); + if ( !p ) + *rp = 0; + else + separate_tail_nbm((NBM)BDY(BDY(p)),0,rp,0); +} + +NBP fnode_to_nbp(FNODE f) +{ + Q r; + int n,i; + NBM m; + V v; + NBP u,u1,u2; + NODE t,b; + + if ( f->id == I_FORMULA ) { + r = eval(f); + NEWNBM(m); + if ( OID(r) == O_N ) { + m->d = 0; m->c = (P)r; m->b = 0; + } else { + v = VR((P)r); + m->d = 1; m->c = (P)ONE; NEWNBMBDY(m,1); + if ( !strcmp(NAME(v),"x") ) NBM_SET(m->b,0); + else NBM_CLR(m->b,0); + } + MKNODE(b,m,0); MKNBP(u,b); + return u; + } else if ( IS_NARYADD(f) ) { + t = (NODE)FA1(f); u = fnode_to_nbp((FNODE)BDY(t)); + for ( t = NEXT(t); t; t = NEXT(t) ) { + u1 = fnode_to_nbp((FNODE)BDY(t)); + addnbp(CO,u,u1,&u2); u = u2; + } + return u; + } else if ( IS_NARYMUL(f) ) { + t = (NODE)FA1(f); u = fnode_to_nbp((FNODE)BDY(t)); + for ( t = NEXT(t); t; t = NEXT(t) ) { + u1 = fnode_to_nbp((FNODE)BDY(t)); + mulnbp(CO,u,u1,&u2); u = u2; + } + return u; + } else if ( IS_BINARYPWR(f) ) { + u = fnode_to_nbp((FNODE)FA1(f)); + r = eval((FNODE)FA2(f)); + pwrnbp(CO,u,r,&u1); + return u1; + } +} + +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) +{ QUOTE q1,q2; FNODE f1,f2; int r; q1 = (QUOTE)ARG0(arg); f1 = (FNODE)BDY(q1); q2 = (QUOTE)ARG1(arg); f2 = (FNODE)BDY(q2); - if ( !q1->normalized ) f1 = fnode_normalize(f1,0); - if ( !q2->normalized ) f2 = fnode_normalize(f2,0); - r = fnode_normalize_comp(f1,f2); + f1 = fnode_normalize(f1,0); + f2 = fnode_normalize(f2,0); + r = nfnode_comp(f1,f2); STOQ(r,*rp); } -INLINE int fnode_is_number(FNODE f) +int fnode_is_var(FNODE f) { Obj obj; + VL vl,t,s; + DCP dc; + if ( fnode_is_coef(f) ) return 0; 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: + 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)); case I_FORMULA: @@ -2200,26 +2953,14 @@ int fnode_is_dependent(FNODE f,V v) } } -FNODE fnode_normalize_add(FNODE a1,FNODE a2,int expand); -FNODE fnode_normalize_mul(FNODE a1,FNODE a2,int expand); -FNODE fnode_normalize_pwr(FNODE a1,FNODE a2,int expand); -FNODE fnode_normalize_mul_coef(Num c,FNODE f,int expand); -FNODE fnode_expand_pwr(FNODE f,int n); -FNODE to_narymul(FNODE f); -FNODE to_naryadd(FNODE f); -FNODE fnode_node_to_naryadd(NODE n); -FNODE fnode_node_to_narymul(NODE n); -void fnode_base_exp(FNODE f,FNODE *bp,FNODE *ep); -void fnode_coef_body(FNODE f,Num *cp,FNODE *bp); - FNODE fnode_normalize(FNODE f,int expand) { FNODE a1,a2,mone,r,b2; NODE n; Q q; - if ( f->normalized && (f->expanded || !expand) ) return f; + if ( f->normalized && (f->expanded == expand) ) return f; STOQ(-1,q); mone = mkfnode(1,I_FORMULA,q); switch ( f->id ) { @@ -2228,7 +2969,7 @@ FNODE fnode_normalize(FNODE f,int expand) break; case I_MINUS: - r = fnode_normalize_mul_coef((Num)q, + r = nfnode_mul_coef((Obj)q, fnode_normalize(FA0(f),expand),expand); break; @@ -2238,21 +2979,21 @@ FNODE fnode_normalize(FNODE f,int expand) a2 = fnode_normalize(FA2(f),expand); switch ( OPNAME(f) ) { case '+': - r = fnode_normalize_add(a1,a2,expand); + r = nfnode_add(a1,a2,expand); break; case '-': - a2 = fnode_normalize_mul_coef((Num)q,a2,expand); - r = fnode_normalize_add(a1,a2,expand); + a2 = nfnode_mul_coef((Obj)q,a2,expand); + r = nfnode_add(a1,a2,expand); break; case '*': - r = fnode_normalize_mul(a1,a2,expand); + r = nfnode_mul(a1,a2,expand); break; case '/': - a2 = fnode_normalize_pwr(a2,mone,expand); - r = fnode_normalize_mul(a1,a2,expand); + a2 = nfnode_pwr(a2,mone,expand); + r = nfnode_mul(a1,a2,expand); break; case '^': - r = fnode_normalize_pwr(a1,a2,expand); + r = nfnode_pwr(a1,a2,expand); break; default: r = mkfnode(3,I_BOP,FA0(f),a1,a2); @@ -2267,7 +3008,7 @@ FNODE fnode_normalize(FNODE f,int expand) r = fnode_normalize(BDY(n),expand); n = NEXT(n); for ( ; n; n = NEXT(n) ) { a1 = fnode_normalize(BDY(n),expand); - r = fnode_normalize_add(r,a1,expand); + r = nfnode_add(r,a1,expand); } break; case '*': @@ -2275,7 +3016,7 @@ FNODE fnode_normalize(FNODE f,int expand) r = fnode_normalize(BDY(n),expand); n = NEXT(n); for ( ; n; n = NEXT(n) ) { a1 = fnode_normalize(BDY(n),expand); - r = fnode_normalize_mul(r,a1,expand); + r = nfnode_mul(r,a1,expand); } break; default: @@ -2323,12 +3064,12 @@ FNODE fnode_apply(FNODE f,FNODE (*func)(),int expand) return r; } -FNODE fnode_normalize_add(FNODE f1,FNODE f2,int expand) +FNODE nfnode_add(FNODE f1,FNODE f2,int expand) { NODE n1,n2,r0,r; FNODE b1,b2; int s; - Num c1,c2,c; + Obj c1,c2,c; if ( IS_ZERO(f1) ) return f2; else if ( IS_ZERO(f2) ) return f1; @@ -2337,14 +3078,14 @@ FNODE fnode_normalize_add(FNODE f1,FNODE f2,int expand r0 = 0; while ( n1 && n2 ) { fnode_coef_body(BDY(n1),&c1,&b1); fnode_coef_body(BDY(n2),&c2,&b2); - if ( (s = fnode_normalize_comp(b1,b2)) > 0 ) { + if ( (s = nfnode_comp(b1,b2)) > 0 ) { NEXTNODE(r0,r); BDY(r) = BDY(n1); n1 = NEXT(n1); } else if ( s < 0 ) { NEXTNODE(r0,r); BDY(r) = BDY(n2); n2 = NEXT(n2); } else { - addnum(0,c1,c2,&c); + arf_add(CO,c1,c2,&c); if ( c ) { - NEXTNODE(r0,r); BDY(r) = fnode_normalize_mul_coef(c,b1,expand); + NEXTNODE(r0,r); BDY(r) = nfnode_mul_coef(c,b1,expand); } n1 = NEXT(n1); n2 = NEXT(n2); } @@ -2358,58 +3099,55 @@ FNODE fnode_normalize_add(FNODE f1,FNODE f2,int expand else if ( r0 ) NEXT(r) = 0; - return fnode_node_to_naryadd(r0); + return fnode_node_to_nary(addfs,r0); } -FNODE fnode_node_to_naryadd(NODE n) +FNODE fnode_node_to_nary(ARF op,NODE n) { - if ( !n ) return mkfnode(1,I_FORMULA,0); - else if ( !NEXT(n) ) return BDY(n); - else return mkfnode(2,I_NARYOP,addfs,n); + if ( !n ) { + if ( op->name[0] == '+' ) + return mkfnode(1,I_FORMULA,NULLP); + else + return mkfnode(1,I_FORMULA,ONE); + } else if ( !NEXT(n) ) return BDY(n); + else return mkfnode(2,I_NARYOP,op,n); } -FNODE fnode_node_to_narymul(NODE n) +FNODE nfnode_mul(FNODE f1,FNODE f2,int expand) { - if ( !n ) return mkfnode(1,I_FORMULA,ONE); - else if ( !NEXT(n) ) return BDY(n); - else return mkfnode(2,I_NARYOP,mulfs,n); -} - -FNODE fnode_normalize_mul(FNODE f1,FNODE f2,int expand) -{ NODE n1,n2,r0,r,r1; FNODE b1,b2,e1,e2,cc,t,t1; FNODE *m; int s; - Num c1,c2,c,e; + Obj c1,c2,c,e; int l1,l,i,j; - if ( IS_ZERO(f1) || IS_ZERO(f2) ) return mkfnode(1,I_FORMULA,0); - else if ( fnode_is_number(f1) ) - return fnode_normalize_mul_coef((Num)eval(f1),f2,expand); - else if ( fnode_is_number(f2) ) - return fnode_normalize_mul_coef((Num)eval(f2),f1,expand); + if ( IS_ZERO(f1) || IS_ZERO(f2) ) return mkfnode(1,I_FORMULA,NULLP); + else if ( fnode_is_coef(f1) ) + return nfnode_mul_coef((Obj)eval(f1),f2,expand); + else if ( fnode_is_coef(f2) ) + return nfnode_mul_coef((Obj)eval(f2),f1,expand); if ( expand && IS_NARYADD(f1) ) { - t = mkfnode(1,I_FORMULA,0); + t = mkfnode(1,I_FORMULA,NULLP); for ( n1 = (NODE)FA1(f1); n1; n1 = NEXT(n1) ) { - t1 = fnode_normalize_mul(BDY(n1),f2,expand); - t = fnode_normalize_add(t,t1,expand); + t1 = nfnode_mul(BDY(n1),f2,expand); + t = nfnode_add(t,t1,expand); } return t; } if ( expand && IS_NARYADD(f2) ) { - t = mkfnode(1,I_FORMULA,0); + t = mkfnode(1,I_FORMULA,NULLP); for ( n2 = (NODE)FA1(f2); n2; n2 = NEXT(n2) ) { - t1 = fnode_normalize_mul(f1,BDY(n2),expand); - t = fnode_normalize_add(t,t1,expand); + t1 = nfnode_mul(f1,BDY(n2),expand); + t = nfnode_add(t,t1,expand); } return t; } fnode_coef_body(f1,&c1,&b1); fnode_coef_body(f2,&c2,&b2); - mulnum(0,c1,c2,&c); - if ( !c ) return mkfnode(1,I_FORMULA,0); + arf_mul(CO,c1,c2,&c); + if ( !c ) return mkfnode(1,I_FORMULA,NULLP); n1 = (NODE)FA1(to_narymul(b1)); n2 = (NODE)FA1(to_narymul(b2)); @@ -2422,9 +3160,19 @@ FNODE fnode_normalize_mul(FNODE f1,FNODE f2,int expand else { fnode_base_exp(m[i-1],&b1,&e1); fnode_base_exp(BDY(r),&b2,&e2); if ( compfnode(b1,b2) ) break; - addnum(0,eval(e1),eval(e2),&e); + arf_add(CO,eval(e1),eval(e2),&e); if ( !e ) i--; - else if ( UNIQ(e) ) + else if ( expand == 2 ) { + if ( INT(e) && SGN((Q)e) < 0 ) { + t1 = mkfnode(3,I_BOP,pwrfs,b1,mkfnode(1,I_FORMULA,e)); + /* r=(r0|rest)->(r0,t1|rest) */ + t = BDY(r); + MKNODE(r1,t1,NEXT(r)); + MKNODE(r,t,r1); + i--; + } else + m[i++] = BDY(r); + } else if ( UNIQ(e) ) m[i-1] = b1; else m[i-1] = mkfnode(3,I_BOP,pwrfs,b1,mkfnode(1,I_FORMULA,e)); @@ -2436,31 +3184,34 @@ FNODE fnode_normalize_mul(FNODE f1,FNODE f2,int expand if ( !UNIQ(c) ) { cc = mkfnode(1,I_FORMULA,c); MKNODE(r1,cc,r); r = r1; } - return fnode_node_to_narymul(r); + return fnode_node_to_nary(mulfs,r); } -FNODE fnode_normalize_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; - Num c,c1,nf2; + Obj c,c1; + Num nf2; int ee; NODE arg,n,t0,t1; Q q; if ( IS_ZERO(f2) ) return mkfnode(1,I_FORMULA,ONE); - else if ( IS_ZERO(f1) ) return mkfnode(1,I_FORMULA,0); - else if ( fnode_is_number(f1) ) { + else if ( IS_ZERO(f1) ) return mkfnode(1,I_FORMULA,NULLP); + else if ( fnode_is_coef(f1) ) { if ( fnode_is_integer(f2) ) { if ( fnode_is_one(f2) ) return f1; 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); } - } else + } else { + f1 = mkfnode(1,I_FORMULA,eval(f1)); return mkfnode(3,I_BOP,pwrfs,f1,f2); + } } else if ( IS_BINARYPWR(f1) ) { b1 = FA1(f1); e1 = FA2(f1); - e = fnode_normalize_mul(e1,f2,expand); + e = nfnode_mul(e1,f2,expand); if ( fnode_is_one(e) ) return b1; else @@ -2469,11 +3220,11 @@ FNODE fnode_normalize_pwr(FNODE f1,FNODE f2,int expand && fnode_is_integer(f2) ) { fnode_coef_body(f1,&c1,&b1); nf2 = (Num)eval(f2); - pwrnum(0,(Num)c1,nf2,&c); + arf_pwr(CO,c1,(Obj)nf2,&c); ee = QTOS((Q)nf2); cc = mkfnode(1,I_FORMULA,c); if ( fnode_is_nonnegative_integer(f2) ) - b = fnode_expand_pwr(b1,ee); + b = fnode_expand_pwr(b1,ee,expand); else { STOQ(-1,q); mone = mkfnode(1,I_FORMULA,q); @@ -2482,36 +3233,48 @@ FNODE fnode_normalize_pwr(FNODE f1,FNODE f2,int expand inv = mkfnode(3,I_BOP,pwrfs,BDY(n),mone); MKNODE(t1,inv,t0); t0 = t1; } - b1 = fnode_node_to_narymul(t0); - b = fnode_expand_pwr(b1,-ee); + b1 = fnode_node_to_nary(mulfs,t0); + b = fnode_expand_pwr(b1,-ee,expand); } if ( fnode_is_one(cc) ) return b; else - return fnode_node_to_narymul(mknode(2,cc,b)); + return fnode_node_to_nary(mulfs,mknode(2,cc,b)); } else if ( expand && fnode_is_integer(f2) && fnode_is_nonnegative_integer(f2) ) { q = (Q)eval(f2); - if ( PL(NM(q)) > 1 ) error("fnode_normalize_pwr : exponent too large"); - return fnode_expand_pwr(f1,QTOS(q)); + if ( PL(NM(q)) > 1 ) error("nfnode_pwr : exponent too large"); + return fnode_expand_pwr(f1,QTOS(q),expand); } else return mkfnode(3,I_BOP,pwrfs,f1,f2); } -FNODE fnode_expand_pwr(FNODE f,int n) +FNODE fnode_expand_pwr(FNODE f,int n,int expand) { - int n1; - FNODE f1,f2; + int n1,i; + FNODE f1,f2,fn; + Q q; if ( !n ) return mkfnode(1,I_FORMULA,ONE); - else if ( IS_ZERO(f) ) return mkfnode(1,I_FORMULA,0); + else if ( IS_ZERO(f) ) return mkfnode(1,I_FORMULA,NULLP); else if ( n == 1 ) return f; else { - n1 = n/2; - f1 = fnode_expand_pwr(f,n1); - f2 = fnode_normalize_mul(f1,f1,1); - if ( n%2 ) f2 = fnode_normalize_mul(f2,f,1); - return f2; + switch ( expand ) { + case 1: + n1 = n/2; + f1 = fnode_expand_pwr(f,n1,expand); + f2 = nfnode_mul(f1,f1,expand); + if ( n%2 ) f2 = nfnode_mul(f2,f,1); + return f2; + case 2: + for ( i = 1, f1 = f; i < n; i++ ) + f1 = nfnode_mul(f1,f,expand); + return f1; + case 0: default: + STOQ(n,q); + fn = mkfnode(1,I_FORMULA,q); + return mkfnode(3,I_BOP,pwrfs,f,fn); + } } } @@ -2549,143 +3312,196 @@ FNODE to_narymul(FNODE f) return r; } -FNODE fnode_normalize_mul_coef(Num c,FNODE f,int expand) +FNODE nfnode_mul_coef(Obj c,FNODE f,int expand) { FNODE b1,cc; - Num c1,c2; + Obj c1,c2; NODE n,r,r0; if ( !c ) - return mkfnode(I_FORMULA,0); + return mkfnode(1,I_FORMULA,NULLP); else { fnode_coef_body(f,&c1,&b1); - mulnum(0,c,c1,&c2); + arf_mul(CO,c,c1,&c2); if ( UNIQ(c2) ) return b1; else { cc = mkfnode(1,I_FORMULA,c2); if ( fnode_is_number(b1) ) { if ( !fnode_is_one(b1) ) - error("fnode_normalize_mul_coef : cannot happen"); + error("nfnode_mul_coef : cannot happen"); else return cc; } else if ( IS_NARYMUL(b1) ) { MKNODE(n,cc,FA1(b1)); - return fnode_node_to_narymul(n); + return fnode_node_to_nary(mulfs,n); } else if ( expand && IS_NARYADD(b1) ) { for ( r0 = 0, n = (NODE)FA1(b1); n; n = NEXT(n) ) { NEXTNODE(r0,r); - BDY(r) = fnode_normalize_mul_coef(c2,BDY(n),expand); + BDY(r) = nfnode_mul_coef(c2,BDY(n),expand); } if ( r0 ) NEXT(r) = 0; - return fnode_node_to_naryadd(r0); + return fnode_node_to_nary(addfs,r0); } else - return fnode_node_to_narymul(mknode(2,cc,b1)); + return fnode_node_to_nary(mulfs,mknode(2,cc,b1)); } } } -void fnode_coef_body(FNODE f,Num *cp,FNODE *bp) +void fnode_coef_body(FNODE f,Obj *cp,FNODE *bp) { FNODE c; - if ( fnode_is_number(f) ) { - *cp = eval(f); *bp = mkfnode(1,I_FORMULA,ONE); + if ( fnode_is_coef(f) ) { + *cp = (Obj)eval(f); *bp = mkfnode(1,I_FORMULA,ONE); } else if ( IS_NARYMUL(f) ) { c=(FNODE)BDY((NODE)FA1(f)); - if ( fnode_is_number(c) ) { - *cp = eval(c); - *bp = fnode_node_to_narymul(NEXT((NODE)FA1(f))); + if ( fnode_is_coef(c) ) { + *cp = (Obj)eval(c); + *bp = fnode_node_to_nary(mulfs,NEXT((NODE)FA1(f))); } else { - *cp = (Num)ONE; *bp = f; + *cp = (Obj)ONE; *bp = f; } } else { - *cp = (Num)ONE; *bp = f; + *cp = (Obj)ONE; *bp = f; } } -int fnode_normalize_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; -int fnode_normalize_comp(FNODE f1,FNODE f2) + switch ( f->id ) { + case I_FORMULA: + if ( fnode_is_coef(f) ) return 0; + else if ( fnode_is_var(f) ) { + if ( !tab ) return 0; + v = VR((P)FA0(f)); + for ( i = 0; tab[i].v; i++ ) + if ( v == tab[i].v ) return tab[i].w; + return 0; + } 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 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; - int r,i1,i2; + int r,i1,i2,ret; char *nm1,*nm2; - FNODE b1,b2,e1,e2,g; - Num ee,ee1,c1,c2; + FNODE b1,b2,e1,e2,g,a1,a2,fn1,fn2,h1,h2; + Num ee,ee1; + Obj c1,c2; + int w1,w2; if ( IS_NARYADD(f1) || IS_NARYADD(f2) ) { f1 = to_naryadd(f1); f2 = to_naryadd(f2); n1 = (NODE)FA1(f1); n2 = (NODE)FA1(f2); - while ( n1 && n2 ) - if ( r = fnode_normalize_comp(BDY(n1),BDY(n2)) ) return r; - else { - n1 = NEXT(n1); n2 = NEXT(n2); - } - return n1?1:(n2?