RCP<const Basic> Mul::diff(const RCP<const Symbol> &x) const
{
RCP<const Basic> r=zero;
for (auto &p: dict_) {
RCP<const Number> coef = coef_;
RCP<const Basic> factor = pow(p.first, p.second)->diff(x);
if (is_a<Integer>(*factor) &&
rcp_static_cast<const Integer>(factor)->is_zero()) continue;
map_basic_basic d = dict_;
d.erase(p.first);
if (is_a_Number(*factor)) {
imulnum(outArg(coef), rcp_static_cast<const Number>(factor));
} else if (is_a<Mul>(*factor)) {
RCP<const Mul> tmp = rcp_static_cast<const Mul>(factor);
imulnum(outArg(coef), tmp->coef_);
for (auto &q: tmp->dict_) {
Mul::dict_add_term_new(outArg(coef), d, q.second, q.first);
}
} else {
RCP<const Basic> exp, t;
Mul::as_base_exp(factor, outArg(exp), outArg(t));
Mul::dict_add_term_new(outArg(coef), d, exp, t);
}
// TODO: speed this up:
r = add(r, Mul::from_dict(coef, std::move(d)));
}
return r;
}
static RCP<const Basic> diff(const Mul &self,
const RCP<const Symbol> &x) {
RCP<const Number> overall_coef = zero;
umap_basic_num add_dict;
for (auto &p: self.dict_) {
RCP<const Number> coef = self.coef_;
RCP<const Basic> factor = pow(p.first, p.second)->diff(x);
if (is_a<Integer>(*factor) &&
rcp_static_cast<const Integer>(factor)->is_zero()) continue;
map_basic_basic d = self.dict_;
d.erase(p.first);
if (is_a_Number(*factor)) {
imulnum(outArg(coef), rcp_static_cast<const Number>(factor));
} else if (is_a<Mul>(*factor)) {
RCP<const Mul> tmp = rcp_static_cast<const Mul>(factor);
imulnum(outArg(coef), tmp->coef_);
for (auto &q: tmp->dict_) {
Mul::dict_add_term_new(outArg(coef), d, q.second, q.first);
}
} else {
RCP<const Basic> exp, t;
Mul::as_base_exp(factor, outArg(exp), outArg(t));
Mul::dict_add_term_new(outArg(coef), d, exp, t);
}
if (d.size() == 0) {
iaddnum(outArg(overall_coef), coef);
} else {
RCP<const Basic> mul = Mul::from_dict(one, std::move(d));
Add::dict_add_term(add_dict, coef, mul);
}
}
return Add::from_dict(overall_coef, std::move(add_dict));
}
RCP<const Basic> Mul::subs(const map_basic_basic &subs_dict) const
{
RCP<const Mul> self = rcp_const_cast<Mul>(rcp(this));
auto it = subs_dict.find(self);
if (it != subs_dict.end())
return it->second;
RCP<const Number> coef = coef_;
map_basic_basic d;
for (auto &p: dict_) {
RCP<const Basic> factor_old = pow(p.first, p.second);
RCP<const Basic> factor = factor_old->subs(subs_dict);
if (factor == factor_old) {
Mul::dict_add_term_new(outArg(coef), d, p.second, p.first);
} else if (is_a<Integer>(*factor) &&
rcp_static_cast<const Integer>(factor)->is_zero()) {
return zero;
} else if (is_a_Number(*factor)) {
imulnum(outArg(coef), rcp_static_cast<const Number>(factor));
} else if (is_a<Mul>(*factor)) {
RCP<const Mul> tmp = rcp_static_cast<const Mul>(factor);
imulnum(outArg(coef), tmp->coef_);
for (auto &q: tmp->dict_) {
Mul::dict_add_term_new(outArg(coef), d, q.second, q.first);
}
} else {
RCP<const Basic> exp, t;
Mul::as_base_exp(factor, outArg(exp), outArg(t));
Mul::dict_add_term_new(outArg(coef), d, exp, t);
}
}
return Mul::from_dict(coef, std::move(d));
}
RCP<const Basic> mul(const RCP<const Basic> &a, const RCP<const Basic> &b)
{
SymEngine::map_basic_basic d;
RCP<const Number> coef = one;
if (SymEngine::is_a<Mul>(*a) && SymEngine::is_a<Mul>(*b)) {
RCP<const Mul> A = rcp_static_cast<const Mul>(a);
RCP<const Mul> B = rcp_static_cast<const Mul>(b);
// This is important optimization, as coef=1 if Mul is inside an Add.
