piranha
0.10
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Polynomial class. More...
#include <piranha/polynomial.hpp>
Public Types | |
template<typename Cf2 > | |
using | rebind = polynomial< Cf2, Key > |
Series rebind alias. | |
using | term_type = term< Cf, Key > |
Alias for term type. | |
using | size_type = typename container_type::size_type |
Size type. More... | |
using | const_iterator = const_iterator_impl |
Const iterator. More... | |
Public Member Functions | |
polynomial ()=default | |
Defaulted default constructor. More... | |
polynomial (const polynomial &)=default | |
Defaulted copy constructor. | |
polynomial (polynomial &&)=default | |
Defaulted move constructor. | |
template<typename Str , str_enabler< Str > = 0> | |
polynomial (Str &&name) | |
Constructor from symbol name. More... | |
~polynomial () | |
Trivial destructor. | |
polynomial & | operator= (const polynomial &other)=default |
Copy assignment operator. More... | |
polynomial & | operator= (polynomial &&other)=default |
Move assignment operator. More... | |
template<typename T > | |
pow_ret_type< T > | pow (const T &x) const |
Override default exponentiation method. More... | |
template<typename Series = polynomial> | |
inverse_type< Series > | invert () const |
Inversion. More... | |
template<typename T = polynomial> | |
integrate_type< T > | integrate (const std::string &name) const |
Integration. More... | |
template<typename T , find_cf_enabler< T > = 0> | |
Cf | find_cf (const T &c) const |
Find coefficient. More... | |
template<typename T , find_cf_init_list_enabler< T > = 0> | |
Cf | find_cf (std::initializer_list< T > l) const |
Find coefficient. More... | |
degree_type< T > | degree () const |
Total degree. More... | |
pdegree_type< T > | degree (const symbol_fset &names) const |
Partial degree. More... | |
ldegree_type< T > | ldegree () const |
Total low degree. More... | |
pldegree_type< T > | ldegree (const symbol_fset &names) const |
Partial low degree. More... | |
polynomial< Cf, Key > | truncate_degree (const T &max_degree) const |
Total degree truncation. More... | |
polynomial< Cf, Key > | truncate_degree (const T &max_degree, const symbol_fset &names) const |
Partial degree truncation. More... | |
t_degree_type< T > | t_degree () const |
Trigonometric degree. More... | |
pt_degree_type< T > | t_degree (const symbol_fset &names) const |
Partial trigonometric degree. More... | |
t_ldegree_type< T > | t_ldegree () const |
Trigonometric low degree. More... | |
pt_ldegree_type< T > | t_ldegree (const symbol_fset &names) const |
Partial trigonometric low degree. More... | |
t_order_type< T > | t_order () const |
Trigonometric order. More... | |
pt_order_type< T > | t_order (const symbol_fset &names) const |
Partial trigonometric order. More... | |
t_lorder_type< T > | t_lorder () const |
Trigonometric low order. More... | |
pt_lorder_type< T > | t_lorder (const symbol_fset &names) const |
Partial trigonometric low order. More... | |
ipow_subs_type< T > | ipow_subs (const std::string &name, const integer &n, const T &x) const |
Substitution. More... | |
ipow_subs_type< T > | ipow_subs (const std::string &name, const Int &n, const T &x) const |
Substitution. More... | |
subs_type< T > | subs (const symbol_fmap< T > &dict) const |
Substitution. More... | |
t_subs_type< T, U > | t_subs (const std::string &name, const T &c, const U &s) const |
Trigonometric substitution. More... | |
size_type | size () const |
Series size. More... | |
bool | empty () const |
Empty test. More... | |
bool | is_single_coefficient () const |
Test for single-coefficient series. More... | |
void | insert (T &&term) |
Insert term. More... | |
void | insert (T &&term) |
Insert generic term with Sign = true . More... | |
polynomial< Cf, Key > | operator+ () const |
Identity operator. More... | |
polynomial< Cf, Key > | operator- () const |
Negation operator. More... | |
void | negate () |
Negate series in-place. More... | |
partial_type< Series > | partial (const std::string &name) const |
Partial derivative. More... | |
const_iterator | begin () const |
Begin iterator. More... | |
const_iterator | end () const |
End iterator. More... | |
polynomial< Cf, Key > | filter (std::function< bool(const std::pair< typename term_type::cf_type, polynomial< Cf, Key > > &)> func) const |
Term filtering. More... | |
