+ return 2;
+}
+
+ex & power::let_op(int i)
+{
+ GINAC_ASSERT(i>=0);
+ GINAC_ASSERT(i<2);
+
+ return i==0 ? basis : exponent;
+}
+
+ex power::map(map_function & f) const
+{
+ return (new power(f(basis), f(exponent)))->setflag(status_flags::dynallocated);
+}
+
+int power::degree(const ex & s) const
+{
+ 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
+ return basis.degree(s) * ex_to<numeric>(exponent).to_int();
+ } else if (basis.has(s))
+ throw(std::runtime_error("power::degree(): undefined degree because of non-integer exponent"));
+ else
+ return 0;
+}
+
+int power::ldegree(const ex & s) const
+{
+ 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
+ return basis.ldegree(s) * ex_to<numeric>(exponent).to_int();
+ } else if (basis.has(s))
+ throw(std::runtime_error("power::ldegree(): undefined degree because of non-integer exponent"));
+ else
+ return 0;
+}
+
+ex power::coeff(const ex & s, int n) const
+{
+ 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;
+ else
+ return _ex0;
+ } else {
+ // basis equal to s
+ if (is_ex_exactly_of_type(exponent, numeric) && ex_to<numeric>(exponent).is_integer()) {
+ // integer exponent
+ int int_exp = ex_to<numeric>(exponent).to_int();
+ if (n == int_exp)
+ return _ex1;
+ else
+ return _ex0;
+ } else {
+ // non-integer exponents are treated as zero
+ if (n == 0)
+ return *this;
+ else
+ return _ex0;
+ }
+ }
+}
+
+/** Perform automatic term rewriting rules in this class. In the following
+ * x, x1, x2,... stand for a symbolic variables of type ex and c, c1, c2...
+ * stand for such expressions that contain a plain number.
+ * - ^(x,0) -> 1 (also handles ^(0,0))
+ * - ^(x,1) -> x
+ * - ^(0,c) -> 0 or exception (depending on the real part of c)
+ * - ^(1,x) -> 1
+ * - ^(c1,c2) -> *(c1^n,c1^(c2-n)) (so that 0<(c2-n)<1, try to evaluate roots, possibly in numerator and denominator of c1)
+ * - ^(^(x,c1),c2) -> ^(x,c1*c2) (c2 integer or -1 < c1 <= 1, case c1=1 should not happen, see below!)
+ * - ^(*(x,y,z),c) -> *(x^c,y^c,z^c) (if c integer)
+ * - ^(*(x,c1),c2) -> ^(x,c2)*c1^c2 (c1>0)
+ * - ^(*(x,c1),c2) -> ^(-x,c2)*c1^c2 (c1<0)
+ *
+ * @param level cut-off in recursive evaluation */
+ex power::eval(int level) const
+{
+ if ((level==1) && (flags & status_flags::evaluated))
+ return *this;
+ else if (level == -max_recursion_level)
+ throw(std::runtime_error("max recursion level reached"));
+
+ const ex & ebasis = level==1 ? basis : basis.eval(level-1);
+ const ex & eexponent = level==1 ? exponent : exponent.eval(level-1);
+
+ bool basis_is_numerical = false;
+ bool exponent_is_numerical = false;
+ const numeric *num_basis;
+ const numeric *num_exponent;
+
+ if (is_ex_exactly_of_type(ebasis, numeric)) {
+ basis_is_numerical = true;
+ num_basis = &ex_to<numeric>(ebasis);
+ }
+ if (is_ex_exactly_of_type(eexponent, numeric)) {
+ exponent_is_numerical = true;
+ num_exponent = &ex_to<numeric>(eexponent);
+ }
+
+ // ^(x,0) -> 1 (0^0 also handled here)
+ if (eexponent.is_zero()) {
+ if (ebasis.is_zero())
+ throw (std::domain_error("power::eval(): pow(0,0) is undefined"));
+ else
+ return _ex1;
+ }
+
+ // ^(x,1) -> x
+ if (eexponent.is_equal(_ex1))
+ return ebasis;
+
+ // ^(0,c1) -> 0 or exception (depending on real value of c1)
+ if (ebasis.is_zero() && exponent_is_numerical) {
+ if ((num_exponent->real()).is_zero())
+ throw (std::domain_error("power::eval(): pow(0,I) is undefined"));
+ else if ((num_exponent->real()).is_negative())
+ throw (pole_error("power::eval(): division by zero",1));
+ else
+ return _ex0;
+ }
+
+ // ^(1,x) -> 1
+ if (ebasis.is_equal(_ex1))
+ return _ex1;
+
+ if (exponent_is_numerical) {
+
+ // ^(c1,c2) -> c1^c2 (c1, c2 numeric(),
+ // except if c1,c2 are rational, but c1^c2 is not)
+ if (basis_is_numerical) {
+ const bool basis_is_crational = num_basis->is_crational();
+ const bool exponent_is_crational = num_exponent->is_crational();
+ if (!basis_is_crational || !exponent_is_crational) {
+ // return a plain float
+ return (new numeric(num_basis->power(*num_exponent)))->setflag(status_flags::dynallocated |
+ status_flags::evaluated |
+ status_flags::expanded);
+ }
+
+ const numeric res = num_basis->power(*num_exponent);
+ if (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-q)<1, q integer
+ if (basis_is_crational && exponent_is_crational
+ && num_exponent->is_real()
+ && !num_exponent->is_integer()) {
+ const numeric n = num_exponent->numer();
+ const numeric m = num_exponent->denom();
+ numeric r;
+ numeric q = iquo(n, m, r);
+ if (r.is_negative()) {
+ r += m;
+ --q;
+ }
+ if (q.is_zero()) { // the exponent was in the allowed range 0<(n/m)<1
+ if (num_basis->is_rational() && !num_basis->is_integer()) {
+ // try it for numerator and denominator separately, in order to
+ // partially simplify things like (5/8)^(1/3) -> 1/2*5^(1/3)
+ const numeric bnum = num_basis->numer();
+ const numeric bden = num_basis->denom();
+ const numeric res_bnum = bnum.power(*num_exponent);
+ const numeric res_bden = bden.power(*num_exponent);
+ if (res_bnum.is_integer())
+ return (new mul(power(bden,-*num_exponent),res_bnum))->setflag(status_flags::dynallocated | status_flags::evaluated);
+ if (res_bden.is_integer())
+ return (new mul(power(bnum,*num_exponent),res_bden.inverse()))->setflag(status_flags::dynallocated | status_flags::evaluated);
+ }
+ return this->hold();
+ } else {
+ // assemble resulting product, but allowing for a re-evaluation,
+ // because otherwise we'll end up with something like
+ // (7/8)^(4/3) -> 7/8*(1/2*7^(1/3))
+ // instead of 7/16*7^(1/3).
+ ex prod = power(*num_basis,r.div(m));
+ return prod*power(*num_basis,q);
+ }
+ }
+ }
+
+ // ^(^(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 (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 (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.is_equal(_num_1)) {
+ 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) &&
+ are_ex_trivially_equal(eexponent,exponent)) {
+ return this->hold();
+ }
+ return (new power(ebasis, eexponent))->setflag(status_flags::dynallocated |
+ status_flags::evaluated);