Happy New Year!
[ginac.git] / ginac / inifcns.cpp
index a9e9b8e..e2a09b1 100644 (file)
@@ -3,7 +3,7 @@
  *  Implementation of GiNaC's initially known functions. */
 
 /*
- *  GiNaC Copyright (C) 1999-2016 Johannes Gutenberg University Mainz, Germany
+ *  GiNaC Copyright (C) 1999-2019 Johannes Gutenberg University Mainz, Germany
  *
  *  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
@@ -109,7 +109,6 @@ static bool func_arg_info(const ex & arg, unsigned inf)
                case info_flags::prime:
                case info_flags::crational_polynomial:
                case info_flags::rational_function:
-               case info_flags::algebraic:
                case info_flags::positive:
                case info_flags::negative:
                case info_flags::nonnegative:
@@ -310,7 +309,7 @@ static ex abs_expand(const ex & arg, unsigned options)
                        else
                                prodseq.push_back(abs(*i));
                }
-               return (new mul(prodseq))->setflag(status_flags::dynallocated | status_flags::expanded);
+               return dynallocate<mul>(prodseq).setflag(status_flags::expanded);
        }
 
        if (options & expand_options::expand_function_args)
@@ -354,9 +353,9 @@ static ex abs_power(const ex & arg, const ex & exp)
 {
        if ((is_a<numeric>(exp) && ex_to<numeric>(exp).is_even()) || exp.info(info_flags::even)) {
                if (arg.info(info_flags::real) || arg.is_equal(arg.conjugate()))
-                       return power(arg, exp);
+                       return pow(arg, exp);
                else
-                       return power(arg, exp/2)*power(arg.conjugate(), exp/2);
+                       return pow(arg, exp/2) * pow(arg.conjugate(), exp/2);
        } else
                return power(abs(arg), exp).hold();
 }
@@ -453,9 +452,8 @@ static ex step_series(const ex & arg,
            && !(options & series_options::suppress_branchcut))
                throw (std::domain_error("step_series(): on imaginary axis"));
        
-       epvector seq;
-       seq.push_back(expair(step(arg_pt), _ex0));
-       return pseries(rel,seq);
+       epvector seq { expair(step(arg_pt), _ex0) };
+       return pseries(rel, std::move(seq));
 }
 
 static ex step_conjugate(const ex& arg)
@@ -532,9 +530,8 @@ static ex csgn_series(const ex & arg,
            && !(options & series_options::suppress_branchcut))
                throw (std::domain_error("csgn_series(): on imaginary axis"));
        
-       epvector seq;
-       seq.push_back(expair(csgn(arg_pt), _ex0));
-       return pseries(rel,seq);
+       epvector seq { expair(csgn(arg_pt), _ex0) };
+       return pseries(rel, std::move(seq));
 }
 
 static ex csgn_conjugate(const ex& arg)
@@ -640,9 +637,8 @@ static ex eta_series(const ex & x, const ex & y,
            (y_pt.info(info_flags::numeric) && y_pt.info(info_flags::negative)) ||
            ((x_pt*y_pt).info(info_flags::numeric) && (x_pt*y_pt).info(info_flags::negative)))
                        throw (std::domain_error("eta_series(): on discontinuity"));
-       epvector seq;
-       seq.push_back(expair(eta(x_pt,y_pt), _ex0));
-       return pseries(rel,seq);
+       epvector seq { expair(eta(x_pt,y_pt), _ex0) };
+       return pseries(rel, std::move(seq));
 }
 
