]> www.ginac.de Git - ginac.git/blobdiff - ginac/normal.cpp
[bugfix] fix elusive bug in quo, rem,...
[ginac.git] / ginac / normal.cpp
index bcb2a398bd8d57b8b8a983c2350963270e3ef3f5..a1e2de48c9f598fd09c915dd026e16211d2fde70 100644 (file)
@@ -6,7 +6,7 @@
  *  computation, square-free factorization and rational function normalization. */
 
 /*
- *  GiNaC Copyright (C) 1999-2015 Johannes Gutenberg University Mainz, Germany
+ *  GiNaC Copyright (C) 1999-2016 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
@@ -196,8 +196,8 @@ static void collect_symbols(const ex &e, sym_desc_vec &v)
  *  @param v  vector of sym_desc structs (filled in) */
 static void get_symbol_stats(const ex &a, const ex &b, sym_desc_vec &v)
 {
-       collect_symbols(a.eval(), v);   // eval() to expand assigned symbols
-       collect_symbols(b.eval(), v);
+       collect_symbols(a, v);
+       collect_symbols(b, v);
        for (auto & it : v) {
                int deg_a = a.degree(it.sym);
                int deg_b = b.degree(it.sym);
@@ -280,18 +280,23 @@ static ex multiply_lcm(const ex &e, const numeric &lcm)
                        lcm_accum *= op_lcm;
                }
                v.push_back(lcm / lcm_accum);
-               return (new mul(v))->setflag(status_flags::dynallocated);
+               return dynallocate<mul>(v);
        } else if (is_exactly_a<add>(e)) {
                size_t num = e.nops();
                exvector v; v.reserve(num);
                for (size_t i=0; i<num; i++)
                        v.push_back(multiply_lcm(e.op(i), lcm));
-               return (new add(v))->setflag(status_flags::dynallocated);
+               return dynallocate<add>(v);
        } else if (is_exactly_a<power>(e)) {
                if (is_a<symbol>(e.op(0)))
                        return e * lcm;
-               else
-                       return pow(multiply_lcm(e.op(0), lcm.power(ex_to<numeric>(e.op(1)).inverse())), e.op(1));
+               else {
+                       numeric root_of_lcm = lcm.power(ex_to<numeric>(e.op(1)).inverse());
+                       if (root_of_lcm.is_rational())
+                               return pow(multiply_lcm(e.op(0), root_of_lcm), e.op(1));
+                       else
+                               return e * lcm;
+               }
        } else
                return e * lcm;
 }
@@ -386,16 +391,16 @@ ex quo(const ex &a, const ex &b, const ex &x, bool check_args)
                        term = rcoeff / blcoeff;
                else {
                        if (!divide(rcoeff, blcoeff, term, false))
-                               return (new fail())->setflag(status_flags::dynallocated);
+                               return dynallocate<fail>();
                }
-               term *= power(x, rdeg - bdeg);
+               term *= pow(x, rdeg - bdeg);
                v.push_back(term);
                r -= (term * b).expand();
                if (r.is_zero())
                        break;
                rdeg = r.degree(x);
        }
-       return (new add(v))->setflag(status_flags::dynallocated);
+       return dynallocate<add>(v);
 }
 
 
@@ -439,9 +444,9 @@ ex rem(const ex &a, const ex &b, const ex &x, bool check_args)
                        term = rcoeff / blcoeff;
                else {
                        if (!divide(rcoeff, blcoeff, term, false))
-                               return (new fail())->setflag(status_flags::dynallocated);
+                               return dynallocate<fail>();
                }
-               term *= power(x, rdeg - bdeg);
+               term *= pow(x, rdeg - bdeg);
                r -= (term * b).expand();
                if (r.is_zero())
                        break;
@@ -501,23 +506,23 @@ ex prem(const ex &a, const ex &b, const ex &x, bool check_args)
                if (bdeg == 0)
                        eb = _ex0;
                else
-                       eb -= blcoeff * power(x, bdeg);
+                       eb -= blcoeff * pow(x, bdeg);
        } else
                blcoeff = _ex1;
 
        int delta = rdeg - bdeg + 1, i = 0;
        while (rdeg >= bdeg && !r.is_zero()) {
                ex rlcoeff = r.coeff(x, rdeg);
-               ex term = (power(x, rdeg - bdeg) * eb * rlcoeff).expand();
+               ex term = (pow(x, rdeg - bdeg) * eb * rlcoeff).expand();
                if (rdeg == 0)
                        r = _ex0;
                else
-                       r -= rlcoeff * power(x, rdeg);
+                       r -= rlcoeff * pow(x, rdeg);
                r = (blcoeff * r).expand() - term;
                rdeg = r.degree(x);
                i++;
        }
-       return power(blcoeff, delta - i) * r;
+       return pow(blcoeff, delta - i) * r;
 }
 
