// Mul (t^exp) to the dict "d"
void Mul::dict_add_term(map_basic_basic &d, const RCP<const Basic> &exp,
const RCP<const Basic> &t)
{
auto it = d.find(t);
if (it == d.end()) {
insert(d, t, exp);
} else {
// Very common case, needs to be fast:
if (is_a_Number(*it->second) && is_a_Number(*exp)) {
RCP<const Number> tmp = rcp_static_cast<const Number>(it->second);
iaddnum(outArg(tmp), rcp_static_cast<const Number>(exp));
if (tmp->is_zero()) {
d.erase(it);
} else {
it->second = tmp;
}
} else {
// General case:
it->second = add(it->second, exp);
if (is_a<Integer>(*it->second) &&
rcp_static_cast<const Integer>(it->second)->is_zero()) {
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(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> log(const RCP<const Basic> &arg)
{
if (eq(*arg, *zero)) {
throw NotImplementedError(
"log(0) is complex infinity. Yet to be implemented");
}
if (eq(*arg, *one))
return zero;
if (eq(*arg, *E))
return one;
if (is_a_Number(*arg)) {
RCP<const Number> _arg = rcp_static_cast<const Number>(arg);
if (not _arg->is_exact()) {
return _arg->get_eval().log(*_arg);
} else if (_arg->is_negative()) {
throw NotImplementedError(
"Imaginary Result. Yet to be implemented");
}
}
if (is_a<Rational>(*arg)) {
RCP<const Integer> num, den;
get_num_den(static_cast<const Rational &>(*arg), outArg(num),
outArg(den));
return sub(log(num), log(den));
}
return make_rcp<const Log>(arg);
}
void Mul::as_base_exp(const RCP<const Basic> &self, const Ptr<RCP<const Basic>> &exp,
const Ptr<RCP<const Basic>> &base)
{
if (is_a_Number(*self)) {
// Always ensure it is of form |num| > |den|
// in case of Integers den = 1
if (is_a<Rational>(*self)) {
RCP<const Rational> self_new = rcp_static_cast<const Rational>(self);
if (abs(self_new->i.get_num()) < abs(self_new->i.get_den())) {
*exp = minus_one;
*base = self_new->rdiv(*rcp_static_cast<const Number>(one));
} else {
*exp = one;
*base = self;
}
} else {
*exp = one;
*base = self;
}
} else if (is_a<Pow>(*self)) {
*exp = rcp_static_cast<const Pow>(self)->exp_;
*base = rcp_static_cast<const Pow>(self)->base_;
} else {
SYMENGINE_ASSERT(!is_a<Mul>(*self));
*exp = one;
*base = self;
}
}
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> Add::subs(const map_basic_basic &subs_dict) const
{
RCP<const Add> self = rcp_const_cast<Add>(rcp(this));
auto it = subs_dict.find(self);
if (it != subs_dict.end())
return it->second;
CSymPy::umap_basic_num d;
RCP<const Number> coef=coef_, coef2;
RCP<const Basic> t;
for (auto &p: dict_) {
RCP<const Basic> term = p.first->subs(subs_dict);
if (term == p.first) {
Add::dict_add_term(d, p.second, p.first);
} else if (is_a<Integer>(*term) &&
rcp_static_cast<const Integer>(term)->is_zero()) {
continue;
} else if (is_a_Number(*term)) {
iaddnum(outArg(coef),
mulnum(p.second, rcp_static_cast<const Number>(term)));
} else if (is_a<Add>(*term)) {
for (auto &q: (rcp_static_cast<const Add>(term))->dict_)
Add::dict_add_term(d, q.second, q.first);
iaddnum(outArg(coef), rcp_static_cast<const Add>(term)->coef_);
} else {
Add::as_coef_term(mul(p.second, term), outArg(coef2), outArg(t));
Add::dict_add_term(d, coef2, t);
}
}
return Add::from_dict(coef, std::move(d));
}
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));
}
static RCP<const Basic> diff(const Pow &self,
const RCP<const Symbol> &x) {
if (is_a_Number(*(self.get_exp())))
return mul(mul(self.get_exp(), pow(self.get_base(), sub(self.get_exp(), one))), self.get_base()->diff(x));
else
return mul(pow(self.get_base(), self.get_exp()), mul(self.get_exp(), log(self.get_base()))->diff(x));
}
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;
}
RCP<const Basic> Pow::diff(const RCP<const Symbol> &x) const
{
if (is_a_Number(*exp_))
return mul(mul(exp_, pow(base_, sub(exp_, one))), base_->diff(x));
else
