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misc.cc
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misc.cc
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/* -*- mode:C++ ; compile-command: "g++ -I.. -I../include -DHAVE_CONFIG_H -DIN_GIAC -DGIAC_GENERIC_CONSTANTS -fno-strict-aliasing -g -c misc.cc -Wall" -*- */
#include "giacPCH.h"
/*
* Copyright (C) 2001, 2007 R. De Graeve, B. Parisse, Institut Fourier, 38402 St Martin d'Heres
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 3 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
using namespace std;
#ifdef HAVE_UNISTD_H
#if !defined NUMWORKS && !defined HP39
#include <dirent.h>
#endif
#include <sys/stat.h>
#include <sys/types.h>
#endif
#include <fstream>
#include <string>
#include "misc.h"
#include "usual.h"
#include "sym2poly.h"
#include "rpn.h"
#include "prog.h"
#include "derive.h"
#include "subst.h"
#include "intg.h"
#include "vecteur.h"
#include "ifactor.h"
#include "solve.h"
#include "modpoly.h"
#include "permu.h"
#include "sym2poly.h"
#include "plot.h"
#include "lin.h"
#include "modpoly.h"
#include "desolve.h"
#include "alg_ext.h"
#include "input_parser.h"
#include "input_lexer.h"
#include "maple.h"
#include "quater.h"
#include "sparse.h"
#include "giacintl.h"
#include "signalprocessing.h"
#if defined GIAC_HAS_STO_38 || defined NSPIRE || defined NSPIRE_NEWLIB || defined FXCG || defined GIAC_GGB || defined USE_GMP_REPLACEMENTS || defined KHICAS
inline bool is_graphe(const giac::gen &g){ return false; }
inline giac::gen _graph_charpoly(const giac::gen &g,const giac::context *){ return g;}
#else
#include "signalprocessing.h"
#include "graphtheory.h"
#endif
#define GIAC_LMCHANGES 1 // changes by L. Marohnić // regression checks
#ifdef KHICAS
#include "kdisplay.h"
const char * mp_hal_input(const char * prompt) ;
#endif
#ifdef HAVE_LIBCURL
#include <curl/curl.h>
#include <curl/easy.h>
#endif
#ifndef NO_NAMESPACE_GIAC
namespace giac {
#endif // ndef NO_NAMESPACE_GIAC
gen _scalar_product(const gen & args,GIAC_CONTEXT){
if ( args.type==_STRNG && args.subtype==-1) return args;
if (args.type!=_VECT || args._VECTptr->size()!=2)
return gensizeerr(contextptr);
vecteur & v=*args._VECTptr;
return scalar_product(v[0],v[1],contextptr);
}
static const char _scalar_product_s []="scalar_product";
static define_unary_function_eval (__scalar_product,&_scalar_product,_scalar_product_s);
define_unary_function_ptr5( at_scalar_product ,alias_at_scalar_product,&__scalar_product,0,true);
static const char _dot_s []="dot";
static define_unary_function_eval (__dot,&_scalar_product,_dot_s);
define_unary_function_ptr5( at_dot ,alias_at_dot,&__dot,0,true);
gen _compare(const gen & args,GIAC_CONTEXT){
if ( args.type==_STRNG && args.subtype==-1) return args;
if (args.type!=_VECT || args._VECTptr->size()!=2)
return gensizeerr(contextptr);
vecteur & v=*args._VECTptr;
return v[0].islesscomplexthan(v[1]);
}
static const char _compare_s []="compare";
static define_unary_function_eval (__compare,&_compare,_compare_s);
define_unary_function_ptr5( at_compare ,alias_at_compare,&__compare,0,true);
gen _preval(const gen & args,GIAC_CONTEXT){
if ( args.type==_STRNG && args.subtype==-1) return args;
if (args.type!=_VECT)
return symbolic(at_preval,args);
vecteur & v=*args._VECTptr;
int s=int(v.size());
if (s<3)
return gentoofewargs("");
gen f(v[0]),x,a,b;
a=v[1];
b=v[2];
if (s==3){
x=vx_var;
if (a.is_symb_of_sommet(at_equal)){
x=a._SYMBptr->feuille[0];
a=a._SYMBptr->feuille[1];
if (b.is_symb_of_sommet(at_equal))
