/* * Copyright (c) 1994-2000 FUJITSU LABORATORIES LIMITED * All rights reserved. * * FUJITSU LABORATORIES LIMITED ("FLL") hereby grants you a limited, * non-exclusive and royalty-free license to use, copy, modify and * redistribute, solely for non-commercial and non-profit purposes, the * computer program, "Risa/Asir" ("SOFTWARE"), subject to the terms and * conditions of this Agreement. For the avoidance of doubt, you acquire * only a limited right to use the SOFTWARE hereunder, and FLL or any * third party developer retains all rights, including but not limited to * copyrights, in and to the SOFTWARE. * * (1) FLL does not grant you a license in any way for commercial * purposes. You may use the SOFTWARE only for non-commercial and * non-profit purposes only, such as academic, research and internal * business use. * (2) The SOFTWARE is protected by the Copyright Law of Japan and * international copyright treaties. If you make copies of the SOFTWARE, * with or without modification, as permitted hereunder, you shall affix * to all such copies of the SOFTWARE the above copyright notice. * (3) An explicit reference to this SOFTWARE and its copyright owner * shall be made on your publication or presentation in any form of the * results obtained by use of the SOFTWARE. * (4) In the event that you modify the SOFTWARE, you shall notify FLL by * e-mail at risa-admin@sec.flab.fujitsu.co.jp of the detailed specification * for such modification or the source code of the modified part of the * SOFTWARE. * * THE SOFTWARE IS PROVIDED AS IS WITHOUT ANY WARRANTY OF ANY KIND. FLL * MAKES ABSOLUTELY NO WARRANTIES, EXPRESSED, IMPLIED OR STATUTORY, AND * EXPRESSLY DISCLAIMS ANY IMPLIED WARRANTY OF MERCHANTABILITY, FITNESS * FOR A PARTICULAR PURPOSE OR NONINFRINGEMENT OF THIRD PARTIES' * RIGHTS. NO FLL DEALER, AGENT, EMPLOYEES IS AUTHORIZED TO MAKE ANY * MODIFICATIONS, EXTENSIONS, OR ADDITIONS TO THIS WARRANTY. * UNDER NO CIRCUMSTANCES AND UNDER NO LEGAL THEORY, TORT, CONTRACT, * OR OTHERWISE, SHALL FLL BE LIABLE TO YOU OR ANY OTHER PERSON FOR ANY * DIRECT, INDIRECT, SPECIAL, INCIDENTAL, PUNITIVE OR CONSEQUENTIAL * DAMAGES OF ANY CHARACTER, INCLUDING, WITHOUT LIMITATION, DAMAGES * ARISING OUT OF OR RELATING TO THE SOFTWARE OR THIS AGREEMENT, DAMAGES * FOR LOSS OF GOODWILL, WORK STOPPAGE, OR LOSS OF DATA, OR FOR ANY * DAMAGES, EVEN IF FLL SHALL HAVE BEEN INFORMED OF THE POSSIBILITY OF * SUCH DAMAGES, OR FOR ANY CLAIM BY ANY OTHER PARTY. EVEN IF A PART * OF THE SOFTWARE HAS BEEN DEVELOPED BY A THIRD PARTY, THE THIRD PARTY * DEVELOPER SHALL HAVE NO LIABILITY IN CONNECTION WITH THE USE, * PERFORMANCE OR NON-PERFORMANCE OF THE SOFTWARE. * * $OpenXM: OpenXM_contrib2/asir2018/builtin/strobj.c,v 1.4 2021/03/25 05:06:06 takayama Exp $ */ #include "ca.h" #include "parse.h" #include "ctype.h" #if defined(PARI) #include "genpari.h" # if !(PARI_VERSION_CODE > 131588) extern jmp_buf environnement; # endif #endif #include #if defined(__GNUC__) #define INLINE inline #elif defined(VISUAL) || defined(__MINGW32__) #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(); void Pwrite_to_tb(); void Ptb_to_string(); void Pclear_tb(); 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 Pnbp_tm(), Pnbp_tt(), Pnbp_tc(), Pnbp_trest(); void Pnbm_deg(), Pnbm_index(); void Pnbm_hp_rest(); void Pnbm_hxky(), Pnbm_xky_rest(); void Pnbm_hv(), Pnbm_tv(), Pnbm_rest(),Pnbm_trest(); void Pquote_to_funargs(),Pfunargs_to_quote(),Pget_function_name(); void 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); char *conv_subs(char *name); char *call_convfunc(char *name); 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}, {"strtoascii",Pstrtoascii,1}, {"asciitostr",Pasciitostr,1}, {"str_len",Pstr_len,1}, {"str_chr",Pstr_chr,3}, {"sub_str",Psub_str,3}, {"write_to_tb",Pwrite_to_tb,2}, {"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}, {"nbp_tm", Pnbp_tm,1}, {"nbp_tt", Pnbp_tt,1}, {"nbp_tc", Pnbp_tc,1}, {"nbp_trest", Pnbp_trest,1}, {"nbm_deg", Pnbm_deg,1}, {"nbm_index", Pnbm_index,1}, {"nbm_hxky", Pnbm_hxky,1}, {"nbm_xky_rest", Pnbm_xky_rest,1}, {"nbm_hp_rest", Pnbm_hp_rest,1}, {"nbm_hv", Pnbm_hv,1}, {"nbm_tv", Pnbm_tv,1}, {"nbm_rest", Pnbm_rest,1}, {"nbm_trest", Pnbm_trest,1}, {"qt_to_nary",Pqt_to_nary,1}, {"qt_to_bin",Pqt_to_bin,2}, {"quotetotex_tb",Pquotetotex_tb,2}, {"quotetotex",Pquotetotex,1}, {"quotetotex_env",Pquotetotex_env,-99999999}, {"flatten_quote",Pflatten_quote,-2}, {"quote_to_funargs",Pquote_to_funargs,1}, {"funargs_to_quote",Pfunargs_to_quote,1}, {"get_function_name",Pget_function_name,1}, {0,0,0}, }; void