SymEngine::UnivariateSeries Class Reference

UnivariateSeries Class. More...

#include <series_generic.h>

Inheritance diagram for SymEngine::UnivariateSeries:

Collaboration diagram for SymEngine::UnivariateSeries:

Public Member Functions
void	accept (Visitor &v) const override
void	accept (EvalRealDoubleVisitorFinal &v) const override
	UnivariateSeries (const UExprDict &sp, const std::string varname, const unsigned degree)
hash_t	__hash__ () const override
int	compare (const Basic &o) const override
bool	operator== (const UnivariateSeries &u) const
RCP< const Basic >	as_basic () const override
umap_int_basic	as_dict () const override
RCP< const Basic >	get_coeff (int) const override
RCP< const Number >	mul (const Number &other) const override
	Multiplication.
RCP< const Number >	pow (const Number &other) const override
	Power.
Public Member Functions inherited from SymEngine::SeriesBase< UExprDict, Expression, UnivariateSeries >
	SeriesBase (UExprDict p, std::string var, unsigned degree)
unsigned	get_degree () const override
const std::string &	get_var () const override
const UExprDict &	get_poly () const
bool	is_zero () const override
bool	is_one () const override
bool	is_minus_one () const override
bool	is_negative () const override
bool	is_positive () const override
bool	is_complex () const override
bool	__eq__ (const Basic &o) const override
	Test equality.
RCP< const Number >	add (const Number &other) const override
	Addition.
RCP< const Number >	mul (const Number &other) const override
	Multiplication.
RCP< const Number >	pow (const Number &other) const override
	Power.
RCP< const Number >	rpow (const Number &other) const override
virtual RCP< const Basic >	as_basic () const =0
virtual umap_int_basic	as_dict () const =0
virtual RCP< const Basic >	get_coeff (int) const =0
virtual unsigned	get_degree () const =0
virtual const std::string &	get_var () const =0
Public Member Functions inherited from SymEngine::Number
virtual bool	is_zero () const =0
virtual bool	is_one () const =0
virtual bool	is_minus_one () const =0
virtual bool	is_negative () const =0
virtual bool	is_positive () const =0
virtual bool	is_complex () const =0
virtual RCP< const Basic >	conjugate () const
virtual bool	is_exact () const
	return true if the number is an exact representation
bool	is_exact_zero () const
virtual Evaluate &	get_eval () const
	Get Evaluate singleton to evaluate numerically.
virtual RCP< const Number >	add (const Number &other) const =0
	Addition.
virtual RCP< const Number >	sub (const Number &other) const
	Subtraction.
virtual RCP< const Number >	rsub (const Number &other) const
virtual RCP< const Number >	mul (const Number &other) const =0
	Multiplication.
virtual RCP< const Number >	div (const Number &other) const
	Division.
virtual RCP< const Number >	rdiv (const Number &other) const
virtual RCP< const Number >	pow (const Number &other) const =0
	Power.
virtual RCP< const Number >	rpow (const Number &other) const =0
vec_basic	get_args () const override
	Returns the list of arguments.
virtual bool	is_perfect_power (bool is_expected=false) const
virtual bool	nth_root (const Ptr< RCP< const Number > > &, unsigned long n) const
Public Member Functions inherited from SymEngine::Basic
TypeID	get_type_code () const
	Basic ()
	Constructor.
	Basic (const Basic &)=delete
	Delete the copy constructor and assignment.
Basic &	operator= (const Basic &)=delete
	Assignment operator in continuation with above.
	Basic (Basic &&)=delete
	Delete the move constructor and assignment.
Basic &	operator= (Basic &&)=delete
	Assignment operator in continuation with above.
virtual hash_t	__hash__ () const =0
hash_t	hash () const
virtual bool	__eq__ (const Basic &o) const =0
	Test equality.
bool	__neq__ (const Basic &o) const
	true if this is not equal to o.
int	__cmp__ (const Basic &o) const
	Comparison operator.
virtual int	compare (const Basic &o) const =0
std::string	__str__ () const
std::string	dumps () const
	Returns a string of the instance serialized.
RCP< const Basic >	subs (const map_basic_basic &subs_dict) const
	Substitutes 'subs_dict' into 'self'.
RCP< const Basic >	xreplace (const map_basic_basic &subs_dict) const
virtual RCP< const Basic >	expand_as_exp () const
	expands the special function in terms of exp function
virtual vec_basic	get_args () const =0
	Returns the list of arguments.
virtual void	accept (Visitor &v) const =0
virtual void	accept (EvalRealDoubleVisitorFinal &v) const =0
RCP< const Basic >	diff (const RCP< const Symbol > &x, bool cache=true) const
Public Member Functions inherited from SymEngine::EnableRCPFromThis< Basic >
RCP< Basic >	rcp_from_this ()
	Get RCP<T> pointer to self (it will cast the pointer to T)
RCP< const Basic >	rcp_from_this () const
	Get RCP<const T> pointer to self (it will cast the pointer to const T)
RCP< const T2 >	rcp_from_this_cast () const
	Get RCP<T2> pointer to self (it will cast the pointer to T2)
unsigned int	use_count () const

