Avoid x^0 and Order(x^0) terms together in series expansion.

At the branch cut, the series expansions of log(), atan(), and atanh()
assembled pseries objects which contained both x^0 and Order(x^0) terms.
This patch removes the extra x^0 term if the order is 0. It also adds
a GINAC_ASSERT for these kinds of invariants to the pseries ctor and
simplifies the loops in pseries' degree(), ldegree(), eval() and evalf()
member functions.

diff --git a/ginac/inifcns_trans.cpp b/ginac/inifcns_trans.cpp
index 9982853961286be457af33ee445339aeb4651f65..98e0caff36aaae386448293c36c4371837513f2e 100644 (file)
--- a/ginac/inifcns_trans.cpp
+++ b/ginac/inifcns_trans.cpp
@@ -265,8 +265,12 @@ static ex log_series(const ex &arg,
                const ex &point = rel.rhs();
                const symbol foo;
                const ex replarg = series(log(arg), s==foo, order).subs(foo==point, subs_options::no_pattern);
-               epvector seq { expair(-I*csgn(arg*I)*Pi, _ex0),
-                              expair(Order(_ex1), order) };
+               epvector seq;
+               if (order > 0) {
+                       seq.reserve(2);
+                       seq.push_back(expair(-I*csgn(arg*I)*Pi, _ex0));
+               }
+               seq.push_back(expair(Order(_ex1), order));
                return series(replarg - I*Pi + pseries(rel, std::move(seq)), rel, order);
        }
        throw do_taylor();  // caught by function::series()
@@ -928,8 +932,12 @@ static ex atan_series(const ex &arg,
                        Order0correction += log((I*arg_pt+_ex_1)/(I*arg_pt+_ex1))*I*_ex_1_2;
                else
                        Order0correction += log((I*arg_pt+_ex1)/(I*arg_pt+_ex_1))*I*_ex1_2;
-               epvector seq { expair(Order0correction, _ex0),
-                              expair(Order(_ex1), order) };
+               epvector seq;
+               if (order > 0) {
+                       seq.reserve(2);
+                       seq.push_back(expair(Order0correction, _ex0));
+               }
+               seq.push_back(expair(Order(_ex1), order));
                return series(replarg - pseries(rel, std::move(seq)), rel, order);
        }
        throw do_taylor();
@@ -1534,8 +1542,12 @@ static ex atanh_series(const ex &arg,
                        Order0correction += log((arg_pt+_ex_1)/(arg_pt+_ex1))*_ex1_2;
                else
                        Order0correction += log((arg_pt+_ex1)/(arg_pt+_ex_1))*_ex_1_2;
-               epvector seq { expair(Order0correction, _ex0),
-                              expair(Order(_ex1), order) };
+               epvector seq;
+               if (order > 0) {
+                       seq.reserve(2);
+                       seq.push_back(expair(Order0correction, _ex0));
+               }
+               seq.push_back(expair(Order(_ex1), order));
                return series(replarg - pseries(rel, std::move(seq)), rel, order);
        }
        throw do_taylor();

