=================================================================== RCS file: /home/cvs/OpenXM_contrib2/asir2000/builtin/strobj.c,v retrieving revision 1.39 retrieving revision 1.114 diff -u -p -r1.39 -r1.114 --- OpenXM_contrib2/asir2000/builtin/strobj.c 2004/03/11 04:52:17 1.39 +++ OpenXM_contrib2/asir2000/builtin/strobj.c 2005/12/19 01:31:43 1.114 @@ -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 1.38 2004/03/11 03:39:39 noro Exp $ + * $OpenXM: OpenXM_contrib2/asir2000/builtin/strobj.c,v 1.113 2005/12/18 06:54:28 noro Exp $ */ #include "ca.h" #include "parse.h" @@ -58,13 +58,29 @@ extern jmp_buf environnement; #endif #include +#if defined(__GNUC__) +#define INLINE inline +#elif defined(VISUAL) +#define INLINE __inline +#else +#define INLINE +#endif + struct TeXSymbol { char *text; char *symbol; }; +#define OPNAME(f) (((ARF)FA0(f))->name[0]) +#define IS_ZERO(f) (((f)->id==I_FORMULA) && FA0(f)==0 ) +#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; +void Psprintf(); void Prtostr(), Pstrtov(), Peval_str(); void Pstrtoascii(), Pasciitostr(); void Pstr_len(), Pstr_chr(), Psub_str(); @@ -75,6 +91,29 @@ void Pstring_to_tb(); void Pquotetotex_tb(); void Pquotetotex(); void Pquotetotex_env(); +void Pflatten_quote(); + +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 Pnbm_deg(); +void Pnbm_hp_rest(); +void Pnbm_hxky(), Pnbm_xky_rest(); +void Pnbm_hv(), Pnbm_rest(); + +void Pquote_to_funargs(),Pfunargs_to_quote(),Pget_function_name(); +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); char *symbol_name(char *name); char *conv_rule(char *name); @@ -84,8 +123,25 @@ 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 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}, {"rtostr",Prtostr,1}, {"strtov",Pstrtov,1}, {"eval_str",Peval_str,1}, @@ -98,9 +154,51 @@ struct ftab str_tab[] = { {"clear_tb",Pclear_tb,1}, {"tb_to_string",Ptb_to_string,1}, {"string_to_tb",Pstring_to_tb,1}, + {"get_quote_id",Pget_quote_id,1}, + + {"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}, + + {"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}, + + {"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}, + {"nbm_deg", Pnbm_deg,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_rest", Pnbm_rest,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}, + {"funargs_to_quote",Pfunargs_to_quote,1}, + {"get_function_name",Pget_function_name,1}, {0,0,0}, }; @@ -118,13 +216,20 @@ int register_symbol_table(Obj arg); int register_conv_rule(Obj arg); int register_conv_func(Obj arg); int register_dp_vars(Obj arg); +int register_dp_vars_origin(Obj arg); +int register_dp_dvars_origin(Obj arg); +int register_dp_dvars_prefix(Obj arg); int register_dp_vars_prefix(Obj arg); int register_dp_vars_hweyl(Obj arg); int register_show_lt(Obj arg); +char *objtostr(Obj obj); static struct TeXSymbol *user_texsymbol; static char **dp_vars; static int dp_vars_len; static char *dp_vars_prefix; +static char *dp_dvars_prefix; +static int dp_vars_origin; +static int dp_dvars_origin; static int show_lt; static FUNC convfunc; static int is_lt; @@ -145,6 +250,9 @@ static struct { {"conv_func",0,register_conv_func}, {"dp_vars",0,register_dp_vars}, {"dp_vars_prefix",0,register_dp_vars_prefix}, + {"dp_dvars_prefix",0,register_dp_dvars_prefix}, + {"dp_vars_origin",0,register_dp_vars_origin}, + {"dp_dvars_origin",0,register_dp_dvars_origin}, {"dp_vars_hweyl",0,register_dp_vars_hweyl}, {"show_lt",0,register_show_lt}, {0,0,0}, @@ -155,39 +263,51 @@ static struct { char *conv_rule(char *name) { char *body,*r; + int len; if ( convfunc ) name = call_convfunc(name); - if ( conv_flag & CONV_DMODE ) { - if ( *name == 'd' ) { - body = conv_flag&CONV_SUBS?conv_subs(name+1):symbol_name(name+1); - if ( !body ) { - r = MALLOC_ATOMIC((strlen(PARTIAL)+1)*sizeof(char)); - strcpy(r,PARTIAL); - } else { - r = MALLOC_ATOMIC((strlen(PARTIAL)+strlen(body)+5) - *sizeof(char)); - sprintf(r,strlen(body)==1?"{%s}_%s":"{%s}_{%s}",PARTIAL,body); - } - return r; - } else - return conv_flag&CONV_SUBS?conv_subs(name):symbol_name(name); - } else - return conv_flag&CONV_SUBS?conv_subs(name):symbol_name(name); + if ( conv_flag & CONV_TABLE ) { + r = symbol_name(name); + if ( r ) return r; + } + if ( (conv_flag & CONV_DMODE) && *name == 'd' ) { + body = conv_rule(name+1); + r = MALLOC_ATOMIC((strlen(PARTIAL)+strlen(body)+5)*sizeof(char)); + if ( !body || !(len=strlen(body)) ) + strcpy(r,PARTIAL); + else if ( len == 1 ) + sprintf(r,"%s_%s",PARTIAL,body); + else + sprintf(r,"%s_{%s}",PARTIAL,body); + return r; + } else + return conv_subs(name); } +int _is_delimiter(char c) +{ + if ( (c == ' ' || c == '_' || c == ',') ) return 1; + else return 0; +} + +int _is_alpha(char c) +{ + if ( isdigit(c) || c == '{' || _is_delimiter(c) ) return 0; + else return 1; +} + char *conv_subs(char *name) { int i,j,k,len,clen,slen,start,level; - char *buf,*head,*r,*h,*brace; + char *buf,*head,*r,*h,*brace,*buf_conv; char **subs; - len = strlen(name); - if ( !len ) return 0; + if ( !name || !(len=strlen(name)) ) return ""; + if ( !