return mul(pow(base_, exp_), mul(exp_, log(base_))->diff(x));
}
RCP<const Basic> add(const RCP<const Basic> &a, const RCP<const Basic> &b)
{
CSymPy::umap_basic_num d;
RCP<const Number> coef;
RCP<const Basic> t;
if (CSymPy::is_a<Add>(*a) && CSymPy::is_a<Add>(*b)) {
coef = (rcp_static_cast<const Add>(a))->coef_;
d = (rcp_static_cast<const Add>(a))->dict_;
for (auto &p: (rcp_static_cast<const Add>(b))->dict_)
Add::dict_add_term(d, p.second, p.first);
iaddnum(outArg(coef), rcp_static_cast<const Add>(b)->coef_);
} else if (CSymPy::is_a<Add>(*a)) {
coef = (rcp_static_cast<const Add>(a))->coef_;
d = (rcp_static_cast<const Add>(a))->dict_;
if (is_a_Number(*b)) {
iaddnum(outArg(coef), rcp_static_cast<const Number>(b));
} else {
RCP<const Number> coef2;
Add::as_coef_term(b, outArg(coef2), outArg(t));
Add::dict_add_term(d, coef2, t);
}
} else if (CSymPy::is_a<Add>(*b)) {
coef = (rcp_static_cast<const Add>(b))->coef_;
d = (rcp_static_cast<const Add>(b))->dict_;
if (is_a_Number(*a)) {
iaddnum(outArg(coef), rcp_static_cast<const Number>(a));
} else {
RCP<const Number> coef2;
Add::as_coef_term(a, outArg(coef2), outArg(t));
Add::dict_add_term(d, coef2, t);
}
} else {
Add::as_coef_term(a, outArg(coef), outArg(t));
Add::dict_add_term(d, coef, t);
Add::as_coef_term(b, outArg(coef), outArg(t));
Add::dict_add_term(d, coef, t);
auto it = d.find(one);
if (it == d.end()) {
coef = zero;
} else {
coef = it->second;
d.erase(it);
}
return Add::from_dict(coef, std::move(d));
}
return Add::from_dict(coef, std::move(d));
}
RCP<const Basic> expand(const RCP<const Basic> &self)
{
if (is_a<Symbol>(*self)) return self;
if (is_a_Number(*self)) return self;
if (is_a<Add>(*self)) return add_expand(rcp_static_cast<const Add>(self));
if (is_a<Mul>(*self)) return mul_expand(rcp_static_cast<const Mul>(self));
if (is_a<Pow>(*self)) return pow_expand(rcp_static_cast<const Pow>(self));
return self;
}
void bvisit(const Number &x)
{
if (not is_a_Number(*pow(the_base, x.rcp_from_this()))) {
if (x.is_positive())
gen_set[one] = x.rcp_from_this_cast<const Number>();
else
gen_set[minus_one]
= mulnum(x.rcp_from_this_cast<const Number>(), minus_one);
}
}
bool Log::is_canonical(const Basic &arg) const
{
// log(0)
if (is_a<Integer>(arg) and static_cast<const Integer &>(arg).is_zero())
return false;
// log(1)
if (is_a<Integer>(arg) and static_cast<const Integer &>(arg).is_one())
return false;
// log(E)
if (eq(arg, *E))
return false;
// Currently not implemented, however should be expanded as `-ipi +
// log(-arg)`
if (is_a_Number(arg) and static_cast<const Number &>(arg).is_negative())
return false;
if (is_a_Number(arg) and not static_cast<const Number &>(arg).is_exact())
return false;
// log(num/den) = log(num) - log(den)
if (is_a<Rational>(arg))
return false;
return true;
}
void Add::as_coef_term(const RCP<Basic> &self,
const Ptr<RCP<Number>> &coef, const Ptr<RCP<Basic>> &term)
{
if (is_a<Mul>(*self)) {
*coef = (rcp_static_cast<Mul>(self))->coef_;
*term = Mul::from_dict(one, (rcp_static_cast<Mul>(self))->dict_);
} else if (is_a_Number(*self)) {
*coef = rcp_static_cast<Number>(self);
*term = one;
} else {
*coef = one;
*term = self;
}
}
RCP<const Boolean> Interval::contains(const RCP<const Basic> &a) const
{
if (not is_a_Number(*a))
return make_rcp<Contains>(a, rcp_from_this_cast<const Set>());
if ((eq(*start_, *a) and left_open_) or (eq(*end_, *a) and right_open_))
return boolean(false);
if (eq(*start_, *a) or eq(*end_, *a))
return boolean(true);
if (eq(*min({end_, a}), *end_))
return boolean(false);
if (eq(*max({start_, a}), *start_))
return boolean(false);
return boolean(true);
}
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));
}
// Very quickly (!) creates the appropriate instance (i.e. Add, Symbol,
// Integer, Mul) depending on the size of the dictionary 'd'.
