- prepared for 1.0.13 release
[ginac.git] / ginac / power.cpp
index 72ec5aa..0730e3c 100644 (file)
@@ -3,7 +3,7 @@
  *  Implementation of GiNaC's symbolic exponentiation (basis^exponent). */
 
 /*
- *  GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
+ *  GiNaC Copyright (C) 1999-2003 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
@@ -33,6 +33,7 @@
 #include "constant.h"
 #include "inifcns.h" // for log() in power::derivative()
 #include "matrix.h"
+#include "indexed.h"
 #include "symbol.h"
 #include "print.h"
 #include "archive.h"
@@ -124,7 +125,7 @@ void power::print(const print_context & c, unsigned level) const
 
                // Integer powers of symbols are printed in a special, optimized way
                if (exponent.info(info_flags::integer)
-                && (is_exactly_a<symbol>(basis) || is_exactly_a<constant>(basis))) {
+                && (is_a<symbol>(basis) || is_a<constant>(basis))) {
                        int exp = ex_to<numeric>(exponent).to_int();
                        if (exp > 0)
                                c.s << '(';
@@ -139,7 +140,7 @@ void power::print(const print_context & c, unsigned level) const
                        c.s << ')';
 
                // <expr>^-1 is printed as "1.0/<expr>" or with the recip() function of CLN
-               } else if (exponent.compare(_num_1) == 0) {
+               } else if (exponent.is_equal(_ex_1)) {
                        if (is_a<print_csrc_cl_N>(c))
                                c.s << "recip(";
                        else
@@ -169,39 +170,39 @@ void power::print(const print_context & c, unsigned level) const
 
        } else {
 
-               if (exponent.is_equal(_ex1_2)) {
-                       if (is_a<print_latex>(c))
-                               c.s << "\\sqrt{";
-                       else
-                               c.s << "sqrt(";
+               bool is_tex = is_a<print_latex>(c);
+
+               if (is_tex && is_exactly_a<numeric>(exponent) && ex_to<numeric>(exponent).is_negative()) {
+
+                       // Powers with negative numeric exponents are printed as fractions in TeX
+                       c.s << "\\frac{1}{";
+                       power(basis, -exponent).eval().print(c);
+                       c.s << "}";
+
+               } else if (exponent.is_equal(_ex1_2)) {
+
+                       // Square roots are printed in a special way
+                       c.s << (is_tex ? "\\sqrt{" : "sqrt(");
                        basis.print(c);
-                       if (is_a<print_latex>(c))
-                               c.s << '}';
-                       else
-                               c.s << ')';
+                       c.s << (is_tex ? '}' : ')');
+
                } else {
-                       if (precedence() <= level) {
-                               if (is_a<print_latex>(c))
-                                       c.s << "{(";
-                               else
-                                       c.s << "(";
-                       }
+
+                       // Ordinary output of powers using '^' or '**'
+                       if (precedence() <= level)
+                               c.s << (is_tex ? "{(" : "(");
                        basis.print(c, precedence());
                        if (is_a<print_python>(c))
                                c.s << "**";
                        else
                                c.s << '^';
-                       if (is_a<print_latex>(c))
+                       if (is_tex)
                                c.s << '{';
                        exponent.print(c, precedence());
-                       if (is_a<print_latex>(c))
+                       if (is_tex)
                                c.s << '}';
-                       if (precedence() <= level) {
-                               if (is_a<print_latex>(c))
-                                       c.s << ")}";
-                               else
-                                       c.s << ')';
-                       }
+                       if (precedence() <= level)
+                               c.s << (is_tex ? ")}" : ")");
                }
        }
 }
@@ -244,7 +245,9 @@ ex power::map(map_function & f) const
 
 int power::degree(const ex & s) const
 {
-       if (is_ex_exactly_of_type(exponent, numeric) && ex_to<numeric>(exponent).is_integer()) {
+       if (is_equal(ex_to<basic>(s)))
+               return 1;
+       else if (is_ex_exactly_of_type(exponent, numeric) && ex_to<numeric>(exponent).is_integer()) {
                if (basis.is_equal(s))
                        return ex_to<numeric>(exponent).to_int();
                else
@@ -257,7 +260,9 @@ int power::degree(const ex & s) const
 