(conv_flag&CONV_SUBS) ) return name; subs = (char **)ALLOCA(len*sizeof(char* )); for ( i = 0, j = 0, start = i; ; j++ ) { - while ( (i < len) && - (name[i] == ' ' || name[i] == '_' || name[i] == ',') ) i++; + while ( (i < len) && _is_delimiter(name[i]) ) i++; start = i; if ( i == len ) break; if ( name[i] == '{' ) { @@ -212,11 +332,12 @@ char *conv_subs(char *name) if ( isdigit(name[i]) ) while ( i < len && isdigit(name[i]) ) i++; else - while ( i < len && (isalpha(name[i]) || name[i] == '\\') ) i++; + while ( i < len && _is_alpha(name[i]) ) i++; slen = i-start; buf = (char *)ALLOCA((slen+1)*sizeof(char)); strncpy(buf,name+start,slen); buf[slen] = 0; - subs[j] = symbol_name(buf); + buf_conv = symbol_name(buf); + subs[j] = buf_conv?buf_conv:buf; } } for ( k = 0, clen = 0; k < j; k++ ) clen += strlen(subs[k]); @@ -295,6 +416,22 @@ int register_symbol_table(Obj arg) return 1; } +int register_dp_vars_origin(Obj arg) +{ + if ( INT(arg) ) { + dp_vars_origin = QTOS((Q)arg); + return 1; + } else return 0; +} + +int register_dp_dvars_origin(Obj arg) +{ + if ( INT(arg) ) { + dp_dvars_origin = QTOS((Q)arg); + return 1; + } else return 0; +} + int register_dp_vars_hweyl(Obj arg) { if ( INT(arg) ) { @@ -322,7 +459,10 @@ int register_conv_rule(Obj arg) int register_conv_func(Obj arg) { - if ( OID(arg) == O_P && (int)(VR((P)arg))->attr == V_SR ) { + if ( !arg ) { + convfunc = 0; + return 1; + } else if ( OID(arg) == O_P && (int)(VR((P)arg))->attr == V_SR ) { convfunc = (FUNC)(VR((P)arg)->priv); /* f must be a function which takes single argument */ return 1; @@ -376,6 +516,20 @@ int register_dp_vars_prefix(Obj arg) } else return 0; } +int register_dp_dvars_prefix(Obj arg) +{ + if ( !arg ) { + dp_dvars_prefix = 0; + return 1; + } else if ( OID(arg) == O_STR ) { + dp_dvars_prefix = BDY((STRING)arg); + return 1; + } else if ( OID(arg) == O_P ) { + dp_dvars_prefix = NAME(VR((P)arg)); + return 1; + } else return 0; +} + void Pquotetotex_env(NODE arg,Obj *rp) { int ac,i; @@ -396,8 +550,10 @@ void Pquotetotex_env(NODE arg,Obj *rp) *rp = (Obj)l; } else if ( ac == 1 && !ARG0(arg) ) { /* set to default */ - for ( i = 0; qtot_env[i].name; i++ ) + for ( i = 0; qtot_env[i].name; i++ ) { + (qtot_env[i].reg)(0); qtot_env[i].value = 0; + } *rp = 0; } else if ( ac == 1 || ac == 2 ) { asir_assert(ARG0(arg),O_STR,"quotetotex_env"); @@ -438,6 +594,486 @@ void Pwrite_to_tb(NODE arg,Q *rp) *rp = 0; } +void Pqt_to_nary(NODE arg,QUOTE *rp) +{ + FNODE f; + + f = fnode_to_nary(BDY((QUOTE)ARG0(arg))); + MKQUOTE(*rp,f); +} + +void Pqt_to_bin(NODE arg,QUOTE *rp) +{ + FNODE f; + int direction; + + direction = QTOS((Q)ARG1(arg)); + f = fnode_to_bin(BDY((QUOTE)ARG0(arg)),direction); + + MKQUOTE(*rp,f); +} + +void Pqt_is_var(NODE arg,Q *rp) +{ + QUOTE q; + int ret; + + q = (QUOTE)ARG0(arg); + 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 Pqt_is_rational(NODE arg,Q *rp) +{ + QUOTE q; + int ret; + + q = (QUOTE)ARG0(arg); + asir_assert(q,O_QUOTE,"qt_is_rational"); + ret = fnode_is_rational(BDY(q)); + STOQ(ret,*rp); +} + +void Pqt_is_integer(NODE arg,Q *rp) +{ + QUOTE q; + int ret; + + q = (QUOTE)ARG0(arg); + asir_assert(q,O_QUOTE,"qt_is_integer"); + ret = fnode_is_integer(BDY(q)); + STOQ(ret,*rp); +} + +void Pqt_is_function(NODE arg,Q *rp) +{ + QUOTE q; + int ret; + + q = (QUOTE)ARG0(arg); + asir_assert(q,O_QUOTE,"qt_is_function"); + if ( q->id == I_FUNC || q->id == I_IFUNC ) + ret = 1; + else + ret = 0; + STOQ(ret,*rp); +} + +void Pqt_is_dependent(NODE arg,Q *rp) +{ + P x; + QUOTE q,v; + int ret; + V var; + + q = (QUOTE)ARG0(arg); + v = (QUOTE)ARG1(arg); + 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; + var = VR(x); + ret = fnode_is_dependent(BDY(q),var); + STOQ(ret,*rp); +} + + +void Pqt_match(NODE arg,Q *rp) +{ + FNODE f,g; + Obj obj; + QUOTE q; + NODE r; + int ret; + + obj = (Obj)ARG0(arg); + ret = qt_match(obj,(Obj)ARG1(arg),&r); + if ( ret ) { + do_assign(r); + *rp = ONE; + } else + *rp = 0; +} + +void Pnqt_match(NODE arg,Q *rp) +{ + QUOTE fq,pq; + FNODE f,p; + int ret; + Q mode; + NODE 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; + } else + *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; + + 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); + + 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) +{ + ARF op; + NODE arg,h0,t,h,valuen; + NODE r,s0,s,pair; + FNODE any,pany,head,tail,a1,a2; + QUOTE q; + int ret; + FNODE value; + int ind; + + 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; + } + + 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 + 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) +{ + NODE t,pair; + int pv; + + QUOTE value; + + for ( t = arg; t; t = NEXT(t) ) { + pair = BDY((LIST)BDY(t)); + pv = (int)FA0((FNODE)BDY((QUOTE)BDY(pair))); + value = (QUOTE)(BDY(NEXT(pair))); + ASSPV(pv,value); + } +} + +/* [[index,fnode],...] */ + +void fnode_do_assign(NODE arg) +{ + NODE t,pair; + 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))); + 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); + } +} + +/* +/* consistency check and merge + */ + +int merge_matching_node(NODE n,NODE a,NODE *rp) +{ + NODE ta,ba,tn,bn; + QUOTE pa,va,pn,vn; + + if ( !n ) { + *rp = a; + return 1; + } + for ( ta = a; ta; ta = NEXT(ta) ) { + ba = BDY((LIST)BDY(ta)); + if ( !ba ) continue; + pa = (QUOTE)BDY(ba); va = (QUOTE)BDY(NEXT(ba)); + for ( tn = n; tn; tn = NEXT(tn) ) { + bn = BDY((LIST)BDY(tn)); + if ( !bn ) continue; + pn = (QUOTE)BDY(bn); vn = (QUOTE)BDY(NEXT(bn)); + if ( !compquote(CO,pa,pn) ) { + if ( !compquote(CO,va,vn) ) break; + else return 0; + } + } + if ( !tn ) { + MKNODE(tn,(pointer)BDY(ta),n); + n = tn; + } + } + *rp = n; + return 1; +} + +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 = qt_match((Obj)BDY(tf),(Obj)BDY(tp),&a); + if ( !ret ) return 0; + ret = merge_matching_node(r,a,&r1); + if ( !ret ) return 0; + else r = r1; + } + *rp = r; + return 1; +} + +/* f = [a,b,c,...] pat = [X,Y,...] rpat matches the rest of f */ + +int qt_match_cons(NODE f,NODE pat,Obj rpat,NODE *rp) { + QUOTE q; + Q id; + FNODE fn; + NODE r,a,tf,tp,r1,arg; + int ret; + LIST list,alist; + + /* matching of the head part */ + if ( length(f) < length(pat) ) return 0; + r = 0; + for ( tf = f, tp = pat; tp; tf = NEXT(tf), tp = NEXT(tp) ) { + 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; + else r = r1; + } + /* matching of the rest */ + MKLIST(list,tf); + STOQ(I_LIST,id); a = mknode(2,id,list); + MKLIST(alist,a); + arg = mknode(1,alist); + Pfunargs_to_quote(arg,&q); + ret = qt_match((Obj)q,rpat,&a); + if ( !ret ) return 0; + ret = merge_matching_node(r,a,&r1); + if ( !ret ) return 0; + *rp = r1; + return 1; +} + +void get_quote_id_arg(QUOTE f,int *id,NODE *r) +{ + LIST fa; + NODE arg,fab; + + arg = mknode(1,f); Pquote_to_funargs(arg,&fa); fab = BDY((LIST)fa); + *id = QTOS((Q)BDY(fab)); *r = NEXT(fab); +} + +/* *rp : [[quote(A),quote(1)],...] */ + +int qt_match(Obj f, Obj pat, NODE *rp) +{ + NODE tf,tp,head,body; + NODE parg,farg,r; + Obj rpat; + LIST fa,l; + int pid,id; + FUNC ff,pf; + int ret; + QUOTE q; + FNODE g; + + if ( !f ) + if ( !pat ) { + *rp = 0; return 1; + } else + return 0; + else if ( OID(pat) == O_LIST ) { + if ( OID(f) == O_LIST ) + return qt_match_node(BDY((LIST)f),BDY((LIST)pat),rp); + else + return 0; + } else if ( OID(pat) == O_QUOTE ) { + pid = ((FNODE)BDY((QUOTE)pat))->id; + switch ( pid ) { + case I_FORMULA: + if ( compquote(CO,f,pat) ) + return 0; + else { + *rp = 0; return 1; + } + break; + + case I_LIST: case I_CONS: + get_quote_id_arg((QUOTE)pat,&pid,&parg); + if ( OID(f) == O_LIST ) + tf = BDY((LIST)f); + else if ( OID(f) == O_QUOTE + && ((FNODE)BDY((QUOTE)f))->id == pid ) { + get_quote_id_arg((QUOTE)f,&id,&farg); + tf = BDY((LIST)BDY(farg)); + } else + return 0; + + tp = BDY((LIST)BDY(parg)); + if ( pid == I_LIST ) + return qt_match_node(tf,tp,rp); + else { + rpat = (Obj)BDY(NEXT(parg)); + return qt_match_cons(tf,tp,rpat,rp); + } + + case I_PVAR: + /* [[pat,f]] */ + r = mknode(2,pat,f); MKLIST(l,r); + *rp = mknode(1,l); + return 1; + + case I_IFUNC: + /* F(X,Y,...) = ... */ + get_quote_id_arg((QUOTE)f,&id,&farg); + get_quote_id_arg((QUOTE)pat,&pid,&parg); + if ( id == I_FUNC ) { + r = mknode(2,BDY(parg),BDY(farg)); MKLIST(l,r); + head = mknode(1,l); + ret = qt_match(BDY(NEXT(farg)), + BDY(NEXT(parg)),&body); + if ( !ret ) return 0; + else return merge_matching_node(head,body,rp); + } else + return 0; + + case I_NARYOP: case I_BOP: case I_FUNC: + /* X+Y = ... */ + /* f(...) = ... */ + if ( OID(f) != O_QUOTE ) return 0; + id = ((FNODE)BDY((QUOTE)f))->id; + if ( pid == I_FUNC ) + ; + else { + /* XXX converting to I_BOP */ + if ( pid == I_NARYOP ) { + g = fnode_to_bin(BDY((QUOTE)pat),1); + MKQUOTE(q,g); pat = (Obj)q; + } + if ( id == I_NARYOP ) { + g = fnode_to_bin(BDY((QUOTE)f),1); + MKQUOTE(q,g); f = (Obj)q; + } + } + 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 qt_match_node(NEXT(farg),NEXT(parg),rp); + + default: + if ( OID(f) != O_QUOTE ) return 0; + id = ((FNODE)BDY((QUOTE)f))->id; + if ( id != pid ) return 0; + get_quote_id_arg((QUOTE)pat,&pid,&parg); + get_quote_id_arg((QUOTE)f,&id,&farg); + return qt_match_node(farg,parg,rp); + } + } +} + void Pquotetotex(NODE arg,STRING *rp) { TB tb; @@ -764,6 +1400,8 @@ char *symbol_name(char *name) { int i; + if ( !name || strlen(name) == 0 ) + return ""; if ( !(conv_flag & CONV_TABLE) ) return name; @@ -774,17 +1412,37 @@ char *symbol_name(char *name) for ( i = 0; texsymbol[i].text; i++ ) if ( !strcmp(texsymbol[i].text,name) ) return texsymbol[i].symbol; - return name; + return 0; } +void Pget_function_name(NODE arg,STRING *rp) +{ + QUOTEARG qa; + ARF f; + char *opname; + + qa = (QUOTEARG)BDY(arg); + if ( !qa || OID(qa) != O_QUOTEARG || qa->type != A_arf ) + *rp = 0; + else { + f = (ARF)BDY(qa); + opname = f->name; + MKSTR(*rp,opname); + } +} + +FNODE strip_paren(FNODE); +void objtotex_tb(Obj obj,TB tb); + void fnodetotex_tb(FNODE f,TB tb) { - NODE n,t,t0; + NODE n,t,t0,args; char vname[BUFSIZ],prefix[BUFSIZ]; char *opname,*vname_conv,*prefix_conv; Obj obj; - int i,len,allzero,elen,elen2; - FNODE fi,f2; + int i,len,allzero,elen,elen2,si; + char *r; + FNODE fi,f2,f1; write_tb(" ",tb); if ( !f ) { @@ -814,48 +1472,102 @@ void fnodetotex_tb(FNODE f,TB tb) /* otherwise => FA1(f), FA2(f) */ case I_BOP: opname = ((ARF)FA0(f))->name; - if ( !strcmp(opname,"+") ) { - fnodetotex_tb((FNODE)FA1(f),tb); - if ( !top_is_minus((FNODE)FA2(f)) ) write_tb(opname,tb); - fnodetotex_tb((FNODE)FA2(f),tb); - } else if ( !strcmp(opname,"-") ) { - if ( FA1(f) ) fnodetotex_tb((FNODE)FA1(f),tb); - write_tb(opname,tb); - fnodetotex_tb((FNODE)FA2(f),tb); - } else