#include "expairseq.h"
#include "add.h"
#include "mul.h"
+#include "ncmul.h"
#include "numeric.h"
#include "inifcns.h"
-#include "relational.h"
+#include "matrix.h"
#include "symbol.h"
#include "print.h"
#include "archive.h"
power::power(const ex & lh, const ex & rh) : basic(TINFO_power), basis(lh), exponent(rh)
{
debugmsg("power ctor from ex,ex",LOGLEVEL_CONSTRUCT);
- GINAC_ASSERT(basis.return_type()==return_types::commutative);
}
+/** Ctor from an ex and a bare numeric. This is somewhat more efficient than
+ * the normal ctor from two ex whenever it can be used. */
power::power(const ex & lh, const numeric & rh) : basic(TINFO_power), basis(lh), exponent(rh)
{
debugmsg("power ctor from ex,numeric",LOGLEVEL_CONSTRUCT);
- GINAC_ASSERT(basis.return_type()==return_types::commutative);
}
//////////
&& (is_ex_exactly_of_type(basis, symbol) || is_ex_exactly_of_type(basis, constant))) {
int exp = ex_to_numeric(exponent).to_int();
if (exp > 0)
- c.s << "(";
+ c.s << '(';
else {
exp = -exp;
if (is_of_type(c, print_csrc_cl_N))
c.s << "1.0/(";
}
print_sym_pow(c, ex_to_symbol(basis), exp);
- c.s << ")";
+ 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
c.s << "1.0/(";
basis.print(c);
- c.s << ")";
+ c.s << ')';
// Otherwise, use the pow() or expt() (CLN) functions
} else {
else
c.s << "pow(";
basis.print(c);
- c.s << ",";
+ c.s << ',';
exponent.print(c);
- c.s << ")";
+ c.s << ')';
}
} else {
if (exponent.is_equal(_ex1_2())) {
- c.s << "sqrt(";
+ if (is_of_type(c, print_latex))
+ c.s << "\\sqrt{";
+ else
+ c.s << "sqrt(";
basis.print(c);
- c.s << ")";
+ if (is_of_type(c, print_latex))
+ c.s << '}';
+ else
+ c.s << ')';
} else {
- if (precedence <= level)
- c.s << "(";
- basis.print(c, precedence);
- c.s << "^";
- exponent.print(c, precedence);
- if (precedence <= level)
- c.s << ")";
+ if (precedence() <= level) {
+ if (is_of_type(c, print_latex))
+ c.s << "{(";
+ else
+ c.s << "(";
+ }
+ basis.print(c, precedence());
+ c.s << '^';
+ if (is_of_type(c, print_latex))
+ c.s << '{';
+ exponent.print(c, precedence());
+ if (is_of_type(c, print_latex))
+ c.s << '}';
+ if (precedence() <= level) {
+ if (is_of_type(c, print_latex))
+ c.s << ")}";
+ else
+ c.s << ')';
+ }
}
}
}
return i==0 ? basis : exponent;
}
+ex power::map(map_func f) const
+{
+ return (new power(f(basis), f(exponent)))->setflag(status_flags::dynallocated);
+}
+
int power::degree(const ex & s) const
{
if (is_exactly_of_type(*exponent.bp,numeric)) {
const ex & ebasis = level==1 ? basis : basis.eval(level-1);
const ex & eexponent = level==1 ? exponent : exponent.eval(level-1);
- bool basis_is_numerical = 0;
- bool exponent_is_numerical = 0;
+ bool basis_is_numerical = false;
+ bool exponent_is_numerical = false;
numeric * num_basis;
numeric * num_exponent;
if (is_exactly_of_type(*ebasis.bp,numeric)) {
- basis_is_numerical = 1;
+ basis_is_numerical = true;
num_basis = static_cast<numeric *>(ebasis.bp);
}
if (is_exactly_of_type(*eexponent.bp,numeric)) {
- exponent_is_numerical = 1;
+ exponent_is_numerical = true;
num_exponent = static_cast<numeric *>(eexponent.bp);
}
if (ebasis.is_equal(_ex1()))
return _ex1();
- if (basis_is_numerical && exponent_is_numerical) {
+ if (exponent_is_numerical) {
+
// ^(c1,c2) -> c1^c2 (c1, c2 numeric(),
// except if c1,c2 are rational, but c1^c2 is not)
- bool basis_is_crational = num_basis->is_crational();
- bool exponent_is_crational = num_exponent->is_crational();
- numeric res = num_basis->power(*num_exponent);
+ if (basis_is_numerical) {
+ bool basis_is_crational = num_basis->is_crational();
+ bool exponent_is_crational = num_exponent->is_crational();
+ numeric res = num_basis->power(*num_exponent);
- if ((!basis_is_crational || !exponent_is_crational)
- || res.is_crational()) {
- return res;