polynomial< Cf, Key > | transform (std::function< std::pair< typename term_type::cf_type, polynomial< Cf, Key > >(const std::pair< typename term_type::cf_type, polynomial< Cf, Key > > &)> func) const |
Term transformation. More... | |
polynomial< Cf, Key > | trim () const |
Trim. More... | |
void | print_tex (std::ostream &os) const |
Print in TeX mode. More... | |
std::size_t | hash () const |
Hash value. More... | |
bool | is_identical (const polynomial< Cf, Key > &other) const |
Check for identical series. More... | |
const symbol_fset & | get_symbol_set () const |
Symbol set getter. More... | |
void | set_symbol_set (const symbol_fset &args) |
Symbol set setter. More... | |
Table-querying methods | |
Methods to query the properties of the internal container used to store the terms. | |
sparsity_info_type | table_sparsity () const |
Table sparsity. More... | |
double | table_load_factor () const |
Table load factor. More... | |
size_type | table_bucket_count () const |
Table bucket count. More... | |
Low-level interface | |
Low-level methods. | |
container_type & | _container () |
Get a mutable reference to the container of terms. More... | |
const container_type & | _container () const |
Get a const reference to the container of terms. More... | |
Static Public Member Functions | |
template<typename U , typename T = polynomial, at_degree_set_enabler< T, U > = 0> | |
static void | set_auto_truncate_degree (const U &max_degree) |
Set total-degree-based auto-truncation. More... | |
template<typename U , typename T = polynomial, at_degree_set_enabler< T, U > = 0> | |
static void | set_auto_truncate_degree (const U &max_degree, const symbol_fset &names) |
Set partial-degree-based auto-truncation. More... | |
template<typename T = polynomial, at_degree_enabler< T > = 0> | |
static void | unset_auto_truncate_degree () |
Disable degree-based auto-truncation. More... | |
template<typename T = polynomial, at_degree_enabler< T > = 0> | |
static std::tuple< int, degree_type< T >, symbol_fset > | get_auto_truncate_degree () |
Query the status of the degree-based auto-truncation mechanism. More... | |
template<typename T = polynomial, um_enabler< T > = 0> | |
static polynomial | untruncated_multiplication (const polynomial &p1, const polynomial &p2) |
Untruncated multiplication. More... | |
template<typename U , typename T = polynomial, tm_enabler< T, U > = 0> | |
static polynomial | truncated_multiplication (const polynomial &p1, const polynomial &p2, const U &max_degree) |
Truncated multiplication (total degree). More... | |
template<typename U , typename T = polynomial, tm_enabler< T, U > = 0> | |
static polynomial | truncated_multiplication (const polynomial &p1, const polynomial &p2, const U &max_degree, const symbol_fset &names) |
Truncated multiplication (partial degree). More... | |
static void | clear_pow_cache () |
Clear the internal cache of natural powers. More... | |
static void | register_custom_derivative (const std::string &name, F func) |
Register custom partial derivative. More... | |
static void | unregister_custom_derivative (const std::string &name) |
Unregister custom partial derivative. More... | |
static void | unregister_all_custom_derivatives () |
Unregister all custom partial derivatives. More... | |
Protected Types | |
using | container_type = hash_set< term_type > |
Container type for terms. | |
Protected Attributes | |
symbol_fset | m_symbol_set |
Symbol set. | |
container_type | m_container |
Terms container. | |
Polynomial class.
This class represents multivariate polynomials as collections of multivariate polynomial terms. Cf
represents the ring over which the polynomial is defined, while Key
represents the monomial type.
Polynomials support an automatic degree-based truncation mechanism, disabled by default, which comes into play during polynomial multiplication. It allows to discard automatically all those terms, generated during series multiplication, whose total or partial degree is greater than a specified limit. This mechanism can be configured via a set of thread-safe static methods, and it is enabled if:
D
,D
is equality-comparable, subtractable and the type resulting from the subtraction is still D
.This class satisfies the piranha::is_series and piranha::is_cf type traits.
Cf
must be suitable for use in piranha::series as first template argument, Key
must be an instance of either piranha::monomial or piranha::kronecker_monomial.
