from libcpp cimport bool from libcpp.string cimport string from libcpp.map cimport map from libcpp.vector cimport vector from cpython.ref cimport PyObject from libcpp.pair cimport pair from libcpp.set cimport set from libcpp.unordered_map cimport unordered_map cdef extern from "" namespace "std": # Cython's libcpp.set does not support multiset in 0.29.x cdef cppclass multiset[T]: cppclass iterator: T& operator*() iterator operator++() nogil iterator operator--() nogil bint operator==(iterator) nogil bint operator!=(iterator) nogil iterator begin() nogil iterator end() nogil iterator insert(T&) nogil cdef extern from 'symengine/mp_class.h' namespace "SymEngine": ctypedef unsigned long mp_limb_t ctypedef struct __mpz_struct: pass ctypedef struct __mpq_struct: pass ctypedef __mpz_struct mpz_t[1] ctypedef __mpq_struct mpq_t[1] cdef cppclass integer_class: integer_class() integer_class(int i) integer_class(integer_class) integer_class(mpz_t) integer_class(const string &s) except + mpz_t get_mpz_t(integer_class &a) const mpz_t get_mpz_t(const integer_class &a) string mp_get_hex_str(const integer_class &a) void mp_set_str(integer_class &a, const string &s) cdef cppclass rational_class: rational_class() rational_class(mpq_t) const mpq_t get_mpq_t(const rational_class &a) cdef extern from "" namespace "SymEngine": cdef enum ENull: null cdef cppclass RCP[T]: T& operator*() nogil # Not yet supported in Cython: # RCP[T]& operator=(RCP[T] &r_ptr) except+ nogil void reset() except+ nogil cdef cppclass Ptr[T]: T& operator*() except+ nogil void print_stack_on_segfault() nogil cdef extern from "" namespace "SymEngine": ctypedef Basic const_Basic "const SymEngine::Basic" # RCP[const_Basic] instead of RCP[const Basic] is because of https://github.com/cython/cython/issues/5478 ctypedef RCP[const_Basic] rcp_const_basic "SymEngine::RCP" #cdef cppclass rcp_const_basic "SymEngine::RCP": # Basic& operator*() nogil # void reset() except+ nogil # pass # Cython has broken support for the following: # ctypedef map[rcp_const_basic, rcp_const_basic] map_basic_basic # So instead we replicate the map features we need here cdef cppclass std_pair_short_rcp_const_basic "std::pair>": short first rcp_const_basic second cdef cppclass std_pair_rcp_const_basic_rcp_const_basic "std::pair, SymEngine::RCP>": rcp_const_basic first rcp_const_basic second cdef cppclass map_basic_basic: map_basic_basic() except + map_basic_basic(map_basic_basic&) except + cppclass iterator: std_pair_rcp_const_basic_rcp_const_basic& operator*() iterator operator++() iterator operator--() bint operator==(iterator) bint operator!=(iterator) rcp_const_basic& operator[](rcp_const_basic&) void clear() bint empty() size_t size() void swap(map_basic_basic&) iterator begin() iterator end() iterator find(rcp_const_basic&) void erase(iterator, iterator) void erase_it(iterator) size_t erase(rcp_const_basic&) pair[iterator, bint] insert(std_pair_rcp_const_basic_rcp_const_basic) except + iterator insert(iterator, std_pair_rcp_const_basic_rcp_const_basic) except + void insert(iterator, iterator) except + ctypedef vector[rcp_const_basic] vec_basic "SymEngine::vec_basic" ctypedef vector[RCP[Symbol]] vec_sym "SymEngine::vec_sym" ctypedef vector[RCP[Integer]] vec_integer "SymEngine::vec_integer" ctypedef map[RCP[Integer], unsigned] map_integer_uint "SymEngine::map_integer_uint" cdef struct RCPIntegerKeyLess cdef struct RCPBasicKeyLess ctypedef set[rcp_const_basic] set_basic "SymEngine::set_basic" ctypedef multiset[rcp_const_basic] multiset_basic "SymEngine::multiset_basic" cdef cppclass Basic: string __str__() except+ nogil unsigned int hash() except+ nogil vec_basic get_args() nogil int __cmp__(const Basic &o) nogil ctypedef RCP[const Number] rcp_const_number "SymEngine::RCP" ctypedef unordered_map[int, rcp_const_basic] umap_int_basic "SymEngine::umap_int_basic" ctypedef unordered_map[int, rcp_const_basic].iterator umap_int_basic_iterator "SymEngine::umap_int_basic::iterator" ctypedef unordered_map[rcp_const_basic, rcp_const_number] umap_basic_num "SymEngine::umap_basic_num" ctypedef unordered_map[rcp_const_basic, rcp_const_number].iterator umap_basic_num_iterator "SymEngine::umap_basic_num::iterator" ctypedef vector[pair[rcp_const_basic, rcp_const_basic]] vec_pair "SymEngine::vec_pair" bool eq(const Basic &a, const Basic &b) except+ nogil bool neq(const Basic &a, const Basic &b) except+ nogil RCP[const Symbol] rcp_static_cast_Symbol "SymEngine::rcp_static_cast"(rcp_const_basic &b) nogil RCP[const PySymbol] rcp_static_cast_PySymbol "SymEngine::rcp_static_cast"(rcp_const_basic &b) except+ nogil RCP[const Integer] rcp_static_cast_Integer "SymEngine::rcp_static_cast"(rcp_const_basic &b) nogil RCP[const Rational] rcp_static_cast_Rational "SymEngine::rcp_static_cast"(rcp_const_basic &b) nogil RCP[const Complex] rcp_static_cast_Complex "SymEngine::rcp_static_cast"(rcp_const_basic &b) nogil RCP[const Number] rcp_static_cast_Number "SymEngine::rcp_static_cast"(rcp_const_basic &b) nogil RCP[const Add] rcp_static_cast_Add "SymEngine::rcp_static_cast"(rcp_const_basic &b) nogil RCP[const Mul] rcp_static_cast_Mul "SymEngine::rcp_static_cast"(rcp_const_basic &b) nogil RCP[const Pow] rcp_static_cast_Pow "SymEngine::rcp_static_cast"(rcp_const_basic &b) nogil RCP[const OneArgFunction] rcp_static_cast_OneArgFunction "SymEngine::rcp_static_cast"(rcp_const_basic &b) nogil RCP[const FunctionSymbol] rcp_static_cast_FunctionSymbol "SymEngine::rcp_static_cast"(rcp_const_basic &b) nogil RCP[const FunctionWrapper] rcp_static_cast_FunctionWrapper "SymEngine::rcp_static_cast"(rcp_const_basic &b) nogil RCP[const Abs] rcp_static_cast_Abs "SymEngine::rcp_static_cast"(rcp_const_basic &b) nogil RCP[const Max] rcp_static_cast_Max "SymEngine::rcp_static_cast"(rcp_const_basic &b) nogil RCP[const Min] rcp_static_cast_Min "SymEngine::rcp_static_cast"(rcp_const_basic &b) nogil RCP[const Infty] rcp_static_cast_Infty "SymEngine::rcp_static_cast"(rcp_const_basic &b) nogil RCP[const Gamma] rcp_static_cast_Gamma "SymEngine::rcp_static_cast"(rcp_const_basic &b) nogil RCP[const Derivative] rcp_static_cast_Derivative "SymEngine::rcp_static_cast"(rcp_const_basic &b) nogil RCP[const Subs] rcp_static_cast_Subs "SymEngine::rcp_static_cast"(rcp_const_basic &b) nogil RCP[const RealDouble] rcp_static_cast_RealDouble "SymEngine::rcp_static_cast"(rcp_const_basic &b) nogil RCP[const ComplexDouble] rcp_static_cast_ComplexDouble "SymEngine::rcp_static_cast"(rcp_const_basic &b) nogil RCP[const ComplexBase] rcp_static_cast_ComplexBase "SymEngine::rcp_static_cast"(rcp_const_basic &b) nogil RCP[const RealMPFR] rcp_static_cast_RealMPFR "SymEngine::rcp_static_cast"(rcp_const_basic &b) nogil RCP[const ComplexMPC] rcp_static_cast_ComplexMPC "SymEngine::rcp_static_cast"(rcp_const_basic &b) nogil RCP[const Log] rcp_static_cast_Log "SymEngine::rcp_static_cast"(rcp_const_basic &b) nogil RCP[const BooleanAtom] rcp_static_cast_BooleanAtom "SymEngine::rcp_static_cast"(rcp_const_basic &b) nogil RCP[const PyNumber] rcp_static_cast_PyNumber "SymEngine::rcp_static_cast"(rcp_const_basic &b) nogil RCP[const PyFunction] rcp_static_cast_PyFunction "SymEngine::rcp_static_cast"(rcp_const_basic &b) nogil RCP[const Boolean] rcp_static_cast_Boolean "SymEngine::rcp_static_cast"(rcp_const_basic &b) nogil RCP[const Set] rcp_static_cast_Set "SymEngine::rcp_static_cast"(rcp_const_basic &b) nogil Ptr[RCP[Basic]] outArg(rcp_const_basic &arg) nogil Ptr[RCP[Integer]] outArg_Integer "SymEngine::outArg>"(RCP[const Integer] &arg) nogil bool is_a[T] (const Basic &b) nogil bool is_a_sub[T] (const Basic &b) nogil rcp_const_basic expand(rcp_const_basic &o, bool deep) except+ nogil void as_numer_denom(rcp_const_basic &x, const Ptr[RCP[Basic]] &numer, const Ptr[RCP[Basic]] &denom) nogil void as_real_imag(rcp_const_basic &x, const Ptr[RCP[Basic]] &real, const Ptr[RCP[Basic]] &imag) nogil void cse(vec_pair &replacements, vec_basic &reduced_exprs, const vec_basic &exprs) except+ nogil cdef extern from "" namespace "SymEngine": rcp_const_basic msubs (rcp_const_basic &x, const map_basic_basic &x) except+ nogil rcp_const_basic ssubs (rcp_const_basic &x, const map_basic_basic &x) except+ nogil rcp_const_basic xreplace (rcp_const_basic &x, const map_basic_basic &x) except+ nogil cdef extern from "" namespace "SymEngine": rcp_const_basic diff "SymEngine::sdiff"(rcp_const_basic &arg, rcp_const_basic &x) except+ nogil cdef extern from "" namespace "SymEngine": cdef cppclass Symbol(Basic): Symbol(string name) nogil string get_name() nogil cdef cppclass Dummy(Symbol): pass cdef extern from "" namespace "SymEngine": cdef cppclass Number(Basic): bool is_positive() nogil bool is_negative() nogil bool is_zero() nogil bool is_one() nogil bool is_minus_one() nogil bool is_complex() nogil pass cdef cppclass NumberWrapper(Basic): pass cdef tribool is_zero(const Basic &x) nogil cdef tribool is_positive(const Basic &x) nogil cdef tribool is_negative(const Basic &x) nogil cdef tribool is_nonnegative(const Basic &x) nogil cdef tribool is_nonpositive(const Basic &x) nogil cdef tribool is_real(const Basic &x) nogil cdef extern from "pywrapper.h" namespace "SymEngine": cdef cppclass PyNumber(NumberWrapper): PyObject* get_py_object() cdef cppclass PyModule: pass cdef cppclass PyFunctionClass: PyObject* call(const vec_basic &vec) cdef cppclass PyFunction: PyObject* get_py_object() cdef