b=b._SYMBptr->feuille[1];
}
}
else
x=v[3];
if (x.type!=_IDNT)
return gentypeerr(contextptr);
return preval(f,x,a,b,contextptr);
}
static const char _preval_s []="preval";
static define_unary_function_eval (__preval,&_preval,_preval_s);
define_unary_function_ptr5( at_preval ,alias_at_preval,&__preval,0,true);
// return suitable gen for interpolation
// if possible return j, if j is too large, return a GF element
gen interpolate_xi(int j,const gen &coeff){
if (coeff.type==_MOD){
}
if (coeff.type!=_USER)
return j;
#ifndef NO_RTTI
if (galois_field * gf=dynamic_cast<galois_field *>(coeff._USERptr)){
if (j<gf->p.val)
return j;
galois_field g(*gf); // copy
g.a=_revlist(_convert(makesequence(j,change_subtype(_BASE,_INT_MAPLECONVERSION),gf->p),context0),context0);
return g;
}
#endif
return j;
}
// characteristic must be large enough to interpolate the resultant
// d1+1 evaluations + there is a probab. of 2/p of bad evaluation
// (d1+1)*p/(p-2)<p -> p>d1+3 + we add some more for safety
// on Galois fields comparison should be (d+1)*p/(p-2)<p^m
// assuming interpolation is done with all fields elements
bool interpolable_resultant(const polynome & P,int d1,gen & coefft,bool extend,GIAC_CONTEXT){
int tt=coefft.type;
if (tt!=_USER)
tt=coefftype(P,coefft);
return interpolable(d1,coefft,extend,contextptr);
}
bool interpolable(int d1,gen & coefft,bool extend,GIAC_CONTEXT){
int tt=coefft.type;
if (tt==_USER){
#ifndef NO_RTTI
if (galois_field * gf=dynamic_cast<galois_field *>(coefft._USERptr)){
gen m=gf->p;
if (!is_integer(m))
return false;
return is_greater(pow(m,gf->P._VECTptr->size()-1,contextptr),d1+20,contextptr);
}
return true;
#endif
}
if (tt==_MOD){
gen m=*(coefft._MODptr+1);
if (!is_integer(m))
return false;
if (is_greater(m,d1+20,contextptr))
return true;
if (!extend || !_isprime(m,contextptr).val)
return false;
// build a suitable field extension...
int n=int(std::ceil(std::log(d1+20.0)/std::log(evalf_double(m,1,contextptr)._DOUBLE_val)));
#ifdef NO_RTTI
return false;
#else
coefft=_galois_field(makesequence(m,n),contextptr);
return true;
#endif
}
return true;
}
vecteur divided_differences(const vecteur & x,const vecteur & y){
vecteur res(y);
int s=int(x.size());
for (int k=1;k<s;++k){
for (int j=s-1;j>=k;--j){
res[j]=(res[j]-res[j-1])/(x[j]-x[j-k]);
}
//CERR << k << res << '\n';
}
return res;
}
gen _lagrange(const gen & args,GIAC_CONTEXT){
if ( args.type==_STRNG && args.subtype==-1) return args;
if (args.type!=_VECT)
return symbolic(at_lagrange,args);
vecteur & v=*args._VECTptr;
int s=int(v.size());
if (s<2)
return gentoofewargs("");
gen v0(v[0]),v1(v[1]),x=vx_var;
if (ckmatrix(v0) && v0._VECTptr->size()==2){
x=v1;
v1=v0._VECTptr->back();
v0=v0._VECTptr->front();
}
if (s>=3)
x=v[2];
if (v0.type!=_VECT && v1.type==_VECT){
gen tmp=v1;
v1=_apply(makesequence(v0,v1),contextptr);
v0=tmp;
}
if (v1.type!=_VECT && v0.type==_VECT)
v1=_apply(makesequence(v1,v0),contextptr);
if ( (v0.type!=_VECT) || (v1.type!=_VECT) )
return gensizeerr(contextptr);
vecteur & vx =*v0._VECTptr;
vecteur & vy=*v1._VECTptr;
s=int(vx.size());
if (!s || vy.size()!=unsigned(s))
return gendimerr(contextptr);
// Using divided difference instead of the theoretical formula
if (x.type==_VECT && x._VECTptr->empty()){
vecteur res;
interpolate(vx,vy,res,0);
return res;
}
vecteur w=divided_differences(vx,vy);
if (x==at_lagrange)
return w;
gen pi(1),res(w[s-1]);
for (int i=s-2;i>=0;--i){
res = res*(x-vx[i])+w[i];
if (i%100==99) // otherwise segfault
res=ratnormal(res,contextptr);
}
return res;
/*
gen res(zero);