This class provides the same guarantee as the base series type it derives from.
Move semantics is equivalent to the move semantics of the base series type it derives from.
Definition at line 149 of file polynomial.hpp.
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inherited |
Const iterator.
Iterator type that can be used to iterate over the terms of the series. The object returned upon dereferentiation is an std::pair
in which the first element is a copy of the coefficient of the term, the second element a single-term instance of Derived
constructed from the term's key and a unitary coefficient.
This iterator is an input iterator which additionally offers the multi-pass guarantee.
Definition at line 1994 of file series.hpp.
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inherited |
Size type.
Used to represent the number of terms in the series. Equivalent to piranha::hash_set::size_type.
Definition at line 1981 of file series.hpp.
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default |
Defaulted default constructor.
Will construct a polynomial with zero terms.
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inlineexplicit |
Constructor from symbol name.
Str
is a C or C++ string.Will construct a univariate polynomial made of a single term with unitary coefficient and exponent, representing the symbolic variable name
. The type of name
must be a string type (either C or C++).
name | name of the symbolic variable that the polynomial will represent. |
unspecified | any exception thrown by:
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Definition at line 480 of file polynomial.hpp.
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inlineinherited |
Get a mutable reference to the container of terms.
Definition at line 2788 of file series.hpp.
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inlineinherited |
Get a const reference to the container of terms.
Definition at line 2796 of file series.hpp.
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inlineinherited |
Begin iterator.
Return an iterator to the first term of the series. The returned iterator will provide, when dereferenced, an std::pair
in which the first element is a copy of the coefficient of the term, whereas the second element is a single-term instance of Derived
built from the term's key and a unitary coefficient.
Note that terms are stored unordered in the series, hence it is not defined which particular term will be returned by calling this method. The only guarantee is that the iterator can be used to transverse all the series' terms until piranha::series::end() is eventually reached.
Calling any non-const method on the series will invalidate the iterators obtained via piranha::series::begin() and piranha::series::end().
unspecified | any exception thrown by:
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Definition at line 2504 of file series.hpp.
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inlinestaticinherited |
Clear the internal cache of natural powers.
This method can be used to clear the cache of natural powers of series maintained by piranha::series::pow().
unspecified | any exception thrown by threading primitives. |
Definition at line 2371 of file series.hpp.
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inlineinherited |
Total degree.
The degree of the series is the maximum degree of its terms. If the series is empty, zero will be returned.
std::overflow_error | if the computation results in an overflow. |
unspecified | any exception thrown by:
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Definition at line 390 of file power_series.hpp.
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inlineinherited |
Partial degree.
The partial degree of the series is the maximum partial degree of its terms. If the series is empty, zero will be returned.
names | names of the variables to be considered in the computation of the degree. |
std::overflow_error | if the computation results in an overflow. |
unspecified | any exception thrown by:
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Definition at line 444 of file power_series.hpp.
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inlineinherited |
Empty test.
true
if size() is nonzero, false
otherwise. Definition at line 2103 of file series.hpp.
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inlineinherited |
End iterator.
Return an iterator one past the last term of the series. See the documentation of piranha::series::begin() on how the returned iterator can be used.
unspecified | any exception thrown by:
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Definition at line 2523 of file series.hpp.
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inlineinherited |
Term filtering.
This method will apply the functor func
to each term in the series, and produce a return series containing all terms in this
for which func
returns true
. Terms are passed to func
in the format resulting from dereferencing the iterators obtained via piranha::series::begin().
func | filtering functor. |
unspecified | any exception thrown by:
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Definition at line 2547 of file series.hpp.
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inline |
Find coefficient.
T
satisfies piranha::has_input_begin_end,Key
can be constructed from the begin/end iterators of c
and a piranha::symbol_fset.This method will first construct a term with zero coefficient and key initialised from the begin/end iterators of c
and the symbol set of this
, and it will then try to locate the term inside this
. If the term is found, its coefficient will be returned. Otherwise, a coefficient initialised from 0 will be returned.
c | the container that will be used to construct the Key to be located. |
Key
corresponds to c
if such term exists, zero otherwise.unspecified | any exception thrown by:
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Definition at line 754 of file polynomial.hpp.
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inline |
Find coefficient.
