refine.cpp

#include <symengine/refine.h>
 
namespace SymEngine
{
 
void RefineVisitor::bvisit(const Abs &x)
{
    auto farg = x.get_arg();
    auto newarg = apply(farg);
    if (is_true(is_nonnegative(*newarg, assumptions_))) {
        result_ = newarg;
    } else if (is_true(is_nonpositive(*newarg, assumptions_))) {
        result_ = neg(newarg);
    } else if (is_a<Conjugate>(*newarg)) {
        result_ = abs(down_cast<const Conjugate &>(*newarg).get_arg());
    } else {
        result_ = abs(newarg);
    }
}
 
void RefineVisitor::bvisit(const Sign &x)
{
    auto farg = x.get_arg();
    auto newarg = apply(farg);
    if (is_true(is_positive(*newarg, assumptions_))) {
        result_ = integer(1);
    } else if (is_true(is_negative(*newarg, assumptions_))) {
        result_ = integer(-1);
    } else if (is_true(is_zero(*newarg, assumptions_))) {
        result_ = integer(0);
    } else {
        result_ = sign(newarg);
    }
}
 
void RefineVisitor::bvisit(const Floor &x)
{
    auto farg = x.get_arg();
    auto newarg = apply(farg);
    if (is_true(is_integer(*newarg, assumptions_))) {
        result_ = newarg;
    } else if (could_extract_minus(*newarg)) {
        result_ = neg(ceiling(neg(newarg)));
    } else {
        result_ = floor(newarg);
    }
}
 
void RefineVisitor::bvisit(const Ceiling &x)
{
    auto farg = x.get_arg();
    auto newarg = apply(farg);
    if (is_true(is_integer(*newarg, assumptions_))) {
        result_ = newarg;
    } else if (could_extract_minus(*newarg)) {
        result_ = neg(floor(neg(newarg)));
    } else {
        result_ = ceiling(newarg);
    }
}
 
void RefineVisitor::bvisit(const Conjugate &x)
{
    auto farg = x.get_arg();
    auto newarg = apply(farg);
    if (is_true(is_real(*newarg, assumptions_))) {
        result_ = newarg;
    } else {
        result_ = conjugate(newarg);
    }
}
 
void RefineVisitor::bvisit(const Max &x)
{
    // positive > nonpositive
    // nonnegative and positive > negative
    vec_basic nonpositive;
    vec_basic negative;
    vec_basic keep;
    bool have_positive = false;
    bool have_nonnegative = false;
    for (auto arg : x.get_args()) {
        auto newarg = apply(arg);
        if (is_true(is_positive(*newarg, assumptions_))) {
            keep.push_back(newarg);
            have_positive = true;
        } else if (is_true(is_nonnegative(*newarg, assumptions_))) {
            keep.push_back(newarg);
            have_nonnegative = true;
        } else if (is_true(is_negative(*newarg, assumptions_))) {
            negative.push_back(newarg);
        } else if (is_true(is_nonpositive(*newarg, assumptions_))) {
            nonpositive.push_back(newarg);
        } else {
            keep.push_back(newarg);
        }
    }
    if (not have_positive and not nonpositive.empty()) {
        std::copy(nonpositive.begin(), nonpositive.end(),
                  std::back_inserter(keep));
    }
    if (not have_nonnegative and not have_positive and not negative.empty()) {
        std::copy(negative.begin(), negative.end(), std::back_inserter(keep));
    }
 
    result_ = max(keep);
}
 
void RefineVisitor::bvisit(const Min &x)
{
    // negative < nonnegative
    // nonpositive and negative < positive
    vec_basic nonnegative;
    vec_basic positive;
    vec_basic keep;
    bool have_negative = false;
    bool have_nonpositive = false;
    for (auto arg : x.get_args()) {
        auto newarg = apply(arg);
        if (is_true(is_negative(*newarg, assumptions_))) {
            keep.push_back(newarg);
            have_negative = true;
        } else if (is_true(is_nonpositive(*newarg, assumptions_))) {
            keep.push_back(newarg);
            have_nonpositive = true;
        } else if (is_true(is_positive(*newarg, assumptions_))) {
            positive.push_back(newarg);
        } else if (is_true(is_nonnegative(*newarg, assumptions_))) {
            nonnegative.push_back(newarg);
        } else {
            keep.push_back(newarg);
        }
    }
    if (not have_negative and not nonnegative.empty()) {
        std::copy(nonnegative.begin(), nonnegative.end(),
                  std::back_inserter(keep));
    }
    if (not have_nonpositive and not have_negative and not positive.empty()) {
        std::copy(positive.begin(), positive.end(), std::back_inserter(keep));
    }
 
    result_ = min(keep);
}
 
void RefineVisitor::bvisit(const Pow &x)
{
    auto exp = x.get_exp();
    auto newexp = apply(exp);
    auto base = x.get_base();
    auto newbase = apply(base);
    // Handle cases when (x**k)**n = x**(k*n) or = abs(x)**(k*n)
    if (is_a<Pow>(*newbase) and is_a_Number(*newexp)) {
        const Pow &inner_pow = down_cast<const Pow &>(*newbase);
        auto inner_exp = inner_pow.get_exp();
        auto inner_base = inner_pow.get_base();
        if (is_true(is_real(*inner_base, assumptions_))
            and is_a_Number(*inner_exp)
            and not down_cast<const Number &>(*inner_exp).is_complex()
            and not down_cast<const Number &>(*newexp).is_complex()) {
            if (is_true(is_positive(*inner_base, assumptions_))) {
                result_ = pow(inner_base, mul(newexp, inner_exp));
            } else {
                result_ = pow(abs(inner_base), mul(newexp, inner_exp));
            }
            return;
        }
    }
    result_ = pow(newbase, newexp);
}
 
void RefineVisitor::bvisit(const Log &x)
{
    auto farg = x.get_arg();
    auto newarg = apply(farg);
    if (is_a<Pow>(*newarg)) {
        auto base = down_cast<const Pow &>(*newarg).get_base();
        if (is_true(is_positive(*base, assumptions_))) {
            auto exp = down_cast<const Pow &>(*newarg).get_exp();
            if (is_true(is_real(*exp, assumptions_))) {
                result_ = mul(exp, log(base));
                return;
            }
        }
    } else if (is_a<Integer>(*newarg)) {
        auto base_exp = mp_perfect_power_decomposition(
            down_cast<const Integer &>(*newarg).as_integer_class());
        if (base_exp.second != 1) {
            result_ = mul(make_rcp<const Integer>(base_exp.second),
                          log(make_rcp<const Integer>(base_exp.first)));
            return;
        }
    }
    result_ = log(newarg);
}
 
void RefineVisitor::bvisit(const Interval &x)
{
    if (eq(*x.get_start(), *SymEngine::infty(-1))
        and eq(*x.get_end(), *SymEngine::infty(1))) {
        result_ = reals();
        return;
    }
    result_ = x.rcp_from_this();
}
 
RCP<const Basic> refine(const RCP<const Basic> &x,
                        const Assumptions *assumptions)
{
    RefineVisitor b(assumptions);
    return b.apply(x);
}
 
} // namespace SymEngine