- }
- GINAC_ASSERT(!num_exponent->is_integer()); // has been handled by now
- // ^(c1,n/m) -> *(c1^q,c1^(n/m-q)), 0<(n/m-h)<1, q integer
- if (basis_is_crational && exponent_is_crational
- && num_exponent->is_real()
- && !num_exponent->is_integer()) {
- numeric n = num_exponent->numer();
- numeric m = num_exponent->denom();
- numeric r;
- numeric q = iquo(n, m, r);
- if (r.is_negative()) {
- r = r.add(m);
- q = q.sub(_num1());
+ if ((!basis_is_crational || !exponent_is_crational)
+ || res.is_crational()) {
+ return res;
}
- if (q.is_zero()) // the exponent was in the allowed range 0<(n/m)<1
- return this->hold();
- else {
- epvector res;
- res.push_back(expair(ebasis,r.div(m)));
- return (new mul(res,ex(num_basis->power_dyn(q))))->setflag(status_flags::dynallocated | status_flags::evaluated);
+ GINAC_ASSERT(!num_exponent->is_integer()); // has been handled by now
+
+ // ^(c1,n/m) -> *(c1^q,c1^(n/m-q)), 0<(n/m-h)<1, q integer
+ if (basis_is_crational && exponent_is_crational
+ && num_exponent->is_real()
+ && !num_exponent->is_integer()) {
+ numeric n = num_exponent->numer();
+ numeric m = num_exponent->denom();
+ numeric r;
+ numeric q = iquo(n, m, r);
+ if (r.is_negative()) {
+ r = r.add(m);
+ q = q.sub(_num1());
+ }
+ if (q.is_zero()) // the exponent was in the allowed range 0<(n/m)<1
+ return this->hold();
+ else {
+ epvector res;
+ res.push_back(expair(ebasis,r.div(m)));
+ return (new mul(res,ex(num_basis->power_dyn(q))))->setflag(status_flags::dynallocated | status_flags::evaluated);
+ }
}
}
- }
- // ^(^(x,c1),c2) -> ^(x,c1*c2)
- // (c1, c2 numeric(), c2 integer or -1 < c1 <= 1,
- // case c1==1 should not happen, see below!)
- if (exponent_is_numerical && is_ex_exactly_of_type(ebasis,power)) {
- const power & sub_power = ex_to_power(ebasis);
- const ex & sub_basis = sub_power.basis;
- const ex & sub_exponent = sub_power.exponent;
- if (is_ex_exactly_of_type(sub_exponent,numeric)) {
- const numeric & num_sub_exponent = ex_to_numeric(sub_exponent);
- GINAC_ASSERT(num_sub_exponent!=numeric(1));
- if (num_exponent->is_integer() || abs(num_sub_exponent)<1)
- return power(sub_basis,num_sub_exponent.mul(*num_exponent));
+ // ^(^(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)) {
+ const power & sub_power = ex_to_power(ebasis);
+ const ex & sub_basis = sub_power.basis;
+ const ex & sub_exponent = sub_power.exponent;
+ if (is_ex_exactly_of_type(sub_exponent,numeric)) {
+ const numeric & num_sub_exponent = ex_to_numeric(sub_exponent);
+ GINAC_ASSERT(num_sub_exponent!=numeric(1));
+ if (num_exponent->is_integer() || (abs(num_sub_exponent) - _num1()).is_negative())
+ return power(sub_basis,num_sub_exponent.mul(*num_exponent));
+ }
}
- }
- // ^(*(x,y,z),c1) -> *(x^c1,y^c1,z^c1) (c1 integer)
- if (exponent_is_numerical && num_exponent->is_integer() &&
- is_ex_exactly_of_type(ebasis,mul)) {
- return expand_mul(ex_to_mul(ebasis), *num_exponent);
- }
+ // ^(*(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_mul(ebasis), *num_exponent);
+ }
- // ^(*(...,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 (exponent_is_numerical && is_ex_exactly_of_type(ebasis,mul)) {
- GINAC_ASSERT(!num_exponent->is_integer()); // should have been handled above
- const mul & mulref = ex_to_mul(ebasis);
- if (!mulref.overall_coeff.is_equal(_ex1())) {
- const numeric & num_coeff = ex_to_numeric(mulref.overall_coeff);
- if (num_coeff.is_real()) {
- if (num_coeff.is_positive()) {
- mul * mulp = new mul(mulref);
- mulp->overall_coeff = _ex1();
- mulp->clearflag(status_flags::evaluated);
- mulp->clearflag(status_flags::hash_calculated);
- return (new mul(power(*mulp,exponent),
- power(num_coeff,*num_exponent)))->setflag(status_flags::dynallocated);
- } else {
- GINAC_ASSERT(num_coeff.compare(_num0())<0);