Key
can be constructed from the begin/end iterators of l
and a piranha::symbol_fset.This method is identical to the other overload with the same name, and it is provided for convenience.
l | the list that will be used to construct the Key to be located. |
Key
corresponds to l
if such term exists, zero otherwise.unspecified | any exception thrown by the other overload. |
Definition at line 774 of file polynomial.hpp.
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inlinestatic |
Query the status of the degree-based auto-truncation mechanism.
This method will return a tuple of three elements describing the status of the degree-based auto-truncation mechanism. The elements of the tuple have the following meaning:
unspecified | any exception thrown by threading primitives or by the involved constructors. |
Definition at line 727 of file polynomial.hpp.
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inlineinherited |
Symbol set getter.
Definition at line 2762 of file series.hpp.
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inlineinherited |
Hash value.
The hash value for a series is zero if the series is empty, otherwise it is computed by adding the hash values of all terms. This ensures that two identical series in which the terms are stored in different order still produce the same hash value.
Note, however, that the arguments of the series are not considered in the hash value and that, in general, two series that compare equal according to operator==() will not have the same hash value (as the equality operator merges the arguments of two series before actually performing the comparison). Instead of operator==(), is_identical() should be used for storing series as keys in associative containers.
unspecified | any exception thrown by computing the hash of a term. |
Definition at line 2730 of file series.hpp.
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inlineinherited |
Insert term.
T
is piranha::series::term_type.This method will insert term
into the series using internally piranha::hash_set::insert.
The insertion algorithm proceeds as follows:
std::invalid_argument
exception is thrown;Sign
is true
) or subtracted (if Sign
is false
) to the existing term's coefficient;Sign
is false
, its coefficient is negated.After any modification to an existing term in the series (e.g., via insertion with negative Sign
or via in-place addition or subtraction of existing coefficients), the term will be checked again for compatibility and ignorability, and, in case the term has become incompatible or ignorable, it will be erased from the series.
The exception safety guarantee upon insertion is that the series will be left in an undefined but valid state. Such a guarantee relies on the fact that the addition/subtraction and negation methods of the coefficient type will leave the coefficient in a valid (possibly undefined) state in face of exceptions.
term | term to be inserted. |
unspecified | any exception thrown by:
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std::invalid_argument | if term is incompatible. |
Definition at line 2161 of file series.hpp.
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inlineinherited |
Insert generic term with Sign = true
.
T
is piranha::series::term_type.Convenience wrapper for the generic insert() method, with Sign
set to true
.
term | term to be inserted. |
unspecified | any exception thrown by generic insert(). |
Definition at line 2177 of file series.hpp.
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inline |
Integration.
This method will attempt to compute the antiderivative of the polynomial term by term. If the term's coefficient does not depend on the integration variable, the result will be calculated via the integration of the corresponding monomial. Integration with respect to a variable appearing to the power of -1 will fail.
Otherwise, a strategy of integration by parts is attempted, its success depending on the integrability of the coefficient and on the value of the exponent of the integration variable. The integration will fail if the exponent is negative or non-integral.
name | integration variable. |
this
with respect to name
.std::invalid_argument | if the integration procedure fails. |
unspecified | any exception thrown by:
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Definition at line 591 of file polynomial.hpp.
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inline |
Inversion.
piranha::polynomial::pow(-1)
is a well-formed expression.unspecified | any exception thrown by piranha::polynomial::pow(). |
Definition at line 557 of file polynomial.hpp.
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inlineinherited |
Substitution.
This method will return an object resulting from the substitution of the integral power of the symbol called name
in this
with the generic object x
.
name | name of the symbol to be substituted. |
n | integral power of the symbol to be substituted. |
x | object used for the substitution. |
unspecified | any exception resulting from:
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Definition at line 224 of file ipow_substitutable_series.hpp.
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inlineinherited |
Substitution.
Int
is a C++ integral type.This is a convenience method that will call the other ipow_subs() overload after converting n
to piranha::integer.
name | name of the symbol to be substituted. |
n | integral power of the symbol to be substituted. |
x | object used for the substitution. |
unspecified | any exception resulting from calling the other ipow_subs() overload, or by constructing a piranha::integer from a C++ integral type. |
Definition at line 252 of file ipow_substitutable_series.hpp.
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inlineinherited |
Check for identical series.