extern from "pywrapper.h" namespace "SymEngine": cdef cppclass PySymbol(Symbol): PySymbol(string name, PyObject* pyobj, bool use_pickle) except + PyObject* get_py_object() except + string wrapper_dumps(const Basic &x) except+ nogil rcp_const_basic wrapper_loads(const string &s) except+ nogil cdef extern from "" namespace "SymEngine": cdef cppclass Integer(Number): Integer(int i) nogil Integer(integer_class i) nogil int compare(const Basic &o) nogil integer_class as_integer_class() nogil RCP[Number] divint(const Integer &other) nogil cdef long mp_get_si(integer_class &i) nogil cdef double mp_get_d(integer_class &i) nogil cdef RCP[const Integer] integer(int i) nogil cdef RCP[const Integer] integer(integer_class i) nogil int i_nth_root(const Ptr[RCP[Integer]] &r, const Integer &a, unsigned long int n) nogil bool perfect_square(const Integer &n) nogil bool perfect_power(const Integer &n) nogil cdef extern from "" namespace "SymEngine": cdef cppclass Rational(Number): rational_class as_rational_class() nogil @staticmethod RCP[const Number] from_two_ints(const long n, const long d) nogil cdef double mp_get_d(rational_class &i) nogil cdef RCP[const Number] from_mpq "SymEngine::Rational::from_mpq"(rational_class r) nogil cdef void get_num_den(const Rational &rat, const Ptr[RCP[Integer]] &num, const Ptr[RCP[Integer]] &den) nogil cdef RCP[const Number] rational(long n, long d) nogil cdef extern from "" namespace "SymEngine": cdef cppclass ComplexBase(Number): RCP[const Number] real_part() nogil RCP[const Number] imaginary_part() nogil cdef cppclass Complex(ComplexBase): pass cdef extern from "" namespace "SymEngine": cdef cppclass RealDouble(Number): RealDouble(double x) nogil double as_double() nogil RCP[const RealDouble] real_double(double d) nogil cdef extern from "" namespace "SymEngine": cdef cppclass ComplexDouble(ComplexBase): ComplexDouble(double complex x) nogil double complex as_complex_double() nogil RCP[const ComplexDouble] complex_double(double complex d) nogil cdef extern from "" namespace "SymEngine": cdef cppclass Constant(Basic): Constant(string name) nogil string get_name() nogil rcp_const_basic I rcp_const_basic E rcp_const_basic pi rcp_const_basic GoldenRatio rcp_const_basic Catalan rcp_const_basic EulerGamma rcp_const_basic Inf rcp_const_basic ComplexInf rcp_const_basic Nan cdef extern from "" namespace "SymEngine": cdef cppclass Infty(Number): pass cdef extern from "" namespace "SymEngine": cdef cppclass NaN(Number): pass cdef extern from "" namespace "SymEngine": cdef rcp_const_basic add(rcp_const_basic &a, rcp_const_basic &b) except+ nogil cdef rcp_const_basic sub(rcp_const_basic &a, rcp_const_basic &b) except+ nogil cdef rcp_const_basic add(const vec_basic &a) except+ nogil cdef cppclass Add(Basic): void as_two_terms(const Ptr[RCP[Basic]] &a, const Ptr[RCP[Basic]] &b) RCP[const Number] get_coef() const umap_basic_num &get_dict() cdef extern from "" namespace "SymEngine": cdef rcp_const_basic mul(rcp_const_basic &a, rcp_const_basic &b) except+ nogil cdef rcp_const_basic div(rcp_const_basic &a, rcp_const_basic &b) except+ nogil cdef rcp_const_basic neg(rcp_const_basic &a) except+ nogil cdef rcp_const_basic mul(const vec_basic &a) except+ nogil cdef cppclass Mul(Basic): void as_two_terms(const Ptr[RCP[Basic]] &a, const Ptr[RCP[Basic]] &b) RCP[const Number] get_coef() const map_basic_basic &get_dict() cdef RCP[const Mul] mul_from_dict "SymEngine::Mul::from_dict"(RCP[const Number] coef, map_basic_basic &d) nogil cdef extern from "" namespace "SymEngine": cdef rcp_const_basic pow(rcp_const_basic &a, rcp_const_basic &b) except+ nogil cdef rcp_const_basic sqrt(rcp_const_basic &x) except+ nogil cdef rcp_const_basic exp(rcp_const_basic &x) except+ nogil cdef cppclass Pow(Basic): rcp_const_basic get_base() nogil rcp_const_basic get_exp() nogil cdef extern from "" namespace "SymEngine": # We need to specialize these for our classes: rcp_const_basic make_rcp_Symbol "SymEngine::make_rcp"(string name) nogil rcp_const_basic make_rcp_Dummy "SymEngine::make_rcp"() nogil rcp_const_basic make_rcp_Dummy "SymEngine::make_rcp"(string name) nogil rcp_const_basic make_rcp_PySymbol "SymEngine::make_rcp"(string name, PyObject * pyobj, bool use_pickle) except + rcp_const_basic make_rcp_Constant "SymEngine::make_rcp"(string name) nogil rcp_const_basic make_rcp_Infty "SymEngine::make_rcp"(RCP[const Number] i) nogil rcp_const_basic make_rcp_NaN "SymEngine::make_rcp"() nogil rcp_const_basic make_rcp_Integer "SymEngine::make_rcp"(int i) nogil rcp_const_basic make_rcp_Integer "SymEngine::make_rcp"(integer_class i) nogil rcp_const_basic make_rcp_Subs "SymEngine::make_rcp"(rcp_const_basic arg, const