// To further speed this up, the upper level code could tell us that we
// are inside an Add, then we don't even have can simply skip the
// following two lines.
if (!(A->coef_->is_one()) || !(B->coef_->is_one()))
coef = mulnum(A->coef_, B->coef_);
d = A->dict_;
for (auto &p: B->dict_)
Mul::dict_add_term_new(outArg(coef), d, p.second, p.first);
} else if (SymEngine::is_a<Mul>(*a)) {
RCP<const Basic> exp;
RCP<const Basic> t;
coef = (rcp_static_cast<const Mul>(a))->coef_;
d = (rcp_static_cast<const Mul>(a))->dict_;
if (is_a_Number(*b)) {
imulnum(outArg(coef), rcp_static_cast<const Number>(b));
} else {
Mul::as_base_exp(b, outArg(exp), outArg(t));
Mul::dict_add_term_new(outArg(coef), d, exp, t);
}
} else if (SymEngine::is_a<Mul>(*b)) {
RCP<const Basic> exp;
RCP<const Basic> t;
coef = (rcp_static_cast<const Mul>(b))->coef_;
d = (rcp_static_cast<const Mul>(b))->dict_;
if (is_a_Number(*a)) {
imulnum(outArg(coef), rcp_static_cast<const Number>(a));
} else {
Mul::as_base_exp(a, outArg(exp), outArg(t));
Mul::dict_add_term_new(outArg(coef), d, exp, t);
}
} else {
RCP<const Basic> exp;
RCP<const Basic> t;
if (is_a_Number(*a)) {
imulnum(outArg(coef), rcp_static_cast<const Number>(a));
} else {
Mul::as_base_exp(a, outArg(exp), outArg(t));
Mul::dict_add_term_new(outArg(coef), d, exp, t);
}
if (is_a_Number(*b)) {
imulnum(outArg(coef), rcp_static_cast<const Number>(b));
} else {
Mul::as_base_exp(b, outArg(exp), outArg(t));
Mul::dict_add_term_new(outArg(coef), d, exp, t);
}
}
return Mul::from_dict(coef, std::move(d));
}
// Mul (t^exp) to the dict "d"
void Mul::dict_add_term_new(const Ptr<RCP<const Number>> &coef, map_basic_basic &d,
const RCP<const Basic> &exp, const RCP<const Basic> &t)
{
auto it = d.find(t);
if (it == d.end()) {
// Don't check for `exp = 0` here
// `pow` for Complex is not expanded by default
if (is_a<Integer>(*exp) && (is_a<Integer>(*t) || is_a<Rational>(*t))) {
imulnum(outArg(*coef), pownum(rcp_static_cast<const Number>(t),
rcp_static_cast<const Number>(exp)));
} else if (is_a<Integer>(*exp) && is_a<Complex>(*t)) {
if (rcp_static_cast<const Integer>(exp)->is_one()) {
imulnum(outArg(*coef), rcp_static_cast<const Number>(t));
} else if (rcp_static_cast<const Integer>(exp)->is_minus_one()) {
idivnum(outArg(*coef), rcp_static_cast<const Number>(t));
} else {
insert(d, t, exp);
}
} else {
insert(d, t, exp);
}
} else {
// Very common case, needs to be fast:
if (is_a_Number(*exp) && is_a_Number(*it->second)) {
RCP<const Number> tmp = rcp_static_cast<const Number>(it->second);
iaddnum(outArg(tmp),
rcp_static_cast<const Number>(exp));
it->second = tmp;
}
else
it->second = add(it->second, exp);
if (is_a<Integer>(*it->second)) {
// `pow` for Complex is not expanded by default
if (is_a<Integer>(*t) || is_a<Rational>(*t)) {
if (!rcp_static_cast<const Integer>(it->second)->is_zero()) {
imulnum(outArg(*coef), pownum(rcp_static_cast<const Number>(t),
rcp_static_cast<const Number>(it->second)));
}
d.erase(it);
} else if (rcp_static_cast<const Integer>(it->second)->is_zero()) {
d.erase(it);
} else if (is_a<Complex>(*t)) {
if (rcp_static_cast<const Integer>(it->second)->is_one()) {
imulnum(outArg(*coef), rcp_static_cast<const Number>(t));
d.erase(it);
} else if (rcp_static_cast<const Integer>(it->second)->is_minus_one()) {
idivnum(outArg(*coef), rcp_static_cast<const Number>(t));
d.erase(it);
}
}
}
}
}
RCP<const Basic> Mul::power_all_terms(const RCP<const Basic> &exp) const
{
CSymPy::map_basic_basic d;
RCP<const Basic> new_coef = pow(coef_, exp);
RCP<const Number> coef_num = one;
RCP<const Basic> new_exp;
for (auto &p: dict_) {
new_exp = mul(p.second, exp);
if (is_a_Number(*new_exp)) {
// No need for additional dict checks here.