-1:0); + for ( ; n1 && n2; n1 = NEXT(n1), n2 = NEXT(n2) ) { + r = nfnode_comp_lex(BDY(n1),BDY(n2)); + if ( r ) return r; + } + if ( !n1 && !n2 ) return 0; + h1 = n1 ? (FNODE)BDY(n1) : mkfnode(1,I_FORMULA,NULLP); + h2 = n2 ? (FNODE)BDY(n2) : mkfnode(1,I_FORMULA,NULLP); + return nfnode_comp_lex(h1,h2); } if ( IS_NARYMUL(f1) || IS_NARYMUL(f2) ) { fnode_coef_body(f1,&c1,&b1); 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); n1 = (NODE)FA1(b1); n2 = (NODE)FA1(b2); - while ( 1 ) { - while ( n1 && n2 && !compfnode(BDY(n1),BDY(n2)) ) { - n1 = NEXT(n1); n2 = NEXT(n2); - } - if ( !n1 || !n2 ) { - return n1?1:(n2?-1:0); - } - fnode_base_exp(BDY(n1),&b1,&e1); - fnode_base_exp(BDY(n2),&b2,&e2); - - if ( r = fnode_normalize_comp(b1,b2) ) { - if ( r > 0 ) - return fnode_normalize_comp(e1,mkfnode(1,I_FORMULA,0)); - else if ( r < 0 ) - return fnode_normalize_comp(mkfnode(1,I_FORMULA,0),e2); - } else { - n1 = NEXT(n1); n2 = NEXT(n2); - if ( fnode_is_number(e1) && fnode_is_number(e2) ) { - /* f1 = t b^e1 ... , f2 = t b^e2 ... */ - subnum(0,eval(e1),eval(e2),&ee); - r = compnum(0,ee,0); - if ( r > 0 ) { - g = mkfnode(3,I_BOP,pwrfs,b1,mkfnode(1,I_FORMULA,ee)); - MKNODE(n1,g,n1); - } else if ( r < 0 ) { - chsgnnum(ee,&ee1); - g = mkfnode(3,I_BOP,pwrfs,b1,mkfnode(1,I_FORMULA,ee1)); - MKNODE(n2,g,n2); - } - } else { - r = fnode_normalize_comp(e1,e2); - if ( r > 0 ) return 1; - else if ( r < 0 ) return -1; - } - } + for ( ; n1 && n2; n1 = NEXT(n1), n2 = NEXT(n2) ) { + r = nfnode_comp_lex(BDY(n1),BDY(n2)); + if ( r ) return r; } + if ( !n1 && !n2 ) return 0; + h1 = n1 ? (FNODE)BDY(n1) : mkfnode(1,I_FORMULA,ONE); + h2 = n2 ? (FNODE)BDY(n2) : mkfnode(1,I_FORMULA,ONE); + return nfnode_comp_lex(h1,h2); } - if ( IS_BINARYPWR(f1) || IS_BINARYPWR(f2) ) - return fnode_normalize_comp_pwr(f1,f2); + if ( IS_BINARYPWR(f1) || IS_BINARYPWR(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,NULLP)); + else if ( r < 0 ) + return nfnode_comp_lex(mkfnode(1,I_FORMULA,NULLP),e2); + } else return nfnode_comp_lex(e1,e2); + } - /* now, IDs of f1 and f2 must be I_FORMULA, I_FUNC, 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 */ switch ( f1->id ) { case I_FORMULA: switch ( f2->id ) { case I_FORMULA: - return arf_comp(CO,FA0(f1),FA0(f2)); - case I_FUNC: case I_PVAR: + return arf_comp(qt_current_ord?qt_current_ord:CO,FA0(f1),FA0(f2)); + case I_FUNC: case I_IFUNC: case I_PVAR: return -1; default: - error("fnode_normalize_comp : undefined"); + error("nfnode_comp_lex : undefined"); } break; - case I_FUNC: + case I_FUNC: case I_FUNC_QARG: switch ( f2->id ) { case I_FORMULA: return 1; - case I_FUNC: + case I_PVAR: case I_IFUNC: + return -1; + case I_FUNC: case I_FUNC_QARG: nm1 = ((FUNC)FA0(f1))->name; nm2 = ((FUNC)FA0(f2))->name; r = strcmp(nm1,nm2); if ( r > 0 ) return 1; @@ -2694,51 +3510,61 @@ int fnode_normalize_comp(FNODE f1,FNODE f2) /* compare args */ n1 = FA0((FNODE)FA1(f1)); n2 = FA0((FNODE)FA1(f2)); while ( n1 && n2 ) - if ( r = fnode_normalize_comp(BDY(n1),BDY(n2)) ) return r; + if ( r = nfnode_comp_lex(BDY(n1),BDY(n2)) ) return r; else { n1 = NEXT(n1); n2 = NEXT(n2); } return n1?1:(n2?