X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fpower.cpp;h=309d529a69cffebb3825f96e2d1bcd13e6ff0916;hp=4c7519ec9c3b75866896555dbf7bfdd5cbd2c046;hb=547db2f0380c03c7d013aa8bda36aa33ff5559e1;hpb=146be3afbf5f340ea81cda30b35b35c158af31c2 diff --git a/ginac/power.cpp b/ginac/power.cpp index 4c7519ec..309d529a 100644 --- a/ginac/power.cpp +++ b/ginac/power.cpp @@ -3,7 +3,7 @@ * Implementation of GiNaC's symbolic exponentiation (basis^exponent). */ /* - * GiNaC Copyright (C) 1999-2002 Johannes Gutenberg University Mainz, Germany + * GiNaC Copyright (C) 1999-2004 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 @@ -23,6 +23,7 @@ #include #include #include +#include #include "power.h" #include "expairseq.h" @@ -31,36 +32,34 @@ #include "ncmul.h" #include "numeric.h" #include "constant.h" +#include "operators.h" #include "inifcns.h" // for log() in power::derivative() #include "matrix.h" +#include "indexed.h" #include "symbol.h" -#include "print.h" +#include "lst.h" #include "archive.h" #include "utils.h" namespace GiNaC { -GINAC_IMPLEMENT_REGISTERED_CLASS(power, basic) +GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(power, basic, + print_func(&power::do_print_dflt). + print_func(&power::do_print_latex). + print_func(&power::do_print_csrc). + print_func(&power::do_print_python). + print_func(&power::do_print_python_repr)) typedef std::vector intvector; ////////// -// default ctor, dtor, copy ctor, assignment operator and helpers +// default constructor ////////// power::power() : inherited(TINFO_power) { } -void power::copy(const power & other) -{ - inherited::copy(other); - basis = other.basis; - exponent = other.exponent; -} - -DEFAULT_DESTROY(power) - ////////// -// other ctors +// other constructors ////////// // all inlined @@ -69,7 +68,7 @@ DEFAULT_DESTROY(power) // archiving ////////// -power::power(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst) +power::power(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst) { n.find_ex("basis", basis, sym_lst); n.find_ex("exponent", exponent, sym_lst); @@ -90,11 +89,58 @@ DEFAULT_UNARCHIVE(power) // public +void power::print_power(const print_context & c, const char *powersymbol, const char *openbrace, const char *closebrace, unsigned level) const +{ + // Ordinary output of powers using '^' or '**' + if (precedence() <= level) + c.s << openbrace << '('; + basis.print(c, precedence()); + c.s << powersymbol; + c.s << openbrace; + exponent.print(c, precedence()); + c.s << closebrace; + if (precedence() <= level) + c.s << ')' << closebrace; +} + +void power::do_print_dflt(const print_dflt & c, unsigned level) const +{ + if (exponent.is_equal(_ex1_2)) { + + // Square roots are printed in a special way + c.s << "sqrt("; + basis.print(c); + c.s << ')'; + + } else + print_power(c, "^", "", "", level); +} + +void power::do_print_latex(const print_latex & c, unsigned level) const +{ + if (is_exactly_a(exponent) && ex_to(exponent).is_negative()) { + + // Powers with negative numeric exponents are printed as fractions + 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 << "\\sqrt{"; + basis.print(c); + c.s << '}'; + + } else + print_power(c, "^", "{", "}", level); +} + static void print_sym_pow(const print_context & c, const symbol &x, int exp) { // Optimal output of integer powers of symbols to aid compiler CSE. // C.f. ISO/IEC 14882:1998, section 1.9 [intro execution], paragraph 15 - // to learn why such a parenthisation is really necessary. + // to learn why such a parenthesation is really necessary. if (exp == 1) { x.print(c); } else if (exp == 2) { @@ -114,96 +160,58 @@ static void print_sym_pow(const print_context & c, const symbol &x, int exp) } } -void power::print(const print_context & c, unsigned level) const +void power::do_print_csrc(const print_csrc & c, unsigned level) const { - if (is_a(c)) { - - inherited::print(c, level); - - } else if (is_a(c)) { - - // Integer powers of symbols are printed in a special, optimized way - if (exponent.info(info_flags::integer) - && (is_exactly_a(basis) || is_exactly_a(basis))) { - int exp = ex_to(exponent).to_int(); - if (exp > 0) - c.s << '('; - else { - exp = -exp; - if (is_a(c)) - c.s << "recip("; - else - c.s << "1.0/("; - } - print_sym_pow(c, ex_to(basis), exp); - c.s << ')'; - - // ^-1 is printed as "1.0/" or with the recip() function of CLN - } else if (exponent.is_equal(_ex_1)) { + // Integer powers of symbols are printed in a special, optimized way + if (exponent.info(info_flags::integer) + && (is_a(basis) || is_a(basis))) { + int exp = ex_to(exponent).to_int(); + if (exp > 0) + c.s << '('; + else { + exp = -exp; if (is_a(c)) c.s << "recip("; else c.s << "1.0/("; - basis.print(c); - c.s << ')'; - - // Otherwise, use the pow() or expt() (CLN) functions - } else { - if (is_a(c)) - c.s << "expt("; - else - c.s << "pow("; - basis.print(c); - c.s << ','; - exponent.print(c); - c.s << ')'; } + print_sym_pow(c, ex_to(basis), exp); + c.s << ')'; - } else if (is_a(c)) { + // ^-1 is printed as "1.0/" or with the recip() function of CLN + } else if (exponent.is_equal(_ex_1)) { + if (is_a(c)) + c.s << "recip("; + else + c.s << "1.0/("; + basis.print(c); + c.s << ')'; - c.s << class_name() << '('; + // Otherwise, use the pow() or expt() (CLN) functions + } else { + if (is_a(c)) + c.s << "expt("; + else + c.s << "pow("; basis.print(c); c.s << ','; exponent.print(c); c.s << ')'; + } +} - } else { +void power::do_print_python(const print_python & c, unsigned level) const +{ + print_power(c, "**", "", "", level); +} - if (exponent.is_equal(_ex1_2)) { - if (is_a(c)) - c.s << "\\sqrt{"; - else - c.s << "sqrt("; - basis.print(c); - if (is_a(c)) - c.s << '}'; - else - c.s << ')'; - } else { - if (precedence() <= level) { - if (is_a(c)) - c.s << "{("; - else - c.s << "("; - } - basis.print(c, precedence()); - if (is_a(c)) - c.s << "**"; - else - c.s << '^'; - if (is_a(c)) - c.s << '{'; - exponent.print(c, precedence()); - if (is_a(c)) - c.s << '}'; - if (precedence() <= level) { - if (is_a(c)) - c.s << ")}"; - else - c.s << ')'; - } - } - } +void power::do_print_python_repr(const print_python_repr & c, unsigned level) const +{ + c.s << class_name() << '('; + basis.print(c); + c.s << ','; + exponent.print(c); + c.s << ')'; } bool power::info(unsigned inf) const @@ -224,14 +232,13 @@ bool power::info(unsigned inf) const return inherited::info(inf); } -unsigned power::nops() const +size_t power::nops() const { return 2; } -ex & power::let_op(int i) +ex power::op(size_t i) const { - GINAC_ASSERT(i>=0); GINAC_ASSERT(i<2); return i==0 ? basis : exponent; @@ -239,14 +246,21 @@ ex & power::let_op(int i) ex power::map(map_function & f) const { - return (new power(f(basis), f(exponent)))->setflag(status_flags::dynallocated); + const ex &mapped_basis = f(basis); + const ex &mapped_exponent = f(exponent); + + if (!are_ex_trivially_equal(basis, mapped_basis) + || !are_ex_trivially_equal(exponent, mapped_exponent)) + return (new power(mapped_basis, mapped_exponent))->setflag(status_flags::dynallocated); + else + return *this; } int power::degree(const ex & s) const { if (is_equal(ex_to(s))) return 1; - else if (is_ex_exactly_of_type(exponent, numeric) && ex_to(exponent).is_integer()) { + else if (is_exactly_a(exponent) && ex_to(exponent).is_integer()) { if (basis.is_equal(s)) return ex_to(exponent).to_int(); else @@ -261,7 +275,7 @@ int power::ldegree(const ex & s) const { if (is_equal(ex_to(s))) return 1; - else if (is_ex_exactly_of_type(exponent, numeric) && ex_to(exponent).is_integer()) { + else if (is_exactly_a(exponent) && ex_to(exponent).is_integer()) { if (basis.is_equal(s)) return ex_to(exponent).to_int(); else @@ -284,7 +298,7 @@ ex power::coeff(const ex & s, int n) const return _ex0; } else { // basis equal to s - if (is_ex_exactly_of_type(exponent, numeric) && ex_to(exponent).is_integer()) { + if (is_exactly_a(exponent) && ex_to(exponent).is_integer()) { // integer exponent int int_exp = ex_to(exponent).to_int(); if (n == int_exp) @@ -330,11 +344,11 @@ ex power::eval(int level) const const numeric *num_basis; const numeric *num_exponent; - if (is_ex_exactly_of_type(ebasis, numeric)) { + if (is_exactly_a(ebasis)) { basis_is_numerical = true; num_basis = &ex_to(ebasis); } - if (is_ex_exactly_of_type(eexponent, numeric)) { + if (is_exactly_a(eexponent)) { exponent_is_numerical = true; num_exponent = &ex_to(eexponent); } @@ -425,11 +439,11 @@ ex power::eval(int level) const // ^(^(x,c1),c2) -> ^(x,c1*c2) // (c1, c2 numeric(), c2 integer or -1 < c1 <= 1, // case c1==1 should not happen, see below!) - if (is_ex_exactly_of_type(ebasis,power)) { + if (is_exactly_a(ebasis)) { const power & sub_power = ex_to(ebasis); const ex & sub_basis = sub_power.basis; const ex & sub_exponent = sub_power.exponent; - if (is_ex_exactly_of_type(sub_exponent,numeric)) { + if (is_exactly_a(sub_exponent)) { const numeric & num_sub_exponent = ex_to(sub_exponent); GINAC_ASSERT(num_sub_exponent!=numeric(1)); if (num_exponent->is_integer() || (abs(num_sub_exponent) - _num1).is_negative()) @@ -438,13 +452,13 @@ ex power::eval(int level) const } // ^(*(x,y,z),c1) -> *(x^c1,y^c1,z^c1) (c1 integer) - if (num_exponent->is_integer() && is_ex_exactly_of_type(ebasis,mul)) { - return expand_mul(ex_to(ebasis), *num_exponent); + if (num_exponent->is_integer() && is_exactly_a(ebasis)) { + return expand_mul(ex_to(ebasis), *num_exponent, 0); } // ^(*(...,x;c1),c2) -> *(^(*(...,x;1),c2),c1^c2) (c1, c2 numeric(), c1>0) // ^(*(...,x;c1),c2) -> *(^(*(...,x;-1),c2),(-c1)^c2) (c1, c2 numeric(), c1<0) - if (is_ex_exactly_of_type(ebasis,mul)) { + if (is_exactly_a(ebasis)) { GINAC_ASSERT(!num_exponent->is_integer()); // should have been handled above const mul & mulref = ex_to(ebasis); if (!mulref.overall_coeff.is_equal(_ex1)) { @@ -475,7 +489,7 @@ ex power::eval(int level) const // ^(nc,c1) -> ncmul(nc,nc,...) (c1 positive integer, unless nc is a matrix) if (num_exponent->is_pos_integer() && ebasis.return_type() != return_types::commutative && - !is_ex_of_type(ebasis,matrix)) { + !is_a(ebasis)) { return ncmul(exvector(num_exponent->to_int(), ebasis), true); } } @@ -509,33 +523,56 @@ ex power::evalf(int level) const return power(ebasis,eexponent); } -ex power::evalm(void) const +ex power::evalm() const { const ex ebasis = basis.evalm(); const ex eexponent = exponent.evalm(); - if (is_ex_of_type(ebasis,matrix)) { - if (is_ex_of_type(eexponent,numeric)) { + if (is_a(ebasis)) { + if (is_exactly_a(eexponent)) { return (new matrix(ex_to(ebasis).pow(eexponent)))->setflag(status_flags::dynallocated); } } return (new power(ebasis, eexponent))->setflag(status_flags::dynallocated); } -ex power::subs(const lst & ls, const lst & lr, bool no_pattern) const -{ - const ex &subsed_basis = basis.subs(ls, lr, no_pattern); - const ex &subsed_exponent = exponent.subs(ls, lr, no_pattern); +// from mul.cpp +extern bool tryfactsubs(const ex &, const ex &, int &, lst &); - if (are_ex_trivially_equal(basis, subsed_basis) - && are_ex_trivially_equal(exponent, subsed_exponent)) - return basic::subs(ls, lr, no_pattern); - else - return power(subsed_basis, subsed_exponent).basic::subs(ls, lr, no_pattern); +ex power::subs(const exmap & m, unsigned options) const +{ + const ex &subsed_basis = basis.subs(m, options); + const ex &subsed_exponent = exponent.subs(m, options); + + if (!are_ex_trivially_equal(basis, subsed_basis) + || !are_ex_trivially_equal(exponent, subsed_exponent)) + return power(subsed_basis, subsed_exponent).subs_one_level(m, options); + + if (!