- if (num_coeff.compare(_num_1())!=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)) {
+ GINAC_ASSERT(!num_exponent->is_integer()); // should have been handled above
+ const mul & mulref = ex_to_mul(ebasis);
+ if (!mulref.overall_coeff.is_equal(_ex1())) {
+ const numeric & num_coeff = ex_to_numeric(mulref.overall_coeff);
+ if (num_coeff.is_real()) {
+ if (num_coeff.is_positive()) {
mul * mulp = new mul(mulref);
- mulp->overall_coeff = _ex_1();
+ mulp->overall_coeff = _ex1();
mulp->clearflag(status_flags::evaluated);
mulp->clearflag(status_flags::hash_calculated);
return (new mul(power(*mulp,exponent),
- power(abs(num_coeff),*num_exponent)))->setflag(status_flags::dynallocated);
+ power(num_coeff,*num_exponent)))->setflag(status_flags::dynallocated);
+ } else {
+ GINAC_ASSERT(num_coeff.compare(_num0())<0);
+ if (num_coeff.compare(_num_1())!=0) {
+ mul * mulp = new mul(mulref);
+ mulp->overall_coeff = _ex_1();
+ mulp->clearflag(status_flags::evaluated);
+ mulp->clearflag(status_flags::hash_calculated);
+ return (new mul(power(*mulp,exponent),
+ power(abs(num_coeff),*num_exponent)))->setflag(status_flags::dynallocated);
+ }
}
}
}
}
+
+ // ^(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)) {
+ return ncmul(exvector(num_exponent->to_int(), ebasis), true);
+ }
}
if (are_ex_trivially_equal(ebasis,basis) &&
return power(ebasis,eexponent);
}
-ex power::subs(const lst & ls, const lst & lr) const
+ex power::evalm(void) const
{
- const ex & subsed_basis=basis.subs(ls,lr);
- const ex & subsed_exponent=exponent.subs(ls,lr);
-
- if (are_ex_trivially_equal(basis,subsed_basis)&&
- are_ex_trivially_equal(exponent,subsed_exponent)) {
- return inherited::subs(ls, lr);
+ ex ebasis = basis.evalm();
+ ex eexponent = exponent.evalm();
+ if (is_ex_of_type(ebasis,matrix)) {
+ if (is_ex_of_type(eexponent,numeric)) {
+ return (new matrix(ex_to_matrix(ebasis).pow(eexponent)))->setflag(status_flags::dynallocated);
+ }
}
-
- return power(subsed_basis, subsed_exponent);
+ 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);
+
+ if (are_ex_trivially_equal(basis, subsed_basis)
+ && are_ex_trivially_equal(exponent, subsed_exponent))
+ return basic::subs(ls, lr, no_pattern);
+ else
+ return ex(power(subsed_basis, subsed_exponent)).bp->basic::subs(ls, lr, no_pattern);
}
ex power::simplify_ncmul(const exvector & v) const
cout << "k_cum[" << i << "]=" << k_cum[i] << endl;
cout << "upper_limit[" << i << "]=" << upper_limit[i] << endl;
}
- for (exvector::const_iterator cit=term.begin(); cit!=term.end(); ++cit) {
- cout << *cit << endl;
- }
+ for_each(term.begin(), term.end(), ostream_iterator<ex>(cout, "\n"));
cout << "end term" << endl;
*/
return (new mul(distrseq,ex_to_numeric(m.overall_coeff).power_dyn(n)))->setflag(status_flags::dynallocated);
}
-/*
-ex power::expand_commutative_3(const ex & basis, const numeric & exponent,
- unsigned options) const
-{
- // obsolete
-
- exvector distrseq;
- epvector splitseq;
-
- const add & addref=static_cast<const add &>(*basis.bp);
-
- splitseq=addref.seq;
- splitseq.pop_back();
- ex first_operands=add(splitseq);
- ex last_operand=addref.recombine_pair_to_ex(*(addref.seq.end()-1));
-
- int n=exponent.to_int();
- for (int k=0; k<=n; k++) {
- distrseq.push_back(binomial(n,k) * power(first_operands,numeric(k))
- * power(last_operand,numeric(n-k)));
- }
- return ex((new add(distrseq))->setflag(status_flags::expanded | status_flags::dynallocated)).expand(options);
-}
-*/
-
/*
ex power::expand_noncommutative(const ex & basis, const numeric & exponent,
unsigned options) const
}
*/
-//////////
-// static member variables
-//////////
-
-// protected
-
-unsigned power::precedence = 60;
-
// helper function
ex sqrt(const ex & a)
git://www.ginac.de / ginac.git / blobdiff