write_tb(char *s,TB tb) { if ( tb->next == tb->size ) { tb->size *= 2; tb->body = (char **)REALLOC(tb->body,tb->size*sizeof(char *)); } tb->body[tb->next] = s; tb->next++; } 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; static int conv_flag; static int dp_vars_hweyl; #define CONV_TABLE (1U<<0) #define CONV_SUBS (1U<<1) #define CONV_DMODE (1U<<2) static struct { char *name; Obj value; int (*reg)(); } qtot_env[] = { {"symbol_table",0,register_symbol_table}, {"conv_rule",0,register_conv_rule}, {"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}, }; #define PARTIAL "\\partial" char *conv_rule(char *name) { char *body,*r; int len; if ( convfunc ) name = call_convfunc(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,*buf_conv; char **subs; 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) && _is_delimiter(name[i]) ) i++; start = i; if ( i == len ) break; if ( name[i] == '{' ) { for ( level = 1, i++; i < len && level; i++ ) { if ( name[i] == '{' ) level++; else if ( name[i] == '}' ) level--; } slen = i-start; if ( slen >= 3 ) { brace = (char *)ALLOCA((slen+1)*sizeof(char)); strncpy(brace,name+start+1,slen-2); brace[slen-2] = 0; buf = conv_subs(brace); subs[j] = (char *)ALLOCA((strlen(buf)+3)*sizeof(char)); if ( strlen(buf) == 1 ) strcpy(subs[j],buf); else sprintf(subs[j],"{%s}",buf); } else subs[j] = "{}"; } else { if ( isdigit(name[i]) ) while ( i < len && isdigit(name[i]) ) i++; else 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; buf_conv = symbol_name(buf); subs[j] = buf_conv?buf_conv:buf; } } for ( k = 0, clen = 0; k < j; k++ ) clen += strlen(subs[k]); /* {subs(0)}_{{subs(1)},...,{subs(j-1)}} => {}:j+1 _:1 ,:j-2 */ h = r = MALLOC_ATOMIC((clen+(j+1)*2+1+(j-2)+1)*sizeof(char)); if ( j == 1 ) sprintf(h,"{%s}",subs[0]); else { sprintf(h,"{%s}_{%s",subs[0],subs[1]); h += strlen(h); for ( k = 2; k < j; k++ ) { sprintf(h,",%s",subs[k]); h += strlen(h); } strcpy(h,"}"); } return r; } char *call_convfunc(char *name) { STRING str,r; NODE arg; MKSTR(str,name); arg = mknode(1,str); r = (STRING)bevalf(convfunc,arg); if ( !r || OID(r) != O_STR ) error("call_convfunc : invalid result"); return BDY(r); } int register_symbol_table(Obj arg) { NODE n,t; Obj b; STRING a0,a1; struct TeXSymbol *uts; int i,len; /* check */ if ( !arg ) { user_texsymbol = 0; return 1; } if ( OID(arg) != O_LIST ) return 0; n = BDY((LIST)arg); len = length(n); uts = (struct TeXSymbol *)MALLOC((len+1)*sizeof(struct TeXSymbol)); for ( i = 0; n; n = NEXT(n), i++ ) { b = (Obj)BDY(n); if ( !b || OID(b) != O_LIST ) return 0; t = BDY((LIST)b); if ( !t || !NEXT(t) ) return 0; a0 = (STRING)BDY(t); a1 = (STRING)BDY(NEXT(t)); if ( !a0 ) return 0; if ( OID(a0) == O_STR ) uts[i].text = BDY(a0); else if ( OID(a0) == O_P ) uts[i].text = NAME(VR((P)a0)); else return 0; if ( !a1 ) return 0; if ( OID(a1) == O_STR ) uts[i].symbol = BDY(a1); else if ( OID(a1) == O_P ) uts[i].symbol = NAME(VR((P)a1)); else return 0; } uts[i].text = 0; uts[i].symbol = 0; user_texsymbol = uts; return 1; } int register_dp_vars_origin(Obj arg) { if ( INT(arg) ) { dp_vars_origin = ZTOS((Q)arg); return 1; } else return 0; } int register_dp_dvars_origin(Obj arg) { if ( INT(arg) ) { dp_dvars_origin = ZTOS((Q)arg); return 1; } else return 0; } int register_dp_vars_hweyl(Obj arg) { if ( INT(arg) ) { dp_vars_hweyl = ZTOS((Q)arg); return 1; } else return 0; } int register_show_lt(Obj arg) { if ( INT(arg) ) { show_lt = ZTOS((Q)arg); return 1; } else return 0; } int register_conv_rule(Obj arg) { if ( INT(arg) ) { conv_flag = ZTOS((Q)arg); convfunc = 0; return 1; } else return 0; } int register_conv_func(Obj arg) { if ( !arg ) { convfunc = 0; return 1; } else if ( OID(arg) == O_P && (long)(VR((P)arg))->attr == V_SR ) { convfunc = (FUNC)(VR((P)arg)->priv); /* f