ca_field_init_qq K ctx

Initializes K to represent the trivial field \(\mathbb{Q}\).

ca_field_init_nf K x ctx

Initializes K to represent the algebraic number field \(\mathbb{Q}(x)\).

ca_field_init_const K func ctx

Initializes K to represent the field \(\mathbb{Q}(x)\) where x is a builtin constant defined by func (example: func = CA_Pi for \(x = \pi\)).

ca_field_init_fx K func x ctx

Initializes K to represent the field \(\mathbb{Q}(a)\) where \(a = f(x)\), given a number x and a builtin univariate function func (example: func = CA_Exp for \(e^x\)).

ca_field_init_fxy K func x y ctx

Initializes K to represent the field \(\mathbb{Q}(a,b)\) where \(a = f(x, y)\).

ca_field_init_multi K len ctx

Initializes K to represent a multivariate field \(\mathbb{Q}(a_1, \ldots, a_n)\) in n extension numbers. The extension numbers must subsequently be assigned one by one using ca_field_set_ext.

ca_field_set_ext K i x_index ctx

Sets the extension number at position i (here indexed from 0) of K to the generator of the field with index x_index in ctx. (It is assumed that the generating field is a univariate field.)

This only inserts a shallow reference: the field at index x_index must be kept alive until K has been cleared.

ca_field_clear K ctx

Clears the field K. This does not clear the individual extension numbers, which are only held as references.

ca_field_print K ctx

Prints a description of the field K to standard output.

ca_field_build_ideal K ctx

Given K with assigned extension numbers, builds the reduction ideal in-place.

ca_field_build_ideal_erf K ctx

Builds relations for error functions present among the extension numbers in K. This heuristic adds relations that are consequences of the functional equations \(\operatorname{erf}(x) = -\operatorname{erf}(-x)\), \(\operatorname{erfc}(x) = 1-\operatorname{erf}(x)\), \(\operatorname{erfi}(x) = -i\operatorname{erf}(ix)\).

ca_field_cmp K1 K2 ctx

Compares the field objects K1 and K2 in a canonical sort order, returning -1, 0 or 1. This only performs a lexicographic comparison of the representations of K1 and K2; the return value does not say anything meaningful about the relative structures of K1 and K2 as mathematical fields.

ca_field_cache_init cache ctx

Initializes cache for use.

ca_field_cache_clear cache ctx

Clears cache, freeing the memory allocated internally. This does not clear the individual extension numbers, which are only held as references.

ca_field_cache_insert_ext cache x len ctx

Adds the field defined by the length-len list of extension numbers x to cache without duplication. If such a field already exists in cache, a pointer to that instance is returned. Otherwise, a field with extension numbers x is inserted into cache and a pointer to that new instance is returned. Upon insertion of a new field, the reduction ideal is constructed via ca_field_build_ideal.