Static Public Member Functions
static RCP< const UnivariateSeries >	create (const RCP< const Symbol > &var, const unsigned int &prec, const UExprDict &s)
static RCP< const UnivariateSeries >	series (const RCP< const Basic > &t, const std::string &x, unsigned int prec)
static UExprDict	var (const std::string &s)
static Expression	convert (const Basic &x)
static int	ldegree (const UExprDict &s)
static UExprDict	mul (const UExprDict &s, const UExprDict &r, unsigned prec)
static UExprDict	pow (const UExprDict &s, int n, unsigned prec)
static Expression	find_cf (const UExprDict &s, const UExprDict &var, int deg)
static Expression	root (Expression &c, unsigned n)
static UExprDict	diff (const UExprDict &s, const UExprDict &var)
static UExprDict	integrate (const UExprDict &s, const UExprDict &var)
static UExprDict	subs (const UExprDict &s, const UExprDict &var, const UExprDict &r, unsigned prec)
static Expression	sin (const Expression &c)
static Expression	cos (const Expression &c)
static Expression	tan (const Expression &c)
static Expression	asin (const Expression &c)
static Expression	acos (const Expression &c)
static Expression	atan (const Expression &c)
static Expression	sinh (const Expression &c)
static Expression	cosh (const Expression &c)
static Expression	tanh (const Expression &c)
static Expression	asinh (const Expression &c)
static Expression	acosh (const Expression &c)
static Expression	atanh (const Expression &c)
static Expression	exp (const Expression &c)
static Expression	log (const Expression &c)
Static Public Member Functions inherited from SymEngine::SeriesBase< UExprDict, Expression, UnivariateSeries >
static const std::list< unsigned int > &	step_list (unsigned int prec)
static UExprDict	series_invert (const UExprDict &s, const UExprDict &var, unsigned int prec)
static UExprDict	series_reverse (const UExprDict &s, const UExprDict &var, unsigned int prec)
static UExprDict	series_nthroot (const UExprDict &s, int n, const UExprDict &var, unsigned int prec)
static UExprDict	series_atan (const UExprDict &s, const UExprDict &var, unsigned int prec)
static UExprDict	series_tan (const UExprDict &s, const UExprDict &var, unsigned int prec)
static UExprDict	series_cot (const UExprDict &s, const UExprDict &var, unsigned int prec)
static UExprDict	_series_sin (const UExprDict &s, unsigned int prec)
static UExprDict	series_sin (const UExprDict &s, const UExprDict &var, unsigned int prec)
static UExprDict	series_csc (const UExprDict &s, const UExprDict &var, unsigned int prec)
static UExprDict	series_asin (const UExprDict &s, const UExprDict &var, unsigned int prec)
static UExprDict	series_acos (const UExprDict &s, const UExprDict &var, unsigned int prec)
static UExprDict	_series_cos (const UExprDict &s, unsigned int prec)
static UExprDict	series_cos (const UExprDict &s, const UExprDict &var, unsigned int prec)
static UExprDict	series_sec (const UExprDict &s, const UExprDict &var, unsigned int prec)
static UExprDict	series_log (const UExprDict &s, const UExprDict &var, unsigned int prec)
static UExprDict	series_exp (const UExprDict &s, const UExprDict &var, unsigned int prec)
static UExprDict	series_lambertw (const UExprDict &s, const UExprDict &var, unsigned int prec)
static UExprDict	series_sinh (const UExprDict &s, const UExprDict &var, unsigned int prec)
static UExprDict	series_cosh (const UExprDict &s, const UExprDict &var, unsigned int prec)
static UExprDict	series_atanh (const UExprDict &s, const UExprDict &var, unsigned int prec)
static UExprDict	series_asinh (const UExprDict &s, const UExprDict &var, unsigned int prec)
static UExprDict	series_tanh (const UExprDict &s, const UExprDict &var, unsigned int prec)
static Expression	sin (const Expression &c)
static Expression	cos (const Expression &c)
static Expression	tan (const Expression &c)
static Expression	asin (const Expression &c)
static Expression	acos (const Expression &c)
static Expression	atan (const Expression &c)
static Expression	sinh (const Expression &c)
static Expression	cosh (const Expression &c)
static Expression	tanh (const Expression &c)
static Expression	asinh (const Expression &c)
static Expression	atanh (const Expression &c)
static Expression	exp (const Expression &c)
static Expression	log (const Expression &c)
Static Public Member Functions inherited from SymEngine::Basic
static RCP< const Basic >	loads (const std::string &)
	Creates an instance of a serialized string.