 
@@ -553,17 +558,17 @@ ex sprem(const ex &a, const ex &b, const ex &x, bool check_args)
                if (bdeg == 0)
                        eb = _ex0;
                else
-                       eb -= blcoeff * power(x, bdeg);
+                       eb -= blcoeff * pow(x, bdeg);
        } else
                blcoeff = _ex1;
 
        while (rdeg >= bdeg && !r.is_zero()) {
                ex rlcoeff = r.coeff(x, rdeg);
-               ex term = (power(x, rdeg - bdeg) * eb * rlcoeff).expand();
+               ex term = (pow(x, rdeg - bdeg) * eb * rlcoeff).expand();
                if (rdeg == 0)
                        r = _ex0;
                else
-                       r -= rlcoeff * power(x, rdeg);
+                       r -= rlcoeff * pow(x, rdeg);
                r = (blcoeff * r).expand() - term;
                rdeg = r.degree(x);
        }
@@ -653,7 +658,7 @@ bool divide(const ex &a, const ex &b, ex &q, bool check_args)
                                else
                                        resv.push_back(a.op(j));
                        }
-                       q = (new mul(resv))->setflag(status_flags::dynallocated);
+                       q = dynallocate<mul>(resv);
                        return true;
                }
        } else if (is_exactly_a<power>(a)) {
@@ -663,7 +668,7 @@ bool divide(const ex &a, const ex &b, ex &q, bool check_args)
                int a_exp = ex_to<numeric>(a.op(1)).to_int();
                ex rem_i;
                if (divide(ab, b, rem_i, false)) {
-                       q = rem_i*power(ab, a_exp - 1);
+                       q = rem_i * pow(ab, a_exp - 1);
                        return true;
                }
 // code below is commented-out because it leads to a significant slowdown
@@ -693,11 +698,11 @@ bool divide(const ex &a, const ex &b, ex &q, bool check_args)
                else
                        if (!divide(rcoeff, blcoeff, term, false))
                                return false;
-               term *= power(x, rdeg - bdeg);
+               term *= pow(x, rdeg - bdeg);
                v.push_back(term);
                r -= (term * b).expand();
                if (r.is_zero()) {
-                       q = (new add(v))->setflag(status_flags::dynallocated);
+                       q = dynallocate<add>(v);
                        return true;
                }
                rdeg = r.degree(x);
@@ -876,11 +881,11 @@ static bool divide_in_z(const ex &a, const ex &b, ex &q, sym_desc_vec::const_ite
                ex term, rcoeff = r.coeff(x, rdeg);
                if (!divide_in_z(rcoeff, blcoeff, term, var+1))
                        break;
-               term = (term * power(x, rdeg - bdeg)).expand();
+               term = (term * pow(x, rdeg - bdeg)).expand();
                v.push_back(term);
                r -= (term * eb).expand();
                if (r.is_zero()) {
-                       q = (new add(v))->setflag(status_flags::dynallocated);
+                       q = dynallocate<add>(v);
 #if USE_REMEMBER
                        dr_remember[ex2(a, b)] = exbool(q, true);
 #endif
@@ -1210,7 +1215,7 @@ ex add::smod(const numeric &xi) const
        }
        GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
        numeric coeff = GiNaC::smod(ex_to<numeric>(overall_coeff), xi);
-       return (new add(std::move(newseq), coeff))->setflag(status_flags::dynallocated);
+       return dynallocate<add>(std::move(newseq), coeff);
 }
 
 ex mul::smod(const numeric &xi) const
@@ -1220,12 +1225,12 @@ ex mul::smod(const numeric &xi) const
                GINAC_ASSERT(!is_exactly_a<numeric>(recombine_pair_to_ex(it)));
        }
 #endif // def DO_GINAC_ASSERT
-       mul * mulcopyp = new mul(*this);
+       mul & mulcopy = dynallocate<mul>(*this);
        GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
-       mulcopyp->overall_coeff = GiNaC::smod(ex_to<numeric>(overall_coeff),xi);
-       mulcopyp->clearflag(status_flags::evaluated);
-       mulcopyp->clearflag(status_flags::hash_calculated);
-       return mulcopyp->setflag(status_flags::dynallocated);
+       mulcopy.overall_coeff = GiNaC::smod(ex_to<numeric>(overall_coeff),xi);
+       mulcopy.clearflag(status_flags::evaluated);
+       mulcopy.clearflag(status_flags::hash_calculated);
+       return mulcopy;
 }
 