Derived
is equality-comparable.This method will return true
if the symbol sets of this
and other
are the same, and other == *this
.
other | argument for the comparison. |
true
if this
and other
are identical, false
otherwise.unspecified | any exception thrown by the comparison operator of Derived . |
Definition at line 2754 of file series.hpp.
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inlineinherited |
Test for single-coefficient series.
A series is considered to be single-coefficient when it is symbolically equivalent to a coefficient. That is, the series is either empty (in which case it is considered to be equivalent to a coefficient constructed from zero) or consisting of a single term with unitary key (in which case the series is considered equivalent to its only coefficient).
true
in case of single-coefficient series, false
otherwise.unspecified | any exception thrown by the is_unitary() method of the key type. |
Definition at line 2118 of file series.hpp.
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inlineinherited |
Total low degree.
The low degree of the series is the minimum low degree of its terms. If the series is empty, zero will be returned.
std::overflow_error | if the computation results in an overflow. |
unspecified | any exception thrown by:
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Definition at line 416 of file power_series.hpp.
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inlineinherited |
Partial low degree.
The partial low degree of the series is the minimum partial low degree of its terms. If the series is empty, zero will be returned.
names | names of the variables to be considered in the computation of the low degree. |
std::overflow_error | if the computation results in an overflow. |
unspecified | any exception thrown by:
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Definition at line 475 of file power_series.hpp.
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inlineinherited |
Negate series in-place.
This method will call math::negate() on the coefficients of all terms. In case of exceptions, the basic exception safety guarantee is provided.
If any term becomes ignorable or incompatible after negation, it will be erased from the series.
unspecified | any exception thrown by math::negate() on the coefficient type. |
Definition at line 2214 of file series.hpp.
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inlineinherited |
Identity operator.
this
, cast to Derived
.unspecified | any exception thrown by the copy constructor. |
Definition at line 2187 of file series.hpp.
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inlineinherited |
Negation operator.
this
on which negate() has been called.unspecified | any exception thrown by:
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Definition at line 2199 of file series.hpp.
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default |
Copy assignment operator.
other | the assignment argument. |
this
.unspecified | any exception thrown by the assignment operator of the base class. |
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default |
Move assignment operator.
other | the assignment argument. |
this
.
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inlineinherited |
Partial derivative.
This method will return the partial derivative of this
with respect to the variable called name
. The method will construct the return value from the output of the differentiation methods of coefficient and key, and via arithmetic and/or term insertion operations.
Note that, contrary to the specialisation of piranha::math::partial() for series types, this method will not take into account custom derivatives registered via piranha::series::register_custom_derivative().
name | name of the argument with respect to which the derivative will be calculated. |
this
with respect to the symbol name
.unspecified | any exception thrown by:
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Definition at line 2405 of file series.hpp.
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inline |
Override default exponentiation method.
x
and the key type can be raised to the power of x
via its exponentiation method.This exponentiation override will check if the polynomial consists of a single-term with non-unitary key. In that case, the return polynomial will consist of a single term with coefficient computed via piranha::math::pow() and key computed via the monomial exponentiation method. Otherwise, the base (i.e., default) exponentiation method will be used.
x | exponent. |
this
to the power of x
.unspecified | any exception thrown by:
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Definition at line 530 of file polynomial.hpp.
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inlineinherited |
Print in TeX mode.
Print series to stream os
in TeX mode. The representation is constructed in the same way as explained in piranha::series::operator<<(), but using piranha::print_tex_coefficient() and the key's TeX printing method instead of the plain printing functions.
os | target stream. |
unspecified | any exception thrown by:
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Definition at line 2654 of file series.hpp.
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inlinestaticinherited |
Register custom partial derivative.
Derived
, and if F
is a type that can be used to construct std::function<partial_type(const Derived &)
, where partial_type
is the type resulting from the partial derivative of Derived
.Register a copy of a callable func
associated to the symbol name
for use by piranha::math::partial(). func
will be used to compute the partial derivative of instances of type Derived
with respect to name
in place of the default partial differentiation algorithm.
It is safe to call this method from multiple threads.
name | symbol for which the custom partial derivative function will be registered. |
func | custom partial derivative function. |
unspecified | any exception thrown by:
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Definition at line 2432 of file series.hpp.
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inlinestatic |
Set total-degree-based auto-truncation.