map_basic_basic &x) nogil rcp_const_basic make_rcp_Derivative "SymEngine::make_rcp"(rcp_const_basic arg, const multiset_basic &x) nogil rcp_const_basic make_rcp_FunctionWrapper "SymEngine::make_rcp"(void* obj, string name, string hash_, const vec_basic &arg, \ void (*dec_ref)(void *), int (*comp)(void *, void *)) nogil rcp_const_basic make_rcp_RealDouble "SymEngine::make_rcp"(double x) nogil rcp_const_basic make_rcp_ComplexDouble "SymEngine::make_rcp"(double complex x) nogil RCP[const PyModule] make_rcp_PyModule "SymEngine::make_rcp"(PyObject* (*) (rcp_const_basic x) except +, \ rcp_const_basic (*)(PyObject*) except +, RCP[const Number] (*)(PyObject*, long bits) except +, rcp_const_basic (*)(PyObject*, rcp_const_basic) except +) except + rcp_const_basic make_rcp_PyNumber "SymEngine::make_rcp"(PyObject*, RCP[const PyModule] x) nogil RCP[const PyFunctionClass] make_rcp_PyFunctionClass "SymEngine::make_rcp"(PyObject* pyobject, string name, RCP[const PyModule] pymodule) nogil rcp_const_basic make_rcp_PyFunction "SymEngine::make_rcp" (const vec_basic &vec, RCP[const PyFunctionClass] pyfunc_class, const PyObject* pyobject) nogil cdef extern from "" namespace "SymEngine": cdef rcp_const_basic sin(rcp_const_basic &arg) except+ nogil cdef rcp_const_basic cos(rcp_const_basic &arg) except+ nogil cdef rcp_const_basic tan(rcp_const_basic &arg) except+ nogil cdef rcp_const_basic cot(rcp_const_basic &arg) except+ nogil cdef rcp_const_basic csc(rcp_const_basic &arg) except+ nogil cdef rcp_const_basic sec(rcp_const_basic &arg) except+ nogil cdef rcp_const_basic asin(rcp_const_basic &arg) except+ nogil cdef rcp_const_basic acos(rcp_const_basic &arg) except+ nogil cdef rcp_const_basic atan(rcp_const_basic &arg) except+ nogil cdef rcp_const_basic acot(rcp_const_basic &arg) except+ nogil cdef rcp_const_basic acsc(rcp_const_basic &arg) except+ nogil cdef rcp_const_basic asec(rcp_const_basic &arg) except+ nogil cdef rcp_const_basic sinh(rcp_const_basic &arg) except+ nogil cdef rcp_const_basic cosh(rcp_const_basic &arg) except+ nogil cdef rcp_const_basic tanh(rcp_const_basic &arg) except+ nogil cdef rcp_const_basic coth(rcp_const_basic &arg) except+ nogil cdef rcp_const_basic csch(rcp_const_basic &arg) except+ nogil cdef rcp_const_basic sech(rcp_const_basic &arg) except+ nogil cdef rcp_const_basic asinh(rcp_const_basic &arg) except+ nogil cdef rcp_const_basic acosh(rcp_const_basic &arg) except+ nogil cdef rcp_const_basic atanh(rcp_const_basic &arg) except+ nogil cdef rcp_const_basic acoth(rcp_const_basic &arg) except+ nogil cdef rcp_const_basic acsch(rcp_const_basic &arg) except+ nogil cdef rcp_const_basic asech(rcp_const_basic &arg) except+ nogil cdef rcp_const_basic function_symbol(string name, const vec_basic &arg) except+ nogil cdef rcp_const_basic abs(rcp_const_basic &arg) except+ nogil cdef rcp_const_basic max(const vec_basic &arg) except+ nogil cdef rcp_const_basic min(const vec_basic &arg) except+ nogil cdef rcp_const_basic gamma(rcp_const_basic &arg) except+ nogil cdef rcp_const_basic atan2(rcp_const_basic &num, rcp_const_basic &den) except+ nogil cdef rcp_const_basic lambertw(rcp_const_basic &arg) except+ nogil cdef rcp_const_basic zeta(rcp_const_basic &s) except+ nogil cdef rcp_const_basic zeta(rcp_const_basic &s, rcp_const_basic &a) except+ nogil cdef rcp_const_basic dirichlet_eta(rcp_const_basic &s) except+ nogil cdef rcp_const_basic kronecker_delta(rcp_const_basic &i, rcp_const_basic &j) except+ nogil cdef rcp_const_basic levi_civita(const vec_basic &arg) except+ nogil cdef rcp_const_basic erf(rcp_const_basic &arg) except+ nogil cdef rcp_const_basic erfc(rcp_const_basic &arg) except+ nogil cdef rcp_const_basic lowergamma(rcp_const_basic &s, rcp_const_basic &x) except+ nogil cdef rcp_const_basic uppergamma(rcp_const_basic &s, rcp_const_basic &x) except+ nogil cdef rcp_const_basic loggamma(rcp_const_basic &arg) except+ nogil cdef rcp_const_basic beta(rcp_const_basic &x, rcp_const_basic &y) except+ nogil cdef rcp_const_basic polygamma(rcp_const_basic &n, rcp_const_basic &x) except+ nogil cdef rcp_const_basic digamma(rcp_const_basic &x) except+ nogil cdef rcp_const_basic trigamma(rcp_const_basic &x) except+ nogil cdef rcp_const_basic sign(rcp_const_basic &x) except+ nogil cdef rcp_const_basic floor(rcp_const_basic &x) except+ nogil cdef rcp_const_basic ceiling(rcp_const_basic &x) except+ nogil cdef rcp_const_basic conjugate(rcp_const_basic &x) except+ nogil cdef rcp_const_basic log(rcp_const_basic &x) except+ nogil cdef rcp_const_basic log(rcp_const_basic &x, rcp_const_basic &y) except+ nogil cdef rcp_const_basic unevaluated_expr(rcp_const_basic &x) except+ nogil cdef cppclass Function(Basic): pass