rewrite.cpp

#include <symengine/visitor.h>
#include <symengine/basic.h>
 
namespace SymEngine
{
 
class RewriteAsExp : public BaseVisitor<RewriteAsExp, TransformVisitor>
{
public:
    using TransformVisitor::bvisit;
 
    RewriteAsExp() : BaseVisitor<RewriteAsExp, TransformVisitor>() {}
 
    void bvisit(const Sin &x)
    {
        auto farg = x.get_arg();
        auto newarg = apply(farg);
        auto expo = mul(I, newarg);
        auto a = exp(expo);
        auto b = exp(neg(expo));
        result_ = div(sub(a, b), mul(integer(2), I));
    }
 
    void bvisit(const Cos &x)
    {
        auto farg = x.get_arg();
        auto newarg = apply(farg);
        auto expo = mul(I, newarg);
        auto a = exp(expo);
        auto b = exp(neg(expo));
        result_ = div(add(a, b), integer(2));
    }
 
    void bvisit(const Tan &x)
    {
        auto farg = x.get_arg();
        auto newarg = apply(farg);
        auto expo = mul(I, newarg);
        auto a = exp(expo);
        auto b = exp(neg(expo));
        result_ = div(sub(a, b), mul(I, add(a, b)));
    }
 
    void bvisit(const Cot &x)
    {
        auto farg = x.get_arg();
        auto newarg = apply(farg);
        auto expo = mul(I, newarg);
        auto a = exp(expo);
        auto b = exp(neg(expo));
        result_ = div(mul(I, add(a, b)), sub(a, b));
    }
 
    void bvisit(const Csc &x)
    {
        auto farg = x.get_arg();
        auto newarg = apply(farg);
        auto expo = mul(I, newarg);
        auto a = exp(expo);
        auto b = exp(neg(expo));
        result_ = div(mul(I, integer(2)), sub(a, b));
    }
 
    void bvisit(const Sec &x)
    {
        auto farg = x.get_arg();
        auto newarg = apply(farg);
        auto expo = mul(I, newarg);
        auto a = exp(expo);
        auto b = exp(neg(expo));
        result_ = div(integer(2), add(a, b));
    }
 
    void bvisit(const Sinh &x)
    {
        auto farg = x.get_arg();
        auto newarg = apply(farg);
        result_ = div(sub(exp(newarg), exp(neg(newarg))), integer(2));
    }
 
    void bvisit(const Cosh &x)
    {
        auto farg = x.get_arg();
        auto newarg = apply(farg);
        result_ = div(add(exp(newarg), exp(neg(newarg))), integer(2));
    }
 
    void bvisit(const Tanh &x)
    {
        auto farg = x.get_arg();
        auto newarg = apply(farg);
        auto pos_exp = exp(newarg);
        auto neg_exp = exp(neg(newarg));
        result_ = div(sub(pos_exp, neg_exp), add(pos_exp, neg_exp));
    }
 
    void bvisit(const Csch &x)
    {
        auto farg = x.get_arg();
        auto newarg = apply(farg);
        auto pos_exp = exp(newarg);
        auto neg_exp = exp(neg(newarg));
        result_ = div(integer(2), sub(pos_exp, neg_exp));
    }
 
    void bvisit(const Sech &x)
    {
        auto farg = x.get_arg();
        auto newarg = apply(farg);
        auto pos_exp = exp(newarg);
        auto neg_exp = exp(neg(newarg));
        result_ = div(integer(2), add(pos_exp, neg_exp));
    }
 
    void bvisit(const Coth &x)
    {
        auto farg = x.get_arg();
        auto newarg = apply(farg);
        auto pos_exp = exp(newarg);
        auto neg_exp = exp(neg(newarg));
        result_ = div(add(pos_exp, neg_exp), sub(pos_exp, neg_exp));
    }
};
 
RCP<const Basic> rewrite_as_exp(const RCP<const Basic> &x)
{
    RewriteAsExp b;
    return b.apply(x);
}
 
class RewriteAsSin : public BaseVisitor<RewriteAsSin, TransformVisitor>
{
public:
    using TransformVisitor::bvisit;
 
    RewriteAsSin() : BaseVisitor<RewriteAsSin, TransformVisitor>() {}
 
    void bvisit(const Cos &x)
    {
        auto farg = x.get_arg();
        auto newarg = apply(farg);
        result_ = sin(unevaluated_expr(add(newarg, div(pi, integer(2)))));
    }
 
    void bvisit(const Tan &x)
    {
        auto farg = x.get_arg();
        auto newarg = apply(farg);
        result_ = div(mul(integer(2), pow(sin(newarg), integer(2))),
                      sin(mul(integer(2), newarg)));
    }
 
    void bvisit(const Cot &x)
    {
        auto farg = x.get_arg();
        auto newarg = apply(farg);
        result_ = div(sin(mul(integer(2), newarg)),
                      mul(integer(2), pow(sin(newarg), integer(2))));
    }
 
    void bvisit(const Csc &x)
    {
        auto farg = x.get_arg();
        auto newarg = apply(farg);
        result_ = div(integer(1), sin(newarg));
    }
 
    void bvisit(const Sec &x)
    {
        auto farg = x.get_arg();
        auto newarg = apply(farg);
        result_ = div(integer(1),
                      sin(unevaluated_expr(add(newarg, div(pi, integer(2))))));
    }
};
 
RCP<const Basic> rewrite_as_sin(const RCP<const Basic> &x)
{
    RewriteAsSin b;
    return b.apply(x);
}
 
class RewriteAsCos : public BaseVisitor<RewriteAsCos, TransformVisitor>
{
public:
    using TransformVisitor::bvisit;
 
    RewriteAsCos() : BaseVisitor<RewriteAsCos, TransformVisitor>() {}
 
    void bvisit(const Sin &x)
    {
        auto farg = x.get_arg();
        auto newarg = apply(farg);
        result_ = cos(unevaluated_expr(sub(newarg, div(pi, integer(2)))));
    }
 
    void bvisit(const Tan &x)
    {
        auto farg = x.get_arg();
        auto newarg = apply(farg);
        result_ = div(cos(unevaluated_expr(sub(newarg, div(pi, integer(2))))),
                      cos(newarg));
    }
 
    void bvisit(const Cot &x)
    {
        auto farg = x.get_arg();
        auto newarg = apply(farg);
        result_ = div(cos(newarg),
                      cos(unevaluated_expr(sub(newarg, div(pi, integer(2))))));
    }
 
    void bvisit(const Csc &x)
    {
        auto farg = x.get_arg();
        auto newarg = apply(farg);
        result_ = div(integer(1),
                      cos(unevaluated_expr(sub(newarg, div(pi, integer(2))))));
    }
 
    void bvisit(const Sec &x)
    {
        auto farg = x.get_arg();
        auto newarg = apply(farg);
        result_ = div(integer(1), cos(newarg));
    }
};
 
RCP<const Basic> rewrite_as_cos(const RCP<const Basic> &x)
{
    RewriteAsCos b;
    return b.apply(x);
}
 
} // namespace SymEngine