Static Public Attributes
static const TypeID	type_code_id = SYMENGINE_UNIVARIATESERIES

Additional Inherited Members
Data Fields inherited from SymEngine::Basic
TypeID	type_code_
Protected Attributes inherited from SymEngine::SeriesBase< UExprDict, Expression, UnivariateSeries >
const UExprDict	p_
const std::string	var_
const unsigned	degree_

Detailed Description

UnivariateSeries Class.

Definition at line 16 of file series_generic.h.

Constructor & Destructor Documentation

UnivariateSeries()

SymEngine::UnivariateSeries::UnivariateSeries ( const UExprDict &  sp, const std::string  varname, const unsigned  degree  )

inline

Definition at line 25 of file series_generic.h.

        : SeriesBase(std::move(sp), varname, degree)
    {
        SYMENGINE_ASSIGN_TYPEID()
    }

Member Function Documentation

__hash__()

hash_t SymEngine::UnivariateSeries::__hash__ ( ) const

overridevirtual

Calculates the hash of the given SymEngine class. Use Basic.hash() which gives a cached version of the hash.

Returns

64-bit integer value for the hash

Implements SymEngine::Basic.

Definition at line 22 of file series_generic.cpp.

{
    hash_t seed = SYMENGINE_UEXPRPOLY;
    hash_combine(seed, get_degree());
    for (const auto &it : p_.dict_) {
        hash_t temp = SYMENGINE_UEXPRPOLY;
        hash_combine<unsigned int>(temp, it.first);
        hash_combine<Basic>(temp, *(it.second.get_basic()));
        seed += temp;
    }
    return seed;
}

accept() [1/2]

void SymEngine::UnivariateSeries::accept ( EvalRealDoubleVisitorFinal &  v ) const

overridevirtual

Implements SymEngine::Basic.

accept() [2/2]

void SymEngine::UnivariateSeries::accept ( Visitor &  v ) const

overridevirtual

Implements SymEngine::Basic.

acos()

Expression SymEngine::UnivariateSeries::acos ( const Expression &  c )

static

Definition at line 202 of file series_generic.cpp.