 
@@ -1237,10 +1242,10 @@ static ex interpolate(const ex &gamma, const numeric &xi, const ex &x, int degre
        numeric rxi = xi.inverse();
        for (int i=0; !e.is_zero(); i++) {
                ex gi = e.smod(xi);
-               g.push_back(gi * power(x, i));
+               g.push_back(gi * pow(x, i));
                e = (e - gi) * rxi;
        }
-       return (new add(g))->setflag(status_flags::dynallocated);
+       return dynallocate<add>(g);
 }
 
 /** Exception thrown by heur_gcd() to signal failure. */
@@ -1563,7 +1568,7 @@ ex gcd(const ex &a, const ex &b, ex *ca, ex *cb, bool check_args, unsigned optio
        int ldeg_b = var->ldeg_b;
        int min_ldeg = std::min(ldeg_a,ldeg_b);
        if (min_ldeg > 0) {
-               ex common = power(x, min_ldeg);
+               ex common = pow(x, min_ldeg);
                return gcd((aex / common).expand(), (bex / common).expand(), ca, cb, false) * common;
        }
 
@@ -1644,14 +1649,14 @@ static ex gcd_pf_pow_pow(const ex& a, const ex& b, ex* ca, ex* cb)
                        if (ca)
                                *ca = _ex1;
                        if (cb)
-                               *cb = power(p, exp_b - exp_a);
-                       return power(p, exp_a);
+                               *cb = pow(p, exp_b - exp_a);
+                       return pow(p, exp_a);
                } else {
                        if (ca)
-                               *ca = power(p, exp_a - exp_b);
+                               *ca = pow(p, exp_a - exp_b);
                        if (cb)
                                *cb = _ex1;
-                       return power(p, exp_b);
+                       return pow(p, exp_b);
                }
        }
 
@@ -1671,11 +1676,11 @@ static ex gcd_pf_pow_pow(const ex& a, const ex& b, ex* ca, ex* cb)
        // a(x) = g(x)^n A(x)^n, b(x) = g(x)^m B(x)^m ==>
        // gcd(a, b) = g(x)^n gcd(A(x)^n, g(x)^(n-m) B(x)^m
        if (exp_a < exp_b) {
-               ex pg =  gcd(power(p_co, exp_a), power(p_gcd, exp_b-exp_a)*power(pb_co, exp_b), ca, cb, false);
-               return power(p_gcd, exp_a)*pg;
+               ex pg =  gcd(pow(p_co, exp_a), pow(p_gcd, exp_b-exp_a)*pow(pb_co, exp_b), ca, cb, false);
+               return pow(p_gcd, exp_a)*pg;
        } else {
-               ex pg = gcd(power(p_gcd, exp_a - exp_b)*power(p_co, exp_a), power(pb_co, exp_b), ca, cb, false);
-               return power(p_gcd, exp_b)*pg;
+               ex pg = gcd(pow(p_gcd, exp_a - exp_b)*pow(p_co, exp_a), pow(pb_co, exp_b), ca, cb, false);
+               return pow(p_gcd, exp_b)*pg;
        }
 }
 
@@ -1694,7 +1699,7 @@ static ex gcd_pf_pow(const ex& a, const ex& b, ex* ca, ex* cb)
        if (p.is_equal(b)) {
                // a = p^n, b = p, gcd = p
                if (ca)
-                       *ca = power(p, a.op(1) - 1);
+                       *ca = pow(p, a.op(1) - 1);
                if (cb)
                        *cb = _ex1;
                return p;
@@ -1712,7 +1717,7 @@ static ex gcd_pf_pow(const ex& a, const ex& b, ex* ca, ex* cb)
                return _ex1;
        }
        // a(x) = g(x)^n A(x)^n, b(x) = g(x) B(x) ==> gcd(a, b) = g(x) gcd(g(x)^(n-1) A(x)^n, B(x))
-       ex rg = gcd(power(p_gcd, exp_a-1)*power(p_co, exp_a), bpart_co, ca, cb, false);
+       ex rg = gcd(pow(p_gcd, exp_a-1)*pow(p_co, exp_a), bpart_co, ca, cb, false);
        return p_gcd*rg;
 }
 