U
can be safely cast to the degree type.Setup the degree-based auto-truncation mechanism to truncate according to the total maximum degree. If the new auto truncation settings are different from the currently active ones, the natural power cache defined in piranha::series will be cleared.
max_degree | maximum total degree that will be retained during automatic truncation. |
unspecified | any exception thrown by:
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Definition at line 637 of file polynomial.hpp.
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inlinestatic |
Set partial-degree-based auto-truncation.
U
can be safely cast to the degree type.Setup the degree-based auto-truncation mechanism to truncate according to the partial degree. If the new auto truncation settings are different from the currently active ones, the natural power cache defined in piranha::series will be cleared.
max_degree | maximum partial degree that will be retained during automatic truncation. |
names | names of the variables that will be considered during the computation of the partial degree. |
unspecified | any exception thrown by:
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Definition at line 676 of file polynomial.hpp.
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inlineinherited |
Symbol set setter.
args | piranha::symbol_fset that will be associated to the series. |
std::invalid_argument | if the series is not empty. |
unspecified | any exception thrown by the copy assignment operator of piranha::symbol_fset. |
Definition at line 2773 of file series.hpp.
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inlineinherited |
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inlineinherited |
Substitution.
T
must be suitable for use in sm_intersect_idx().This method will return an object resulting from the substitution in this
of the symbols in dict
with the mapped values.
dict | a dictionary mapping a set of symbols to the values that will be substituted for them. |
unspecified | any exception resulting from:
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Definition at line 218 of file substitutable_series.hpp.
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inlineinherited |
Trigonometric degree.
unspecified | any exception resulting from the computation and comparison of the degree of the individual terms. |
Definition at line 204 of file trigonometric_series.hpp.
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inlineinherited |
Partial trigonometric degree.
names | the names of the variables to be considered in the computation. |
unspecified | any exception resulting from the computation and comparison of the degree of the individual terms. |
Definition at line 226 of file trigonometric_series.hpp.
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inlineinherited |
Trigonometric low degree.
unspecified | any exception resulting from the computation and comparison of the degree of the individual terms. |
Definition at line 248 of file trigonometric_series.hpp.
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inlineinherited |
Partial trigonometric low degree.
names | the names of the variables to be considered in the computation. |
unspecified | any exception resulting from the computation and comparison of the degree of the individual terms. |
Definition at line 270 of file trigonometric_series.hpp.
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inlineinherited |
Trigonometric low order.
unspecified | any exception resulting from the computation and comparison of the order of the individual terms. |
Definition at line 335 of file trigonometric_series.hpp.
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inlineinherited |
Partial trigonometric low order.
names | the names of the variables to be considered in the computation. |
unspecified | any exception resulting from the computation and comparison of the order of the individual terms. |
Definition at line 357 of file trigonometric_series.hpp.
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inlineinherited |
Trigonometric order.
unspecified | any exception resulting from the computation and comparison of the order of the individual terms. |
Definition at line 292 of file trigonometric_series.hpp.
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inlineinherited |
Partial trigonometric order.
names | the names of the variables to be considered in the computation. |
unspecified | any exception resulting from the computation and comparison of the order of the individual terms. |
Definition at line 314 of file trigonometric_series.hpp.
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inlineinherited |
Trigonometric substitution.
Trigonometric substitution is the substitution of the cosine and sine of name
for c
and s
.
name | name of the symbol that will be subject to substitution. |
c | cosine of name . |
s | sine of name . |
unspecified | any exception resulting from:
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Definition at line 219 of file t_substitutable_series.hpp.
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inlineinherited |
Table bucket count.
Definition at line 2263 of file series.hpp.
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inlineinherited |
Table load factor.
Will call piranha::hash_set::load_factor() on the internal terms container and return the result.
Definition at line 2255 of file series.hpp.
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inlineinherited |
Table sparsity.
Will call piranha::hash_set::evaluate_sparsity() on the internal terms container and return the result.
unspecified | any exception thrown by piranha::hash_set::evaluate_sparsity(). |
Definition at line 2244 of file series.hpp.
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inlineinherited |
Term transformation.
This method will apply the functor func
to each term in the series, and will use the return value of the functor to construct a new series. Terms are passed to func
in the same format resulting from dereferencing the iterators obtained via piranha::series::begin(), and func
is expected to produce a return value of the same type.
