Module Author: William A. Stein (was@math.harvard.edu)
Section Author: William A. Stein (was@math.harvard.edu)
The integer_ring module defines the following functions:
-
Compute and return a Chinese Remainder Theorem basis for the list
of coprime integers. An alternative xgcd
function
can be passed as the second argument.
-
Compute and return the prime factorization of the integer
,
as a list of pairs
, where each
is prime and
.
The integer ring
has the following methods:
-
Return 0 as a Pythin int.
-
Return
True
, since elements of the integers do not have
to be printed with parenthesis around them, when they
are coefficients, e.g., in a polynomial.
-
Return
False
.
-
Return the string
"Z"
.
-
Return a random integer between
and
,
including both endpoints.
-
Return
, which is the root of unity of largest order in
.
Note, this is not the Riemann zeta function. it is a member function
of the IntegerRing class, and should be thought of in the sense
of
, a primitive
th root of unity. This function is
available for certain other fields, e.g., number fields.
Release 0.3, documentation updated on April 21, 2005.
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