@@ -1737,10 +1742,10 @@ static ex gcd_pf_mul(const ex& a, const ex& b, ex* ca, ex* cb)
                part_b = part_cb;
        }
        if (ca)
-               *ca = (new mul(acc_ca))->setflag(status_flags::dynallocated);
+               *ca = dynallocate<mul>(acc_ca);
        if (cb)
                *cb = part_b;
-       return (new mul(g))->setflag(status_flags::dynallocated);
+       return dynallocate<mul>(g);
 }
 
 /** Compute LCM (Least Common Multiple) of multivariate polynomials in Z[X].
@@ -1771,7 +1776,7 @@ ex lcm(const ex &a, const ex &b, bool check_args)
  *  Yun's algorithm.  Used internally by sqrfree().
  *
  *  @param a  multivariate polynomial over Z[X], treated here as univariate
- *            polynomial in x.
+ *            polynomial in x (needs not be expanded).
  *  @param x  variable to factor in
  *  @return   vector of factors sorted in ascending degree */
 static exvector sqrfree_yun(const ex &a, const symbol &x)
@@ -1780,6 +1785,9 @@ static exvector sqrfree_yun(const ex &a, const symbol &x)
        ex w = a;
        ex z = w.diff(x);
        ex g = gcd(w, z);
+       if (g.is_zero()) {
+               return res;
+       }
        if (g.is_equal(_ex1)) {
                res.push_back(a);
                return res;
@@ -1787,6 +1795,9 @@ static exvector sqrfree_yun(const ex &a, const symbol &x)
        ex y;
        do {
                w = quo(w, g, x);
+               if (w.is_zero()) {
+                       return res;
+               }
                y = quo(z, g, x);
                z = y - w.diff(x);
                g = gcd(w, z);
@@ -1798,7 +1809,7 @@ static exvector sqrfree_yun(const ex &a, const symbol &x)
 
 /** Compute a square-free factorization of a multivariate polynomial in Q[X].
  *
- *  @param a  multivariate polynomial over Q[X]
+ *  @param a  multivariate polynomial over Q[X] (needs not be expanded)
  *  @param l  lst of variables to factor in, may be left empty for autodetection
  *  @return   a square-free factorization of \p a.
  *
@@ -1833,8 +1844,8 @@ static exvector sqrfree_yun(const ex &a, const symbol &x)
  */
 ex sqrfree(const ex &a, const lst &l)
 {
-       if (is_exactly_a<numeric>(a) ||     // algorithm does not trap a==0
-           is_a<symbol>(a))        // shortcut
+       if (is_exactly_a<numeric>(a) ||
+           is_a<symbol>(a))        // shortcuts
                return a;
 
        // If no lst of variables to factorize in was specified we have to
@@ -1876,7 +1887,7 @@ ex sqrfree(const ex &a, const lst &l)
        ex result = _ex1;
        int p = 1;
        for (auto & it : factors)
-               result *= power(it, p++);
+               result *= pow(it, p++);
 
        // Yun's algorithm does not account for constant factors.  (For univariate
        // polynomials it works only in the monic case.)  We can correct this by
@@ -1992,7 +2003,7 @@ static ex replace_with_symbol(const ex & e, exmap & repl, exmap & rev_lookup)
        // Otherwise create new symbol and add to list, taking care that the
        // replacement expression doesn't itself contain symbols from repl,
        // because subs() is not recursive
-       ex es = (new symbol)->setflag(status_flags::dynallocated);
+       ex es = dynallocate<symbol>();
        repl.insert(std::make_pair(es, e_replaced));
        rev_lookup.insert(std::make_pair(e_replaced, es));
        return es;
@@ -2016,7 +2027,7 @@ static ex replace_with_symbol(const ex & e, exmap & repl)
        // Otherwise create new symbol and add to list, taking care that the
        // replacement expression doesn't itself contain symbols from repl,
        // because subs() is not recursive
-       ex es = (new symbol)->setflag(status_flags::dynallocated);
+       ex es = dynallocate<symbol>();
        repl.insert(std::make_pair(es, e_replaced));
        return es;
 }
@@ -2024,36 +2035,27 @@ static ex replace_with_symbol(const ex & e, exmap & repl)
 