for (int i=0;i<s;++i){
gen pix(plus_one),pix0(plus_one),x0(vx[i]);
for (int j=0;j<s;++j){
if (j==i)
continue;
pix=pix*(x-vx[j]);
pix0=pix0*(x0-vx[j]);
}
res=res+vy[i]*rdiv(pix,pix0);
}
return res;
*/
}
static const char _lagrange_s []="lagrange";
static define_unary_function_eval (__lagrange,&_lagrange,_lagrange_s);
define_unary_function_ptr5( at_lagrange ,alias_at_lagrange,&__lagrange,0,true);
gen _reorder(const gen & args,GIAC_CONTEXT){
if ( args.type==_STRNG && args.subtype==-1) return args;
if (args.type!=_VECT)
return symbolic(at_reorder,args);
vecteur & v=*args._VECTptr;
int s=int(v.size());
if (s<2)
return gentoofewargs("");
gen e(v[0]),l(v[1]);
if (e.type<=_POLY) return e;
if (l.type!=_VECT)
return gensizeerr(contextptr);
vecteur w(*l._VECTptr);
lvar(e,w);
e=e2r(e,w,contextptr);
return r2e(e,w,contextptr);
}
static const char _reorder_s []="reorder";
static define_unary_function_eval (__reorder,&_reorder,_reorder_s);
define_unary_function_ptr5( at_reorder ,alias_at_reorder,&__reorder,0,true);
gen _adjoint_matrix(const gen & args,GIAC_CONTEXT){
if ( args.type==_STRNG && args.subtype==-1) return args;
if (args.type!=_VECT)
return symbolic(at_adjoint_matrix,args);
matrice mr(*args._VECTptr);
if (!is_squarematrix(mr))
return gensizeerr(contextptr);
matrice m_adj;
vecteur p_car;
p_car=mpcar(mr,m_adj,true,true,contextptr);
return makevecteur(p_car,m_adj);
}
static const char _adjoint_matrix_s []="adjoint_matrix";
static define_unary_function_eval (__adjoint_matrix,&_adjoint_matrix,_adjoint_matrix_s);
define_unary_function_ptr5( at_adjoint_matrix ,alias_at_adjoint_matrix,&__adjoint_matrix,0,true);
gen _equal2diff(const gen & args,GIAC_CONTEXT){
if ( args.type==_STRNG && args.subtype==-1) return args;
return apply(args,equal2diff);
}
static const char _equal2diff_s []="equal2diff";
static define_unary_function_eval (__equal2diff,&_equal2diff,_equal2diff_s);
define_unary_function_ptr5( at_equal2diff ,alias_at_equal2diff,&__equal2diff,0,true);
static gen equal2list(const gen & arg){
if ( !is_equal(arg))
return makevecteur(arg,zero);
return arg._SYMBptr->feuille;
}
gen _equal2list(const gen & args,GIAC_CONTEXT){
if ( args.type==_STRNG && args.subtype==-1) return args;
return apply(args,equal2list);
}
static const char _equal2list_s []="equal2list";
static define_unary_function_eval (__equal2list,&_equal2list,_equal2list_s);
define_unary_function_ptr5( at_equal2list ,alias_at_equal2list,&__equal2list,0,true);
gen _rank(const gen & args,GIAC_CONTEXT){
if ( args.type==_STRNG && args.subtype==-1) return args;
if (args.type!=_VECT)
return gentypeerr(contextptr); // return symbolic(at_adjoint_matrix,args);
matrice mr(*args._VECTptr);
if (!ckmatrix(mr))
return gensizeerr(contextptr);
mr=mrref(mr,contextptr);
int r=int(mr.size());
for (;r;--r){
if (!is_zero(mr[r-1]))
break;
}
return r;
}
static const char _rank_s []="rank";
static define_unary_function_eval (__rank,&_rank,_rank_s);
define_unary_function_ptr5( at_rank ,alias_at_rank,&__rank,0,true);
gen _sec(const gen & args,GIAC_CONTEXT){
if ( args.type==_STRNG && args.subtype==-1) return args;
return inv(cos(args,contextptr),contextptr);
}
static const char _sec_s []="sec";
static define_unary_function_eval (__sec,&_sec,_sec_s);
define_unary_function_ptr5( at_sec ,alias_at_sec,&__sec,0,true);
gen _csc(const gen & args,GIAC_CONTEXT){
if ( args.type==_STRNG && args.subtype==-1) return args;
return inv(sin(args,contextptr),contextptr);
}
static const char _csc_s []="csc";
static define_unary_function_eval (__csc,&_csc,_csc_s);