// If d.size() > 1 then it just returns Add. This means that the dictionary
// must be in canonical form already. For d.size == 1, it returns Mul, Pow,
// Symbol or Integer, depending on the expression.
RCP<Basic> Add::from_dict(const RCP<Number> &coef, const umap_basic_int &d)
{
if (d.size() == 0) {
return coef;
} else if (d.size() == 1 && coef->is_zero()) {
auto p = d.begin();
if (is_a<Integer>(*(p->second))) {
if (rcp_static_cast<Integer>(p->second)->is_zero()) {
return zero;
}
if (rcp_static_cast<Integer>(p->second)->is_one()) {
return p->first;
}
if (is_a<Mul>(*(p->first))) {
return Mul::from_dict(p->second,
rcp_static_cast<Mul>(p->first)->dict_);
}
map_basic_basic m;
if (is_a<Pow>(*(p->first))) {
insert(m, rcp_static_cast<Pow>(p->first)->base_,
rcp_static_cast<Pow>(p->first)->exp_);
} else {
insert(m, p->first, one);
}
return rcp(new Mul(p->second, m));
}
map_basic_basic m;
if (is_a_Number(*p->second)) {
if (is_a<Mul>(*(p->first))) {
return Mul::from_dict(p->second,
rcp_static_cast<Mul>(p->first)->dict_);
}
if (is_a<Pow>(*p->first)) {
insert(m, rcp_static_cast<Pow>(p->first)->base_,
rcp_static_cast<Pow>(p->first)->exp_);
} else {
insert(m, p->first, one);
}
return rcp(new Mul(p->second, m));
} else {
insert(m, p->first, one);
insert(m, p->second, one);
return rcp(new Mul(one, m));
}
} else {
return rcp(new Add(coef, d));
}
}
RCP<const Basic> pow(const RCP<const Basic> &a, const RCP<const Basic> &b)
{
if (eq(b, zero)) return one;
if (eq(b, one)) return a;
if (eq(a, zero)) return zero;
if (eq(a, one)) return one;
if (is_a_Number(*a) && is_a<Integer>(*b))
return pownum(rcp_static_cast<const Number>(a), rcp_static_cast<const Integer>(b));
if (is_a<Mul>(*a))
return rcp_static_cast<const Mul>(a)->power_all_terms(b);
if (is_a<Pow>(*a)) {
RCP<const Pow> A = rcp_static_cast<const Pow>(a);
return pow(A->base_, mul(A->exp_, b));
}
return rcp(new Pow(a, b));
}
void Add::as_coef_term(const RCP<const Basic> &self,
const Ptr<RCP<const Number>> &coef, const Ptr<RCP<const Basic>> &term)
{
if (is_a<Mul>(*self)) {
*coef = (rcp_static_cast<const Mul>(self))->coef_;
// We need to copy our 'dict_' here, as 'term' has to have its own.