if ( !strcmp(opname,"*") ) { - fnodetotex_tb((FNODE)FA1(f),tb); - write_tb(" ",tb); - /* XXX special care for DP */ - f2 = (FNODE)FA2(f); - 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 ) + switch ( opname[0] ) { + case '+': + fnodetotex_tb((FNODE)FA1(f),tb); + if ( !top_is_minus((FNODE)FA2(f)) ) write_tb(opname,tb); + fnodetotex_tb((FNODE)FA2(f),tb); + break; + case '-': + if ( FA1(f) ) fnodetotex_tb((FNODE)FA1(f),tb); + write_tb(opname,tb); + fnodetotex_tb((FNODE)FA2(f),tb); + break; + case '*': + fnodetotex_tb((FNODE)FA1(f),tb); + write_tb(" ",tb); + /* XXX special care for DP */ + f2 = (FNODE)FA2(f); + 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((FNODE)FA2(f),tb); + } else fnodetotex_tb((FNODE)FA2(f),tb); - } else + break; + case '/': + write_tb("\\frac{",tb); + fnodetotex_tb((FNODE)FA1(f),tb); + write_tb("} {",tb); fnodetotex_tb((FNODE)FA2(f),tb); - } else if ( !strcmp(opname,"/") ) { - write_tb("\\frac{",tb); - fnodetotex_tb((FNODE)FA1(f),tb); - write_tb("} {",tb); - fnodetotex_tb((FNODE)FA2(f),tb); - write_tb("}",tb); - } else if ( !strcmp(opname,"^") ) { - fnodetotex_tb((FNODE)FA1(f),tb); - write_tb("^{",tb); - fnodetotex_tb((FNODE)FA2(f),tb); - write_tb("} ",tb); - } else if ( !strcmp(opname,"%") ) { - fnodetotex_tb((FNODE)FA1(f),tb); - write_tb(" {\\rm mod}\\, ",tb); - fnodetotex_tb((FNODE)FA2(f),tb); - } else - error("invalid binary operator"); + write_tb("}",tb); + break; + case '^': + 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); + break; + case '%': + fnodetotex_tb((FNODE)FA1(f),tb); + write_tb(" {\\rm mod}\\, ",tb); + fnodetotex_tb((FNODE)FA2(f),tb); + break; + default: + error("invalid binary operator"); + break; + } break; + case I_NARYOP: + args = (NODE)FA1(f); + switch ( OPNAME(f) ) { + case '+': + fnodetotex_tb((FNODE)BDY(args),tb); + for ( args = NEXT(args); args; args = NEXT(args) ) { + write_tb("+",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); args = NEXT(args); + } + for ( ; args; args = NEXT(args) ) { + f2 = (FNODE)BDY(args); + 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; + } + break; case I_COP: switch( (cid)FA0(f) ) { @@ -871,12 +1583,12 @@ void fnodetotex_tb(FNODE f,TB tb) break; case C_GT: fnodetotex_tb((FNODE)FA1(f),tb); - write_tb(" \\gt ",tb); + write_tb(" > ",tb); fnodetotex_tb((FNODE)FA2(f),tb); break; case C_LT: fnodetotex_tb((FNODE)FA1(f),tb); - write_tb(" \\lt ",tb); + write_tb(" < ",tb); fnodetotex_tb((FNODE)FA2(f),tb); break; case C_GE: @@ -906,12 +1618,12 @@ void fnodetotex_tb(FNODE f,TB tb) break; case L_GT: fnodetotex_tb((FNODE)FA1(f),tb); - write_tb(" \\gt ",tb); + write_tb(" > ",tb); fnodetotex_tb((FNODE)FA2(f),tb); break; case L_LT: fnodetotex_tb((FNODE)FA1(f),tb); - write_tb(" \\lt ",tb); + write_tb(" < ",tb); fnodetotex_tb((FNODE)FA2(f),tb); break; case L_GE: @@ -970,11 +1682,17 @@ void fnodetotex_tb(FNODE f,TB tb) /* function */ case I_FUNC: - opname = conv_rule(((FUNC)FA0(f))->name); - write_tb(opname,tb); - write_tb("(",tb); - fargstotex_tb(opname,FA1(f),tb); - write_tb(")",tb); + if ( !strcmp(((FUNC)FA0(f))->name,"@pi") ) + write_tb("\\pi",tb); + else if ( !strcmp(((FUNC)FA0(f))->name,"@e") ) + write_tb("e",tb); + else { + opname = conv_rule(((FUNC)FA0(f))->name); + write_tb(opname,tb); + write_tb("(",tb); + fargstotex_tb(opname,FA1(f),tb); + write_tb(")",tb); + } break; /* XXX */ @@ -1014,20 +1732,33 @@ void fnodetotex_tb(FNODE f,TB tb) vname_conv = conv_rule(vname); } else { if ( dp_vars_hweyl ) { - if ( i < elen2 ) + if ( i < elen2 ) { strcpy(prefix,dp_vars_prefix?dp_vars_prefix:"x"); - else if ( i < elen ) - strcpy(prefix,"\\partial"); - else + prefix_conv = conv_rule(prefix); + vname_conv = (char *)ALLOCA(strlen(prefix_conv)+50); + si = i+dp_vars_origin; + sprintf(vname_conv,(si>=0&&si<10)?"%s_%d":"%s_{%d}", + prefix_conv,si); + } else if ( i < elen ) { + strcpy(prefix, + dp_dvars_prefix?dp_dvars_prefix:"\\partial"); + prefix_conv = conv_rule(prefix); + vname_conv = (char *)ALLOCA(strlen(prefix_conv)+50); + si = i+dp_dvars_origin-elen2; + sprintf(vname_conv,(si>=0&&si<10)?"%s_%d":"%s_{%d}", + prefix_conv,si); + } else { strcpy(prefix,"h"); - } else + vname_conv = conv_rule(prefix); + } + } else { strcpy(prefix,dp_vars_prefix?dp_vars_prefix:"x"); - prefix_conv = conv_rule(prefix); - vname_conv = (char *)ALLOCA(strlen(prefix_conv)+50); - if ( i < 10 ) - sprintf(vname_conv,"%s_%d",prefix_conv,i); - else - sprintf(vname_conv,"%s_{%d}",prefix_conv,i); + prefix_conv = conv_rule(prefix); + vname_conv = (char *)ALLOCA(strlen(prefix_conv)+50); + si = i+dp_vars_origin; + sprintf(vname_conv,(si>=0&&si<10)?"