The return series is first initialised as an empty series. For each input term t
, the return value of func
is used to construct a new temporary series from the multiplication of t.first
and t.second
. Each temporary series is then added to the return value series.
This method requires the coefficient type to be multipliable by Derived
.
func | transforming functor. |
unspecified | any exception thrown by:
|
Definition at line 2585 of file series.hpp.
|
inlineinherited |
Trim.
This method will return a series mathematically equivalent to this
in which discardable arguments have been removed from the internal set of symbols. Which symbols are removed depends on the trimming method trim_identify()
of the key type (e.g., in a polynomial a symbol can be discarded if its exponent is zero in all monomials).
If the coefficient type is an instance of piranha::series, trim() will be called recursively on the coefficients while building the return value.
this
.unspecified | any exception thrown by:
|
Definition at line 2619 of file series.hpp.
|
inlineinherited |
Total degree truncation.
This method can be used to eliminate the parts of a series whose degree is greater than max_degree
. This includes the elimination of whole terms, but also the recursive truncation of coefficients via the piranha::math::truncate_degree() function, if supported by the coefficient. It must be noted that, in general, this method is not guaranteed to eliminate all the parts whose degree is greater than max_degree
(in particular, in the current implementation there is no truncation implemented for keys - a key is kept as-is or completely eliminated).
max_degree | maximum allowed total degree. |
this
.unspecified | any exception thrown by:
|
Definition at line 510 of file power_series.hpp.
|
inlineinherited |
Partial degree truncation.
This method is equivalent to the other overload, the only difference being that the partial degree is considered in the computation.
max_degree | maximum allowed partial degree. |
names | names of the variables to be considered in the computation of the partial degree. |
this
.unspecified | any exception thrown by:
|
Definition at line 543 of file power_series.hpp.
|
inlinestatic |
Truncated multiplication (total degree).
U
can be safely cast to the degree type of the calling piranha::polynomial.This function will return the product of p1
and p2
, truncated to the maximum total degree of max_degree
(regardless of the current automatic truncation settings). Note that this function is available only if the operands are of the same type and no type promotions affect the coefficient types during multiplication.
p1 | the first operand. |
p2 | the second operand. |
max_degree | the maximum total degree in the result. |
p1
and p2
.unspecified | any exception thrown by:
|
Definition at line 835 of file polynomial.hpp.
|
inlinestatic |
Truncated multiplication (partial degree).
U
can be safely cast to the degree type of the calling piranha::polynomial.This function will return the product of p1
and p2
, truncated to the maximum partial degree of max_degree
(regardless of the current automatic truncation settings). Note that this function is available only if the operands are of the same type and no type promotions affect the coefficient types during multiplication.
p1 | the first operand. |
p2 | the second operand. |
max_degree | the maximum degree in the result. |
names | the set of the symbols that will be considered in the computation of the degree. |
p1
and p2
.unspecified | any exception thrown by:
|
Definition at line 872 of file polynomial.hpp.
|
inlinestaticinherited |
Unregister all custom partial derivatives.
Derived
.Will unregister all custom derivatives currently registered via register_custom_derivative(). It is safe to call this method from multiple threads.
unspecified | any exception thrown by failure(s) in threading primitives. |
Definition at line 2478 of file series.hpp.
|
inlinestaticinherited |
Unregister custom partial derivative.
Derived
.Unregister the custom partial derivative function associated to the symbol name
. If no custom partial derivative was previously registered using register_custom_derivative(), calling this function will be a no-op.
It is safe to call this method from multiple threads.
name | symbol for which the custom partial derivative function will be unregistered. |
unspecified | any exception thrown by:
|
Definition at line 2459 of file series.hpp.
|
inlinestatic |
Disable degree-based auto-truncation.
Disable the degree-based auto-truncation mechanism.
unspecified | any exception thrown by:
|
Definition at line 701 of file polynomial.hpp.
|
inlinestatic |
Untruncated multiplication.
This function will return the product of p1
and p2
, computed without truncation (regardless of the current automatic truncation settings). Note that this function is available only if the operands are of the same type and no type promotions affect the coefficient types during multiplication.
p1 | the first operand. |
p2 | the second operand. |
p1
and p2
.unspecified | any exception thrown by:
|
Definition at line 800 of file polynomial.hpp.