cdef cppclass OneArgFunction(Function): rcp_const_basic get_arg() nogil cdef cppclass TrigFunction(OneArgFunction): pass cdef cppclass Sin(TrigFunction): pass cdef cppclass Cos(TrigFunction): pass cdef cppclass Tan(TrigFunction): pass cdef cppclass Cot(TrigFunction): pass cdef cppclass Csc(TrigFunction): pass cdef cppclass Sec(TrigFunction): pass cdef cppclass ASin(TrigFunction): pass cdef cppclass ACos(TrigFunction): pass cdef cppclass ATan(TrigFunction): pass cdef cppclass ACot(TrigFunction): pass cdef cppclass ACsc(TrigFunction): pass cdef cppclass ASec(TrigFunction): pass cdef cppclass HyperbolicFunction(OneArgFunction): pass cdef cppclass Sinh(HyperbolicFunction): pass cdef cppclass Cosh(HyperbolicFunction): pass cdef cppclass Tanh(HyperbolicFunction): pass cdef cppclass Coth(HyperbolicFunction): pass cdef cppclass Csch(HyperbolicFunction): pass cdef cppclass Sech(HyperbolicFunction): pass cdef cppclass ASinh(HyperbolicFunction): pass cdef cppclass ACosh(HyperbolicFunction): pass cdef cppclass ATanh(HyperbolicFunction): pass cdef cppclass ACoth(HyperbolicFunction): pass cdef cppclass ACsch(HyperbolicFunction): pass cdef cppclass ASech(HyperbolicFunction): pass cdef cppclass FunctionSymbol(Function): string get_name() nogil cdef cppclass FunctionWrapper(FunctionSymbol): FunctionWrapper(void* obj, string name, string hash_, const vec_basic &arg, \ void (*dec_ref)(void *), int (*comp)(void *, void *)) void* get_object() cdef cppclass Derivative(Basic): Derivative(const rcp_const_basic &arg, const vec_basic &x) nogil rcp_const_basic get_arg() nogil multiset_basic get_symbols() nogil cdef cppclass Subs(Basic): Subs(const rcp_const_basic &arg, const map_basic_basic &x) nogil rcp_const_basic get_arg() nogil vec_basic get_variables() nogil vec_basic get_point() nogil cdef cppclass Abs(OneArgFunction): pass cdef cppclass Max(Function): pass cdef cppclass Min(Function): pass cdef cppclass Gamma(OneArgFunction): pass cdef cppclass ATan2(Function): pass cdef cppclass LambertW(OneArgFunction): pass cdef cppclass Zeta(Function): pass cdef cppclass Dirichlet_eta(OneArgFunction): pass cdef cppclass KroneckerDelta(Function): pass cdef cppclass LeviCivita(Function): pass cdef cppclass Erf(OneArgFunction): pass cdef cppclass Erfc(OneArgFunction): pass cdef cppclass LowerGamma(Function): pass cdef cppclass UpperGamma(Function): pass cdef cppclass LogGamma(OneArgFunction): pass cdef cppclass Beta(Function): pass cdef cppclass PolyGamma(Function): pass cdef cppclass Sign(OneArgFunction): pass cdef cppclass Floor(OneArgFunction): pass cdef cppclass Ceiling(OneArgFunction): pass cdef cppclass Conjugate(OneArgFunction): pass cdef cppclass UnevaluatedExpr(OneArgFunction): pass cdef cppclass Log(Function): pass cdef extern from "": # These come from mpfr.h, but don't include mpfr.h to not break # builds without mpfr ctypedef struct __mpfr_struct: pass ctypedef __mpfr_struct mpfr_t[1] ctypedef __mpfr_struct* mpfr_ptr ctypedef const __mpfr_struct* mpfr_srcptr ctypedef long mpfr_prec_t ctypedef enum mpfr_rnd_t: MPFR_RNDN MPFR_RNDZ MPFR_RNDU MPFR_RNDD MPFR_RNDA MPFR_RNDF MPFR_RNDNA cdef extern from "" namespace "SymEngine": cdef cppclass mpfr_class: mpfr_class() nogil mpfr_class(mpfr_prec_t prec) nogil mpfr_class(string s, mpfr_prec_t prec, unsigned base) nogil mpfr_class(mpfr_t m) nogil mpfr_ptr get_mpfr_t() nogil cdef cppclass RealMPFR(Number): RealMPFR(mpfr_class) nogil mpfr_class as_mpfr() nogil mpfr_prec_t get_prec() nogil RCP[const RealMPFR] real_mpfr(mpfr_class t) nogil cdef extern from "": # These come from mpc.h, but don't include mpc.h to not break # builds without mpc ctypedef struct __mpc_struct: pass ctypedef __mpc_struct mpc_t[1] ctypedef __mpc_struct* mpc_ptr ctypedef const __mpc_struct* mpc_srcptr cdef extern from "" namespace "SymEngine": cdef cppclass mpc_class: mpc_class() nogil mpc_class(mpfr_prec_t prec) nogil mpc_class(mpc_t m) nogil mpc_ptr get_mpc_t() nogil mpc_class(string s, mpfr_prec_t prec, unsigned base) nogil cdef cppclass ComplexMPC(ComplexBase): ComplexMPC(mpc_class) nogil mpc_class as_mpc() nogil mpfr_prec_t get_prec() nogil RCP[const ComplexMPC] complex_mpc(mpc_class t) nogil cdef extern from "" namespace "SymEngine": cdef cppclass MatrixBase: const unsigned nrows() nogil const unsigned ncols() nogil rcp_const_basic get(unsigned i, unsigned j) nogil rcp_const_basic set(unsigned i, unsigned j, rcp_const_basic e) nogil string __str__() except+ nogil bool eq(const MatrixBase &) nogil rcp_const_basic det() nogil void inv(MatrixBase &) bool is_square() nogil void add_matrix(const MatrixBase &other, MatrixBase &result) nogil void mul_matrix(const MatrixBase &other, MatrixBase &result) nogil void elementwise_mul_matrix(const MatrixBase &other, MatrixBase &result) nogil void conjugate(MatrixBase &result) nogil void conjugate_transpose(MatrixBase &result) nogil void add_scalar(rcp_const_basic k, MatrixBase &result) nogil void mul_scalar(rcp_const_basic k, MatrixBase &result) nogil void transpose(MatrixBase &result) nogil void submatrix(MatrixBase &result, unsigned row_start, unsigned col_start, unsigned row_end, unsigned col_end, unsigned row_step, unsigned col_step) nogil void LU(MatrixBase &L, MatrixBase &U) nogil void LDL(MatrixBase &L, MatrixBase &D) nogil void LU_solve(const MatrixBase &b, MatrixBase &x) nogil void FFLU(MatrixBase &LU) nogil void FFLDU(MatrixBase &L, MatrixBase &D, MatrixBase &U) nogil void QR(MatrixBase &Q, MatrixBase &R) nogil void cholesky(MatrixBase &L) nogil cdef cppclass DenseMatrix(MatrixBase): DenseMatrix() DenseMatrix(unsigned i, unsigned j) nogil DenseMatrix(unsigned i, unsigned j, const vec_basic &v) nogil void resize(unsigned i, unsigned j) nogil void row_join(const DenseMatrix &B) nogil void col_join(const DenseMatrix &B) nogil void row_insert(const DenseMatrix &B, unsigned pos) nogil void col_insert(const DenseMatrix &B, unsigned pos) nogil void row_del(unsigned k) nogil void col_del(unsigned k) nogil rcp_const_basic trace() nogil tribool is_zero() nogil tribool is_real() nogil tribool is_diagonal() nogil tribool is_symmetric() nogil tribool is_hermitian() nogil tribool is_weakly_diagonally_dominant() nogil tribool is_strictly_diagonally_dominant() nogil tribool is_positive_definite() nogil tribool is_negative_definite() nogil DenseMatrix* static_cast_DenseMatrix "static_cast"(const MatrixBase *a) void inverse_FFLU "SymEngine::inverse_fraction_free_LU"(const DenseMatrix &A, DenseMatrix &B) except+ nogil void pivoted_LU_solve (const DenseMatrix &A, const DenseMatrix &b, DenseMatrix &x) except+ nogil void inverse_GJ "SymEngine::inverse_gauss_jordan"(const DenseMatrix &A, DenseMatrix &B) except+ nogil void FFLU_solve "SymEngine::fraction_free_LU_solve"(const DenseMatrix &A, const DenseMatrix &b, DenseMatrix &x) except+ nogil void FFGJ_solve "SymEngine::fraction_free_gauss_jordan_solve"(const DenseMatrix &A, const DenseMatrix &b, DenseMatrix &x) except+ nogil void LDL_solve "SymEngine::LDL_solve"(const DenseMatrix &A, const DenseMatrix &b, DenseMatrix &x) except+ nogil void jacobian "SymEngine::sjacobian"(const DenseMatrix &A, const DenseMatrix &x, DenseMatrix &result) except+ nogil void diff "SymEngine::sdiff"(const DenseMatrix &A, rcp_const_basic &x, DenseMatrix &result) except+ nogil void eye (DenseMatrix &A, int k) nogil void diag(DenseMatrix &A, vec_basic &v, int k) nogil void ones(DenseMatrix &A) nogil void zeros(DenseMatrix &A) nogil void row_exchange_dense(DenseMatrix &A, unsigned i, unsigned j) nogil void row_mul_scalar_dense(DenseMatrix &A, unsigned i, rcp_const_basic &c) nogil void row_add_row_dense(DenseMatrix &A, unsigned i, unsigned j, rcp_const_basic &c) nogil void column_exchange_dense(DenseMatrix &A, unsigned i, unsigned j) nogil void dot(const DenseMatrix &A, const DenseMatrix &B, DenseMatrix &C) nogil void cross(const DenseMatrix &A, const DenseMatrix &B, DenseMatrix &C) nogil cdef extern from "": void pivoted_LU (const DenseMatrix &A, DenseMatrix &L, DenseMatrix &U, vector[pair[int, int]] &P) except+ nogil cdef extern from "" namespace "SymEngine": int probab_prime_p(const Integer &a, int reps) RCP[const Integer] nextprime (const Integer &a) nogil RCP[const Integer] gcd(const Integer &a, const Integer &b) nogil RCP[const Integer] lcm(const Integer &a, const Integer &b) nogil void gcd_ext(const Ptr[RCP[Integer]] &g, const Ptr[RCP[Integer]] &s, const Ptr[RCP[Integer]] &t, const Integer &a, const Integer &b) nogil RCP[const Integer] mod "SymEngine::mod_f"(const Integer &n, const Integer &d) except+ nogil RCP[const Integer] quotient "SymEngine::quotient_f"(const Integer &n, const Integer &d) except+ nogil void quotient_mod "SymEngine::quotient_mod_f"(const Ptr[RCP[Integer]] &q, const Ptr[RCP[Integer]] &mod, const Integer &n, const Integer &d) except+ nogil int mod_inverse(const Ptr[RCP[Integer]] &b, const Integer &a, const Integer &m) nogil bool crt(const Ptr[RCP[Integer]] &R, const vec_integer &rem, const vec_integer &mod) nogil RCP[const Integer] fibonacci(unsigned long n) nogil void fibonacci2(const Ptr[RCP[Integer]] &g, const Ptr[RCP[Integer]] &s, unsigned long n) nogil RCP[const Integer] lucas(unsigned long n) nogil void lucas2(const Ptr[RCP[Integer]] &g, const Ptr[RCP[Integer]] &s, unsigned long n) nogil RCP[const Integer] binomial(const Integer &n,unsigned long k) nogil RCP[const Integer] factorial(unsigned long