(options & subs_options::algebraic)) + return subs_one_level(m, options); + + for (exmap::const_iterator it = m.begin(); it != m.end(); ++it) { + int nummatches = std::numeric_limits::max(); + lst repls; + if (tryfactsubs(*this, it->first, nummatches, repls)) + return (ex_to((*this) * power(it->second.subs(ex(repls), subs_options::no_pattern) / it->first.subs(ex(repls), subs_options::no_pattern), nummatches))).subs_one_level(m, options); + } + + return subs_one_level(m, options); +} + +ex power::eval_ncmul(const exvector & v) const +{ + return inherited::eval_ncmul(v); } -ex power::simplify_ncmul(const exvector & v) const +ex power::conjugate() const { - return inherited::simplify_ncmul(v); + ex newbasis = basis.conjugate(); + ex newexponent = exponent.conjugate(); + if (are_ex_trivially_equal(basis, newbasis) && are_ex_trivially_equal(exponent, newexponent)) { + return *this; + } + return (new power(newbasis, newexponent))->setflag(status_flags::dynallocated); } // protected @@ -571,12 +608,12 @@ int power::compare_same_type(const basic & other) const return exponent.compare(o.exponent); } -unsigned power::return_type(void) const +unsigned power::return_type() const { return basis.return_type(); } -unsigned power::return_type_tinfo(void) const +unsigned power::return_type_tinfo() const { return basis.return_type_tinfo(); } @@ -590,7 +627,7 @@ ex power::expand(unsigned options) const const ex expanded_exponent = exponent.expand(options); // x^(a+b) -> x^a * x^b - if (is_ex_exactly_of_type(expanded_exponent, add)) { + if (is_exactly_a(expanded_exponent)) { const add &a = ex_to(expanded_exponent); exvector distrseq; distrseq.reserve(a.seq.size() + 1); @@ -605,8 +642,8 @@ ex power::expand(unsigned options) const if (ex_to(a.overall_coeff).is_integer()) { const numeric &num_exponent = ex_to(a.overall_coeff); int int_exponent = num_exponent.to_int(); - if (int_exponent > 0 && is_ex_exactly_of_type(expanded_basis, add)) - distrseq.push_back(expand_add(ex_to(expanded_basis), int_exponent)); + if (int_exponent > 0 && is_exactly_a(expanded_basis)) + distrseq.push_back(expand_add(ex_to(expanded_basis), int_exponent, options)); else distrseq.push_back(power(expanded_basis, a.overall_coeff)); } else @@ -614,10 +651,10 @@ ex power::expand(unsigned options) const // Make sure that e.g. (x+y)^(1+a) -> x*(x+y)^a + y*(x+y)^a ex r = (new mul(distrseq))->setflag(status_flags::dynallocated); - return r.expand(); + return r.expand(options); } - if (!is_ex_exactly_of_type(expanded_exponent, numeric) || + if (!is_exactly_a(expanded_exponent) || !ex_to(expanded_exponent).is_integer()) { if (are_ex_trivially_equal(basis,expanded_basis) && are_ex_trivially_equal(exponent,expanded_exponent)) { return this->hold(); @@ -631,12 +668,12 @@ ex power::expand(unsigned options) const int int_exponent = num_exponent.to_int(); // (x+y)^n, n>0 - if (int_exponent > 0 && is_ex_exactly_of_type(expanded_basis,add)) - return expand_add(ex_to(expanded_basis), int_exponent); + if (int_exponent > 0 && is_exactly_a(expanded_basis)) + return expand_add(ex_to(expanded_basis), int_exponent, options); // (x*y)^n -> x^n * y^n - if (is_ex_exactly_of_type(expanded_basis,mul)) - return expand_mul(ex_to(expanded_basis), num_exponent); + if (is_exactly_a(expanded_basis)) + return expand_mul(ex_to(expanded_basis), num_exponent, options, true); // cannot expand further if (are_ex_trivially_equal(basis,expanded_basis) && are_ex_trivially_equal(exponent,expanded_exponent)) @@ -655,31 +692,35 @@ 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 +ex power::expand_add(const add & a, int n, unsigned options) const { if (n==2) - return expand_add_2(a); - - int m = a.nops(); - exvector sum; - sum.reserve((n+1)*(m-1)); + return expand_add_2(a, options); + + const size_t 