Пример #1
0
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;
}
Пример #2
0
 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));
 }
Пример #3
0
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));
}
Пример #4
0
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));
}
Пример #5
0
// 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);
                }
            }
        }
    }
}
Пример #6
0
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)));
    }
}
Пример #7
0
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));
}
Пример #8
0
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;
}
Пример #9
0
// 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))));
                }
            }
        }
    }
}