 int power::ldegree(const ex & s) const 
 {
-       if (is_ex_exactly_of_type(exponent, numeric) && ex_to<numeric>(exponent).is_integer()) {
+       if (is_equal(ex_to<basic>(s)))
+               return 1;
+       else if (is_ex_exactly_of_type(exponent, numeric) && ex_to<numeric>(exponent).is_integer()) {
                if (basis.is_equal(s))
                        return ex_to<numeric>(exponent).to_int();
                else
@@ -270,7 +275,9 @@ int power::ldegree(const ex & s) const
 
 ex power::coeff(const ex & s, int n) const
 {
-       if (!basis.is_equal(s)) {
+       if (is_equal(ex_to<basic>(s)))
+               return n==1 ? _ex1 : _ex0;
+       else if (!basis.is_equal(s)) {
                // basis not equal to s
                if (n == 0)
                        return *this;
@@ -649,31 +656,35 @@ ex power::expand(unsigned options) const
 // non-virtual functions in this class
 //////////
 
-/** expand a^n where a is an add and n is an integer.
+/** expand a^n where a is an add and n is a positive integer.
  *  @see power::expand */
 ex power::expand_add(const add & a, int n) const
 {
        if (n==2)
                return expand_add_2(a);
-       
-       int m = a.nops();
-       exvector sum;
-       sum.reserve((n+1)*(m-1));
+
+       const int m = a.nops();
+       exvector result;
+       // The number of terms will be the number of combinatorial compositions,
+       // i.e. the number of unordered arrangement of m nonnegative integers
+       // which sum up to n.  It is frequently written as C_n(m) and directly
+       // related with binomial coefficients:
+       result.reserve(binomial(numeric(n+m-1), numeric(m-1)).to_int());
        intvector k(m-1);
        intvector k_cum(m-1); // k_cum[l]:=sum(i=0,l,k[l]);
        intvector upper_limit(m-1);
        int l;
-       
-       for (int l=0; l<m-1; l++) {
+
+       for (int l=0; l<m-1; ++l) {
                k[l] = 0;
                k_cum[l] = 0;
                upper_limit[l] = n;
        }
-       
+
        while (true) {
                exvector term;
                term.reserve(m+1);
-               for (l=0; l<m-1; l++) {
+               for (l=0; l<m-1; ++l) {
                        const ex & b = a.op(l);
                        GINAC_ASSERT(!is_exactly_a<add>(b));
                        GINAC_ASSERT(!is_exactly_a<power>(b) ||
@@ -687,7 +698,7 @@ ex power::expand_add(const add & a, int n) const
                        else
                                term.push_back(power(b,k[l]));
                }
-               
+
                const ex & b = a.op(l);
                GINAC_ASSERT(!is_exactly_a<add>(b));
                GINAC_ASSERT(!is_exactly_a<power>(b) ||
@@ -700,38 +711,35 @@ ex power::expand_add(const add & a, int n) const
                        term.push_back(expand_mul(ex_to<mul>(b),numeric(n-k_cum[m-2])));
                else
                        term.push_back(power(b,n-k_cum[m-2]));
-               
+
                numeric f = binomial(numeric(n),numeric(k[0]));
-               for (l=1; l<m-1; l++)
+               for (l=1; l<m-1; ++l)
                        f *= binomial(numeric(n-k_cum[l-1]),numeric(k[l]));
-               
+
                term.push_back(f);
-               
-               // TODO: Can we optimize this?  Alex seemed to think so...
-               sum.push_back((new mul(term))->setflag(status_flags::dynallocated));
-               
+
+               result.push_back((new mul(term))->setflag(status_flags::dynallocated));
+
                // increment k[]
                l = m-2;
                while ((l>=0) && ((++k[l])>upper_limit[l])) {
-                       k[l] = 0;    
+                       k[l] = 0;
                        --l;
                }
                if (l<0) break;
-               
+
                // recalc k_cum[] and upper_limit[]
-               if (l==0)
-                       k_cum[0] = k[0];
-               else
-                       k_cum[l] = k_cum[l-1]+k[l];
-               
-               for (int i=l+1; i<m-1; i++)
+               k_cum[l] = (l==0 ? k[0] : k_cum[l-1]+k[l]);
+
+               for (int i=l+1; i<m-1; ++i)
                        k_cum[i] = k_cum[i-1]+k[i];
-               
-               for (int i=l+1; i<m-1; i++)
+
+               for (int i=l+1; i<m-1; ++i)
                        upper_limit[i] = n-k_cum[i-1];
        }
-       return (new add(sum))->setflag(status_flags::dynallocated |
-                                      status_flags::expanded );
+
+       return (new add(result))->setflag(status_flags::dynallocated |
+                                         status_flags::expanded);
 }
 