define_unary_function_ptr5( at_csc ,alias_at_csc,&__csc,0,true);
gen _cot(const gen & args,GIAC_CONTEXT){
if ( args.type==_STRNG && args.subtype==-1) return args;
return rdiv(cos(args,contextptr),sin(args,contextptr),contextptr);
}
static const char _cot_s []="cot";
static define_unary_function_eval (__cot,&_cot,_cot_s);
define_unary_function_ptr5( at_cot ,alias_at_cot,&__cot,0,true);
gen _asec(const gen & args,GIAC_CONTEXT){
if ( args.type==_STRNG && args.subtype==-1) return args;
return acos(inv(args,contextptr),contextptr);
}
static const char _asec_s []="asec";
static define_unary_function_eval (__asec,&_asec,_asec_s);
define_unary_function_ptr5( at_asec ,alias_at_asec,&__asec,0,true);
static const char _arcsec_s []="arcsec";
static define_unary_function_eval (__arcsec,&_asec,_arcsec_s);
define_unary_function_ptr5( at_arcsec ,alias_at_arcsec,&__arcsec,0,true);
gen _acsc(const gen & args,GIAC_CONTEXT){
if ( args.type==_STRNG && args.subtype==-1) return args;
return asin(inv(args,contextptr),contextptr);
}
static const char _acsc_s []="acsc";
static define_unary_function_eval (__acsc,&_acsc,_acsc_s);
define_unary_function_ptr5( at_acsc ,alias_at_acsc,&__acsc,0,true);
static const char _arccsc_s []="arccsc";
static define_unary_function_eval (__arccsc,&_acsc,_arccsc_s);
define_unary_function_ptr5( at_arccsc ,alias_at_arccsc,&__arccsc,0,true);
gen _acot(const gen & args,GIAC_CONTEXT){
if ( args.type==_STRNG && args.subtype==-1) return args;
if (is_zero(args))
//grad
return angle_radian(contextptr)?cst_pi_over_2:(angle_degree(contextptr)?90:100);
#if 0
if (abs_calc_mode(contextptr)==38)
return cst_pi_over_2-atan(args,contextptr);
#endif
return atan(inv(args,contextptr),contextptr);
}
static const char _acot_s []="acot";
static define_unary_function_eval (__acot,&_acot,_acot_s);
define_unary_function_ptr5( at_acot ,alias_at_acot,&__acot,0,true);
static const char _arccot_s []="arccot";
static define_unary_function_eval (__arccot,&_acot,_arccot_s);
define_unary_function_ptr5( at_arccot ,alias_at_arccot,&__arccot,0,true);
// args=[u'*v,v] or [[F,u'*v],v] -> [F+u*v,-u*v']
// a third argument would be the integration var
// if v=0 returns F+integrate(u'*v,x)
gen _ibpu(const gen & args,GIAC_CONTEXT) {
if ( args.type==_STRNG && args.subtype==-1) return args;
if ( (args.type!=_VECT) || (args._VECTptr->size()<2) )
return symbolic(at_ibpu,args);
vecteur & w=*args._VECTptr;
gen X(vx_var),x(vx_var),a,b;
bool bound=false;
if (w.size()>=3)
x=X=w[2];
if (is_equal(x))
x=x._SYMBptr->feuille[0];
if (w.size()>=5)
X=symb_equal(x,symb_interval(w[3],w[4]));
if (is_equal(X) && X._SYMBptr->feuille[1].is_symb_of_sommet(at_interval)){
a=X._SYMBptr->feuille[1]._SYMBptr->feuille[0];
b=X._SYMBptr->feuille[1]._SYMBptr->feuille[1];
bound=true;
}
gen u,v(w[1]),uprimev,F;
if (w.front().type==_VECT){
vecteur & ww=*w.front()._VECTptr;
if (ww.size()!=2)
return gensizeerr(contextptr);
F=ww.front();
uprimev=ww.back();
}
else
uprimev=w.front();
if (is_zero(v) || is_one(v)){
gen tmp=integrate_gen(uprimev,x,contextptr);
if (is_undef(tmp)) return tmp;
if (bound)
tmp=preval(tmp,x,a,b,contextptr);
return tmp+F;
}
gen uprime(normal(rdiv(uprimev,v,contextptr),contextptr));
u=integrate_gen(uprime,x,contextptr);
if (is_undef(u)) return u;
if (bound)
F += preval(u*v,x,a,b,contextptr);
else
F += u*v;
return makevecteur(F,normal(-u*derive(v,x,contextptr),contextptr));
}
static const char _ibpu_s []="ibpu";
static define_unary_function_eval (__ibpu,&_ibpu,_ibpu_s);
define_unary_function_ptr5( at_ibpu ,alias_at_ibpu,&__ibpu,0,true);