diff --git a/ginac/pseries.cpp b/ginac/pseries.cpp
index 12f4fedebd8c36c49b0a51e55db595afe997fa20..2d0b7adc24ccbd95ef531ea1ce637466941fdaa5 100644 (file)
--- a/ginac/pseries.cpp
+++ b/ginac/pseries.cpp
@@ -71,6 +71,19 @@ pseries::pseries() { }
 pseries::pseries(const ex &rel_, const epvector &ops_)
   : seq(ops_)
 {
+#ifdef DO_GINAC_ASSERT
+       auto i = seq.begin();
+       while (i != seq.end()) {
+               auto ip1 = i+1;
+               if (ip1 != seq.end())
+                       GINAC_ASSERT(!is_order_function(i->rest));
+               else
+                       break;
+               GINAC_ASSERT(is_a<numeric>(i->coeff));
+               GINAC_ASSERT(ex_to<numeric>(i->coeff) < ex_to<numeric>(ip1->coeff));
+               ++i;
+       }
+#endif // def DO_GINAC_ASSERT
        GINAC_ASSERT(is_a<relational>(rel_));
        GINAC_ASSERT(is_a<symbol>(rel_.lhs()));
        point = rel_.rhs();
@@ -79,6 +92,19 @@ pseries::pseries(const ex &rel_, const epvector &ops_)
 pseries::pseries(const ex &rel_, epvector &&ops_)
   : seq(std::move(ops_))
 {
+#ifdef DO_GINAC_ASSERT
+       auto i = seq.begin();
+       while (i != seq.end()) {
+               auto ip1 = i+1;
+               if (ip1 != seq.end())
+                       GINAC_ASSERT(!is_order_function(i->rest));
+               else
+                       break;
+               GINAC_ASSERT(is_a<numeric>(i->coeff));
+               GINAC_ASSERT(ex_to<numeric>(i->coeff) < ex_to<numeric>(ip1->coeff));
+               ++i;
+       }
+#endif // def DO_GINAC_ASSERT
        GINAC_ASSERT(is_a<relational>(rel_));
        GINAC_ASSERT(is_a<symbol>(rel_.lhs()));
        point = rel_.rhs();
@@ -290,25 +316,17 @@ ex pseries::op(size_t i) const
  *  series is examined termwise. */
 int pseries::degree(const ex &s) const
 {
-       if (var.is_equal(s)) {
-               // Return last exponent
-               if (seq.size())
-                       return ex_to<numeric>((seq.end()-1)->coeff).to_int();
-               else
-                       return 0;
-       } else {
-               epvector::const_iterator it = seq.begin(), itend = seq.end();
-               if (it == itend)
-                       return 0;
-               int max_pow = std::numeric_limits<int>::min();
-               while (it != itend) {
-                       int pow = it->rest.degree(s);
-                       if (pow > max_pow)
-                               max_pow = pow;
-                       ++it;
-               }
-               return max_pow;
-       }
+       if (seq.empty())
+               return 0;
+
+       if (var.is_equal(s))
+               // Return last/greatest exponent
+               return ex_to<numeric>((seq.end()-1)->coeff).to_int();
+
+       int max_pow = std::numeric_limits<int>::min();
+       for (auto & it : seq)
+               max_pow = std::max(max_pow, it.rest.degree(s));
+       return max_pow;
 }
 
 /** Return degree of lowest power of the series.  This is usually the exponent
@@ -318,25 +336,17 @@ int pseries::degree(const ex &s) const
  *  I.e.: (1-x) + (1-x)^2 + Order((1-x)^3) has ldegree(x) 1, not 0. */
 int pseries::ldegree(const ex &s) const
 {
-       if (var.is_equal(s)) {
-               // Return first exponent
-               if (seq.size())
-                       return ex_to<numeric>((seq.begin())->coeff).to_int();
-               else
-                       return 0;
-       } else {
-               epvector::const_iterator it = seq.begin(), itend = seq.end();
-               if (it == itend)
-                       return 0;
-               int min_pow = std::numeric_limits<int>::max();
-               while (it != itend) {
-                       int pow = it->rest.ldegree(s);
-                       if (pow < min_pow)
-                               min_pow = pow;
-                       ++it;
-               }
-               return min_pow;
-       }
+       if (seq.empty())
+               return 0;
+
+       if (var.is_equal(s))
+               // Return first/smallest exponent
+               return ex_to<numeric>((seq.begin())->coeff).to_int();
+
+       int min_pow = std::numeric_limits<int>::max();
+       for (auto & it : seq)
+               min_pow = std::min(min_pow, it.rest.degree(s));
+       return min_pow;
 }
 
 /** Return coefficient of degree n in power series if s is the expansion
@@ -389,15 +399,13 @@ ex pseries::eval() const
        if (flags & status_flags::evaluated) {
                return *this;
        }
-       
+
        // Construct a new series with evaluated coefficients
        epvector new_seq;
        new_seq.reserve(seq.size());
-       epvector::const_iterator it = seq.begin(), itend = seq.end();
-       while (it != itend) {
-               new_seq.push_back(expair(it->rest, it->coeff));
-               ++it;
-       }
+       for (auto & it : seq)
+               new_seq.push_back(expair(it.rest, it.coeff));
+
        return dynallocate<pseries>(relational(var,point), std::move(new_seq)).setflag(status_flags::evaluated);
 }
 
@@ -413,11 +421,9 @@ ex pseries::evalf(int level) const
        // Construct a new series with evaluated coefficients
        epvector new_seq;
        new_seq.reserve(seq.size());
-       epvector::const_iterator it = seq.begin(), itend = seq.end();
-       while (it != itend) {
-               new_seq.push_back(expair(it->rest.evalf(level-1), it->coeff));
-               ++it;
-       }
+       for (auto & it : seq)
+               new_seq.push_back(expair(it.rest, it.coeff));
+
        return dynallocate<pseries>(relational(var,point), std::move(new_seq)).setflag(status_flags::evaluated);
 }