 /** Function object to be applied by basic::normal(). */
 struct normal_map_function : public map_function {
-       int level;
-       normal_map_function(int l) : level(l) {}
-       ex operator()(const ex & e) override { return normal(e, level); }
+       ex operator()(const ex & e) override { return normal(e); }
 };
 
 /** Default implementation of ex::normal(). It normalizes the children and
  *  replaces the object with a temporary symbol.
  *  @see ex::normal */
-ex basic::normal(exmap & repl, exmap & rev_lookup, int level) const
+ex basic::normal(exmap & repl, exmap & rev_lookup) const
 {
        if (nops() == 0)
-               return (new lst(replace_with_symbol(*this, repl, rev_lookup), _ex1))->setflag(status_flags::dynallocated);
-       else {
-               if (level == 1)
-                       return (new lst(replace_with_symbol(*this, repl, rev_lookup), _ex1))->setflag(status_flags::dynallocated);
-               else if (level == -max_recursion_level)
-                       throw(std::runtime_error("max recursion level reached"));
-               else {
-                       normal_map_function map_normal(level - 1);
-                       return (new lst(replace_with_symbol(map(map_normal), repl, rev_lookup), _ex1))->setflag(status_flags::dynallocated);
-               }
-       }
+               return dynallocate<lst>({replace_with_symbol(*this, repl, rev_lookup), _ex1});
+
+       normal_map_function map_normal;
+       return dynallocate<lst>({replace_with_symbol(map(map_normal), repl, rev_lookup), _ex1});
 }
 
 
 /** Implementation of ex::normal() for symbols. This returns the unmodified symbol.
  *  @see ex::normal */
-ex symbol::normal(exmap & repl, exmap & rev_lookup, int level) const
+ex symbol::normal(exmap & repl, exmap & rev_lookup) const
 {
-       return (new lst(*this, _ex1))->setflag(status_flags::dynallocated);
+       return dynallocate<lst>({*this, _ex1});
 }
 
 
@@ -2061,7 +2063,7 @@ ex symbol::normal(exmap & repl, exmap & rev_lookup, int level) const
  *  into re+I*im and replaces I and non-rational real numbers with a temporary
  *  symbol.
  *  @see ex::normal */
-ex numeric::normal(exmap & repl, exmap & rev_lookup, int level) const
+ex numeric::normal(exmap & repl, exmap & rev_lookup) const
 {
        numeric num = numer();
        ex numex = num;
@@ -2077,7 +2079,7 @@ ex numeric::normal(exmap & repl, exmap & rev_lookup, int level) const
        }
 
        // Denominator is always a real integer (see numeric::denom())
-       return (new lst(numex, denom()))->setflag(status_flags::dynallocated);
+       return dynallocate<lst>({numex, denom()});
 }
 
 
@@ -2095,11 +2097,11 @@ static ex frac_cancel(const ex &n, const ex &d)
 
        // Handle trivial case where denominator is 1
        if (den.is_equal(_ex1))
-               return (new lst(num, den))->setflag(status_flags::dynallocated);
+               return dynallocate<lst>({num, den});
 
        // Handle special cases where numerator or denominator is 0
        if (num.is_zero())
-               return (new lst(num, _ex1))->setflag(status_flags::dynallocated);
+               return dynallocate<lst>({num, _ex1});
        if (den.expand().is_zero())
                throw(std::overflow_error("frac_cancel: division by zero in frac_cancel"));
 
@@ -2138,30 +2140,25 @@ static ex frac_cancel(const ex &n, const ex &d)
 
        // Return result as list
 //std::clog << " returns num = " << num << ", den = " << den << ", pre_factor = " << pre_factor << std::endl;
-       return (new lst(num * pre_factor.numer(), den * pre_factor.denom()))->setflag(status_flags::dynallocated);
+       return dynallocate<lst>({num * pre_factor.numer(), den * pre_factor.denom()});
 }
 