must be a function which takes single argument */ return 1; } else return 0; } int register_dp_vars(Obj arg) { int l,i; char **r; NODE n; STRING a; if ( !arg ) { dp_vars = 0; dp_vars_len = 0; return 1; } else if ( OID(arg) != O_LIST ) return 0; else { n = BDY((LIST)arg); l = length(n); r = (char **)MALLOC_ATOMIC(l*sizeof(char *)); for ( i = 0; i < l; i++, n = NEXT(n) ) { a = (STRING)BDY(n); if ( !a ) return 0; if ( OID(a) == O_STR ) r[i] = BDY(a); else if ( OID(a) == O_P ) r[i] = NAME(VR((P)a)); else return 0; } dp_vars = r; dp_vars_len = l; return 1; } } int register_dp_vars_prefix(Obj arg) { if ( !arg ) { dp_vars_prefix = 0; return 1; } else if ( OID(arg) == O_STR ) { dp_vars_prefix = BDY((STRING)arg); return 1; } else if ( OID(arg) == O_P ) { dp_vars_prefix = NAME(VR((P)arg)); return 1; } 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; char *name; NODE n,n0; STRING s; LIST l; ac = argc(arg); if ( !ac ) { n0 = 0; for ( i = 0; qtot_env[i].name; i++ ) { NEXTNODE(n0,n); MKSTR(s,qtot_env[i].name); BDY(n) = (pointer)s; NEXTNODE(n0,n); BDY(n) = (Q)qtot_env[i].value; } NEXT(n) = 0; MKLIST(l,n0); *rp = (Obj)l; } else if ( ac == 1 && !ARG0(arg) ) { /* set to default */ 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"); name = BDY((STRING)ARG0(arg)); for ( i = 0; qtot_env[i].name; i++ ) if ( !strcmp(qtot_env[i].name,name) ) { if ( ac == 2 ) { if ( (qtot_env[i].reg)((Obj)ARG1(arg)) ) qtot_env[i].value = (Obj)ARG1(arg); else error("quotetotex_env : invalid argument"); } *rp = qtot_env[i].value; return; } *rp = 0; } else *rp = 0; } void Pwrite_to_tb(NODE arg,Q *rp) { int i; Obj obj; TB tb; asir_assert(ARG1(arg),O_TB,"write_to_tb"); obj = ARG0(arg); if ( !obj ) write_tb("",ARG1(arg)); else if ( OID(obj) == O_STR ) write_tb(BDY((STRING)obj),ARG1(arg)); else if ( OID(obj) == O_TB ) { tb = (TB)obj; for ( i = 0; i < tb->next; i++ ) write_tb(tb->body[i],ARG1(arg)); } *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 = ZTOS((Q)ARG1(arg)); f = fnode_to_bin(BDY((QUOTE)ARG0(arg)),direction); MKQUOTE(*rp,f); } void Pqt_is_var(NODE arg,Z *rp) { QUOTE q; int ret; q = (QUOTE)ARG0(arg); asir_assert(q,O_QUOTE,"qt_is_var"); ret = fnode_is_var(BDY(q)); STOZ(ret,*rp); } void Pqt_is_coef(NODE arg,Z *rp) { QUOTE q; int ret; q = (QUOTE)ARG0(arg); asir_assert(q,O_QUOTE,"qt_is_coef"); ret = fnode_is_coef(BDY(q)); STOZ(ret,*rp); } void Pqt_is_number(NODE arg,Z *rp) { QUOTE q; int ret; q = (QUOTE)ARG0(arg); asir_assert(q,O_QUOTE,"qt_is_number"); ret = fnode_is_number(BDY(q)); STOZ(ret,*rp); } void Pqt_is_rational(NODE arg,Z *rp) { QUOTE q; int ret; q = (QUOTE)ARG0(arg); asir_assert(q,O_QUOTE,"qt_is_rational"); ret = fnode_is_rational(BDY(q)); STOZ(ret,*rp); } void Pqt_is_integer(NODE arg,Z *rp) { QUOTE q; int ret; q = (QUOTE)ARG0(arg); asir_assert(q,O_QUOTE,"qt_is_integer"); ret = fnode_is_integer(BDY(q)); STOZ(ret,*rp); } void Pqt_is_function(NODE arg,Z *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; STOZ(ret,*rp); } void Pqt_is_dependent(NODE arg,Z *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); STOZ(ret,*rp); } void Pqt_match(NODE arg,Z *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,Z *rp) { QUOTE fq,pq; FNODE f,p; int ret; Z mode; NODE r; mode = argc(arg)==3 ? (Z)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; Z mode; int m; obj = (Obj)ARG0(arg); rule = BDY((LIST)ARG1(arg)); mode = (Z)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 = ZTOS(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 = (long)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; long pv; FNODE f; QUOTE value; QUOTEARG qa; for ( t = arg; t; t = NEXT(t) ) { pair = (NODE)BDY(t); pv = (long)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; Z 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); STOZ(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 = ZTOS((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,(QUOTE)f,(QUOTE)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); } } /* XXX */ return 0; } void Pquotetotex(NODE arg,STRING *rp) { TB tb; NEWTB(tb); /* XXX for DP */ is_lt = 1; fnodetotex_tb(BDY((QUOTE)ARG0(arg)),tb); tb_to_string(tb,rp); } void Pquotetotex_tb(NODE