map_basic_basic d2 = (rcp_static_cast<const Mul>(self))->dict_;
*term = Mul::from_dict(one, std::move(d2));
} else if (is_a_Number(*self)) {
*coef = rcp_static_cast<const Number>(self);
*term = one;
} else {
*coef = one;
*term = self;
}
}
RCP<const Basic> log(const RCP<const Basic> &arg)
{
if (eq(arg, zero)) {
throw std::runtime_error("log(0) is complex infinity. Yet to be implemented");
}
if (eq(arg, one)) return zero;
if (eq(arg, E)) return one;
if (is_a_Number(*arg) &&
rcp_static_cast<const Number>(arg)->is_negative()) {
throw std::runtime_error("Imaginary Result. Yet to be implemented");
}
if (is_a<Rational>(*arg)) {
RCP<const Integer> num, den;
get_num_den(rcp_static_cast<const Rational>(arg), outArg(num), outArg(den));
return sub(log(num), log(den));
}
return rcp(new Log(arg));
}
bool Log::is_canonical(const RCP<const Basic> &arg)
{
if (arg == null) return false;
// log(0)
if (is_a<Integer>(*arg) && rcp_static_cast<const Integer>(arg)->is_zero())
return false;
// log(1)
if (is_a<Integer>(*arg) && rcp_static_cast<const Integer>(arg)->is_one())
return false;
// log(E)
if (eq(arg, E))
return false;
// Currently not implemented, however should be expanded as `-ipi + log(-arg)`
if (is_a_Number(*arg) && rcp_static_cast<const Number>(arg)->is_negative())
return false;
// log(num/den) = log(num) - log(den)
if (is_a<Rational>(*arg))
return false;
return true;
}
void Add::coef_dict_add_term(const Ptr<RCP<const Number>> &coef, umap_basic_num &d,
const RCP<const Number> &c, const RCP<const Basic> &term)
{
if (is_a_Number(*term)) {
iaddnum(coef, mulnum(c, rcp_static_cast<const Number>(term)));
} else if (is_a<Add>(*term)) {
if (c->is_one()) {
for (const auto &q: (rcp_static_cast<const Add>(term))->dict_)
Add::dict_add_term(d, q.second, q.first);
iaddnum(coef, rcp_static_cast<const Add>(term)->coef_);
} else {
Add::dict_add_term(d, c, term);
}
} else {
RCP<const Number> coef2;
RCP<const Basic> t;
Add::as_coef_term(term, outArg(coef2), outArg(t));
Add::dict_add_term(d, mulnum(c, coef2), t);
}
}
void Mul::as_base_exp(const RCP<const Basic> &self, const Ptr<RCP<const Basic>> &exp,
const Ptr<RCP<const Basic>> &base)
{
if (is_a<Symbol>(*self)) {
*exp = one;
*base = self;
} else if (is_a_Number(*self)) {
// Always ensure it is of form |num| > |den|
// in case of Integers den = 1
if (is_a<Rational>(*self)) {
RCP<const Rational> self_new = rcp_static_cast<const Rational>(self);
if (abs(self_new->i.get_num()) < abs(self_new->i.get_den())) {
*exp = minus_one;
*base = self_new->rdiv(*rcp_static_cast<const Number>(one));
} else {
*exp = one;
*base = self;
}
} else {
*exp = one;
*base = self;
}
} else if (is_a<Pow>(*self)) {
*exp = rcp_static_cast<const Pow>(self)->exp_;
*base = rcp_static_cast<const Pow>(self)->base_;
} else if (is_a<Add>(*self)) {
*exp = one;
*base = self;
} else if (is_a<Log>(*self)) {
*exp = one;
*base = self;
} else if (is_a_sub<Function>(*self)) {
*exp = one;
*base = self;
} else {
std::cout << "as_base_exp: " << *self << std::endl;
throw std::runtime_error("Not implemented yet.");
}
}
RCP<const Basic> Add::diff(const RCP<const Symbol> &x) const
{
CSymPy::umap_basic_num d;
RCP<const Number> coef=zero, coef2;
RCP<const Basic> t;
for (auto &p: dict_) {
RCP<const Basic> term = p.first->diff(x);
if (is_a<Integer>(*term) && rcp_static_cast<const Integer>(term)->is_zero()) {
continue;
} else if (is_a_Number(*term)) {
iaddnum(outArg(coef),
mulnum(p.second, rcp_static_cast<const Number>(term)));
} else if (is_a<Add>(*term)) {
for (auto &q: (rcp_static_cast<const Add>(term))->dict_)
Add::dict_add_term(d, q.second, q.first);
iaddnum(outArg(coef), rcp_static_cast<const Add>(term)->coef_);
} else {
Add::as_coef_term(mul(p.second, term), outArg(coef2), outArg(t));
Add::dict_add_term(d, coef2, t);
}
}
return Add::from_dict(coef, std::move(d));
}
// Very quickly (!) creates the appropriate instance (i.e. Add, Symbol,
// Integer, Mul) depending on the size of the dictionary 'd'.