{
    return SymEngine::acos(c.get_basic());
}

as_basic()

RCP< const Basic > SymEngine::UnivariateSeries::as_basic ( ) const

overridevirtual

Implements SymEngine::SeriesCoeffInterface.

Definition at line 42 of file series_generic.cpp.

{
    return p_.get_basic(var_);
}

as_dict()

umap_int_basic SymEngine::UnivariateSeries::as_dict ( ) const

overridevirtual

Implements SymEngine::SeriesCoeffInterface.

Definition at line 47 of file series_generic.cpp.

{
    umap_int_basic map;
    for (const auto &it : p_.get_dict())
        if (it.second != 0)
            map[it.first] = it.second.get_basic();
    return map;
}

asin()

Expression SymEngine::UnivariateSeries::asin ( const Expression &  c )

static

Definition at line 197 of file series_generic.cpp.

{
    return SymEngine::asin(c.get_basic());
}

asinh()

Expression SymEngine::UnivariateSeries::asinh ( const Expression &  c )

static

Definition at line 227 of file series_generic.cpp.

{
    return SymEngine::asinh(c.get_basic());
}

atan()

Expression SymEngine::UnivariateSeries::atan ( const Expression &  c )

static

Definition at line 207 of file series_generic.cpp.

{
    return SymEngine::atan(c.get_basic());
}

atanh()

Expression SymEngine::UnivariateSeries::atanh ( const Expression &  c )

static

Definition at line 232 of file series_generic.cpp.

{
    return SymEngine::atanh(c.get_basic());
}

compare()

int SymEngine::UnivariateSeries::compare ( const Basic &  o ) const

overridevirtual

Returns -1, 0, 1 for this < o, this == o, this > o. This method is used when you want to sort things like x+y+z into canonical order. This function assumes that o is the same type as this. Use __cmp__ if you want general comparison.

Implements SymEngine::Basic.

Definition at line 35 of file series_generic.cpp.

{
    SYMENGINE_ASSERT(is_a<UnivariateSeries>(other))
    const UnivariateSeries &o_ = down_cast<const UnivariateSeries &>(other);
    return p_.compare(o_.get_poly());
}

convert()

Expression SymEngine::UnivariateSeries::convert ( const Basic &  x )

static

Definition at line 69 of file series_generic.cpp.

{
    return Expression(x.rcp_from_this());
}

cos()

Expression SymEngine::UnivariateSeries::cos ( const Expression &  c )

static

Definition at line 187 of file series_generic.cpp.

{
    return SymEngine::cos(c.get_basic());
}

cosh()

Expression SymEngine::UnivariateSeries::cosh ( const Expression &  c )

static

Definition at line 217 of file series_generic.cpp.

{
    return SymEngine::cosh(c.get_basic());
}

create()

static RCP< const UnivariateSeries > SymEngine::UnivariateSeries::create ( const RCP< const Symbol > &  var, const unsigned int &  prec, const UExprDict &  s  )

inlinestatic

Definition at line 32 of file series_generic.h.

    {
        return make_rcp<const UnivariateSeries>(std::move(s), var->get_name(),
                                                prec);
    }

diff()

UExprDict SymEngine::UnivariateSeries::diff ( const UExprDict &  s, const UExprDict &  var  )

static

Definition at line 142 of file series_generic.cpp.

{
    if (var.get_dict().size() == 1 and var.get_dict().at(1) == Expression(1)) {
        map_int_Expr d;
        for (const auto &p : s.get_dict()) {
            if (p.first != 0)
                d[p.first - 1] = p.second * p.first;
        }
        return UExprDict(d);
    } else {
        return UExprDict({{0, Expression(0)}});
    }
}

exp()

Expression SymEngine::UnivariateSeries::exp ( const Expression &  c )

static

Definition at line 237 of file series_generic.cpp.

{
    return SymEngine::exp(c.get_basic());
}

find_cf()

Expression SymEngine::UnivariateSeries::find_cf ( const UExprDict &  s, const UExprDict &  var, int  deg  )

static

Definition at line 128 of file series_generic.cpp.