// The dict should be of standard form before this is
// called.
if (rcp_static_cast<const Number>(new_exp)->is_zero()) {
continue;
} else {
Mul::dict_add_term_new(outArg(coef_num), d, new_exp, p.first);
}
} else {
Mul::dict_add_term_new(outArg(coef_num), d, new_exp, p.first);
}
}
if (is_a_Number(*new_coef)) {
imulnum(outArg(coef_num), rcp_static_cast<const Number>(new_coef));
return Mul::from_dict(coef_num, std::move(d));
} else {
// TODO: this can be made faster probably:
return mul(mul(new_coef, coef_num), Mul::from_dict(one, std::move(d)));
}
}
RCP<const Basic> Mul::power_all_terms(const RCP<const Basic> &exp) const
{
SymEngine::map_basic_basic d;
RCP<const Basic> new_coef = pow(coef_, exp);
RCP<const Number> coef_num = one;
RCP<const Basic> new_exp;
for (auto &p: dict_) {
new_exp = mul(p.second, exp);
if (is_a_Number(*new_exp)) {
// No need for additional dict checks here.
// The dict should be of standard form before this is
// called.
if (rcp_static_cast<const Number>(new_exp)->is_zero()) {
continue;
} else {
Mul::dict_add_term_new(outArg(coef_num), d, new_exp, p.first);
}
} else {
Mul::dict_add_term_new(outArg(coef_num), d, new_exp, p.first);
}
}
if (is_a_Number(*new_coef)) {
imulnum(outArg(coef_num), rcp_static_cast<const Number>(new_coef));
} else if (is_a<Mul>(*new_coef)) {
RCP<const Mul> tmp = rcp_static_cast<const Mul>(new_coef);
imulnum(outArg(coef_num), tmp->coef_);
for (auto &q: tmp->dict_) {
Mul::dict_add_term_new(outArg(coef_num), d, q.second, q.first);
}
} else {
RCP<const Basic> _exp, t;
Mul::as_base_exp(new_coef, outArg(_exp), outArg(t));
Mul::dict_add_term_new(outArg(coef_num), d, _exp, t);
}
return Mul::from_dict(coef_num, std::move(d));
}
RCP<const Basic> pow_expand(const RCP<const Pow> &self)
{
RCP<const Basic> _base = expand(self->base_);
bool negative_pow = false;
if (! is_a<Integer>(*self->exp_) || ! is_a<Add>(*_base)) {
if (neq(_base, self->base_)) {
return pow(_base, self->exp_);
} else {
return self;
}
}
map_vec_mpz r;
int n = rcp_static_cast<const Integer>(self->exp_)->as_int();
if (n < 0) {
n = -n;
negative_pow = true;
}
RCP<const Add> base = rcp_static_cast<const Add>(_base);
umap_basic_num base_dict = base->dict_;
if (! (base->coef_->is_zero())) {
// Add the numerical coefficient into the dictionary. This
// allows a little bit easier treatment below.
insert(base_dict, base->coef_, one);
}
int m = base_dict.size();
multinomial_coefficients_mpz(m, n, r);
umap_basic_num rd;
// This speeds up overall expansion. For example for the benchmark
// (y + x + z + w)^60 it improves the timing from 135ms to 124ms.
rd.reserve(2*r.size());
RCP<const Number> add_overall_coeff=zero;
for (auto &p: r) {
auto power = p.first.begin();
auto i2 = base_dict.begin();
map_basic_basic d;
RCP<const Number> overall_coeff=one;
for (; power != p.first.end(); ++power, ++i2) {
if (*power > 0) {
RCP<const Integer> exp = rcp(new Integer(*power));
RCP<const Basic> base = i2->first;
if (is_a<Integer>(*base)) {
imulnum(outArg(overall_coeff),
rcp_static_cast<const Number>(
rcp_static_cast<const Integer>(base)->powint(*exp)));
} else if (is_a<Symbol>(*base)) {
Mul::dict_add_term(d, exp, base);
} else {
RCP<const Basic> exp2, t, tmp;
tmp = pow(base, exp);
if (is_a<Mul>(*tmp)) {
for (auto &p: (rcp_static_cast<const Mul>(tmp))->dict_) {
Mul::dict_add_term_new(outArg(overall_coeff), d,
p.second, p.first);
}
imulnum(outArg(overall_coeff), (rcp_static_cast<const Mul>(tmp))->coef_);
} else {
Mul::as_base_exp(tmp, outArg(exp2), outArg(t));
Mul::dict_add_term_new(outArg(overall_coeff), d, exp2, t);
}
}
if (!(i2->second->is_one())) {
if (is_a<Integer>(*(i2->second)) || is_a<Rational>(*(i2->second))) {
imulnum(outArg(overall_coeff),
pownum(i2->second,
rcp_static_cast<const Number>(exp)));
} else if (is_a<Complex>(*(i2->second))) {