gen _changebase(const gen & args,GIAC_CONTEXT){
if ( args.type==_STRNG && args.subtype==-1) return args;
if (args.type!=_VECT)
return symbolic(at_changebase,args);
vecteur & v=*args._VECTptr;
if (v.size()!=2)
return gentypeerr(contextptr);
gen a=v.front(),p=v.back();
if (!is_squarematrix(p))
return gensizeerr(contextptr);
return minv(*p._VECTptr,contextptr)*a*p;
}
static const char _changebase_s []="changebase";
static define_unary_function_eval (__changebase,&_changebase,_changebase_s);
define_unary_function_ptr5( at_changebase ,alias_at_changebase,&__changebase,0,true);
static gen epsilon2zero(const gen & g,GIAC_CONTEXT){
switch (g.type){
case _DOUBLE_:
if (fabs(g._DOUBLE_val)<epsilon(contextptr))
return zero;
else
return g;
case _CPLX:
return epsilon2zero(re(g,contextptr),contextptr)+cst_i*epsilon2zero(im(g,contextptr),contextptr);
case _SYMB:
return symbolic(g._SYMBptr->sommet,epsilon2zero(g._SYMBptr->feuille,contextptr));
case _VECT:
return apply(g,epsilon2zero,contextptr);
default:
return g;
}
}
gen _epsilon2zero(const gen & args,GIAC_CONTEXT){
if ( args.type==_STRNG && args.subtype==-1) return args;
if (args.type==_VECT && args.subtype==_SEQ__VECT && args._VECTptr->size()==2){
gen p=evalf_double(args._VECTptr->back(),1,contextptr);
if (p.type==_DOUBLE_ && p._DOUBLE_val>0){
double eps=epsilon(contextptr);
epsilon(p._DOUBLE_val,contextptr);
gen res=epsilon2zero(args._VECTptr->front(),contextptr);
epsilon(eps,contextptr);
return res;
}
}
return epsilon2zero(args,contextptr);
}
static const char _epsilon2zero_s []="epsilon2zero";
static define_unary_function_eval (__epsilon2zero,&_epsilon2zero,_epsilon2zero_s);
define_unary_function_ptr5( at_epsilon2zero ,alias_at_epsilon2zero,&__epsilon2zero,0,true);
gen _suppress(const gen & args,GIAC_CONTEXT){
if ( args.type==_STRNG && args.subtype==-1) return args;
if (args.type!=_VECT)
return symbolic(at_suppress,args);
vecteur & v=*args._VECTptr;
if (v.size()==3 && v[1].type==_INT_ && v[2].type==_INT_){
int i1=v[1].val-array_start(contextptr); //(xcas_mode(contextptr)!=0 || abs_calc_mode(contextptr)==38);
int i2=v[2].val-array_start(contextptr); //(xcas_mode(contextptr)!=0 || abs_calc_mode(contextptr)==38);
if (i1 >i2 || i1<0 || i2 < 0)
return gendimerr(contextptr);
if (v[0].type==_VECT){
vecteur w=*v[0]._VECTptr;
if (i1>=int(w.size()) || i2>=int(w.size()))
return gendimerr(contextptr);
return gen(mergevecteur(vecteur(w.begin(),w.begin()+i1),vecteur(w.begin()+i2+1,w.end())),v[0].subtype);
}
if (v[0].type==_STRNG){
string s=*v[0]._STRNGptr;
if (i1>=int(s.size()) || i2>=int(s.size()))
return gendimerr(contextptr);
return string2gen(s.substr(0,i1)+s.substr(i2+1,s.size()-i2-1),false);
}
return gensizeerr(contextptr);
}
if (v.size()!=2)
return gentypeerr(contextptr);
gen l=v.front(),i=v.back();
if (i.is_symb_of_sommet(at_deuxpoints))
return _suppress(makesequence(l,i[1],i[2]-1),contextptr);
if (i.is_symb_of_sommet(at_interval))
return _suppress(makesequence(l,i[1],i[2]),contextptr);
int ii=0;
if (i.type==_VECT){
i=sortad(*i._VECTptr,false,contextptr);
if (i.type==_VECT){
const_iterateur it=i._VECTptr->begin(),itend=i._VECTptr->end();
for (;it!=itend;++it){
l=_suppress(makesequence(l,*it),contextptr);
}
return l;
}
}
if (i.type==_INT_ )
ii=i.val-array_start(contextptr); //(xcas_mode(contextptr)!=0 || abs_calc_mode(contextptr)==38);
if (l.type==_STRNG){
string res;
string & s=*l._STRNGptr;
int n=int(s.size());
if (i.type==_INT_ && ii>=0 && ii<n)
res=s.substr(0,ii)+s.substr(ii+1,n-ii-1);