{
    if (s.get_dict().count(deg) == 0)
        return Expression(0);
    else
        return (s.get_dict()).at(deg);
}

get_coeff()

RCP< const Basic > SymEngine::UnivariateSeries::get_coeff ( int  deg ) const

overridevirtual

Implements SymEngine::SeriesCoeffInterface.

Definition at line 56 of file series_generic.cpp.

{
    if (p_.get_dict().count(deg) == 0)
        return zero;
    else
        return p_.get_dict().at(deg).get_basic();
}

integrate()

UExprDict SymEngine::UnivariateSeries::integrate ( const UExprDict &  s, const UExprDict &  var  )

static

Definition at line 156 of file series_generic.cpp.

{
    map_int_Expr dict;
    for (auto &it : s.get_dict()) {
        if (it.first != -1) {
            dict.insert(std::pair<int, Expression>(it.first + 1,
                                                   it.second / (it.first + 1)));
        } else {
            throw NotImplementedError("Not Implemented");
        }
    }
 
    return UExprDict(dict);
}

ldegree()

int SymEngine::UnivariateSeries::ldegree ( const UExprDict &  s )

static

Definition at line 74 of file series_generic.cpp.

{
    return s.get_dict().begin()->first;
}

log()

Expression SymEngine::UnivariateSeries::log ( const Expression &  c )

static

Definition at line 242 of file series_generic.cpp.

{
    return SymEngine::log(c.get_basic());
}

mul() [1/2]

RCP< const Number > SymEngine::SeriesBase< Poly, Coeff, Series >::mul ( const Number &  other ) const

inlineoverridevirtual

Multiplication.

Implements SymEngine::Number.

Definition at line 110 of file series.h.

    {
        if (is_a<Series>(other)) {
            const Series &o = down_cast<const Series &>(other);
            auto deg = std::min(degree_, o.degree_);
            if (var_ != o.var_) {
                throw NotImplementedError(
                    "Multivariate Series not implemented");
            }
            return make_rcp<Series>(Series::mul(p_, o.p_, deg), var_, deg);
        } else if (other.get_type_code() < Series::type_code_id) {
            Poly p = Series::series(other.rcp_from_this(), var_, degree_)->p_;
            return make_rcp<Series>(Series::mul(p_, p, degree_), var_, degree_);
        } else {
            return other.mul(*this);
        }
    }

mul() [2/2]

UExprDict SymEngine::UnivariateSeries::mul ( const UExprDict &  s, const UExprDict &  r, unsigned  prec  )

static

Definition at line 79 of file series_generic.cpp.

{
    map_int_Expr p;
    for (auto &it1 : a.get_dict()) {
        for (auto &it2 : b.get_dict()) {
            int exp = it1.first + it2.first;
            if (exp < (int)prec) {
                p[exp] += it1.second * it2.second;
            } else {
                break;
            }
        }
    }
    return UExprDict(p);
}

pow() [1/2]

RCP< const Number > SymEngine::SeriesBase< Poly, Coeff, Series >::pow ( const Number &  other ) const

inlineoverridevirtual

Power.

Implements SymEngine::Number.

Definition at line 128 of file series.h.

    {
        auto deg = degree_;
        Poly p;
        if (is_a<Series>(other)) {
            const Series &o = down_cast<const Series &>(other);
            deg = std::min(deg, o.degree_);
            if (var_ != o.var_) {
                throw NotImplementedError(
                    "Multivariate Series not implemented");
            }
            p = o.p_;
        } else if (is_a<Integer>(other)) {
            if (other.is_negative()) {
                p = Series::pow(
                    p_,
                    (numeric_cast<int>(
                        down_cast<const Integer &>(other).neg()->as_int())),
                    deg);
                p = Series::series_invert(p, Series::var(var_), deg);
                return make_rcp<Series>(p, var_, deg);
            }
            p = Series::pow(
                p_,
                numeric_cast<int>((down_cast<const Integer &>(other).as_int())),
                deg);
            return make_rcp<Series>(p, var_, deg);
        } else if (other.get_type_code() < Series::type_code_id) {
            p = Series::series(other.rcp_from_this(), var_, degree_)->p_;
        } else {
            return other.rpow(*this);
        }
        p = Series::series_exp(
            Poly(p * Series::series_log(p_, Series::var(var_), deg)),
            Series::var(var_), deg);
        return make_rcp<Series>(p, var_, deg);
    }

pow() [2/2]