-1:0); } break; - case I_PVAR: - return -1; default: - error("fnode_normalize_comp : undefined"); + error("nfnode_comp_lex : undefined"); } case I_PVAR: switch ( f2->id ) { - case I_FORMULA: case I_FUNC: + case I_FORMULA: case I_FUNC: case I_FUNC_QARG: return 1; + case I_IFUNC: + return -1; case I_PVAR: i1 = (int)FA0(f1); i2 = (int)FA0(f2); if ( i1 > i2 ) return 1; else if ( i1 < i2 ) return -1; else return 0; default: - error("fnode_normalize_comp : undefined"); + error("nfnode_comp_lex : undefined"); } break; + case I_IFUNC: + switch ( f2->id ) { + case I_FORMULA: case I_FUNC: case I_FUNC_QARG: case I_PVAR: + return 1; + case I_IFUNC: + i1 = (int)FA0((FNODE)FA0(f1)); + i2 = (int)FA0((FNODE)FA0(f2)); + if ( i1 > i2 ) return 1; + else if ( i1 < i2 ) return -1; + else { + /* compare args */ + n1 = FA0((FNODE)FA1(f1)); n2 = FA0((FNODE)FA1(f2)); + while ( n1 && n2 ) + if ( r = nfnode_comp_lex(BDY(n1),BDY(n2)) ) return r; + else { + n1 = NEXT(n1); n2 = NEXT(n2); + } + return n1?1:(n2?-1:0); + } + break; + + default: + error("nfnode_comp_lex : undefined"); + } + break; default: - error("fnode_normalize_comp : undefined"); + error("nfnode_comp_lex : undefined"); } } -int fnode_normalize_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 = fnode_normalize_comp(b1,b2) ) { - if ( r > 0 ) - return fnode_normalize_comp(e1,mkfnode(1,I_FORMULA,0)); - else if ( r < 0 ) - return fnode_normalize_comp(mkfnode(1,I_FORMULA,0),e2); - } else return fnode_normalize_comp(e1,e2); -} - NODE append_node(NODE a1,NODE a2) { NODE t,t0; @@ -2754,19 +3580,27 @@ NODE append_node(NODE a1,NODE a2) } } -int fnode_normalize_match(FNODE f,FNODE pat,NODE *rp) +int nfnode_match(FNODE f,FNODE pat,NODE *rp) { NODE m,m1,m2,base,exp,fa,pa,n; LIST l; QUOTE qp,qf; - FNODE fbase,fexp,a; + FNODE fbase,fexp,a,fh; FUNC ff,pf; int r; + if ( !pat ) + if ( !f ) { + *rp = 0; + return 1; + } else + return 0; + else if ( !f ) + return 0; switch ( pat->id ) { case I_PVAR: /* [[pat,f]] */ - *rp = mknode(1,mknode(2,(int)FA0(pat),f),0); + *rp = mknode(1,mknode(2,(int)FA0(pat),f)); return 1; case I_FORMULA: @@ -2778,32 +3612,39 @@ int fnode_normalize_match(FNODE f,FNODE pat,NODE *rp) case I_BOP: /* OPNAME should be "^" */ if ( !IS_BINARYPWR(pat) ) - error("fnode_normalize_match : invalid BOP"); + error("nfnode_match : invalid BOP"); if ( IS_BINARYPWR(f) ) { fbase = FA1(f); fexp = FA2(f); } else { fbase = f; fexp = mkfnode(1,I_FORMULA,ONE); } - if ( !fnode_normalize_match(fbase,FA1(pat),&base) ) return 0; - a = rewrite_fnode(FA2(pat),base); - if ( !fnode_normalize_match(fexp,a,&exp) ) return 0; + if ( !nfnode_match(fbase,FA1(pat),&base) ) return 0; + a = rewrite_fnode(FA2(pat),base,0); + if ( !nfnode_match(fexp,a,&exp) ) return 0; else { *rp = append_node(base,exp); return 1; } break; - case I_FUNC: + case I_FUNC: case I_IFUNC: if ( f->id != I_FUNC ) return 0; - ff = (FUNC)FA0(f); pf = (FUNC)FA0(pat); - if ( strcmp(ff->fullname,pf->fullname) ) return 0; + ff = (FUNC)FA0(f); + if ( pat->id == I_FUNC ) { + pf = (FUNC)FA0(pat); + if ( strcmp(ff->fullname,pf->fullname) ) return 0; + m = 0; + } else { + /* XXX : I_FUNC_HEAD is a dummy id to pass FUNC */ + fh = mkfnode(1,I_FUNC_HEAD,FA0(f)); + m = mknode(1,mknode(2,FA0((FNODE)FA0(pat)),fh),NULLP); + } /* FA1(f) and FA1(pat) are I_LIST */ fa = (NODE)FA0((FNODE)FA1(f)); pa = (NODE)FA0((FNODE)FA1(pat)); - m = 0; while ( fa && pa ) { - a = rewrite_fnode(BDY(pa),m); - if ( !fnode_normalize_match(BDY(fa),a,&m1) ) return 0; + a = rewrite_fnode(BDY(pa),m,0); + if ( !nfnode_match(BDY(fa),a,&m1) ) return 0; m = append_node(m1,m); fa = NEXT(fa); pa = NEXT(pa); } @@ -2815,15 +3656,15 @@ int fnode_normalize_match(FNODE f,FNODE pat,NODE *rp) case I_NARYOP: if ( IS_NARYADD(pat) ) - return fnode_normalize_match_naryadd(f,pat,rp); + return nfnode_match_naryadd(f,pat,rp); else if ( IS_NARYMUL(pat) ) - return fnode_normalize_match_narymul(f,pat,rp); + return nfnode_match_narymul(f,pat,rp); else - error("fnode_normalize_match : invalid NARYOP"); + error("nfnode_match : invalid NARYOP"); break; default: - error("fnode_normalize_match : invalid pattern"); + error("nfnode_match : invalid pattern"); } } @@ -2838,14 +3679,14 @@ FNODE fnode_removeith_naryadd(FNODE p,int i) l = length(a); if ( i < 0 || i >= l ) error("fnode_removeith_naryadd: invalid index"); else if ( i == 0 ) - return fnode_node_to_naryadd(NEXT(a)); + return fnode_node_to_nary(addfs,NEXT(a)); else { for ( r0 = 0, k = 0, t = a; k < i; k++, t = NEXT(t) ) { NEXTNODE(r0,r); BDY(r) = BDY(t); } NEXT(r) = NEXT(t); - return fnode_node_to_naryadd(r0); + return fnode_node_to_nary(addfs,r0); } } @@ -2859,7 +3700,7 @@ FNODE fnode_left_narymul(FNODE p,int i) a = (NODE)FA1(p); l = length(a); if ( i < 0 || i >= l ) error("fnode_left_narymul : invalid index"); - if ( i == 0 ) return mkfnode(1,I_FORMULA,ONE); + if ( i == 0 ) return 0; else if ( i == 1 ) return (FNODE)BDY(a); else { for ( r0 = 0, k = 0, t = a; k < i; k++, t = NEXT(t) ) { @@ -2867,7 +3708,7 @@ FNODE fnode_left_narymul(FNODE p,int i) BDY(r) = BDY(t); } NEXT(r) = 0; - return fnode_node_to_narymul(r0); + return fnode_node_to_nary(mulfs,r0); } } @@ -2880,14 +3721,14 @@ FNODE fnode_right_narymul(FNODE p,int i) a = (NODE)FA1(p); l = length(a); if ( i < 0 || i >= l ) error("fnode_right_narymul : invalid index"); - if ( i == l-1 ) return mkfnode(1,I_FORMULA,ONE); + if ( i == l-1 ) return 0; else { for ( k = 0, t = a; k <= i; k++, t = NEXT(t) ); - return fnode_node_to_narymul(t); + return fnode_node_to_nary(mulfs,t); } } -int fnode_normalize_match_naryadd(FNODE f,FNODE p,NODE *rp) +int nfnode_match_naryadd(FNODE f,FNODE p,NODE *rp) { int fl,pl,fi,pi; NODE fa,pa,t,s,m,m1; @@ -2899,7 +3740,7 @@ int fnode_normalize_match_naryadd(FNODE f,FNODE p,NODE if ( fl < pl ) return 0; else if ( pl == 1 ) { if ( fl == 1 ) - return fnode_normalize_match(BDY(fa),BDY(pa),rp); + return nfnode_match(BDY(fa),BDY(pa),rp); else return 0; } else { @@ -2909,24 +3750,24 @@ int fnode_normalize_match_naryadd(FNODE f,FNODE p,NODE /* all are I_PVAR */ m = 0; for ( t = pa, s = fa; NEXT(t); t = NEXT(t), s = NEXT(s) ) { - fnode_normalize_match(BDY(s),BDY(t),&m1); + nfnode_match(BDY(s),BDY(t),&m1); m = append_node(m1,m); } if ( !NEXT(s) ) fr = (FNODE)BDY(s); else fr = mkfnode(2,I_NARYOP,FA0(f),s); - fnode_normalize_match(fr,BDY(t),&m1); + nfnode_match(fr,BDY(t),&m1); *rp = append_node(m1,m); return 1; } else { pivot = (FNODE)BDY(t); pr = fnode_removeith_naryadd(p,pi); for ( s = fa, fi = 0; s; s = NEXT(s), fi++ ) { - if ( fnode_normalize_match(BDY(s),pivot,&m) ) { + if ( nfnode_match(BDY(s),pivot,&m) ) { fr = fnode_removeith_naryadd(f,fi); - prr = rewrite_fnode(pr,m); - if ( fnode_normalize_match(fr,prr,&m1) ) { + prr = rewrite_fnode(pr,m,0); + if ( nfnode_match(fr,prr,&m1) ) { *rp = append_node(m,m1); return 1; } @@ -2937,7 +3778,7 @@ int fnode_normalize_match_naryadd(FNODE f,FNODE p,NODE } } -int fnode_normalize_match_narymul(FNODE f,FNODE p,NODE *rp) +int nfnode_match_narymul(FNODE f,FNODE p,NODE *rp) { int fl,pl,fi,pi; NODE fa,pa,t,s,m,m1; @@ -2949,7 +3790,7 @@ int fnode_normalize_match_narymul(FNODE f,FNODE p,NODE if ( fl < pl ) return 0; else if ( pl == 1 ) { if ( fl == 1 ) - return fnode_normalize_match(BDY(fa),BDY(pa),rp); + return nfnode_match(BDY(fa),BDY(pa),rp); else return 0; } else { @@ -2959,16 +3800,16 @@ int fnode_normalize_match_narymul(FNODE f,FNODE p,NODE /* all are I_PVAR */ m = 0; for ( t = pa, s = fa; NEXT(t); t = NEXT(t), s = NEXT(s) ) { - pr = rewrite_fnode(BDY(t),m); - if ( !fnode_normalize_match(BDY(s),pr,&m1) ) return 0; + pr = rewrite_fnode(BDY(t),m,0); + if ( !nfnode_match(BDY(s),pr,&m1) ) return 0; m = append_node(m1,m); } if ( !NEXT(s) ) fr = (FNODE)BDY(s); else fr = mkfnode(2,I_NARYOP,FA0(f),s); - pr = rewrite_fnode(BDY(t),m); - if ( !fnode_normalize_match(fr,pr,&m1) ) return 0; + pr = rewrite_fnode(BDY(t),m,0); + if ( !nfnode_match(fr,pr,&m1) ) return 0; *rp = append_node(m1,m); return 1; } else { @@ -2977,14 +3818,15 @@ int fnode_normalize_match_narymul(FNODE f,FNODE p,NODE pright = fnode_right_narymul(p,pi); /* XXX : incomplete */ for ( s = fa, fi = 0; s; s = NEXT(s), fi++ ) { - if ( fnode_normalize_match(BDY(s),pivot,&m) ) { + if ( fi < pi ) continue; + if ( nfnode_match(BDY(s),pivot,&m) ) { fleft = fnode_left_narymul(f,fi); - pleft1 = rewrite_fnode(pleft,m); - if ( fnode_normalize_match(fleft,pleft1,&m1) ) { + pleft1 = rewrite_fnode(pleft,m,0); + if ( nfnode_match(fleft,pleft1,&m1) ) { m = append_node(m1,m); fright = fnode_right_narymul(f,fi); - pright1 = rewrite_fnode(pright,m); - if ( fnode_normalize_match(fright,pright1,&m1) ) { + pright1 = rewrite_fnode(pright,m,0); + if ( nfnode_match(fright,pright1,&m1) ) { *rp = append_node(m1,m); return 1; } @@ -2993,5 +3835,57 @@ int fnode_normalize_match_narymul(FNODE f,FNODE p,NODE } return 0; } + } +} + +NODE nfnode_pvars(FNODE pat,NODE found) +{ + int ind; + NODE prev,t; + int *pair; + + switch ( pat->id ) { + case I_PVAR: + ind = (int)FA0(pat); + for ( prev = 0, t = found; t; prev = t, t = NEXT(t) ) { + pair = (int *)BDY(t); + if ( pair[0] == ind ) { + pair[1]++; + return found; + } + } + pair = (int *)MALLOC_ATOMIC(sizeof(int)*2); + pair[0] = ind; pair[1] = 1; + if ( !prev ) + MKNODE(found,pair,0); + else + MKNODE(NEXT(prev),pair,0); + return found; + + case I_FORMULA: + return found; + + case I_BOP: + /* OPNAME should be "^" */ + if ( !IS_BINARYPWR(pat) ) + error("nfnode_pvar : invalid BOP"); + found = nfnode_pvars(FA1(pat),found); + found = nfnode_pvars(FA2(pat),found); + return found; + + case I_FUNC: + t = (NODE)FA0((FNODE)FA1(pat)); + for ( ; t; t = NEXT(t) ) + found = nfnode_pvars(BDY(t),found); + return found; + + case I_NARYOP: + t = (NODE)FA1(pat); + for ( ; t; t = NEXT(t) ) + found = nfnode_pvars(BDY(t),found); + return found; + + default: + error("nfnode_match : invalid pattern"); } }