6. Rings

CLN has a class of abstract rings.

                         Ring
                       cl_ring
                      <cl_ring.h>

Rings can be compared for equality:

bool operator== (const cl_ring&, const cl_ring&)
bool operator!= (const cl_ring&, const cl_ring&): These compare two rings for equality.

Given a ring R, the following members can be used.

void R->fprint (cl_ostream stream, const cl_ring_element& x)
cl_boolean R->equal (const cl_ring_element& x, const cl_ring_element& y)
cl_ring_element R->zero ()
cl_boolean R->zerop (const cl_ring_element& x)
cl_ring_element R->plus (const cl_ring_element& x, const cl_ring_element& y)
cl_ring_element R->minus (const cl_ring_element& x, const cl_ring_element& y)
cl_ring_element R->uminus (const cl_ring_element& x)
cl_ring_element R->one ()
cl_ring_element R->canonhom (const cl_I& x)
cl_ring_element R->mul (const cl_ring_element& x, const cl_ring_element& y)
cl_ring_element R->square (const cl_ring_element& x)
cl_ring_element R->expt_pos (const cl_ring_element& x, const cl_I& y)

The following rings are built-in.

cl_null_ring cl_0_ring: The null ring, containing only zero.
cl_complex_ring cl_C_ring: The ring of complex numbers. This corresponds to the type cl_N.
cl_real_ring cl_R_ring: The ring of real numbers. This corresponds to the type cl_R.
cl_rational_ring cl_RA_ring: The ring of rational numbers. This corresponds to the type cl_RA.
cl_integer_ring cl_I_ring: The ring of integers. This corresponds to the type cl_I.

Type tests can be performed for any of cl_C_ring, cl_R_ring, cl_RA_ring, cl_I_ring:

cl_boolean instanceof (const cl_number& x, const cl_number_ring& R): Tests whether the given number is an element of the number ring R.