 static ex eta_conjugate(const ex & x, const ex & y)
@@ -745,9 +741,8 @@ static ex Li2_series(const ex &x, const relational &rel, int order, unsigned opt
                        // substitute the argument's series expansion
                        ser = ser.subs(s==x.series(rel, order), subs_options::no_pattern);
                        // maybe that was terminating, so add a proper order term
-                       epvector nseq;
-                       nseq.push_back(expair(Order(_ex1), order));
-                       ser += pseries(rel, nseq);
+                       epvector nseq { expair(Order(_ex1), order) };
+                       ser += pseries(rel, std::move(nseq));
                        // reexpanding it will collapse the series again
                        return ser.series(rel, order);
                        // NB: Of course, this still does not allow us to compute anything
@@ -770,9 +765,8 @@ static ex Li2_series(const ex &x, const relational &rel, int order, unsigned opt
                        // substitute the argument's series expansion
                        ser = ser.subs(s==x.series(rel, order), subs_options::no_pattern);
                        // maybe that was terminating, so add a proper order term
-                       epvector nseq;
-                       nseq.push_back(expair(Order(_ex1), order));
-                       ser += pseries(rel, nseq);
+                       epvector nseq { expair(Order(_ex1), order) };
+                       ser += pseries(rel, std::move(nseq));
                        // reexpanding it will collapse the series again
                        return ser.series(rel, order);
                }
@@ -794,7 +788,7 @@ static ex Li2_series(const ex &x, const relational &rel, int order, unsigned opt
                                seq.push_back(expair((replarg.op(i)/power(s-foo,i)).series(foo==point,1,options).op(0).subs(foo==s, subs_options::no_pattern),i));
                        // append an order term:
                        seq.push_back(expair(Order(_ex1), replarg.nops()-1));
-                       return pseries(rel, seq);
+                       return pseries(rel, std::move(seq));
                }
        }
        // all other cases should be safe, by now:
@@ -1004,11 +998,10 @@ static ex Order_eval(const ex & x)
 static ex Order_series(const ex & x, const relational & r, int order, unsigned options)
 {
        // Just wrap the function into a pseries object
-       epvector new_seq;
        GINAC_ASSERT(is_a<symbol>(r.lhs()));
        const symbol &s = ex_to<symbol>(r.lhs());
-       new_seq.push_back(expair(Order(_ex1), numeric(std::min(x.ldegree(s), order))));
-       return pseries(r, new_seq);
+       epvector new_seq { expair(Order(_ex1), numeric(std::min(x.ldegree(s), order))) };
+       return pseries(r, std::move(new_seq));
 }
 
 static ex Order_conjugate(const ex & x)
@@ -1045,13 +1038,31 @@ REGISTER_FUNCTION(Order, eval_func(Order_eval).
 // Solve linear system
 //////////
 
+static void insert_symbols(exset &es, const ex &e)
+{
+       if (is_a<symbol>(e)) {
+               es.insert(e);
+       } else {
+               for (const ex &sube : e) {
+                       insert_symbols(es, sube);
+               }
+       }
+}
+
+static exset symbolset(const ex &e)
+{
+       exset s;
+       insert_symbols(s, e);
+       return s;
+}
+
 ex lsolve(const ex &eqns, const ex &symbols, unsigned options)
 {
        // solve a system of linear equations
        if (eqns.info(info_flags::relation_equal)) {
                if (!symbols.info(info_flags::symbol))
                        throw(std::invalid_argument("lsolve(): 2nd argument must be a symbol"));
-               const ex sol = lsolve(lst(eqns),lst(symbols));
+               const ex sol = lsolve(lst{eqns}, lst{symbols});
                
                GINAC_ASSERT(sol.nops()==1);
                GINAC_ASSERT(is_exactly_a<relational>(sol.op(0)));
@@ -1060,20 +1071,20 @@ ex lsolve(const ex &eqns, const ex &symbols, unsigned options)
        }
        