%s_%d":"%s_{%d}", + prefix_conv,si); + } } if ( fi->id == I_FORMULA && UNIQ(FA0(fi)) ) { len = strlen(vname_conv); @@ -1060,16 +1791,7 @@ void fnodetotex_tb(FNODE f,TB tb) /* internal object */ case I_FORMULA: - obj = (Obj)FA0(f); - if ( obj && OID(obj) == O_P ) { - opname = conv_rule(VR((P)obj)->name); - } else { - len = estimate_length(CO,obj); - opname = (char *)MALLOC_ATOMIC(len+1); - soutput_init(opname); - sprintexpr(CO,obj); - } - write_tb(opname,tb); + objtotex_tb((Obj)FA0(f),tb); break; /* program variable */ @@ -1085,6 +1807,151 @@ 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; + char *r; + + len = estimate_length(CO,obj); + r = (char *)MALLOC_ATOMIC(len+1); + soutput_init(r); + sprintexpr(CO,obj); + return r; +} + +void Psprintf(NODE arg,STRING *rp) +{ + STRING string; + char *s,*t,*r; + int argc,n,len; + NODE node; + + string = (STRING)ARG0(arg); + asir_assert(string,O_STR,"sprintf"); + s = BDY(string); + for(n = 0, t = s; *t; t++) { + if (*t=='%' && *(t+1)=='a') { + n++; + } + } + for(node = NEXT(arg), argc = 0, len = strlen(s); node; node = NEXT(node), argc++) { + len += estimate_length(CO,BDY(node)); + } + if (argc < n) { + error("sprintf: invalid argument"); + } + r = (char *)MALLOC_ATOMIC(len); + for(node = NEXT(arg), t = r; *s; s++) { + if (*s=='%' && *(s+1)=='a') { + strcpy(t,objtostr(BDY(node))); + node = NEXT(node); + t = strchr(t,0); + s++; + }else { + *t++ = *s; + } + } + *t = 0; + MKSTR(*rp,r); +} + void fnodenodetotex_tb(NODE n,TB tb) { for ( ; n; n = NEXT(n) ) { @@ -1152,9 +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); @@ -1164,7 +2035,1719 @@ int top_is_minus(FNODE f) return opname[0]=='-'; } } + case I_NARYOP: + return top_is_minus((FNODE)BDY((NODE)FA1(f))); + default: return 0; + } +} + +FNODE flatten_fnode(FNODE,char *); + +void Pflatten_quote(NODE arg,Obj *rp) +{ + FNODE f; + QUOTE q; + + if ( !ARG0(arg) || OID((Obj)ARG0(arg)) != O_QUOTE ) + *rp = (Obj)ARG0(arg); + else if ( argc(arg) == 1 ) { + f = flatten_fnode(BDY((QUOTE)ARG0(arg)),"+"); + f = flatten_fnode(f,"*"); + MKQUOTE(q,f); + *rp = (Obj)q; + } else { + f = flatten_fnode(BDY((QUOTE)ARG0(arg)),BDY((STRING)ARG1(arg))); + MKQUOTE(q,f); + *rp = (Obj)q; + } +} + +void Pget_quote_id(NODE arg,Q *rp) +{ + FNODE f; + QUOTE q; + + q = (QUOTE)ARG0(arg); + if ( !q || OID(q) != O_QUOTE ) + error("get_quote_id : invalid argument"); + f = BDY(q); + STOQ((int)f->id,*rp); +} + +void Pquote_to_funargs(NODE arg,LIST *rp) +{ + fid_spec_p spec; + QUOTE q; + QUOTEARG qa; + FNODE f; + STRING s; + QUOTE r; + int i; + Q id,a; + LIST l; + NODE t0,t,w,u,u0; + + q = (QUOTE)ARG0(arg); + if ( !q || OID(q) != O_QUOTE ) + error("quote_to_funargs : invalid argument"); + f = BDY(q); + if ( !f ) { + MKLIST(*rp,0); + return; + } + get_fid_spec(f->id,&spec); + if ( !spec ) + error("quote_to_funargs : not supported yet"); + t0 = 0; + STOQ((int)f->id,id); + NEXTNODE(t0,t); + BDY(t) = (pointer)id; + for ( i = 0; spec->type[i] != A_end; i++ ) { + NEXTNODE(t0,t); + switch ( spec->type[i] ) { + case A_fnode: + MKQUOTE(r,(FNODE)f->arg[i]); + BDY(t) = (pointer)r; + break; + case A_int: + STOQ((int)f->arg[i],a); + BDY(t) = (pointer)a; + break; + case A_str: + MKSTR(s,(char *)f->arg[i]); + BDY(t) = (pointer)s; + break; + case A_internal: + BDY(t) = (pointer)f->arg[i]; + break; + case A_node: + w = (NODE)f->arg[i]; + for ( u0 = 0; w; w = NEXT(w) ){ + NEXTNODE(u0,u); + MKQUOTE(r,(FNODE)BDY(w)); + BDY(u) = (pointer)r; + } + if ( u0 ) NEXT(u) = 0; + MKLIST(l,u0); + BDY(t) = (pointer)l; + break; + default: + MKQUOTEARG(qa,spec->type[i],f->arg[i]); + BDY(t) = (pointer)qa; + break; + } + } + if ( t0 ) NEXT(t) = 0; + MKLIST(*rp,t0); +} + +void Pfunargs_to_quote(NODE arg,QUOTE *rp) +{ + fid_spec_p spec; + QUOTE q; + QUOTEARG qa; + FNODE f; + STRING s; + QUOTE r,b; + int i; + LIST l; + fid id; + Obj a; + NODE t0,t,u0,u,w; + + l = (LIST)ARG0(arg); + if ( !l || OID(l) != O_LIST || !(t=BDY(l)) ) + error("funargs_to_quote : invalid argument"); + t = BDY(l); + id = (fid)QTOS((Q)BDY(t)); t = NEXT(t); + get_fid_spec(id,&spec); + if ( !spec ) + error("funargs_to_quote : not supported yet"); + for ( i = 0; spec->type[i] != A_end; i++ ); + NEWFNODE(f,i); + f->id = id; + for ( i = 0; spec->type[i] != A_end; i++, t = NEXT(t) ) { + if ( !t ) + error("funargs_to_quote : argument mismatch"); + a = (Obj)BDY(t); + switch ( spec->type[i] ) { + case A_fnode: + if ( !a || OID(a) != O_QUOTE ) + error("funargs_to_quote : invalid argument"); + f->arg[i] = BDY((QUOTE)a); + break; + case A_int: + if ( !INT(a) ) + error("funargs_to_quote : invalid argument"); + f->arg[i] = (pointer)QTOS((Q)a); + break; + case A_str: + if ( !a || OID(a) != O_STR ) + error("funargs_to_quote : invalid argument"); + f->arg[i] = (pointer)BDY((STRING)a); + break; + case A_internal: + f->arg[i] = (pointer)a; + break; + case A_node: + if ( !a || OID(a) != O_LIST ) + error("funargs_to_quote : invalid argument"); + u0 = 0; + for ( w = BDY((LIST)a); w; w = NEXT(w) ) { + NEXTNODE(u0,u); + b = (QUOTE)BDY(w); + if ( !b || OID(b) != O_QUOTE ) + error("funargs_to_quote : invalid argument"); + BDY(u) = BDY(b); + } + if ( u0 ) NEXT(u) = 0; + f->arg[i] = (pointer)u0; + break; + default: + if ( !a || OID(a) != O_QUOTEARG || + ((QUOTEARG)a)->type != spec->type[i] ) + error("funargs_to_quote : invalid argument"); + f->arg[i] = BDY((QUOTEARG)a); + break; + } + } + MKQUOTE(*rp,f); +} + +VL reordvars(VL vl0,NODE head) +{ + VL vl,svl,tvl; + int i,j; + NODE n; + P t; + V *va; + V v; + + 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("qt_normalize : invalid argument"); + q = (QUOTE)ARG0(arg); + if ( ac == 2 ) + expand = QTOS((Q)ARG1(arg)); + if ( !q || OID(q) != O_QUOTE ) + *rp = q; + else { + f = fnode_normalize(BDY(q),expand); + MKQUOTE(r,f); + *rp = r; + } +} + +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 = ONE; m1->b = m->b; + MKNODE(n,m1,0); + MKNBP(*rp,n); + } +} + +void Pnbp_hc(NODE arg, Q *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 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_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 = 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 = 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); +} + +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 = (Q)r; m->b = 0; + } else { + v = VR((P)r); + m->d = 1; m->c = 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); + f1 = fnode_normalize(f1,0); + f2 = fnode_normalize(f2,0); + r = nfnode_comp(f1,f2); + STOQ(r,*rp); +} + +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: + obj = FA0(f); + if ( !obj ) return 1; + else if ( OID(obj) == O_QUOTE ) + return fnode_is_number(BDY((QUOTE)obj)); + else if ( NUM(obj) ) return 1; + else return 0; + + case I_BOP: + return fnode_is_number(FA1(f)) && fnode_is_number(FA2(f)); + + default: + return 0; + } +} + +int fnode_is_rational(FNODE f) +{ + Obj obj; + + switch ( f->id ) { + case I_MINUS: case I_PAREN: + return fnode_is_number(FA0(f)); + + case I_FORMULA: + obj = FA0(f); + if ( !obj ) return 1; + else if ( OID(obj) == O_QUOTE ) + return fnode_is_rational(BDY((QUOTE)obj)); + else if ( NUM(obj) && RATN(obj) ) return 1; + else return 0; + + case I_BOP: + if ( !strcmp(((ARF)FA0(f))->name,"^") ) + return fnode_is_rational(FA1(f)) && fnode_is_integer(FA2(f)); + else + return fnode_is_rational(FA1(f)) && fnode_is_rational(FA2(f)); + + default: + return 0; + } +} + +int fnode_is_integer(FNODE f) +{ + Obj obj; + + switch ( f->id ) { + case I_MINUS: case I_PAREN: + return fnode_is_integer(FA0(f)); + + case I_FORMULA: + obj = FA0(f); + if ( !obj ) return 1; + else if ( OID(obj) == O_QUOTE ) + return fnode_is_integer(BDY((QUOTE)obj)); + else if ( INT(obj)) return 1; + else return 0; + + case I_BOP: + switch ( ((ARF)FA0(f))->name[0] ) { + case '^': + return fnode_is_integer(FA1(f)) + && fnode_is_nonnegative_integer(FA2(f)); + case '/': + return fnode_is_integer(FA1(f)) && + ( fnode_is_one(FA2(f)) || fnode_is_minusone(FA2(f)) ); + default: + return fnode_is_integer(FA1(f)) && fnode_is_integer(FA2(f)); + } + break; + + default: + return 0; + } +} + +int fnode_is_nonnegative_integer(FNODE f) +{ + Q n; + + n = eval(f); + if ( !n || (INT(n) && SGN(n) > 0) ) return 1; + else return 0; +} + +int fnode_is_one(FNODE f) +{ + Q n; + + n = eval(f); + if ( UNIQ(n) ) return 1; + else return 0; +} + +int fnode_is_minusone(FNODE f) +{ + Q n; + + n = eval(f); + if ( MUNIQ(n) ) return 1; + else return 0; +} + +int fnode_is_dependent(FNODE f,V v) +{ + Obj obj; + FNODE arg; + NODE t; + + switch ( f->id ) { + case I_MINUS: case I_PAREN: + return fnode_is_dependent(FA0(f),v); + + case I_FORMULA: + obj = FA0(f); + if ( !obj ) return 0; + else if ( OID(obj) == O_QUOTE ) + return fnode_is_dependent(BDY((QUOTE)obj),v); + else if ( obj_is_dependent(obj,v) ) return 1; + else return 0; + + case I_BOP: + return fnode_is_dependent(FA1(f),v) || fnode_is_dependent(FA2(f),v); + + case I_FUNC: + arg = (FNODE)FA1(f); + for ( t = FA0(arg); t; t = NEXT(t) ) + if ( fnode_is_dependent(BDY(t),v) ) return 1; + return 0; + + default: + return 0; + } +} + + +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; + STOQ(-1,q); + mone = mkfnode(1,I_FORMULA,q); + switch ( f->id ) { + case I_PAREN: + r = fnode_normalize(FA0(f),expand); + break; + + case I_MINUS: + r = nfnode_mul_coef((Obj)q, + fnode_normalize(FA0(f),expand),expand); + break; + + case I_BOP: + /* arf fnode fnode */ + a1 = fnode_normalize(FA1(f),expand); + a2 = fnode_normalize(FA2(f),expand); + switch ( OPNAME(f) ) { + case '+': + r = nfnode_add(a1,a2,expand); + break; + case '-': + a2 = nfnode_mul_coef((Obj)q,a2,expand); + r = nfnode_add(a1,a2,expand); + break; + case '*': + r = nfnode_mul(a1,a2,expand); + break; + case '/': + a2 = nfnode_pwr(a2,mone,expand); + r = nfnode_mul(a1,a2,expand); + break; + case '^': + r = nfnode_pwr(a1,a2,expand); + break; + default: + r = mkfnode(3,I_BOP,FA0(f),a1,a2); + break; + } + break; + + case I_NARYOP: + switch ( OPNAME(f) ) { + case '+': + n = (NODE)FA1(f); + r = fnode_normalize(BDY(n),expand); n = NEXT(n); + for ( ; n; n = NEXT(n) ) { + a1 = fnode_normalize(BDY(n),expand); + r = nfnode_add(r,a1,expand); + } + break; + case '*': + n = (NODE)FA1(f); + r = fnode_normalize(BDY(n),expand); n = NEXT(n); + for ( ; n; n = NEXT(n) ) { + a1 = fnode_normalize(BDY(n),expand); + r = nfnode_mul(r,a1,expand); + } + break; + default: + error("fnode_normallize : cannot happen"); + } + break; + + default: + return fnode_apply(f,fnode_normalize,expand); + } + r->normalized = 1; + r->expanded = expand; + return r; +} + +FNODE fnode_apply(FNODE f,FNODE (*func)(),int expand) +{ + fid_spec_p spec; + FNODE r; + int i,n; + NODE t,t0,s; + + get_fid_spec(f->id,&spec); + for ( n = 0; spec->type[n] != A_end; n++ ); + NEWFNODE(r,n); r->id = f->id; + for ( i = 0; i < n; i++ ) { + switch ( spec->type[i] ) { + case A_fnode: + r->arg[i] = func(f->arg[i],expand); + break; + case A_node: + s = (NODE)f->arg[i]; + for ( t0 = 0; s; s = NEXT(s) ) { + NEXTNODE(t0,t); + BDY(t) = (pointer)func((FNODE)BDY(s),expand); + } + if ( t0 ) NEXT(t) = 0; + r->arg[i] = t0; + break; + default: + r->arg[i] = f->arg[i]; + break; + } + } + return r; +} + +FNODE nfnode_add(FNODE f1,FNODE f2,int expand) +{ + NODE n1,n2,r0,r; + FNODE b1,b2; + int s; + Obj c1,c2,c; + + if ( IS_ZERO(f1) ) return f2; + else if ( IS_ZERO(f2) ) return f1; + f1 = to_naryadd(f1); f2 = to_naryadd(f2); + n1 = (NODE)FA1(f1); n2 = (NODE)FA1(f2); + r0 = 0; + while ( n1 && n2 ) { + fnode_coef_body(BDY(n1),&c1,&b1); fnode_coef_body(BDY(n2),&c2,&b2); + 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 { + arf_add(CO,c1,c2,&c); + if ( c ) { + NEXTNODE(r0,r); BDY(r) = nfnode_mul_coef(c,b1,expand); + } + n1 = NEXT(n1); n2 = NEXT(n2); + } + } + if ( n1 ) + if ( r0 ) NEXT(r) = n1; + else r0 = n1; + else if ( n2 ) + if ( r0 ) NEXT(r) = n2; + else r0 = n2; + else if ( r0 ) + NEXT(r) = 0; + + return fnode_node_to_nary(addfs,r0); +} + +FNODE fnode_node_to_nary(ARF op,NODE 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 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; + 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_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); + for ( n1 = (NODE)FA1(f1); n1; n1 = NEXT(n1) ) { + 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); + for ( n2 = (NODE)FA1(f2); n2; n2 = NEXT(n2) ) { + 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); + arf_mul(CO,c1,c2,&c); + if ( !c ) return mkfnode(1,I_FORMULA,0); + + + n1 = (NODE)FA1(to_narymul(b1)); n2 = (NODE)FA1(to_narymul(b2)); + l1 = length(n1); l = l1+length(n2); + m = (FNODE *)ALLOCA(l*sizeof(FNODE)); + for ( r = n1, i = 0; i < l1; r = NEXT(r), i++ ) m[i] = BDY(r); + for ( r = n2; r; r = NEXT(r) ) { + if ( i == 0 ) + m[i++] = BDY(r); + else { + fnode_base_exp(m[i-1],&b1,&e1); fnode_base_exp(BDY(r),&b2,&e2); + if ( compfnode(b1,b2) ) break; + arf_add(CO,eval(e1),eval(e2),&e); + if ( !e ) i--; + 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)); + } + } + for ( j = i-1; j >= 0; j-- ) { + MKNODE(r1,m[j],r); r = r1; + } + if ( !UNIQ(c) ) { + cc = mkfnode(1,I_FORMULA,c); MKNODE(r1,cc,r); r = r1; + } + 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; + 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_coef(f1) ) { + if ( fnode_is_integer(f2) ) { + if ( fnode_is_one(f2) ) return f1; + else { + arf_pwr(CO,eval(f1),(Obj)eval(f2),&c); + return mkfnode(1,I_FORMULA,c); + } + } 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); + if ( fnode_is_one(e) ) + return b1; + else + return mkfnode(3,I_BOP,FA0(f1),b1,e); + } else if ( expand && IS_NARYMUL(f1) && fnode_is_number(f2) + && fnode_is_integer(f2) ) { + fnode_coef_body(f1,&c1,&b1); + nf2 = (Num)eval(f2); + 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,expand); + else { + STOQ(-1,q); + mone = mkfnode(1,I_FORMULA,q); + b1 = to_narymul(b1); + for ( t0 = 0, n = (NODE)FA1(b1); n; n = NEXT(n) ) { + inv = mkfnode(3,I_BOP,pwrfs,BDY(n),mone); + MKNODE(t1,inv,t0); t0 = t1; + } + 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_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("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,int expand) +{ + 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 ( n == 1 ) return f; + else { + 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); + } + } +} + +/* f = b^e */ +void fnode_base_exp(FNODE f,FNODE *bp,FNODE *ep) +{ + if ( IS_BINARYPWR(f) ) { + *bp = FA1(f); *ep = FA2(f); + } else { + *bp = f; *ep = mkfnode(1,I_FORMULA,ONE); + } +} + +FNODE to_naryadd(FNODE f) +{ + FNODE r; + NODE n; + + if ( IS_NARYADD(f) ) return f; + + NEWFNODE(r,2); r->id = I_NARYOP; + FA0(r) = addfs; MKNODE(n,f,0); FA1(r) = n; + return r; +} + +FNODE to_narymul(FNODE f) +{ + FNODE r; + NODE n; + + if ( IS_NARYMUL(f) ) return f; + + NEWFNODE(r,2); r->id = I_NARYOP; + FA0(r) = mulfs; MKNODE(n,f,0); FA1(r) = n; + return r; +} + +FNODE nfnode_mul_coef(Obj c,FNODE f,int expand) +{ + FNODE b1,cc; + Obj c1,c2; + NODE n,r,r0; + + if ( !c ) + return mkfnode(I_FORMULA,0); + else { + fnode_coef_body(f,&c1,&b1); + 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("nfnode_mul_coef : cannot happen"); + else + return cc; + } else if ( IS_NARYMUL(b1) ) { + MKNODE(n,cc,FA1(b1)); + 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_nary(addfs,r0); + } else + return fnode_node_to_nary(mulfs,mknode(2,cc,b1)); + } + } +} + +void fnode_coef_body(FNODE f,Obj *cp,FNODE *bp) +{ + FNODE c; + + 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_coef(c) ) { + *cp = (Obj)eval(c); + *bp = fnode_node_to_nary(mulfs,NEXT((NODE)FA1(f))); + } else { + *cp = (Obj)ONE; *bp = f; + } + } else { + *cp = (Obj)ONE; *bp = f; + } +} + +int nfnode_weight(struct wtab *tab,FNODE f) +{ + NODE n; + int w,w1; + int i; + Q a2; + V v; + + switch ( f->id ) { + case I_FORMULA: + if ( fnode_is_coef(f) ) return 0; + else if ( fnode_is_var(f) ) { + if ( !tab ) return 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,ret; + char *nm1,*nm2; + 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); + 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,0); + h2 = n2 ? (FNODE)BDY(n2) : mkfnode(1,I_FORMULA,0); + 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 arf_comp(CO,c1,c2); + b1 = to_narymul(b1); b2 = to_narymul(b2); + n1 = (NODE)FA1(b1); n2 = (NODE)FA1(b2); + 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) ) { + 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_FUNC_QARG > I_FORMULA */ + switch ( f1->id ) { + case I_FORMULA: + switch ( f2->id ) { + case I_FORMULA: + 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_lex : undefined"); + } + break; + 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_QARG: + nm1 = ((FUNC)FA0(f1))->name; nm2 = ((FUNC)FA0(f2))->name; + r = strcmp(nm1,nm2); + if ( r > 0 ) return 1; + else if ( r < 0 ) 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"); + } + case I_PVAR: + switch ( f2->id ) { + 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("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("nfnode_comp_lex : undefined"); + } +} + +NODE append_node(NODE a1,NODE a2) +{ + NODE t,t0; + + if ( !a1 ) + return a2; + else { + for ( t0 = 0; a1; a1 = NEXT(a1) ) { + NEXTNODE(t0,t); BDY(t) = BDY(a1); + } + NEXT(t) = a2; + return t0; + } +} + +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,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)); + return 1; + + case I_FORMULA: + if ( f->id == I_FORMULA && !arf_comp(CO,(Obj)FA0(f),(Obj)FA0(pat)) ) { + *rp = 0; return 1; + } else + return 0; + + case I_BOP: + /* OPNAME should be "^" */ + if ( !IS_BINARYPWR(pat) ) + 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 ( !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_IFUNC: + if ( f->id != I_FUNC ) 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),0); + } + /* FA1(f) and FA1(pat) are I_LIST */ + fa = (NODE)FA0((FNODE)FA1(f)); + pa = (NODE)FA0((FNODE)FA1(pat)); + while ( fa && pa ) { + 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); + } + if ( fa || pa ) return 0; + else { + *rp = m; + return 1; + } + + case I_NARYOP: + if ( IS_NARYADD(pat) ) + return nfnode_match_naryadd(f,pat,rp); + else if ( IS_NARYMUL(pat) ) + return nfnode_match_narymul(f,pat,rp); + else + error("nfnode_match : invalid NARYOP"); + break; + + default: + error("nfnode_match : invalid pattern"); + } +} + +/* remove i-th element */ + +FNODE fnode_removeith_naryadd(FNODE p,int i) +{ + int k,l; + NODE t,r0,r,a; + + a = (NODE)FA1(p); + l = length(a); + if ( i < 0 || i >= l ) error("fnode_removeith_naryadd: invalid index"); + else if ( i == 0 ) + 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_nary(addfs,r0); + } + +} + +/* a0,...,a(i-1) */ +FNODE fnode_left_narymul(FNODE p,int i) +{ + int k,l; + NODE t,r0,r,a; + + a = (NODE)FA1(p); + l = length(a); + if ( i < 0 || i >= l ) error("fnode_left_narymul : invalid index"); + 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) ) { + NEXTNODE(r0,r); + BDY(r) = BDY(t); + } + NEXT(r) = 0; + return fnode_node_to_nary(mulfs,r0); + } +} + +/* a(i+1),...,a(l-1) */ +FNODE fnode_right_narymul(FNODE p,int i) +{ + NODE a,t; + int l,k; + + a = (NODE)FA1(p); + l = length(a); + if ( i < 0 || i >= l ) error("fnode_right_narymul : invalid index"); + if ( i == l-1 ) return 0; + else { + for ( k = 0, t = a; k <= i; k++, t = NEXT(t) ); + return fnode_node_to_nary(mulfs,t); + } +} + +int nfnode_match_naryadd(FNODE f,FNODE p,NODE *rp) +{ + int fl,pl,fi,pi; + NODE fa,pa,t,s,m,m1; + FNODE fr,pr,prr,pivot; + + f = to_naryadd(f); + fa = (NODE)FA1(f); fl = length(fa); + pa = (NODE)FA1(p); pl = length(pa); + if ( fl < pl ) return 0; + else if ( pl == 1 ) { + if ( fl == 1 ) + return nfnode_match(BDY(fa),BDY(pa),rp); + else + return 0; + } else { + for ( t = pa, pi = 0; t; t = NEXT(t), pi++ ) + if ( ((FNODE)BDY(t))->id != I_PVAR ) break; + if ( !t ) { + /* all are I_PVAR */ + m = 0; + for ( t = pa, s = fa; NEXT(t); t = NEXT(t), s = NEXT(s) ) { + 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); + 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 ( nfnode_match(BDY(s),pivot,&m) ) { + fr = fnode_removeith_naryadd(f,fi); + prr = rewrite_fnode(pr,m,0); + if ( nfnode_match(fr,prr,&m1) ) { + *rp = append_node(m,m1); + return 1; + } + } + } + return 0; + } + } +} + +int nfnode_match_narymul(FNODE f,FNODE p,NODE *rp) +{ + int fl,pl,fi,pi; + NODE fa,pa,t,s,m,m1; + FNODE fr,pr,pleft,pleft1,pright,pright1,fleft,fright,pivot; + + f = to_narymul(f); + fa = (NODE)FA1(f); fl = length(fa); + pa = (NODE)FA1(p); pl = length(pa); + if ( fl < pl ) return 0; + else if ( pl == 1 ) { + if ( fl == 1 ) + return nfnode_match(BDY(fa),BDY(pa),rp); + else + return 0; + } else { + for ( t = pa, pi = 0; t; t = NEXT(t), pi++ ) + if ( ((FNODE)BDY(t))->id != I_PVAR ) break; + if ( !t ) { + /* 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,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,0); + if ( !nfnode_match(fr,pr,&m1) ) return 0; + *rp = append_node(m1,m); + return 1; + } else { + pivot = (FNODE)BDY(t); + pleft = fnode_left_narymul(p,pi); + pright = fnode_right_narymul(p,pi); + /* XXX : incomplete */ + for ( s = fa, fi = 0; s; s = NEXT(s), fi++ ) { + if ( fi < pi ) continue; + if ( nfnode_match(BDY(s),pivot,&m) ) { + fleft = fnode_left_narymul(f,fi); + 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,0); + if ( nfnode_match(fright,pright1,&m1) ) { + *rp = append_node(m1,m); + return 1; + } + } + } + } + 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"); } }