if (i.type==_STRNG){
string & remove=*i._STRNGptr;
int removen=int(remove.size());
for (int j=0;j<n;++j){
int k=int(remove.find(s[j]));
if (k<0 || k>=removen)
res += s[j];
}
}
return string2gen(res,false);
}
if ( (l.type!=_VECT) || (i.type!=_INT_) )
return gensizeerr(contextptr);
const_iterateur it=l._VECTptr->begin(),itend=l._VECTptr->end();
vecteur res;
res.reserve(itend-it);
for (int j=0;it!=itend;++it,++j){
if (j!=ii)
res.push_back(*it);
}
return gen(res,l.subtype);
}
static const char _suppress_s []="suppress";
static define_unary_function_eval (__suppress,&_suppress,_suppress_s);
define_unary_function_ptr5( at_suppress ,alias_at_suppress,&__suppress,0,true);
void adjust_pixels_dim(const vecteur & V,int & I,int &J){
const_iterateur it=V.begin(),itend=V.end();
for (;it!=itend;++it){
gen g=remove_at_pnt(*it);
if (g.is_symb_of_sommet(at_pixon) && g._SYMBptr->feuille.type==_VECT){
vecteur &v=*g._SYMBptr->feuille._VECTptr;
if (v[0].type!=_INT_ || v[1].type!=_INT_)
continue;
int psx=0,psy=0;
if (v.size()>3 && v[3].type==_INT_){
if (v[3].val>0) psy=v[3].val; else psx=-v[3].val;
}
if (I<v[0].val+psx)
I=v[0].val+psx;
if (J<v[1].val+psy)
J=v[1].val+psy;
}
}
++I; ++J;
}
void cleanup_pixels(vecteur & V){
V=merge_pixon(V);
// find dimensions
int I=screen_w,J=screen_h;
adjust_pixels_dim(V,I,J);
vector<bool> used(I*J);
for (int i=screen_w;i<I;++i){
for (int j=screen_h;j<J;++j)
used[i*J+j]=true;
}
vecteur W;
iterateur it=V.end(),itend=V.begin();
for (--it;it>=itend;--it){
W.push_back(*it);
gen g=remove_at_pnt(*it);
if (g.is_symb_of_sommet(at_pixon) && g._SYMBptr->feuille.type==_VECT){
vecteur &v=*g._SYMBptr->feuille._VECTptr;
if (v[0].type!=_INT_ || v[1].type!=_INT_)
continue;
int psx=0,psy=0;
if (v.size()>3 && v[3].type==_INT_){
if (v[3].val>0) psy=v[3].val; else psx=-v[3].val;
}
// look if pixels are already in use
int di=v[0].val,dj=v[1].val,i,j;
for (i=giacmax(di,0);i<=di+psx;++i){
for (j=giacmax(dj,0);j<=dj+psy;++j){
bool b=used[i*J+j];
if (!b)
break;
}
if (j<=dj+psy)
break;
}
if (i>di+psx) // all pixels were already used, clean up this pixel
W.pop_back();
else {
// mark pixels
for (i=giacmax(di,0);i<=di+psx;++i){
for (j=giacmax(dj,0);j<=dj+psy;++j){
used[i*J+j]=true;
}
}
}
}
}
reverse(W.begin(),W.end());
V.swap(W);
}
#if defined GIAC_HAS_STO_38 || defined FXCG || defined NSPIRE
const int pixel_lines=1; // 320; // calculator screen 307K
const int pixel_cols=1; // 240;
#else
#ifdef KHICAS
const int pixel_lines=320;
const int pixel_cols=240;
#else
const int pixel_lines=1024;
const int pixel_cols=768;
#endif
#endif
#ifdef KHICAS
void clear_pixel_buffer(){
}
vecteur get_pixel_v(){
return vecteur(0);
}
#else
int pixel_buffer[pixel_lines][pixel_cols];
void clear_pixel_buffer(){
for (int i=0;i<pixel_lines;++i){
int * ptr=pixel_buffer[i];
int * ptrend = ptr+pixel_cols;
for (;ptr<ptrend;++ptr){
*ptr=int(FL_WHITE);
}
}
}
static gen & pixel_v(){
static gen * ptr=0;
if (ptr==0){
clear_pixel_buffer();
ptr=new gen(makevecteur(0));
}
return *ptr;
}
vecteur get_pixel_v(){
return *pixel_v()._VECTptr;
}
void pixel_v_clear(){
pixel_v()._VECTptr->clear();
}
void cleanup_pixel_v(){
cleanup_pixels(*pixel_v()._VECTptr);
}
void pixel_v_push_back(const gen & b){
pixel_v()._VECTptr->push_back(b);
}
#endif
gen _clear(const gen & args,GIAC_CONTEXT){
if ( args.type==_STRNG && args.subtype==-1) return args;
if (args.type==_VECT && args._VECTptr->empty()){
#ifdef KHICAS
os_fill_rect(0,0,pixel_lines,pixel_cols,_WHITE);
#else // KHICAS
#ifdef GIAC_HAS_STO_38
static gen RECT_P(identificateur("RECT_P"));
