#12236: random element madness
--------------------------------+-------------------------------------------
Reporter: mariah | Owner: AlexGhitza
Type: defect | Status: new
Priority: minor | Milestone: sage-4.8
Component: basic arithmetic | Keywords:
Work_issues: | Upstream: N/A
Reviewer: | Author:
Merged: | Dependencies:
--------------------------------+-------------------------------------------
The following output is generated by the code below using
sage-4.7.2:
{{{
R: Univariate Quotient Polynomial Ring in xbar over Ring of integers
modulo 2 with modulus x^4 + 1
S: Quotient of Univariate Quotient Polynomial Ring in xbar over Integer
Ring with modulus x^4 + 1 by the ideal (2)
Now these two rings are isomorphic, but constructed in different orders,
so it is not that surprising that SAGE considers them to be different:
R == S: False
And random_element on R seems sensible:
[xbar^3 + xbar + 1, xbar^3 + xbar^2 + 1, xbar^2 + xbar, xbar^2, 1, xbar^2
+ xbar, xbar^3, xbar^3, xbar^3 + xbar^2, xbar^2 + xbar + 1]
But random_element on S just doesn't make sense on several levels:
[2, 1, -2, 2, 2, 0, 1, 0, 2, -2]
1) Why are there no polynomial powers?
2) Why are the integers not reduced modulo 2?
}}}
Here is the code:
{{{
def print_random_elements(R, num_elts=10):
R_elts = [R.random_element() for i in range(num_elts)]
print R_elts
def madness():
U.<x> = ZZ[]
f = x^4 + 1
p = 2
num_elts = 10
S = U.quotient(f).quotient(p)
#S.<x> = Integers(p)[]
#S1 = S.quotient(f)
R = (Integers(p)['x']).quotient(f)
print 'R:', R
print 'S:', S
print '''Now these two rings are isomorphic, but constructed in
different
orders, so it is not that surprising that SAGE considers them to
be different:'''
print "R == S:", R == S
print 'And random_element on R seems sensible:'
print_random_elements(R)
print "But random_element on S just doesn't make sense on several
levels:"
print_random_elements(S)
print "1) Why are there no polynomial powers?"
print "2) Why are the integers not reduced modulo %s?" % p
madness()
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12236>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To post to this group, send email to [email protected].
To unsubscribe from this group, send email to
[email protected].
For more options, visit this group at
http://groups.google.com/group/sage-trac?hl=en.