arg,Q *rp) { int i; TB tb; asir_assert(ARG1(arg),O_TB,"quotetotex_tb"); /* XXX for DP */ is_lt = 1; fnodetotex_tb(BDY((QUOTE)ARG0(arg)),ARG1(arg)); *rp = 0; } void Pstring_to_tb(NODE arg,TB *rp) { TB tb; asir_assert(ARG0(arg),O_STR,"string_to_tb"); NEWTB(tb); tb->body[0] = BDY((STRING)ARG0(arg)); tb->next++; *rp = tb; } void Ptb_to_string(NODE arg,STRING *rp) { TB tb; asir_assert(ARG0(arg),O_TB,"tb_to_string"); tb = (TB)ARG0(arg); tb_to_string(tb,rp); } void tb_to_string(TB tb,STRING *rp) { int j,len; char *all,*p,*q; for ( j = 0, len = 0; j < tb->next; j++ ) len += strlen(tb->body[j]); all = (char *)MALLOC_ATOMIC((len+1)*sizeof(char)); for ( j = 0, p = all; j < tb->next; j++ ) for ( q = tb->body[j]; *q; *p++ = *q++ ); *p = 0; MKSTR(*rp,all); } void Pclear_tb(NODE arg,Q *rp) { TB tb; int j; asir_assert(ARG0(arg),O_TB,"clear_tb"); tb = (TB)ARG0(arg); for ( j = 0; j < tb->next; j++ ) tb->body[j] = 0; tb->next = 0; *rp = 0; } void Pstr_len(arg,rp) NODE arg; Z *rp; { Obj obj; TB tb; int r,i; obj = (Obj)ARG0(arg); if ( !obj || (OID(obj) != O_STR && OID(obj) != O_TB) ) error("str_len : invalid argument"); if ( OID(obj) == O_STR) r = strlen(BDY((STRING)obj)); else if ( OID(obj) == O_TB ) { tb = (TB)obj; for ( r = i = 0; i < tb->next; i++ ) r += strlen(tb->body[i]); } STOZ(r,*rp); } void Pstr_chr(arg,rp) NODE arg; Z *rp; { STRING str,terminator; Z start; char *p,*ind; int chr,spos,r; str = (STRING)ARG0(arg); start = (Z)ARG1(arg); terminator = (STRING)ARG2(arg); asir_assert(str,O_STR,"str_chr"); asir_assert(start,O_N,"str_chr"); asir_assert(terminator,O_STR,"str_chr"); p = BDY(str); spos = ZTOS(start); chr = BDY(terminator)[0]; if ( spos > (int)strlen(p) ) r = -1; else { ind = strchr(p+spos,chr); if ( ind ) r = ind-p; else r = -1; } STOZ(r,*rp); } void Psub_str(arg,rp) NODE arg; STRING *rp; { STRING str; Q head,tail; char *p,*r; int spos,epos,len; str = (STRING)ARG0(arg); head = (Q)ARG1(arg); tail = (Q)ARG2(arg); asir_assert(str,O_STR,"sub_str"); asir_assert(head,O_N,"sub_str"); asir_assert(tail,O_N,"sub_str"); p = BDY(str); spos = ZTOS(head); epos = ZTOS(tail); len = strlen(p); if ( (spos >= len) || (epos < spos) ) { *rp = 0; return; } if ( epos >= len ) epos = len-1; len = epos-spos+1; r = (char *)MALLOC(len+1); strncpy(r,p+spos,len); r[len] = 0; MKSTR(*rp,r); } void Pstrtoascii(arg,rp) NODE arg; LIST *rp; { STRING str; char *p; int len,i; NODE n,n1; Z q; str = (STRING)ARG0(arg); asir_assert(str,O_STR,"strtoascii"); p = BDY(str); len = strlen(p); for ( i = len-1, n = 0; i >= 0; i-- ) { UTOZ((unsigned int)p[i],q); MKNODE(n1,q,n); n = n1; } MKLIST(*rp,n); } void Pasciitostr(arg,rp) NODE arg; STRING *rp; { LIST list; unsigned char *p; int len,i,j; NODE n; Z q; list = (LIST)ARG0(arg); asir_assert(list,O_LIST,"asciitostr"); n = BDY(list); len = length(n); p = MALLOC_ATOMIC(len+1); for ( i = 0; i < len; i++, n = NEXT(n) ) { q = (Z)BDY(n); asir_assert(q,O_N,"asciitostr"); j = ZTOS(q); if ( j >= 256 || j <= 0 ) error("asciitostr : argument out of range"); p[i] = j; } p[i] = 0; MKSTR(*rp,(char *)p); } void Peval_str(arg,rp) NODE arg; Obj *rp; { FNODE fnode; SNODE snode; char *cmd; #if defined(PARI) void recover(int); recover(0); # if !(PARI_VERSION_CODE > 131588) if ( setjmp(environnement) ) { avma = top; recover(1); resetenv(""); } # endif #endif cmd = BDY((STRING)ARG0(arg)); #if 0 exprparse_create_var(0,cmd,&fnode); *rp = eval(fnode); #else exprparse_create_var(0,cmd,&snode); *rp = evalstat(snode); #endif } void Prtostr(arg,rp) NODE arg; STRING *rp; { char *b; int len; len = estimate_length(CO,ARG0(arg)); b = (char *)MALLOC_ATOMIC(len+1); soutput_init(b); sprintexpr(CO,ARG0(arg)); MKSTR(*rp,b); } void Pstrtov(arg,rp) NODE arg; P *rp; { char *p; FUNC f; p = BDY((STRING)ARG0(arg)); #if 0 if ( !islower(*p) ) *rp = 0; else { for ( t = p+1; t && (isalnum(*t) || *t == '_'); t++ ); if ( *t ) *rp = 0; else makevar(p,rp); } #else /* search global variables */ gen_searchf_searchonly(p,&f,1); if ( f ) makesrvar(f,rp); else makevar(p,rp); #endif } static struct TeXSymbol texsymbol[] = { {"sin","\\sin"}, {"cos","\\cos"}, {"tan","\\tan"}, {"sinh","\\sinh"}, {"cosh","\\cosh"}, {"tanh","\\tanh"}, {"exp","\\exp"}, {"log","\\log"}, /* Greek