UExprDict SymEngine::UnivariateSeries::pow ( const UExprDict &  s, int  n, unsigned  prec  )

static

Definition at line 96 of file series_generic.cpp.

{
    if (exp < 0) {
        SYMENGINE_ASSERT(base.size() == 1)
        map_int_Expr dict;
        dict[-(base.get_dict().begin()->first)]
            = 1 / base.get_dict().begin()->second;
        return pow(UExprDict(dict), -exp, prec);
    }
    if (exp == 0) {
        if (base == 0 or base.get_dict().size() == 0) {
            throw DomainError("Error: 0**0 is undefined.");
        } else {
            return UExprDict(1);
        }
    }
 
    UExprDict x(base);
    UExprDict y(1);
    while (exp > 1) {
        if (exp % 2 == 0) {
            x = mul(x, x, prec);
            exp /= 2;
        } else {
            y = mul(x, y, prec);
            x = mul(x, x, prec);
            exp = (exp - 1) / 2;
        }
    }
    return mul(x, y, prec);
}

root()

Expression SymEngine::UnivariateSeries::root ( Expression &  c, unsigned  n  )

static

Definition at line 137 of file series_generic.cpp.

{
    return SymEngine::pow(c, 1 / Expression(n));
}

series()

RCP< const UnivariateSeries > SymEngine::UnivariateSeries::series ( const RCP< const Basic > &  t, const std::string &  x, unsigned int  prec  )

static

Definition at line 12 of file series_generic.cpp.

{
    UExprDict p({{1, Expression(1)}});
    SeriesVisitor<UExprDict, Expression, UnivariateSeries> visitor(std::move(p),
                                                                   x, prec);
    return visitor.series(t);
}

sin()

Expression SymEngine::UnivariateSeries::sin ( const Expression &  c )

static

Definition at line 182 of file series_generic.cpp.

{
    return SymEngine::sin(c.get_basic());
}

sinh()

Expression SymEngine::UnivariateSeries::sinh ( const Expression &  c )

static

Definition at line 212 of file series_generic.cpp.

{
    return SymEngine::sinh(c.get_basic());
}

subs()

UExprDict SymEngine::UnivariateSeries::subs ( const UExprDict &  s, const UExprDict &  var, const UExprDict &  r, unsigned  prec  )

static

Definition at line 171 of file series_generic.cpp.

{
    UExprDict result({{1, Expression(1)}});
 
    for (auto &i : s.get_dict())
        result += i.second * pow(r, i.first, prec);
 
    return result;
}

tan()

Expression SymEngine::UnivariateSeries::tan ( const Expression &  c )

static

Definition at line 192 of file series_generic.cpp.

{
    return SymEngine::tan(c.get_basic());
}

tanh()

Expression SymEngine::UnivariateSeries::tanh ( const Expression &  c )

static

Definition at line 222 of file series_generic.cpp.

{
    return SymEngine::tanh(c.get_basic());
}

var()

UExprDict SymEngine::UnivariateSeries::var ( const std::string &  s )

static

Definition at line 64 of file series_generic.cpp.

{
    return UExprDict({{1, Expression(1)}});
}

Field Documentation

type_code_id

const TypeID SymEngine::UnivariateSeries::type_code_id = SYMENGINE_UNIVARIATESERIES

static

Type_code_id shared by all instances

Definition at line 24 of file series_generic.h.

---

The documentation for this class was generated from the following files:

• /home/runner/work/symengine/symengine/symengine/series_generic.h
• /home/runner/work/symengine/symengine/symengine/series_generic.cpp