 
 /** Implementation of ex::normal() for a sum. It expands terms and performs
  *  fractional addition.
  *  @see ex::normal */
-ex add::normal(exmap & repl, exmap & rev_lookup, int level) const
+ex add::normal(exmap & repl, exmap & rev_lookup) const
 {
-       if (level == 1)
-               return (new lst(replace_with_symbol(*this, repl, rev_lookup), _ex1))->setflag(status_flags::dynallocated);
-       else if (level == -max_recursion_level)
-               throw(std::runtime_error("max recursion level reached"));
-
        // Normalize children and split each one into numerator and denominator
        exvector nums, dens;
        nums.reserve(seq.size()+1);
        dens.reserve(seq.size()+1);
        for (auto & it : seq) {
-               ex n = ex_to<basic>(recombine_pair_to_ex(it)).normal(repl, rev_lookup, level-1);
+               ex n = ex_to<basic>(recombine_pair_to_ex(it)).normal(repl, rev_lookup);
                nums.push_back(n.op(0));
                dens.push_back(n.op(1));
        }
-       ex n = ex_to<numeric>(overall_coeff).normal(repl, rev_lookup, level-1);
+       ex n = ex_to<numeric>(overall_coeff).normal(repl, rev_lookup);
        nums.push_back(n.op(0));
        dens.push_back(n.op(1));
        GINAC_ASSERT(nums.size() == dens.size());
@@ -2202,29 +2199,23 @@ ex add::normal(exmap & repl, exmap & rev_lookup, int level) const
 /** Implementation of ex::normal() for a product. It cancels common factors
  *  from fractions.
  *  @see ex::normal() */
-ex mul::normal(exmap & repl, exmap & rev_lookup, int level) const
+ex mul::normal(exmap & repl, exmap & rev_lookup) const
 {
-       if (level == 1)
-               return (new lst(replace_with_symbol(*this, repl, rev_lookup), _ex1))->setflag(status_flags::dynallocated);
-       else if (level == -max_recursion_level)
-               throw(std::runtime_error("max recursion level reached"));
-
        // Normalize children, separate into numerator and denominator
        exvector num; num.reserve(seq.size());
        exvector den; den.reserve(seq.size());
        ex n;
        for (auto & it : seq) {
-               n = ex_to<basic>(recombine_pair_to_ex(it)).normal(repl, rev_lookup, level-1);
+               n = ex_to<basic>(recombine_pair_to_ex(it)).normal(repl, rev_lookup);
                num.push_back(n.op(0));
                den.push_back(n.op(1));
        }
-       n = ex_to<numeric>(overall_coeff).normal(repl, rev_lookup, level-1);
+       n = ex_to<numeric>(overall_coeff).normal(repl, rev_lookup);
        num.push_back(n.op(0));
        den.push_back(n.op(1));
 
        // Perform fraction cancellation
-       return frac_cancel((new mul(num))->setflag(status_flags::dynallocated),
-                          (new mul(den))->setflag(status_flags::dynallocated));
+       return frac_cancel(dynallocate<mul>(num), dynallocate<mul>(den));
 }
 
 
@@ -2232,16 +2223,11 @@ ex mul::normal(exmap & repl, exmap & rev_lookup, int level) const
  *  distributes integer exponents to numerator and denominator, and replaces
  *  non-integer powers by temporary symbols.
  *  @see ex::normal */
-ex power::normal(exmap & repl, exmap & rev_lookup, int level) const
+ex power::normal(exmap & repl, exmap & rev_lookup) const
 {
-       if (level == 1)
-               return (new lst(replace_with_symbol(*this, repl, rev_lookup), _ex1))->setflag(status_flags::dynallocated);
-       else if (level == -max_recursion_level)
-               throw(std::runtime_error("max recursion level reached"));
-
        // Normalize basis and exponent (exponent gets reassembled)
-       ex n_basis = ex_to<basic>(basis).normal(repl, rev_lookup, level-1);
-       ex n_exponent = ex_to<basic>(exponent).normal(repl, rev_lookup, level-1);
+       ex n_basis = ex_to<basic>(basis).normal(repl, rev_lookup);
+       ex n_exponent = ex_to<basic>(exponent).normal(repl, rev_lookup);
        n_exponent = n_exponent.op(0) / n_exponent.op(1);
 
        if (n_exponent.info(info_flags::integer)) {
@@ -2249,12 +2235,12 @@ ex power::normal(exmap & repl, exmap & rev_lookup, int level) const
                if (n_exponent.info(info_flags::positive)) {
 
                        // (a/b)^n -> {a^n, b^n}
-                       return (new lst(power(n_basis.op(0), n_exponent), power(n_basis.op(1), n_exponent)))->setflag(status_flags::dynallocated);
+                       return dynallocate<lst>({pow(n_basis.op(0), n_exponent), pow(n_basis.op(1), n_exponent)});
 