        // syntax checks
-       if (!eqns.info(info_flags::list)) {
-               throw(std::invalid_argument("lsolve(): 1st argument must be a list or an equation"));
+       if (!(eqns.info(info_flags::list) || eqns.info(info_flags::exprseq))) {
+               throw(std::invalid_argument("lsolve(): 1st argument must be a list, a sequence, or an equation"));
        }
        for (size_t i=0; i<eqns.nops(); i++) {
                if (!eqns.op(i).info(info_flags::relation_equal)) {
                        throw(std::invalid_argument("lsolve(): 1st argument must be a list of equations"));
                }
        }
-       if (!symbols.info(info_flags::list)) {
-               throw(std::invalid_argument("lsolve(): 2nd argument must be a list or a symbol"));
+       if (!(symbols.info(info_flags::list) || symbols.info(info_flags::exprseq))) {
+               throw(std::invalid_argument("lsolve(): 2nd argument must be a list, a sequence, or a symbol"));
        }
        for (size_t i=0; i<symbols.nops(); i++) {
                if (!symbols.op(i).info(info_flags::symbol)) {
-                       throw(std::invalid_argument("lsolve(): 2nd argument must be a list of symbols"));
+                       throw(std::invalid_argument("lsolve(): 2nd argument must be a list or a sequence of symbols"));
                }
        }
        
@@ -1084,8 +1095,10 @@ ex lsolve(const ex &eqns, const ex &symbols, unsigned options)
        
        for (size_t r=0; r<eqns.nops(); r++) {
                const ex eq = eqns.op(r).op(0)-eqns.op(r).op(1); // lhs-rhs==0
+               const exset syms = symbolset(eq);
                ex linpart = eq;
                for (size_t c=0; c<symbols.nops(); c++) {
+                       if (syms.count(symbols.op(c)) == 0) continue;
                        const ex co = eq.coeff(ex_to<symbol>(symbols.op(c)),1);
                        linpart -= co*symbols.op(c);
                        sys(r,c) = co;
@@ -1095,11 +1108,13 @@ ex lsolve(const ex &eqns, const ex &symbols, unsigned options)
        }
        
        // test if system is linear and fill vars matrix
+       const exset sys_syms = symbolset(sys);
+       const exset rhs_syms = symbolset(rhs);
        for (size_t i=0; i<symbols.nops(); i++) {
                vars(i,0) = symbols.op(i);
-               if (sys.has(symbols.op(i)))
+               if (sys_syms.count(symbols.op(i)) != 0)
                        throw(std::logic_error("lsolve: system is not linear"));
-               if (rhs.has(symbols.op(i)))
+               if (rhs_syms.count(symbols.op(i)) != 0)
                        throw(std::logic_error("lsolve: system is not linear"));
        }
        
@@ -1109,12 +1124,12 @@ ex lsolve(const ex &eqns, const ex &symbols, unsigned options)
        } catch (const std::runtime_error & e) {
                // Probably singular matrix or otherwise overdetermined system:
                // It is consistent to return an empty list
-               return lst();
+               return lst{};
        }
        GINAC_ASSERT(solution.cols()==1);
        GINAC_ASSERT(solution.rows()==symbols.nops());
        
-       // return list of equations of the form lst(var1==sol1,var2==sol2,...)
+       // return list of equations of the form lst{var1==sol1,var2==sol2,...}
        lst sollist;
        for (size_t i=0; i<symbols.nops(); i++)
                sollist.append(symbols.op(i)==solution(i,0));
@@ -1224,7 +1239,7 @@ fsolve(const ex& f_in, const symbol& x, const numeric& x1, const numeric& x2)
                        // determined by the secant between the values xx[0] and xx[1].
                        // Don't set the secant_weight to one because that could disturb
                        // the convergence in some corner cases!
-                       static const double secant_weight = 0.984375;  // == 63/64 < 1
+                       constexpr double secant_weight = 0.984375;  // == 63/64 < 1
                        numeric xxmid = (1-secant_weight)*0.5*(xx[0]+xx[1])
                            + secant_weight*(xx[0]+fx[0]*(xx[0]-xx[1])/(fx[1]-fx[0]));
                        ex fxmid_ = f.subs(x == xxmid).evalf();