=================================================================== RCS file: /home/cvs/OpenXM_contrib2/asir2000/builtin/strobj.c,v retrieving revision 1.104 retrieving revision 1.111 diff -u -p -r1.104 -r1.111 --- OpenXM_contrib2/asir2000/builtin/strobj.c 2005/11/30 05:08:00 1.104 +++ OpenXM_contrib2/asir2000/builtin/strobj.c 2005/12/18 01:44:16 1.111 @@ -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 1.103 2005/11/30 04:51:46 noro Exp $ + * $OpenXM: OpenXM_contrib2/asir2000/builtin/strobj.c,v 1.110 2005/12/14 09:06:54 noro Exp $ */ #include "ca.h" #include "parse.h" @@ -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; @@ -92,13 +93,15 @@ 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 Pnquote_comp(); -void Pnquote_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 Pquote_to_nbp(); +void Pqt_to_nbp(); void Pshuffle_mul(), Pharmonic_mul(); void Pnbp_hm(), Pnbp_ht(), Pnbp_hc(), Pnbp_rest(); void Pnbm_deg(); @@ -107,8 +110,8 @@ void Pnbm_hxky(), Pnbm_xky_rest(); void Pnbm_hv(), Pnbm_rest(); 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); @@ -120,7 +123,22 @@ 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}, @@ -138,19 +156,25 @@ 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_match",Pquote_match,2}, - {"quote_match_rewrite",Pquote_match_rewrite,-4}, + {"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}, - {"nquote_comp",Pnquote_comp,2}, - {"nquote_match",Pnquote_match,-3}, - {"quote_to_nbp",Pquote_to_nbp,1}, + {"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}, @@ -165,8 +189,8 @@ struct ftab str_tab[] = { {"nbm_hv", Pnbm_hv,1}, {"nbm_rest", Pnbm_rest,1}, - {"quote_to_nary",Pquote_to_nary,1}, - {"quote_to_bin",Pquote_to_bin,2}, + {"qt_to_nary",Pqt_to_nary,1}, + {"qt_to_bin",Pqt_to_bin,2}, {"quotetotex_tb",Pquotetotex_tb,2}, {"quotetotex",Pquotetotex,1}, @@ -570,9 +594,7 @@ 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; @@ -580,7 +602,7 @@ 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; @@ -591,46 +613,68 @@ 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 @@ -638,7 +682,7 @@ 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; @@ -647,8 +691,8 @@ 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; @@ -658,7 +702,7 @@ 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; @@ -666,14 +710,8 @@ 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; @@ -681,7 +719,7 @@ void Pquote_match(NODE arg,Q *rp) *rp = 0; } -void Pnquote_match(NODE arg,Q *rp) +void Pnqt_match(NODE arg,Q *rp) { QUOTE fq,pq; FNODE f,p; @@ -690,8 +728,8 @@ void Pnquote_match(NODE arg,Q *rp) NODE r; mode = argc(arg)==3 ? (Q)ARG2(arg) : 0; - fq = (QUOTE)ARG0(arg); Pquote_normalize(mknode(2,fq,mode),&fq); f = (FNODE)BDY(fq); - pq = (QUOTE)ARG1(arg); Pquote_normalize(mknode(2,pq,mode),&pq); p = (FNODE)BDY(pq); + 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); @@ -700,48 +738,98 @@ void Pnquote_match(NODE arg,Q *rp) *rp = 0; } +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; -FNODE rewrite_fnode(FNODE,NODE); + 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); -extern Obj VOIDobj; + m = QTOS(mode); + r = nfnode_match_rewrite(f,p,c,a,m); + if ( r ) { + MKQUOTE(q,r); + *rp = (Obj)q; + } else + *rp = obj; +} -void Pquote_match_rewrite(NODE arg,Obj *rp) +/* 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) @@ -818,14 +906,14 @@ 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; @@ -837,7 +925,7 @@ 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; @@ -849,7 +937,7 @@ 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; @@ -861,7 +949,7 @@ 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; @@ -880,7 +968,7 @@ 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; @@ -899,7 +987,7 @@ 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 ) { @@ -926,10 +1014,10 @@ 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: @@ -945,7 +1033,7 @@ 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); @@ -973,7 +1061,7 @@ 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; @@ -981,7 +1069,7 @@ 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); } } } @@ -1344,6 +1432,7 @@ void Pget_function_name(NODE arg,STRING *rp) } FNODE strip_paren(FNODE); +void objtotex_tb(Obj obj,TB tb); void fnodetotex_tb(FNODE f,TB tb) { @@ -1352,7 +1441,6 @@ 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; @@ -1420,7 +1508,14 @@ 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); @@ -1437,43 +1532,41 @@ 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: @@ -1698,33 +1791,7 @@ 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 */ @@ -1740,6 +1807,103 @@ 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; @@ -1855,9 +2019,13 @@ 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); @@ -2048,17 +2216,132 @@ 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); if ( ac == 2 ) expand = QTOS((Q)ARG1(arg)); @@ -2073,7 +2356,7 @@ void Pquote_normalize(NODE arg,QUOTE *rp) NBP fnode_to_nbp(FNODE f); -void Pquote_to_nbp(NODE arg,NBP *rp) +void Pqt_to_nbp(NODE arg,NBP *rp) { QUOTE q; FNODE f; @@ -2302,8 +2585,20 @@ NBP fnode_to_nbp(FNODE f) } } -void Pnquote_comp(NODE arg,Q *rp) +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(f); + STOQ(w,*rp); +} + +void Pnqt_comp(NODE arg,Q *rp) +{ QUOTE q1,q2; FNODE f1,f2; int r; @@ -2316,12 +2611,72 @@ void Pnquote_comp(NODE arg,Q *rp) 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: @@ -2460,19 +2815,7 @@ int fnode_is_dependent(FNODE f,V v) } } -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(Num 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_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; @@ -2488,7 +2831,7 @@ FNODE fnode_normalize(FNODE f,int expand) break; case I_MINUS: - r = nfnode_mul_coef((Num)q, + r = nfnode_mul_coef((Obj)q, fnode_normalize(FA0(f),expand),expand); break; @@ -2501,7 +2844,7 @@ FNODE fnode_normalize(FNODE f,int expand) r = nfnode_add(a1,a2,expand); break; case '-': - a2 = nfnode_mul_coef((Num)q,a2,expand); + a2 = nfnode_mul_coef((Obj)q,a2,expand); r = nfnode_add(a1,a2,expand); break; case '*': @@ -2588,7 +2931,7 @@ 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; @@ -2602,7 +2945,7 @@ FNODE nfnode_add(FNODE f1,FNODE f2,int expand) } 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) = nfnode_mul_coef(c,b1,expand); } @@ -2618,37 +2961,34 @@ FNODE nfnode_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,0); + 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) -{ - if ( !n ) return mkfnode(1,I_FORMULA,ONE); - else if ( !NEXT(n) ) return BDY(n); - else return mkfnode(2,I_NARYOP,mulfs,n); -} - FNODE nfnode_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 nfnode_mul_coef((Num)eval(f1),f2,expand); - else if ( fnode_is_number(f2) ) - return nfnode_mul_coef((Num)eval(f2),f1,expand); + 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); @@ -2668,7 +3008,7 @@ FNODE nfnode_mul(FNODE f1,FNODE f2,int expand) } 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); @@ -2682,7 +3022,7 @@ FNODE nfnode_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) ) m[i-1] = b1; @@ -2696,28 +3036,31 @@ FNODE nfnode_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 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 ( 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 = nfnode_mul(e1,f2,expand); @@ -2729,7 +3072,7 @@ FNODE nfnode_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) ) @@ -2742,13 +3085,13 @@ FNODE nfnode_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); + 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); @@ -2821,17 +3164,17 @@ FNODE to_narymul(FNODE f) 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; - Num c1,c2; + Obj c1,c2; NODE n,r,r0; if ( !c ) return mkfnode(I_FORMULA,0); 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); @@ -2842,54 +3185,121 @@ FNODE nfnode_mul_coef(Num c,FNODE f,int expand) 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) = 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 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) ) { + v = VR((P)FA0(f)); + for ( i = 0; tab[i].v; i++ ) + if ( v == tab[i].v ) return tab[i].w; + return w; + } 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,ret; char *nm1,*nm2; 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) ) { f1 = to_naryadd(f1); f2 = to_naryadd(f2); n1 = (NODE)FA1(f1); n2 = (NODE)FA1(f2); 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 { n1 = NEXT(n1); n2 = NEXT(n2); } @@ -2898,7 +3308,7 @@ int nfnode_comp(FNODE f1,FNODE f2) 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 ) { @@ -2911,11 +3321,11 @@ int nfnode_comp(FNODE f1,FNODE f2) fnode_base_exp(BDY(n1),&b1,&e1); fnode_base_exp(BDY(n2),&b2,&e2); - if ( r = nfnode_comp(b1,b2) ) { + if ( r = nfnode_comp_lex(b1,b2) ) { 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 ) - return nfnode_comp(mkfnode(1,I_FORMULA,0),e2); + return nfnode_comp_lex(mkfnode(1,I_FORMULA,0),e2); } else { n1 = NEXT(n1); n2 = NEXT(n2); if ( fnode_is_number(e1) && fnode_is_number(e2) ) { @@ -2931,36 +3341,44 @@ int nfnode_comp(FNODE f1,FNODE f2) MKNODE(n2,g,n2); } } else { - r = nfnode_comp(e1,e2); + r = nfnode_comp_lex(e1,e2); if ( r > 0 ) return 1; else if ( r < 0 ) return -1; } } } } - if ( IS_BINARYPWR(f1) || IS_BINARYPWR(f2) ) - return nfnode_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,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 */ - /* I_IFUNC > I_PVAR > I_FUNC > I_FORMULA */ + /* 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)); + 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("nfnode_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_PVAR: case I_IFUNC: return -1; - case I_FUNC: + 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; @@ -2969,7 +3387,7 @@ int nfnode_comp(FNODE f1,FNODE f2) /* compare args */ n1 = FA0((FNODE)FA1(f1)); n2 = FA0((FNODE)FA1(f2)); 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 { n1 = NEXT(n1); n2 = NEXT(n2); } @@ -2977,11 +3395,11 @@ int nfnode_comp(FNODE f1,FNODE f2) } break; default: - error("nfnode_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; @@ -2991,12 +3409,12 @@ int nfnode_comp(FNODE f1,FNODE f2) else if ( i1 < i2 ) return -1; else return 0; default: - error("nfnode_comp : undefined"); + error("nfnode_comp_lex : undefined"); } break; case I_IFUNC: switch ( f2->id ) { - case I_FORMULA: case I_FUNC: case I_PVAR: + case I_FORMULA: case I_FUNC: case I_FUNC_QARG: case I_PVAR: return 1; case I_IFUNC: i1 = (int)FA0((FNODE)FA0(f1)); @@ -3007,7 +3425,7 @@ int nfnode_comp(FNODE f1,FNODE f2) /* compare args */ n1 = FA0((FNODE)FA1(f1)); n2 = FA0((FNODE)FA1(f2)); 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 { n1 = NEXT(n1); n2 = NEXT(n2); } @@ -3016,29 +3434,14 @@ int nfnode_comp(FNODE f1,FNODE f2) break; default: - error("nfnode_comp : undefined"); + error("nfnode_comp_lex : undefined"); } break; 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 t,t0; @@ -3093,7 +3496,7 @@ int nfnode_match(FNODE f,FNODE pat,NODE *rp) fbase = f; fexp = mkfnode(1,I_FORMULA,ONE); } if ( !nfnode_match(fbase,FA1(pat),&base) ) return 0; - a = rewrite_fnode(FA2(pat),base); + a = rewrite_fnode(FA2(pat),base,0); if ( !nfnode_match(fexp,a,&exp) ) return 0; else { *rp = append_node(base,exp); @@ -3117,7 +3520,7 @@ int nfnode_match(FNODE f,FNODE pat,NODE *rp) fa = (NODE)FA0((FNODE)FA1(f)); pa = (NODE)FA0((FNODE)FA1(pat)); while ( fa && pa ) { - a = rewrite_fnode(BDY(pa),m); + 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); @@ -3153,14 +3556,14 @@ 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); } } @@ -3182,7 +3585,7 @@ 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); } } @@ -3198,7 +3601,7 @@ FNODE fnode_right_narymul(FNODE p,int i) 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); } } @@ -3240,7 +3643,7 @@ int nfnode_match_naryadd(FNODE f,FNODE p,NODE *rp) for ( s = fa, fi = 0; s; s = NEXT(s), fi++ ) { if ( nfnode_match(BDY(s),pivot,&m) ) { fr = fnode_removeith_naryadd(f,fi); - prr = rewrite_fnode(pr,m); + prr = rewrite_fnode(pr,m,0); if ( nfnode_match(fr,prr,&m1) ) { *rp = append_node(m,m1); return 1; @@ -3274,7 +3677,7 @@ int nfnode_match_narymul(FNODE f,FNODE p,NODE *rp) /* 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); + pr = rewrite_fnode(BDY(t),m,0); if ( !nfnode_match(BDY(s),pr,&m1) ) return 0; m = append_node(m1,m); } @@ -3282,7 +3685,7 @@ int nfnode_match_narymul(FNODE f,FNODE p,NODE *rp) fr = (FNODE)BDY(s); else fr = mkfnode(2,I_NARYOP,FA0(f),s); - pr = rewrite_fnode(BDY(t),m); + pr = rewrite_fnode(BDY(t),m,0); if ( !nfnode_match(fr,pr,&m1) ) return 0; *rp = append_node(m1,m); return 1; @@ -3295,11 +3698,11 @@ int nfnode_match_narymul(FNODE f,FNODE p,NODE *rp) if ( fi < pi ) continue; if ( nfnode_match(BDY(s),pivot,&m) ) { fleft = fnode_left_narymul(f,fi); - pleft1 = rewrite_fnode(pleft,m); + 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); + pright1 = rewrite_fnode(pright,m,0); if ( nfnode_match(fright,pright1,&m1) ) { *rp = append_node(m1,m); return 1;