                } else if (n_exponent.info(info_flags::negative)) {
 
                        // (a/b)^-n -> {b^n, a^n}
-                       return (new lst(power(n_basis.op(1), -n_exponent), power(n_basis.op(0), -n_exponent)))->setflag(status_flags::dynallocated);
+                       return dynallocate<lst>({pow(n_basis.op(1), -n_exponent), pow(n_basis.op(0), -n_exponent)});
                }
 
        } else {
@@ -2262,32 +2248,32 @@ ex power::normal(exmap & repl, exmap & rev_lookup, int level) const
                if (n_exponent.info(info_flags::positive)) {
 
                        // (a/b)^x -> {sym((a/b)^x), 1}
-                       return (new lst(replace_with_symbol(power(n_basis.op(0) / n_basis.op(1), n_exponent), repl, rev_lookup), _ex1))->setflag(status_flags::dynallocated);
+                       return dynallocate<lst>({replace_with_symbol(pow(n_basis.op(0) / n_basis.op(1), n_exponent), repl, rev_lookup), _ex1});
 
                } else if (n_exponent.info(info_flags::negative)) {
 
                        if (n_basis.op(1).is_equal(_ex1)) {
 
                                // a^-x -> {1, sym(a^x)}
-                               return (new lst(_ex1, replace_with_symbol(power(n_basis.op(0), -n_exponent), repl, rev_lookup)))->setflag(status_flags::dynallocated);
+                               return dynallocate<lst>({_ex1, replace_with_symbol(pow(n_basis.op(0), -n_exponent), repl, rev_lookup)});
 
                        } else {
 
                                // (a/b)^-x -> {sym((b/a)^x), 1}
-                               return (new lst(replace_with_symbol(power(n_basis.op(1) / n_basis.op(0), -n_exponent), repl, rev_lookup), _ex1))->setflag(status_flags::dynallocated);
+                               return dynallocate<lst>({replace_with_symbol(pow(n_basis.op(1) / n_basis.op(0), -n_exponent), repl, rev_lookup), _ex1});
                        }
                }
        }
 
        // (a/b)^x -> {sym((a/b)^x, 1}
-       return (new lst(replace_with_symbol(power(n_basis.op(0) / n_basis.op(1), n_exponent), repl, rev_lookup), _ex1))->setflag(status_flags::dynallocated);
+       return dynallocate<lst>({replace_with_symbol(pow(n_basis.op(0) / n_basis.op(1), n_exponent), repl, rev_lookup), _ex1});
 }
 
 
 /** Implementation of ex::normal() for pseries. It normalizes each coefficient
  *  and replaces the series by a temporary symbol.
  *  @see ex::normal */
-ex pseries::normal(exmap & repl, exmap & rev_lookup, int level) const
+ex pseries::normal(exmap & repl, exmap & rev_lookup) const
 {
        epvector newseq;
        for (auto & it : seq) {
@@ -2296,7 +2282,7 @@ ex pseries::normal(exmap & repl, exmap & rev_lookup, int level) const
                        newseq.push_back(expair(restexp, it.coeff));
        }
        ex n = pseries(relational(var,point), std::move(newseq));
-       return (new lst(replace_with_symbol(n, repl, rev_lookup), _ex1))->setflag(status_flags::dynallocated);
+       return dynallocate<lst>({replace_with_symbol(n, repl, rev_lookup), _ex1});
 }
 
 
@@ -2310,13 +2296,12 @@ ex pseries::normal(exmap & repl, exmap & rev_lookup, int level) const
  *  expression can be treated as a rational function). normal() is applied
  *  recursively to arguments of functions etc.
  *
- *  @param level maximum depth of recursion
  *  @return normalized expression */
-ex ex::normal(int level) const
+ex ex::normal() const
 {
        exmap repl, rev_lookup;
 
-       ex e = bp->normal(repl, rev_lookup, level);
+       ex e = bp->normal(repl, rev_lookup);
        GINAC_ASSERT(is_a<lst>(e));
 
        // Re-insert replaced symbols
@@ -2337,7 +2322,7 @@ ex ex::numer() const
 {
        exmap repl, rev_lookup;
 
-       ex e = bp->normal(repl, rev_lookup, 0);
+       ex e = bp->normal(repl, rev_lookup);
        GINAC_ASSERT(is_a<lst>(e));
 
        // Re-insert replaced symbols
@@ -2357,7 +2342,7 @@ ex ex::denom() const
 {
        exmap repl, rev_lookup;
 