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(b)); GINAC_ASSERT(!is_exactly_a(b) || @@ -688,12 +729,12 @@ ex power::expand_add(const add & a, int n) const !is_exactly_a(ex_to(b).basis) || !is_exactly_a(ex_to(b).basis) || !is_exactly_a(ex_to(b).basis)); - if (is_ex_exactly_of_type(b,mul)) - term.push_back(expand_mul(ex_to(b),numeric(k[l]))); + if (is_exactly_a(b)) + term.push_back(expand_mul(ex_to(b), numeric(k[l]), options, true)); else term.push_back(power(b,k[l])); } - + const ex & b = a.op(l); GINAC_ASSERT(!is_exactly_a(b)); GINAC_ASSERT(!is_exactly_a(b) || @@ -702,54 +743,51 @@ ex power::expand_add(const add & a, int n) const !is_exactly_a(ex_to(b).basis) || !is_exactly_a(ex_to(b).basis) || !is_exactly_a(ex_to(b).basis)); - if (is_ex_exactly_of_type(b,mul)) - term.push_back(expand_mul(ex_to(b),numeric(n-k_cum[m-2]))); + if (is_exactly_a(b)) + term.push_back(expand_mul(ex_to(b), numeric(n-k_cum[m-2]), options, true)); else term.push_back(power(b,n-k_cum[m-2])); - + numeric f = binomial(numeric(n),numeric(k[0])); - for (l=1; lsetflag(status_flags::dynallocated)); - + + result.push_back(ex((new mul(term))->setflag(status_flags::dynallocated)).expand(options)); + // 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; isetflag(status_flags::dynallocated | - status_flags::expanded ); + + return (new add(result))->setflag(status_flags::dynallocated | + status_flags::expanded); } /** Special case of power::expand_add. Expands a^2 where a is an add. * @see power::expand_add */ -ex power::expand_add_2(const add & a) const +ex power::expand_add_2(const add & a, unsigned options) const { epvector sum; - unsigned a_nops = a.nops(); + size_t 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) { @@ -764,24 +802,24 @@ ex power::expand_add_2(const add & a) const !is_exactly_a(ex_to(r).basis) || !is_exactly_a(ex_to(r).basis)); - if (are_ex_trivially_equal(c,_ex1)) { - if (is_ex_exactly_of_type(r,mul)) { - sum.push_back(expair(expand_mul(ex_to(r),_num2), + if (c.is_equal(_ex1)) { + if (is_exactly_a(r)) { + sum.push_back(expair(expand_mul(ex_to(r), _num2, options, true), _ex1)); } else { sum.push_back(expair((new power(r,_ex2))->setflag(status_flags::dynallocated), _ex1)); } } else { - if (is_ex_exactly_of_type(r,mul)) { - sum.push_back(expair(expand_mul(ex_to(r),_num2), + if (is_exactly_a(r)) { + sum.push_back(a.combine_ex_with_coeff_to_pair(expand_mul(ex_to(r), _num2, options, true), ex_to(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(c).power_dyn(_num2))); } } - + for (epvector::const_iterator cit1=cit0+1; cit1!=last; ++cit1) { const ex & r1 = cit1->rest; const ex & c1 = cit1->coeff; @@ -807,28 +845,44 @@ 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 +ex power::expand_mul(const mul & m, const numeric & n, unsigned options, bool from_expand) const { + GINAC_ASSERT(n.is_integer()); + if (n.is_zero()) return _ex1; - + epvector distrseq; distrseq.reserve(m.seq.size()); + bool need_reexpand = false; + 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_exactly_a(cit->rest)) { + 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((*cit).coeff).mul(n))); + numeric new_coeff = ex_to(cit->coeff).mul(n); + if (from_expand && is_exactly_a(cit->rest) && new_coeff.is_pos_integer()) { + // this happens when e.g. (a+b)^(1/2) gets squared and + // the resulting product needs to be reexpanded + need_reexpand = true; + } + distrseq.push_back(expair(cit->rest, new_coeff)); } ++cit; } - return (new mul(distrseq,ex_to(m.overall_coeff).power_dyn(n)))->setflag(status_flags::dynallocated); + + const mul & result = static_cast((new mul(distrseq, ex_to(m.overall_coeff).power_dyn(n)))->setflag(status_flags::dynallocated)); + if (need_reexpand) + return ex(result).expand(options); + if (from_expand) + return result.setflag(status_flags::expanded); + return result; } } // namespace GiNaC