RCP<const Number> tmp = rcp_static_cast<const Complex>(i2->second)->pow(*exp);
imulnum(outArg(overall_coeff), tmp);
}
}
}
}
RCP<const Basic> term = Mul::from_dict(overall_coeff, std::move(d));
RCP<const Number> coef2 = rcp(new Integer(p.second));
if (is_a_Number(*term)) {
iaddnum(outArg(add_overall_coeff),
mulnum(rcp_static_cast<const Number>(term), coef2));
} else {
if (is_a<Mul>(*term) &&
!(rcp_static_cast<const Mul>(term)->coef_->is_one())) {
// Tidy up things like {2x: 3} -> {x: 6}
imulnum(outArg(coef2),
rcp_static_cast<const Mul>(term)->coef_);
// We make a copy of the dict_:
map_basic_basic d2 = rcp_static_cast<const Mul>(term)->dict_;
term = Mul::from_dict(one, std::move(d2));
}
Add::dict_add_term(rd, coef2, term);
}
}
RCP<const Basic> result = Add::from_dict(add_overall_coeff, std::move(rd));
if (negative_pow) result = pow(result, minus_one);
return result;
}
// Mul (t**exp) to the dict "d"
void Mul::dict_add_term_new(const Ptr<RCP<const Number>> &coef, map_basic_basic &d,
const RCP<const Basic> &exp, const RCP<const Basic> &t)
{
auto it = d.find(t);
if (it == d.end()) {
// Don't check for `exp = 0` here
// `pow` for Complex is not expanded by default
if (is_a<Integer>(*t) || is_a<Rational>(*t)) {
if (is_a<Integer>(*exp)) {
imulnum(outArg(*coef), pownum(rcp_static_cast<const Number>(t),
rcp_static_cast<const Number>(exp)));
} else if (is_a<Rational>(*exp)) {
// Here we make the exponent postive and a fraction between
// 0 and 1.
mpz_class q, r, num, den;
num = rcp_static_cast<const Rational>(exp)->i.get_num();
den = rcp_static_cast<const Rational>(exp)->i.get_den();
mpz_fdiv_qr(q.get_mpz_t(), r.get_mpz_t(), num.get_mpz_t(),
den.get_mpz_t());
insert(d, t, Rational::from_mpq(mpq_class(r, den)));
imulnum(outArg(*coef), pownum(rcp_static_cast<const Number>(t),
rcp_static_cast<const Number>(integer(q))));
} else {
insert(d, t, exp);
}
} else if (is_a<Integer>(*exp) && is_a<Complex>(*t)) {
if (rcp_static_cast<const Integer>(exp)->is_one()) {
imulnum(outArg(*coef), rcp_static_cast<const Number>(t));
} else if (rcp_static_cast<const Integer>(exp)->is_minus_one()) {
idivnum(outArg(*coef), rcp_static_cast<const Number>(t));
} else {
insert(d, t, exp);
}
} else {
insert(d, t, exp);
}
} else {
// Very common case, needs to be fast:
if (is_a_Number(*exp) && is_a_Number(*it->second)) {
RCP<const Number> tmp = rcp_static_cast<const Number>(it->second);
iaddnum(outArg(tmp),
rcp_static_cast<const Number>(exp));
it->second = tmp;
}
else
it->second = add(it->second, exp);
if (is_a<Integer>(*it->second)) {
// `pow` for Complex is not expanded by default
if (is_a<Integer>(*t) || is_a<Rational>(*t)) {
if (!rcp_static_cast<const Integer>(it->second)->is_zero()) {
imulnum(outArg(*coef), pownum(rcp_static_cast<const Number>(t),
rcp_static_cast<const Number>(it->second)));
}
d.erase(it);
} else if (rcp_static_cast<const Integer>(it->second)->is_zero()) {
d.erase(it);
} else if (is_a<Complex>(*t)) {
if (rcp_static_cast<const Integer>(it->second)->is_one()) {
imulnum(outArg(*coef), rcp_static_cast<const Number>(t));
d.erase(it);
} else if (rcp_static_cast<const Integer>(it->second)->is_minus_one()) {
idivnum(outArg(*coef), rcp_static_cast<const Number>(t));
d.erase(it);
}
}
} else if (is_a<Rational>(*it->second)) {
if (is_a_Number(*t)) {
mpz_class q, r, num, den;
num = rcp_static_cast<const Rational>(it->second)->i.get_num();
den = rcp_static_cast<const Rational>(it->second)->i.get_den();
// Here we make the exponent postive and a fraction between
// 0 and 1.
if (num > den || num < 0) {
mpz_fdiv_qr(q.get_mpz_t(), r.get_mpz_t(), num.get_mpz_t(),
den.get_mpz_t());
it->second = Rational::from_mpq(mpq_class(r, den));
imulnum(outArg(*coef), pownum(rcp_static_cast<const Number>(t),
rcp_static_cast<const Number>(integer(q))));
}
}
}
}
}