n) nogil bool divides(const Integer &a, const Integer &b) nogil int factor(const Ptr[RCP[Integer]] &f, const Integer &n, double B1) nogil int factor_lehman_method(const Ptr[RCP[Integer]] &f, const Integer &n) nogil int factor_pollard_pm1_method(const Ptr[RCP[Integer]] &f, const Integer &n, unsigned B, unsigned retries) nogil int factor_pollard_rho_method(const Ptr[RCP[Integer]] &f, const Integer &n, unsigned retries) nogil void prime_factors(vec_integer &primes, const Integer &n) except+ nogil void prime_factor_multiplicities(map_integer_uint &primes, const Integer &n) except+ nogil RCP[const Number] bernoulli(unsigned long n) except+ nogil bool primitive_root(const Ptr[RCP[Integer]] &g, const Integer &n) nogil void primitive_root_list(vec_integer &roots, const Integer &n) nogil RCP[const Integer] totient(RCP[const Integer] n) nogil RCP[const Integer] carmichael(RCP[const Integer] n) nogil bool multiplicative_order(const Ptr[RCP[Integer]] &o, RCP[const Integer] a, RCP[const Integer] n) nogil int legendre(const Integer &a, const Integer &n) nogil int jacobi(const Integer &a, const Integer &n) nogil int kronecker(const Integer &a, const Integer &n) nogil void nthroot_mod_list(vec_integer &roots, RCP[const Integer] n, RCP[const Integer] a, RCP[const Integer] m) nogil bool nthroot_mod(const Ptr[RCP[Integer]] &root, RCP[const Integer] n, RCP[const Integer] a, RCP[const Integer] m) nogil bool powermod(const Ptr[RCP[Integer]] &powm, RCP[const Integer] a, RCP[const Number] b, RCP[const Integer] m) nogil void powermod_list(vec_integer &powm, RCP[const Integer] a, RCP[const Number] b, RCP[const Integer] m) nogil cdef extern from "" namespace "SymEngine": void sieve_generate_primes "SymEngine::Sieve::generate_primes"(vector[unsigned] &primes, unsigned limit) nogil cdef cppclass sieve_iterator "SymEngine::Sieve::iterator": sieve_iterator() sieve_iterator(unsigned limit) nogil unsigned next_prime() nogil cdef extern from "" namespace "SymEngine": bool has_symbol(const Basic &b, const Basic &x) except+ nogil rcp_const_basic coeff(const Basic &b, const Basic &x, const Basic &n) except+ nogil set_basic free_symbols(const Basic &b) except+ nogil set_basic free_symbols(const MatrixBase &b) except+ nogil unsigned count_ops(const vec_basic &a) nogil cdef extern from "" namespace "SymEngine": cdef cppclass Boolean(Basic): RCP[const Boolean] logical_not() except+ nogil cdef cppclass BooleanAtom(Boolean): bool get_val() nogil cdef cppclass Relational(Boolean): pass cdef cppclass Equality(Relational): pass cdef cppclass Unequality(Relational): pass cdef cppclass LessThan(Relational): pass cdef cppclass StrictLessThan(Relational): pass cdef cppclass Piecewise(Basic): pass cdef cppclass Contains(Boolean): pass cdef cppclass And(Boolean): pass cdef cppclass Or(Boolean): pass cdef cppclass Not(Boolean): pass cdef cppclass Xor(Boolean): pass rcp_const_basic boolTrue rcp_const_basic boolFalse cdef RCP[const Boolean] Eq(rcp_const_basic &lhs) except+ nogil cdef RCP[const Boolean] Eq(rcp_const_basic &lhs, rcp_const_basic &rhs) except+ nogil cdef RCP[const Boolean] Ne(rcp_const_basic &lhs, rcp_const_basic &rhs) except+ nogil cdef RCP[const Boolean] Ge(rcp_const_basic &lhs, rcp_const_basic &rhs) except+ nogil cdef RCP[const Boolean] Gt(rcp_const_basic &lhs, rcp_const_basic &rhs) except+ nogil cdef RCP[const Boolean] Le(rcp_const_basic &lhs, rcp_const_basic &rhs) except+ nogil cdef RCP[const Boolean] Lt(rcp_const_basic &lhs, rcp_const_basic &rhs) except+ nogil ctypedef Boolean const_Boolean "const SymEngine::Boolean" ctypedef vector[pair[rcp_const_basic, RCP[const_Boolean]]] PiecewiseVec; ctypedef vector[RCP[Boolean]] vec_boolean "SymEngine::vec_boolean" ctypedef set[RCP[Boolean]] set_boolean "SymEngine::set_boolean" cdef RCP[const Boolean] logical_and(set_boolean &s) except+ nogil cdef RCP[const Boolean] logical_nand(set_boolean &s) except+ nogil cdef RCP[const Boolean] logical_or(set_boolean &s) except+ nogil cdef RCP[const Boolean] logical_not(RCP[const Boolean] &s) except+ nogil cdef RCP[const Boolean] logical_nor(set_boolean &s) except+ nogil cdef RCP[const Boolean] logical_xor(vec_boolean &s) except+ nogil cdef RCP[const Boolean] logical_xnor(vec_boolean &s) except+ nogil cdef rcp_const_basic piecewise(PiecewiseVec vec) except+ nogil cdef RCP[const Boolean] contains(rcp_const_basic &expr, RCP[const Set] &set) nogil cdef extern from "" namespace "SymEngine": cdef cppclass EvalfDomain: pass cdef EvalfDomain EvalfComplex "SymEngine::EvalfDomain::Complex" cdef EvalfDomain EvalfReal "SymEngine::EvalfDomain::Real" cdef EvalfDomain EvalfSymbolic "SymEngine::EvalfDomain::Symbolic" rcp_const_basic evalf(const Basic &b, unsigned