Letters (lower case) */ {"alpha","\\alpha"}, {"beta","\\beta"}, {"gamma","\\gamma"}, {"delta","\\delta"}, {"epsilon","\\epsilon"}, {"varepsilon","\\varepsilon"}, {"zeta","\\zeta"}, {"eta","\\eta"}, {"theta","\\theta"}, {"vartheta","\\vartheta"}, {"iota","\\iota"}, {"kappa","\\kappa"}, {"lambda","\\lambda"}, {"mu","\\mu"}, {"nu","\\nu"}, {"xi","\\xi"}, {"pi","\\pi"}, {"varpi","\\varpi"}, {"rho","\\rho"}, {"sigma","\\sigma"}, {"varsigma","\\varsigma"}, {"tau","\\tau"}, {"upsilon","\\upsilon"}, {"phi","\\phi"}, {"varphi","\\varphi"}, {"chi","\\chi"}, {"omega","\\omega"}, /* Greek Letters, (upper case) */ {"ggamma","\\Gamma"}, {"ddelta","\\Delta"}, {"ttheta","\\Theta"}, {"llambda","\\Lambda"}, {"xxi","\\Xi"}, {"ppi","\\Pi"}, {"ssigma","\\Sigma"}, {"uupsilon","\\Upsilon"}, {"pphi","\\Phi"}, {"ppsi","\\Psi"}, {"oomega","\\Omega"}, /* Our own mathematical functions */ {"algebra_tensor","\\otimes"}, {"base_where","{\\rm \\ where \\ }"}, /* Mathematical constants */ {"c_pi","\\pi"}, {"c_i","\\sqrt{-1}"}, /* Temporary */ {0,0} }; char *symbol_name(char *name) { int i; if ( !name || strlen(name) == 0 ) return ""; if ( !(conv_flag & CONV_TABLE) ) return name; if ( user_texsymbol ) for ( i = 0; user_texsymbol[i].text; i++ ) if ( !strcmp(user_texsymbol[i].text,name) ) return user_texsymbol[i].symbol; for ( i = 0; texsymbol[i].text; i++ ) if ( !strcmp(texsymbol[i].text,name) ) return texsymbol[i].symbol; return 0; } void Pget_function_name(NODE arg,STRING *rp) { QUOTEARG qa; qa = (QUOTEARG)BDY(arg); if ( !qa || OID(qa) != O_QUOTEARG ) { *rp = 0; return; } switch ( qa->type ) { case A_arf: MKSTR(*rp,((ARF)BDY(qa))->name); break; case A_func: MKSTR(*rp,((FUNC)BDY(qa))->name); break; default: *rp = 0; break; } } FNODE strip_paren(FNODE); void objtotex_tb(Obj obj,TB tb); void fnodetotex_tb(FNODE f,TB tb) { NODE n,t,t0,args; char vname[BUFSIZ],prefix[BUFSIZ]; char *opname,*vname_conv,*prefix_conv; Obj obj; int i,len,allzero,elen,elen2,si; char *r; FNODE fi,f2,f1; write_tb(" ",tb); if ( !f ) { write_tb("0",tb); return; } switch ( f->id ) { /* unary operators */ case I_NOT: write_tb("\\neg (",tb); fnodetotex_tb((FNODE)FA0(f),tb); write_tb(")",tb); break; case I_PAREN: write_tb("(",tb); fnodetotex_tb((FNODE)FA0(f),tb); write_tb(")",tb); break; case I_MINUS: write_tb("-",tb); fnodetotex_tb((FNODE)FA0(f),tb); break; /* binary operators */ /* arg list */ /* I_AND, I_OR => FA0(f), FA1(f) */ /* otherwise => FA1(f), FA2(f) */ case I_BOP: opname = ((ARF)FA0(f))->name; 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); break; case '/': write_tb("\\frac{",tb); fnodetotex_tb((FNODE)FA1(f),tb); write_tb("} {",tb); fnodetotex_tb((FNODE)FA2(f),tb); 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) ) { case C_EQ: fnodetotex_tb((FNODE)FA1(f),tb); write_tb(" = ",tb); fnodetotex_tb((FNODE)FA2(f),tb); break; case C_NE: fnodetotex_tb((FNODE)FA1(f),tb); write_tb(" \\neq ",tb); fnodetotex_tb((FNODE)FA2(f),tb); break; case C_GT: fnodetotex_tb((FNODE)FA1(f),tb); write_tb(" > ",tb); fnodetotex_tb((FNODE)FA2(f),tb); break; case C_LT: fnodetotex_tb((FNODE)FA1(f),tb); write_tb(" < ",tb); fnodetotex_tb((FNODE)FA2(f),tb); break; case C_GE: fnodetotex_tb((FNODE)FA1(f),tb); write_tb(" \\geq ",tb); fnodetotex_tb((FNODE)FA2(f),tb); break; case C_LE: fnodetotex_tb((FNODE)FA1(f),tb); write_tb(" \\leq ",tb); fnodetotex_tb((FNODE)FA2(f),tb); break; } break; case I_LOP: switch( (lid)FA0(f) ) { case L_EQ: fnodetotex_tb((FNODE)FA1(f),tb); write_tb(" = ",tb); fnodetotex_tb((FNODE)FA2(f),tb); break; case L_NE: fnodetotex_tb((FNODE)FA1(f),tb); write_tb(" \\neq ",tb); fnodetotex_tb((FNODE)FA2(f),tb); break; case L_GT: fnodetotex_tb((FNODE)FA1(f),tb); write_tb(" > ",tb); fnodetotex_tb((FNODE)FA2(f),tb); break; case L_LT: fnodetotex_tb((FNODE)FA1(f),tb); write_tb(" < ",tb); fnodetotex_tb((FNODE)FA2(f),tb); break; case L_GE: fnodetotex_tb((FNODE)FA1(f),tb); write_tb(" \\geq ",tb); fnodetotex_tb((FNODE)FA2(f),tb); break; case L_LE: fnodetotex_tb((FNODE)FA1(f),tb); write_tb(" \\leq ",tb); fnodetotex_tb((FNODE)FA2(f),tb); break; case L_AND: fnodetotex_tb((FNODE)FA1(f),tb); write_tb(" {\\rm \\ and\\ } ",tb); fnodetotex_tb((FNODE)FA2(f),tb); break; case L_OR: fnodetotex_tb((FNODE)FA1(f),tb); write_tb(" {\\rm \\ or\\ } ",tb); fnodetotex_tb((FNODE)FA2(f),tb); break; case L_NOT: /* XXX : L_NOT is a unary operator */ write_tb("\\neg (",tb); fnodetotex_tb((FNODE)FA1(f),tb); write_tb(")",tb); return; default: return; } break; case I_AND: fnodetotex_tb((FNODE)FA0(f),tb); write_tb(" {\\rm \\ and\\ } ",tb); fnodetotex_tb((FNODE)FA1(f),tb); break; case I_OR: fnodetotex_tb((FNODE)FA0(f),tb); write_tb(" {\\rm \\ or\\ } ",tb); fnodetotex_tb((FNODE)FA1(f),tb); break; /* ternary operators */ case I_CE: error("fnodetotex_tb : not implemented yet"); break; /* lists */ case I_LIST: write_tb(" [ ",tb); n = (NODE)FA0(f); fnodenodetotex_tb(n,tb); write_tb("]",tb); break; /* function */ case I_FUNC: 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 */ case I_CAR: opname = conv_rule("car"); write_tb(opname,tb); write_tb("(",tb); fargstotex_tb(opname,FA0(f),tb); write_tb(")",tb); break; case I_CDR: opname = conv_rule("cdr"); write_tb(opname,tb); write_tb("(",tb); fargstotex_tb(opname,FA0(f),tb); write_tb(")",tb); break; /* exponent vector */ case I_EV: n = (NODE)FA0(f); if ( dp_vars_hweyl ) { elen = length(n); elen2 = elen>>1; elen = elen2<<1; } allzero = 1; if ( show_lt && is_lt ) write_tb("\\underline{",tb); for ( t0 = 0, i = 0; n; n = NEXT(n), i++ ) { fi = (FNODE)BDY(n); if ( fi->id == I_FORMULA && !FA0(fi) ) continue; allzero = 0; if ( dp_vars && i < dp_vars_len ) { strcpy(vname,dp_vars[i]); vname_conv = conv_rule(vname); } else { if ( dp_vars_hweyl ) { if ( i < elen2 ) { strcpy(prefix,dp_vars_prefix?dp_vars_prefix:"x"); 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"); 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); 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); opname = MALLOC_ATOMIC(len+2); sprintf(opname,"%s ",vname_conv); write_tb(opname,tb); } else { len = strlen(vname_conv); /* 2: ^{ */ opname = MALLOC_ATOMIC(len+1+2); sprintf(opname,"%s^{",vname_conv); write_tb(opname,tb); fnodetotex_tb((FNODE)BDY(n),tb); write_tb("} ",tb); } } /* XXX */ if ( allzero ) write_tb(" 1 ",tb); if ( show_lt && is_lt ) { write_tb("}",tb); is_lt = 0; } break; /* string */ case I_STR: write_tb((char *)FA0(f),tb); break; /* internal object */ case I_FORMULA: objtotex_tb((Obj)FA0(f),tb); break; /* program variable */ case I_PVAR: if ( FA1(f) ) error("fnodetotex_tb : not implemented yet"); GETPVNAME(FA0(f),opname); write_tb(opname,tb); break; default: error("fnodetotex_tb : not implemented yet"); return; } } 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 ( cmpz(DEG(dc),ONE) ) { write_tb("^",tb); if ( INT(DEG(dc)) && sgnz(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+1); 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) ) { is_lt = 1; fnodetotex_tb((FNODE)BDY(n),tb); if ( NEXT(n) ) write_tb(", ",tb); } } void fargstotex_tb(char *name,FNODE f,TB tb) { NODE n; if ( !strcmp(name,"matrix") ) { error("fargstotex_tb : not implemented yet"); } else if ( !strcmp(name,"vector") ) { error("fargstotex_tb : not implemented yet"); } else { if ( f->id == I_LIST ) { n = (NODE)FA0(f); fnodenodetotex_tb(n,tb); } else fnodetotex_tb(f,tb); } } int top_is_minus(FNODE f) { char *opname; int len; Obj obj; if ( !f ) return 0; switch ( f->id ) { case I_MINUS: return 1; case I_BOP: opname = ((ARF)FA0(f))->name; switch ( opname[0] ) { case '+': case '*': case '/': case '^': case '%': return top_is_minus((FNODE)FA1(f)); case '-': if ( FA1(f) ) return top_is_minus((FNODE)FA1(f)); else return 1; default: return 0; } break; case I_COP: return top_is_minus((FNODE)FA1(f)); case I_LOP: if ( (lid)FA0(f) == L_NOT ) return 0; else return top_is_minus((FNODE)FA1(f)); case I_AND: case I_OR: return top_is_minus((FNODE)FA0(f)); case I_FORMULA: obj = (Obj)FA0(f); if ( !obj ) return 0; else { switch ( OID(obj) ) { 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); opname = (char *)MALLOC_ATOMIC(len+1); soutput_init(opname); sprintexpr(CO,obj); 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,Z *rp) { FNODE f; QUOTE q; q = (QUOTE)ARG0(arg); if ( !q || OID(q) != O_QUOTE ) error("get_quote_id : invalid argument"); f = BDY(q); STOZ((long)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; Z 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; STOZ((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: STOZ((long)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)ZTOS((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)ZTOS((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 *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 = ZTOS((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 = ZTOS((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 = (P)ONE; m1->b = m->b; MKNODE(n,m1,0); MKNBP(*rp,n); } } void Pnbp_hc(NODE arg, P *rp) { NBP p; NBM m; p = (NBP)ARG0(arg); if ( !p ) *rp = 0; else { m = (NBM)BDY(BDY(p)); *rp = m->c; } } void Pnbp_rest(NODE arg, NBP *rp) { NBP p; NODE n; p = (NBP)ARG0(arg); if ( !p ) *rp = 0; else { n = BDY(p); if ( !NEXT(n) ) *rp = 0; else MKNBP(*rp,NEXT(n)); } } void Pnbp_tm(NODE arg, NBP *rp) { NBP p; NODE n; NBM m; p = (NBP)ARG0(arg); if ( !p ) *rp = 0; else { for ( n = BDY(p); NEXT(n); n = NEXT(n) ); m = (NBM)BDY(n); MKNODE(n,m,0); MKNBP(*rp,n); } } void Pnbp_tt(NODE arg, NBP *rp) { NBP p; NODE n; NBM m,m1; p = (NBP)ARG0(arg); if ( !p ) *rp = 0; else { for ( n = BDY(p); NEXT(n); n = NEXT(n) ); m = (NBM)BDY(n); NEWNBM(m1); m1->d = m->d; m1->c = (P)ONE; m1->b = m->b; MKNODE(n,m1,0); MKNBP(*rp,n); } } void Pnbp_tc(NODE arg, P *rp) { NBP p; NBM m; NODE n; p = (NBP)ARG0(arg); if ( !p ) *rp = 0; else { for ( n = BDY(p); NEXT(n); n = NEXT(n) ); m = (NBM)BDY(n); *rp = m->c; } } void Pnbp_trest(NODE arg, NBP *rp) { NBP p; NODE n,r,r0; p = (NBP)ARG0(arg); if ( !p ) *rp = 0; else { n = BDY(p); for ( r0 = 0; NEXT(n); n = NEXT(n) ) { NEXTNODE(r0,r); BDY(r) = (pointer)BDY(n); } if ( r0 ) { NEXT(r) = 0; MKNBP(*rp,r0); } else *rp = 0; } } void Pnbm_deg(NODE arg, Z *rp) { NBP p; NBM m; p = (NBP)ARG0(arg); if ( !p ) STOZ(-1,*rp); else { m = (NBM)BDY(BDY(p)); STOZ(m->d,*rp); } } void Pnbm_index(NODE arg, Z *rp) { NBP p; NBM m; unsigned int *b; int d,i,r; p = (NBP)ARG0(arg); if ( !p ) STOZ(0,*rp); else { m = (NBM)BDY(BDY(p)); d = m->d; if ( d > 32 ) error("nbm_index : weight too large"); b = m->b; for ( r = 0, i = d-2; i > 0; i-- ) if ( !NBM_GET(b,i) ) r |= (1<<(d-2-i)); STOZ(r,*rp); } } void Pnbm_hp_rest(NODE arg, LIST *rp) { NBP p,h,r; NBM m,m1; NODE n; int *b,*b1; int d,d1,v,i,j,k; p = (NBP)ARG0(arg); if ( !p ) MKLIST(*rp,0); else { m = (NBM)BDY(BDY(p)); b = (int *)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 = (int *)m1->b; m1->d = i; m1->c = (P)ONE; if ( v ) for ( j = 0; j < i; j++ ) NBM_SET(b1,j); else for ( j = 0; j < i; j++ ) NBM_CLR(b1,j); MKNODE(n,m1,0); MKNBP(h,n); d1 = d-i; NEWNBM(m1); NEWNBMBDY(m1,d1); b1 = (int *)m1->b; m1->d = d1; m1->c = (P)ONE; for ( j = 0, k = i; j < d1; j++, k++ ) if ( NBM_GET(b,k) ) NBM_SET(b1,j); else NBM_CLR(b1,j); MKNODE(n,m1,0); MKNBP(r,n); n = mknode(2,h,r); MKLIST(*rp,n); } } } void Pnbm_hxky(NODE arg, NBP *rp) { NBP p; p = (NBP)ARG0(arg); if ( !p ) *rp = 0; else separate_xky_nbm((NBM)BDY(BDY(p)),0,rp,0); } void Pnbm_xky_rest(NODE arg,NBP *rp) { NBP p; p = (NBP)ARG0(arg); if ( !p ) *rp = 0; else separate_xky_nbm((NBM)BDY(BDY(p)),0,0,rp); } void Pnbm_hv(NODE arg, NBP *rp) { NBP p; p = (NBP)ARG0(arg); if ( !p ) *rp = 0; else separate_nbm((NBM)BDY(BDY(p)),0,rp,0); } void Pnbm_rest(NODE arg, NBP *rp) { NBP p; p = (NBP)ARG0(arg); if ( !p ) *rp = 0; else separate_nbm((NBM)BDY(BDY(p)),0,0,rp); } void Pnbm_tv(NODE arg, NBP *rp) { NBP p; p = (NBP)ARG0(arg); if ( !p ) *rp = 0; else separate_tail_nbm((NBM)BDY(BDY(p)),0,0,rp); } void Pnbm_trest(NODE arg, NBP *rp) { NBP p; p = (NBP)ARG0(arg); if ( !p ) *rp = 0; else separate_tail_nbm((NBM)BDY(BDY(p)),0,rp,0); } NBP fnode_to_nbp(FNODE f) { Z r; int n,i; NBM m; V v; NBP u,u1,u2; NODE t,b; if ( f->id == I_FORMULA ) { r = eval(f); NEWNBM(m); if ( OID(r) == O_N ) { m->d = 0; m->c = (P)r; m->b = 0; } else { v = VR((P)r); m->d = 1; m->c = (P)ONE; NEWNBMBDY(m,1); if ( !strcmp(NAME(v),"x") ) NBM_SET(m->b,0); else NBM_CLR(m->b,0); } MKNODE(b,m,0); MKNBP(u,b); return u; } else if ( IS_NARYADD(f) ) { t = (NODE)FA1(f); u = fnode_to_nbp((FNODE)BDY(t)); for ( t = NEXT(t); t; t = NEXT(t) ) { u1 = fnode_to_nbp((FNODE)BDY(t)); addnbp(CO,u,u1,&u2); u = u2; } return u; } else if ( IS_NARYMUL(f) ) { t = (NODE)FA1(f); u = fnode_to_nbp((FNODE)BDY(t)); for ( t = NEXT(t); t; t = NEXT(t) ) { u1 = fnode_to_nbp((FNODE)BDY(t)); mulnbp(CO,u,u1,&u2); u = u2; } return u; } else if ( IS_BINARYPWR(f) ) { u = fnode_to_nbp((FNODE)FA1(f)); r = eval((FNODE)FA2(f)); pwrnbp(CO,u,r,&u1); return u1; } /* XXX */ return 0; } void Pnqt_weight(NODE arg,Z *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); STOZ(w,*rp); } void Pnqt_comp(NODE arg,Z *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); STOZ(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 ( !cmpz(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) { Z n; n = (Z)eval(f); if ( !n || (INT(n) && sgnz(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; Z q; if ( f->normalized && (f->expanded == expand) ) return f; STOZ(-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,NULLP); 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,NULLP); else if ( fnode_is_coef(f1) ) return nfnode_mul_coef((Obj)eval(f1),f2,expand); else if ( fnode_is_coef(f2) ) return nfnode_mul_coef((Obj)eval(f2),f1,expand); if ( expand && IS_NARYADD(f1) ) { t = mkfnode(1,I_FORMULA,NULLP); 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,NULLP); 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,NULLP); 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) && sgnz((Z)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; Z q; if ( IS_ZERO(f2) ) return mkfnode(1,I_FORMULA,ONE); else if ( IS_ZERO(f1) ) return mkfnode(1,I_FORMULA,NULLP); else if ( fnode_is_coef(f1) ) { if ( fnode_is_integer(f2) ) { if ( fnode_is_one(f2) ) return f1; else { 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 = ZTOS((Q)nf2); cc = mkfnode(1,I_FORMULA,c); if ( fnode_is_nonnegative_integer(f2) ) b = fnode_expand_pwr(b1,ee,expand); else { STOZ(-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 = (Z)eval(f2); if ( !smallz(q) ) error("nfnode_pwr : exponent too large"); return fnode_expand_pwr(f1,ZTOS(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; Z q; if ( !n ) return mkfnode(1,I_FORMULA,ONE); else if ( IS_ZERO(f) ) return mkfnode(1,I_FORMULA,NULLP); 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: STOZ(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(1,I_FORMULA,NULLP); 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)); } } /* XXX */ return 0; } 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 = ZTOS(a2); } else w = nfnode_weight(tab,FA2(f)); return nfnode_weight(tab,FA1(f))*w; default: error("nfnode_weight : not_implemented"); return 0; } } 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,NULLP); h2 = n2 ? (FNODE)BDY(n2) : mkfnode(1,I_FORMULA,NULLP); return nfnode_comp_lex(h1,h2); } if ( IS_NARYMUL(f1) || IS_NARYMUL(f2) ) { fnode_coef_body(f1,&c1,&b1); fnode_coef_body(f2,&c2,&b2); if ( !compfnode(b1,b2) ) return 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) ) != 0 ) { if ( r > 0 ) return nfnode_comp_lex(e1,mkfnode(1,I_FORMULA,NULLP)); else if ( r < 0 ) return nfnode_comp_lex(mkfnode(1,I_FORMULA,NULLP),e2); } else return nfnode_comp_lex(e1,e2); } /* now, IDs of f1 and f2 must be I_FORMULA, I_FUNC, 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)) ) != 0 ) 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 = (long)FA0(f1); i2 = (long)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 = (long)FA0((FNODE)FA0(f1)); i2 = (long)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)) ) != 0 ) return r; else { n1 = NEXT(n1); n2 = NEXT(n2); } return n1?1:(n2?-1:0); } break; default: error("nfnode_comp_lex : undefined"); return 0; } break; default: error("nfnode_comp_lex : undefined"); return 0; } return 0; } 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,(long)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),NULLP); } /* 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"); return 0; } return 0; } /* 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); } /* XXX */ return 0; } /* 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 = (long)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"); return 0; } }