 
@@ -743,7 +751,7 @@ ex power::expand_add_2(const add & a) const
        unsigned a_nops = a.nops();
        sum.reserve((a_nops*(a_nops+1))/2);
        epvector::const_iterator last = a.seq.end();
-       
+
        // power(+(x,...,z;c),2)=power(+(x,...,z;0),2)+2*c*+(x,...,z;0)+c*c
        // first part: ignore overall_coeff and expand other terms
        for (epvector::const_iterator cit0=a.seq.begin(); cit0!=last; ++cit0) {
@@ -768,10 +776,10 @@ ex power::expand_add_2(const add & a) const
                        }
                } else {
                        if (is_ex_exactly_of_type(r,mul)) {
-                               sum.push_back(expair(expand_mul(ex_to<mul>(r),_num2),
+                               sum.push_back(a.combine_ex_with_coeff_to_pair(expand_mul(ex_to<mul>(r),_num2),
                                                     ex_to<numeric>(c).power_dyn(_num2)));
                        } else {
-                               sum.push_back(expair((new power(r,_ex2))->setflag(status_flags::dynallocated),
+                               sum.push_back(a.combine_ex_with_coeff_to_pair((new power(r,_ex2))->setflag(status_flags::dynallocated),
                                                     ex_to<numeric>(c).power_dyn(_num2)));
                        }
                }
@@ -801,28 +809,30 @@ ex power::expand_add_2(const add & a) const
        return (new add(sum))->setflag(status_flags::dynallocated | status_flags::expanded);
 }
 
-/** Expand factors of m in m^n where m is a mul and n is and integer
+/** Expand factors of m in m^n where m is a mul and n is and integer.
  *  @see power::expand */
 ex power::expand_mul(const mul & m, const numeric & n) const
 {
+       GINAC_ASSERT(n.is_integer());
+
        if (n.is_zero())
                return _ex1;
-       
+
        epvector distrseq;
        distrseq.reserve(m.seq.size());
        epvector::const_iterator last = m.seq.end();
        epvector::const_iterator cit = m.seq.begin();
        while (cit!=last) {
-               if (is_ex_exactly_of_type((*cit).rest,numeric)) {
-                       distrseq.push_back(m.combine_pair_with_coeff_to_pair(*cit,n));
+               if (is_ex_exactly_of_type(cit->rest,numeric)) {
+                       distrseq.push_back(m.combine_pair_with_coeff_to_pair(*cit, n));
                } else {
                        // it is safe not to call mul::combine_pair_with_coeff_to_pair()
                        // since n is an integer
-                       distrseq.push_back(expair((*cit).rest, ex_to<numeric>((*cit).coeff).mul(n)));
+                       distrseq.push_back(expair(cit->rest, ex_to<numeric>(cit->coeff).mul(n)));
                }
                ++cit;
        }
-       return (new mul(distrseq,ex_to<numeric>(m.overall_coeff).power_dyn(n)))->setflag(status_flags::dynallocated);
+       return (new mul(distrseq, ex_to<numeric>(m.overall_coeff).power_dyn(n)))->setflag(status_flags::dynallocated);
 }
 
 } // namespace GiNaC