-       ex e = bp->normal(repl, rev_lookup, 0);
+       ex e = bp->normal(repl, rev_lookup);
        GINAC_ASSERT(is_a<lst>(e));
 
        // Re-insert replaced symbols
@@ -2377,7 +2362,7 @@ ex ex::numer_denom() const
 {
        exmap repl, rev_lookup;
 
-       ex e = bp->normal(repl, rev_lookup, 0);
+       ex e = bp->normal(repl, rev_lookup);
        GINAC_ASSERT(is_a<lst>(e));
 
        // Re-insert replaced symbols
@@ -2517,7 +2502,7 @@ ex numeric::to_polynomial(exmap & repl) const
 ex power::to_rational(exmap & repl) const
 {
        if (exponent.info(info_flags::integer))
-               return power(basis.to_rational(repl), exponent);
+               return pow(basis.to_rational(repl), exponent);
        else
                return replace_with_symbol(*this, repl);
 }
@@ -2527,17 +2512,17 @@ ex power::to_rational(exmap & repl) const
 ex power::to_polynomial(exmap & repl) const
 {
        if (exponent.info(info_flags::posint))
-               return power(basis.to_rational(repl), exponent);
+               return pow(basis.to_rational(repl), exponent);
        else if (exponent.info(info_flags::negint))
        {
                ex basis_pref = collect_common_factors(basis);
                if (is_exactly_a<mul>(basis_pref) || is_exactly_a<power>(basis_pref)) {
                        // (A*B)^n will be automagically transformed to A^n*B^n
-                       ex t = power(basis_pref, exponent);
+                       ex t = pow(basis_pref, exponent);
                        return t.to_polynomial(repl);
                }
                else
-                       return power(replace_with_symbol(power(basis, _ex_1), repl), -exponent);
+                       return pow(replace_with_symbol(pow(basis, _ex_1), repl), -exponent);
        } 
        else
                return replace_with_symbol(*this, repl);
@@ -2556,7 +2541,7 @@ ex expairseq::to_rational(exmap & repl) const
        if (oc.info(info_flags::numeric))
                return thisexpairseq(std::move(s), overall_coeff);
        else
-               s.push_back(combine_ex_with_coeff_to_pair(oc, _ex1));
+               s.push_back(expair(oc, _ex1));
        return thisexpairseq(std::move(s), default_overall_coeff());
 }
 
@@ -2572,7 +2557,7 @@ ex expairseq::to_polynomial(exmap & repl) const
        if (oc.info(info_flags::numeric))
                return thisexpairseq(std::move(s), overall_coeff);
        else
-               s.push_back(combine_ex_with_coeff_to_pair(oc, _ex1));
+               s.push_back(expair(oc, _ex1));
        return thisexpairseq(std::move(s), default_overall_coeff());
 }
 
@@ -2628,7 +2613,7 @@ static ex find_common_factor(const ex & e, ex & factor, exmap & repl)
                                                        else
                                                                v.push_back(t.op(k));
                                                }
-                                               t = (new mul(v))->setflag(status_flags::dynallocated);
+                                               t = dynallocate<mul>(v);
                                                goto term_done;
                                        }
                                }
@@ -2638,7 +2623,7 @@ static ex find_common_factor(const ex & e, ex & factor, exmap & repl)
                        t = x;
 term_done:     ;
                }
-               return (new add(terms))->setflag(status_flags::dynallocated);
+               return dynallocate<add>(terms);
 
        } else if (is_exactly_a<mul>(e)) {
 
@@ -2648,7 +2633,7 @@ term_done:        ;
                for (size_t i=0; i<num; i++)
                        v.push_back(find_common_factor(e.op(i), factor, repl));
 
-               return (new mul(v))->setflag(status_flags::dynallocated);
+               return dynallocate<mul>(v);
 
        } else if (is_exactly_a<power>(e)) {
                const ex e_exp(e.op(1));
@@ -2656,8 +2641,8 @@ term_done:        ;
                        ex eb = e.op(0).to_polynomial(repl);
                        ex factor_local(_ex1);
                        ex pre_res = find_common_factor(eb, factor_local, repl);
-                       factor *= power(factor_local, e_exp);
-                       return power(pre_res, e_exp);
+                       factor *= pow(factor_local, e_exp);
+                       return pow(pre_res, e_exp);
                        
                } else
                        return e.to_polynomial(repl);