_of(makesequence(RECT_P,args),contextptr);
#else
clear_pixel_buffer();
#endif // else HP
pixel_v_clear();
history_plot(contextptr).clear();
#endif // else KHICAS
return 1;
}
gen g=eval(args,1,contextptr);
if (g.type==_STRNG)
g=string2gen("",false);
else {
if (g.type!=_VECT)
return gensizeerr(contextptr);
g=gen(vecteur(0),args.subtype);
}
if (args.type==_STRNG || args.type==_VECT)
return g;
return sto(g,args,contextptr);
}
static const char _clear_s []="clear";
static define_unary_function_eval_quoted (__clear,&_clear,_clear_s);
define_unary_function_ptr5( at_clear ,alias_at_clear,&__clear,_QUOTE_ARGUMENTS,true);
#ifdef KHICAS
gen _show_pixels(const gen & args,GIAC_CONTEXT){
return undef;
}
#else
gen _show_pixels(const gen & args,GIAC_CONTEXT){
#ifdef GIAC_HAS_STO_38
static gen FREEZE(identificateur("FREEZE"));
return _of(makesequence(FREEZE,args),contextptr);
#else
#if defined(EMCC) || defined(EMCC2)
return get_pixel_v();
#else
return makesequence(symb_equal(change_subtype(_AXES,_INT_PLOT),0),get_pixel_v());
#endif // EMCC
#endif // STO_38
}
#endif // KHICAS
static const char _show_pixels_s []="show_pixels";
static define_unary_function_eval (__show_pixels,&_show_pixels,_show_pixels_s);
define_unary_function_ptr5( at_show_pixels ,alias_at_show_pixels,&__show_pixels,0,true);
gen _show(const gen & args,GIAC_CONTEXT){
return history_plot(contextptr);
}
static const char _show_s []="show";
static define_unary_function_eval (__show,&_show,_show_s);
define_unary_function_ptr5( at_show ,alias_at_show,&__show,0,true);
gen _insert(const gen & args,GIAC_CONTEXT){
if ( args.type==_STRNG && args.subtype==-1) return args;
if (args.type!=_VECT)
return gensizeerr(contextptr);
vecteur & v=*args._VECTptr;
if (v.size()!=3)
return gensizeerr(contextptr);
gen i=v[1];
if (!is_integral(i) || i.type!=_INT_)
return gensizeerr(contextptr);
int ii=i.val-array_start(contextptr); //(xcas_mode(contextptr)!=0 || abs_calc_mode(contextptr)==38);
if (v[0].type==_VECT){
vecteur w=*v[0]._VECTptr;
if (ii<0 || ii>int(w.size()))
return gendimerr(contextptr);
w.insert(w.begin()+ii,v[2]);
return gen(w,v[0].subtype);
}
if (v[0].type==_STRNG){
string s=*v[0]._STRNGptr;
if (ii<0 || ii>int(s.size()))
return gendimerr(contextptr);
string add=(v[2].type==_STRNG)?*v[2]._STRNGptr:v[2].print(contextptr);
s=s.substr(0,ii)+add+s.substr(ii,s.size()-ii);
return string2gen(s,false);
}
return gensizeerr(contextptr);
}
static const char _insert_s []="insert";
static define_unary_function_eval (__insert,&_insert,_insert_s);
define_unary_function_ptr5( at_insert ,alias_at_insert,&__insert,0,true);
gen _pop(const gen & args,GIAC_CONTEXT){
if ( args.type==_STRNG && args.subtype==-1) return args;
if (args.type==_VECT && args.subtype==_SEQ__VECT && args._VECTptr->size()==2 ){
if (args._VECTptr->front().type==_MAP){
const gen & m=args._VECTptr->front();
const gen & indice=args._VECTptr->back();
gen_map::iterator it=m._MAPptr->find(indice),itend=m._MAPptr->end();
if (it==itend)
return gensizeerr(gettext("Bad index")+indice.print(contextptr));
m._MAPptr->erase(it);
return 1;
}
if (args._VECTptr->back().type==_INT_){
int pos=args._VECTptr->back().val;
gen g=args._VECTptr->front();
if (pos>=0 && g.type==_VECT && g._VECTptr->size()>pos){
gen res=(*g._VECTptr)[pos];
g._VECTptr->erase(g._VECTptr->begin()+pos);
return res;
}
}
}
if (args.type!=_VECT || args._VECTptr->empty())
return gensizeerr(contextptr);
gen res=args._VECTptr->back();
args._VECTptr->pop_back();
return res;
}
static const char _pop_s []="pop";
