* Implementation of GiNaC's initially known functions. */
/*
- * GiNaC Copyright (C) 1999-2015 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
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:
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)
{
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();
}
&& !(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)
&& !(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)
(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)
// 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
// 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);
}
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:
return binomial(x, y).hold();
}
-// At the moment the numeric evaluation of a binomail function always
+// At the moment the numeric evaluation of a binomial function always
// gives a real number, but if this would be implemented using the gamma
// function, also complex conjugation should be changed (or rather, deleted).
static ex binomial_conjugate(const ex & x, const ex & y)
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)
// 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)));
}
// 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"));
}
}
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;
}
// 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"));
}
} 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));
// 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();
git://www.ginac.de / ginac.git / blobdiff