// If d.size() > 1 then it just returns Add. This means that the dictionary
// must be in canonical form already. For d.size == 1, it returns Mul, Pow,
// Symbol or Integer, depending on the expression.
RCP<const Basic> Add::from_dict(const RCP<const Number> &coef, umap_basic_num &&d)
{
if (d.size() == 0) {
return coef;
} else if (d.size() == 1 && coef->is_zero()) {
auto p = d.begin();
if (is_a<Integer>(*(p->second))) {
if (rcp_static_cast<const Integer>(p->second)->is_zero()) {
return zero;
}
if (rcp_static_cast<const Integer>(p->second)->is_one()) {
return p->first;
}
if (is_a<Mul>(*(p->first))) {
#if !defined(WITH_CSYMPY_THREAD_SAFE) && defined(WITH_CSYMPY_RCP)
if (rcp_static_cast<const Mul>(p->first)->refcount_ == 1) {
// We can steal the dictionary:
// Cast away const'ness, so that we can move 'dict_', since
// 'p->first' will be destroyed when 'd' is at the end of
// this function, so we "steal" its dict_ to avoid an
// unnecessary copy. We know the refcount_ is one, so
// nobody else is using the Mul except us.
const map_basic_basic &d2 =
rcp_static_cast<const Mul>(p->first)->dict_;
map_basic_basic &d3 = const_cast<map_basic_basic &>(d2);
return Mul::from_dict(p->second, std::move(d3));
} else {
#else
{
#endif
// We need to copy the dictionary:
map_basic_basic d2 =
rcp_static_cast<const Mul>(p->first)->dict_;
return Mul::from_dict(p->second, std::move(d2));
}
}
map_basic_basic m;
if (is_a<Pow>(*(p->first))) {
insert(m, rcp_static_cast<const Pow>(p->first)->base_,
rcp_static_cast<const Pow>(p->first)->exp_);
} else {
insert(m, p->first, one);
}
return rcp(new Mul(p->second, std::move(m)));
}
map_basic_basic m;
if (is_a_Number(*p->second)) {
if (is_a<Mul>(*(p->first))) {
#if !defined(WITH_CSYMPY_THREAD_SAFE) && defined(WITH_CSYMPY_RCP)
if (rcp_static_cast<const Mul>(p->first)->refcount_ == 1) {
// We can steal the dictionary:
// Cast away const'ness, so that we can move 'dict_', since
// 'p->first' will be destroyed when 'd' is at the end of
// this function, so we "steal" its dict_ to avoid an
// unnecessary copy. We know the refcount_ is one, so
// nobody else is using the Mul except us.
const map_basic_basic &d2 =
rcp_static_cast<const Mul>(p->first)->dict_;
map_basic_basic &d3 = const_cast<map_basic_basic &>(d2);
return Mul::from_dict(p->second, std::move(d3));
} else {
#else
{
#endif
// We need to copy the dictionary:
map_basic_basic d2 =
rcp_static_cast<const Mul>(p->first)->dict_;
return Mul::from_dict(p->second, std::move(d2));
}
}
if (is_a<Pow>(*p->first)) {
insert(m, rcp_static_cast<const Pow>(p->first)->base_,
rcp_static_cast<const Pow>(p->first)->exp_);
} else {
insert(m, p->first, one);
}
return rcp(new Mul(p->second, std::move(m)));
} else {
insert(m, p->first, one);
insert(m, p->second, one);
return rcp(new Mul(one, std::move(m)));
}
} else {
return rcp(new Add(coef, std::move(d)));
}
}
// Adds (coef*t) to the dict "d"
// Assumption: "t" does not have any numerical coefficients, those are in "coef"
void Add::dict_add_term(umap_basic_num &d, const RCP<const Number> &coef,
const RCP<const Basic> &t)
{
auto it = d.find(t);
if (it == d.end()) {
// Not found, add it in if it is nonzero:
if (!(coef->is_zero())) insert(d, t, coef);
} else {
iaddnum(outArg(it->second), coef);
if (it->second->is_zero()) d.erase(it);