long bits, EvalfDomain domain) except+ nogil cdef extern from "" namespace "SymEngine": double eval_double(const Basic &b) except+ nogil double complex eval_complex_double(const Basic &b) except+ nogil cdef extern from "" namespace "SymEngine": cdef cppclass LambdaRealDoubleVisitor: LambdaRealDoubleVisitor() nogil void init(const vec_basic &x, const vec_basic &b, bool cse) except+ nogil void call(double *r, const double *x) nogil cdef cppclass LambdaComplexDoubleVisitor: LambdaComplexDoubleVisitor() nogil void init(const vec_basic &x, const vec_basic &b, bool cse) except+ nogil void call(double complex *r, const double complex *x) nogil cdef extern from "" namespace "SymEngine": cdef cppclass LLVMVisitor: LLVMVisitor() nogil void init(const vec_basic &x, const vec_basic &b, bool cse, int opt_level) except+ nogil const string& dumps() nogil void loads(const string&) nogil cdef cppclass LLVMFloatVisitor(LLVMVisitor): void call(float *r, const float *x) nogil cdef cppclass LLVMDoubleVisitor(LLVMVisitor): void call(double *r, const double *x) nogil cdef cppclass LLVMLongDoubleVisitor(LLVMVisitor): void call(long double *r, const long double *x) nogil cdef extern from "" namespace "SymEngine": cdef cppclass SeriesCoeffInterface: rcp_const_basic as_basic() except+ nogil umap_int_basic as_dict() except+ nogil rcp_const_basic get_coeff(int) except+ nogil ctypedef RCP[const SeriesCoeffInterface] rcp_const_seriescoeffinterface "SymEngine::RCP" rcp_const_seriescoeffinterface series "SymEngine::series"(rcp_const_basic &ex, RCP[const Symbol] &var, unsigned int prec) except+ nogil cdef extern from "" namespace "SymEngine": void eval_mpfr(mpfr_t result, const Basic &b, mpfr_rnd_t rnd) except+ nogil cdef extern from "" namespace "SymEngine": void eval_mpc(mpc_t result, const Basic &b, mpfr_rnd_t rnd) except+ nogil cdef extern from "" namespace "SymEngine": rcp_const_basic parse(const string &n) except+ nogil cdef extern from "" namespace "SymEngine": cdef cppclass Set(Basic): RCP[const Set] set_intersection(RCP[const Set] &o) except+ nogil RCP[const Set] set_union(RCP[const Set] &o) except+ nogil RCP[const Set] set_complement(RCP[const Set] &o) except+ nogil RCP[const Boolean] contains(rcp_const_basic &a) except+ nogil cdef cppclass Interval(Set): pass cdef cppclass EmptySet(Set): pass cdef cppclass Reals(Set): pass cdef cppclass Rationals(Set): pass cdef cppclass Integers(Set): pass cdef cppclass UniversalSet(Set): pass cdef cppclass FiniteSet(Set): pass cdef cppclass Union(Set): pass cdef cppclass Complement(Set): pass cdef cppclass ConditionSet(Set): pass cdef cppclass ImageSet(Set): pass ctypedef set[RCP[Set]] set_set "SymEngine::set_set" cdef rcp_const_basic interval(RCP[const Number] &start, RCP[const Number] &end, bool l, bool r) except+ nogil cdef RCP[const EmptySet] emptyset() except+ nogil cdef RCP[const Reals] reals() except+ nogil cdef RCP[const Rationals] rationals() except+ nogil cdef RCP[const Integers] integers() except+ nogil cdef RCP[const UniversalSet] universalset() except+ nogil cdef RCP[const Set] finiteset(set_basic &container) except+ nogil cdef RCP[const Set] set_union(set_set &a) except+ nogil cdef RCP[const Set] set_intersection(set_set &a) except+ nogil cdef RCP[const Set] set_complement_helper(RCP[const Set] &container, RCP[const Set] &universe) except+ nogil cdef RCP[const Set] set_complement(RCP[const Set] &universe, RCP[const Set] &container) except+ nogil cdef RCP[const Set] conditionset(rcp_const_basic &sym, RCP[const Boolean] &condition) except+ nogil cdef RCP[const Set] imageset(rcp_const_basic &sym, rcp_const_basic &expr, RCP[const Set] &base) except+ nogil cdef extern from "" namespace "SymEngine": cdef RCP[const Set] solve(rcp_const_basic &f, RCP[const Symbol] &sym) except+ nogil cdef RCP[const Set] solve(rcp_const_basic &f, RCP[const Symbol] &sym, RCP[const Set] &domain) except+ nogil cdef vec_basic linsolve(const vec_basic &eqs, const vec_sym &syms) except+ nogil cdef extern from "symengine/tribool.h" namespace "SymEngine": cdef cppclass tribool: pass # tribool is an enum class cdef bool is_true(tribool) nogil cdef bool is_false(tribool) nogil cdef bool is_indeterminate(tribool) nogil cdef extern from "symengine/tribool.h" namespace "SymEngine::tribool": cdef tribool indeterminate cdef tribool trifalse cdef tribool tritrue cdef extern from "" namespace "SymEngine": string ccode(const Basic &x) except+ nogil string latex(const Basic &x) except+ nogil string latex(const DenseMatrix &x, unsigned max_rows, unsigned max_cols) except+ nogil string unicode(const Basic &x) except+ nogil ## Defined in 'symengine/cwrapper.cpp' cdef struct CRCPBasic: rcp_const_basic m