static define_unary_function_eval (__pop,&_pop,_pop_s);
define_unary_function_ptr5( at_pop ,alias_at_pop,&__pop,0,true);
static int valuation(const polynome & p){
if (p.coord.empty())
return -1;
return p.coord.back().index.front();
}
gen _valuation(const gen & args,GIAC_CONTEXT){
if ( args.type==_STRNG && args.subtype==-1) return args;
gen p,x;
if (args.type!=_VECT){
x=vx_var;
p=args;
}
else {
vecteur & v=*args._VECTptr;
int s=int(v.size());
if (!s)
return minus_inf;
if (s==2 && is_integer(v[0]) && is_integer(v[1])){
if (is_zero(v[0]))
return plus_inf;
mpz_t a,b,q,r;
mpz_init(q); mpz_init(r);
if (v[0].type==_INT_)
mpz_init_set_si(a,v[0].val);
else
mpz_init_set(a,*v[0]._ZINTptr);
if (v[1].type==_INT_)
mpz_init_set_si(b,v[1].val);
else
mpz_init_set(b,*v[1]._ZINTptr);
int res=0;
for (;;++res){
mpz_fdiv_qr(q,r,a,b);
if (mpz_cmp_si(r,0)!=0){
mpz_clear(r); mpz_clear(q); mpz_clear(a); mpz_clear(b);
return res;
}
mpz_set(a,q);
}
}
if ( (args.subtype==_POLY1__VECT) || (s!=2) || (v[1].type!=_IDNT) ){
int j=s;
for (;j;--j){
if (!is_zero(v[j-1]))
break;
}
return s-j;
}
x=v.back();
p=v.front();
}
vecteur lv(1,x);
lvar(p,lv);
gen aa=e2r(p,lv,contextptr),aan,aad;
if (is_zero(aa))
return minus_inf;
fxnd(aa,aan,aad);
if ( (aad.type==_POLY) && (aad._POLYptr->lexsorted_degree() ) )
return gensizeerr(contextptr);
if (aan.type!=_POLY)
return zero;
int res=valuation(*aan._POLYptr);
if (res==-1)
return minus_inf;
else
return res;
}
static const char _valuation_s []="valuation";
static define_unary_function_eval (__valuation,&_valuation,_valuation_s);
define_unary_function_ptr5( at_valuation ,alias_at_valuation,&__valuation,0,true);
static const char _ldegree_s []="ldegree";
static define_unary_function_eval (__ldegree,&_valuation,_ldegree_s);
define_unary_function_ptr5( at_ldegree ,alias_at_ldegree,&__ldegree,0,true);
int sum_degree(const index_m & v1,int vars){
int i=0;
for (index_t::const_iterator it=v1.begin();it!=v1.end() && it!=v1.begin()+vars;++it)
i=i+(*it);
return(i);
}
int total_degree(const polynome & p,int vars) {
std::vector< monomial<gen> >::const_iterator it=p.coord.begin();
std::vector< monomial<gen> >::const_iterator it_end=p.coord.end();
int res=0;
for (;it!=it_end;++it){
int temp=sum_degree(it->index,vars);
if (res<temp)
res=temp;
}
return res;
}
gen _degree_(const gen & args,bool total,GIAC_CONTEXT){
if ( args.type==_STRNG && args.subtype==-1) return args;
gen p,x;
if (args.type!=_VECT){
p=args;
if (calc_mode(contextptr)==1)
x=ggb_var(p);
else
x=vx_var;
}
else {
vecteur & v=*args._VECTptr;
int s=int(v.size());
if ( (args.subtype==_POLY1__VECT) || (s!=2) || (v[1].type!=_IDNT && v[1].type!=_VECT) )
return s-1;
x=v.back();
p=v.front();
}
if (p.type==_POLY){
if (x.type==_INT_ && x.val>=0 && x.val<p._POLYptr->dim)
return p._POLYptr->degree(x.val);
else {
vecteur res(p._POLYptr->dim);
index_t idx(p._POLYptr->degree());
for (int i=0;i<p._POLYptr->dim;++i)
res[i]=idx[i];
return res;
}
}
vecteur lv(1,x);
if (x.type==_VECT)
lv=*x._VECTptr;
lvar(p,lv);
gen aa=e2r(p,lv,contextptr),aan,aad;
if (is_zero(aa))
return zero;
fxnd(aa,aan,aad);
if (x.type==_VECT){
if (total){
int deg=0;
if (aad.type==_POLY)
deg -= total_degree(*aad._POLYptr,int(x._VECTptr->size()));
if (aan.type==_POLY)
deg += total_degree(*aan._POLYptr,int(x._VECTptr->size()));
return deg;
}
int s=int(x._VECTptr->size());
vecteur res(s);
for (int i=0;i<s;++i){
int deg=0;
if (aad.type==_POLY)
deg -= aad._POLYptr->degree(i);;
if (aan.type!=_POLY)
res[i]=deg;
else
res[i]=deg+aan._POLYptr->degree(i);
}
return res;
}