}
}
RCP<const Basic> pow(const RCP<const Basic> &a, const RCP<const Basic> &b)
{
if (eq(b, zero)) return one;
if (eq(b, one)) return a;
if (eq(a, zero)) return zero;
if (eq(a, one)) return one;
if (eq(a, minus_one)) {
if (is_a<Integer>(*b)) {
return is_a<Integer>(*div(b, integer(2))) ? one : minus_one;
} else if (is_a<Rational>(*b) &&
(rcp_static_cast<const Rational>(b)->i.get_num() == 1) &&
(rcp_static_cast<const Rational>(b)->i.get_den() == 2)) {
return I;
}
}
if (is_a_Number(*a) && is_a_Number(*b)) {
if (is_a<Integer>(*b)) {
if (is_a<Rational>(*a)) {
RCP<const Rational> exp_new = rcp_static_cast<const Rational>(a);
return exp_new->powrat(*rcp_static_cast<const Integer>(b));
} else if (is_a<Integer>(*a)) {
RCP<const Integer> exp_new = rcp_static_cast<const Integer>(a);
return exp_new->powint(*rcp_static_cast<const Integer>(b));
} else if (is_a<Complex>(*a)) {
RCP<const Complex> exp_new = rcp_static_cast<const Complex>(a);
RCP<const Integer> pow_new = rcp_static_cast<const Integer>(b);
RCP<const Number> res = exp_new->pow(*pow_new);
return res;
} else {
throw std::runtime_error("Not implemented");
}
} else if (is_a<Rational>(*b)) {
mpz_class q, r, num, den;
num = rcp_static_cast<const Rational>(b)->i.get_num();
den = rcp_static_cast<const Rational>(b)->i.get_den();
if (num > den || num < 0) {
mpz_fdiv_qr(q.get_mpz_t(), r.get_mpz_t(), num.get_mpz_t(),
den.get_mpz_t());
} else {
return rcp(new Pow(a, b));
}
// Here we make the exponent postive and a fraction between
// 0 and 1. We multiply numerator and denominator appropriately
// to achieve this
if (is_a<Rational>(*a)) {
RCP<const Rational> exp_new = rcp_static_cast<const Rational>(a);
RCP<const Basic> frac =
div(exp_new->powrat(Integer(q)), integer(exp_new->i.get_den()));
RCP<const Basic> surds =
mul(rcp(new Pow(integer(exp_new->i.get_num()), div(integer(r), integer(den)))),
rcp(new Pow(integer(exp_new->i.get_den()), sub(one, div(integer(r), integer(den))))));
return mul(frac, surds);
} else if (is_a<Integer>(*a)) {
RCP<const Integer> exp_new = rcp_static_cast<const Integer>(a);
RCP<const Number> frac = exp_new->powint(Integer(q));
map_basic_basic surd;
if ((exp_new->is_negative()) && (2 * r == den)) {
frac = mulnum(frac, I);
exp_new = exp_new->mulint(*minus_one);
// if exp_new is one, no need to add it to dict
if (exp_new->is_one())
return frac;
surd[exp_new] = div(integer(r), integer(den));
} else {
surd[exp_new] = div(integer(r), integer(den));
}
return rcp(new Mul(frac, std::move(surd)));
} else if (is_a<Complex>(*a)) {
return rcp(new Pow(a, b));
} else {
throw std::runtime_error("Not implemented");
}
} else if (is_a<Complex>(*b)) {
return rcp(new Pow(a, b));
} else {
throw std::runtime_error("Not implemented");
}
}
if (is_a<Mul>(*a) && is_a<Integer>(*b)) {
// Convert (x*y)^b = x^b*y^b, where 'b' is an integer. This holds for
// any complex 'x', 'y' and integer 'b'.
return rcp_static_cast<const Mul>(a)->power_all_terms(b);
}
if (is_a<Pow>(*a) && is_a<Integer>(*b)) {
// Convert (x^y)^b = x^(b*y), where 'b' is an integer. This holds for
// any complex 'x', 'y' and integer 'b'.
RCP<const Pow> A = rcp_static_cast<const Pow>(a);
return pow(A->base_, mul(A->exp_, b));
}
return rcp(new Pow(a, b));
}
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;
}