I've attached a patch that takes care of 1) only and updated
http://sagetrac.org/sage_trac/ticket/980 . The individual degree
distribution is a little better:
{{{
sage: GF(10007)['x,y,q'].random_element(6,10)
-2005*x^6 + 2400*x^4*y^2 - 3609*x^3*y^3 + 488*x*y^5 - 3093*x^4*y*q +
3482*x*y*q^3 - 989*x^2*y*q - 3529*x*q^3 - 3957*x
}}}
But note that most of the time for the example at the beginning of the
thread, we still get 6,7 out of 9 terms most of the time. I still
don't think this is a bug: we are not creating a polynomial with 9
terms in it, but picking one with at most 9 terms.
{{{
sage: GF(10007)['x,y'].random_element(4,9)
797*x^4 - 439*x^2*y^2 - 1457*x*y^3 - 2348*y^4 - 1721*x^3 - 1885*x^2*y
- 1760*x*y^2 + 310*y
}}}
didier
2007/10/24, Steffen <[EMAIL PROTECTED]>:
>
>
>
> On Oct 24, 5:45 am, "didier deshommes" <[EMAIL PROTECTED]> wrote:
> > 2007/10/23, Steffen <[EMAIL PROTECTED]>:
> >
> > > Exactly, thats one of two points. The maximum degree in every variable
> > > is (maximum total degree of resulting polynomial) / (number of
> > > varialbes of the polynomial). Thus for example GF(10007)
> > > ['x,y,z'].random_element(5,9) will be limited in every variable to
> > > degree 5/3 = 1 !!!. This is not what the upper definition says.
> > > The second point is about the number of coefficients that are set to
> > > 0. This might a point to argue about, but if I create a random
> > > polynomial with a (maximum number of terms to generate) then I expect
> > > that the 0 occurs with the same probability and thus as often as every
> > > other element. Thats why I am not happy if 20% or more of the
> > > parameters are 0.
> >
> > I filed out a bug report about those 2 issues:
> > 1) Degrees can severely restricted.
> > 2) The polynomials returned can be too sparse
> >
> > I plan to post a patch addressing your concerns (I can especially see
> > how 1) can be annoying). Random poly generation will most likely be
> > slower, so for now I'm planning to keep the current behavior around,
> > even if it is not the default.
> >
> > didier
>
> Thanks, I will wait for didiers patch. If I then have any additional
> requirements I will implement them via an optional flag or smth
> similar.
>
> Steffen
>
>
> >
>
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diff -r 1a19787af98d sage/rings/polynomial/multi_polynomial_ring_generic.pyx
--- a/sage/rings/polynomial/multi_polynomial_ring_generic.pyx Sun Oct 21
10:13:32 2007 -0700
+++ b/sage/rings/polynomial/multi_polynomial_ring_generic.pyx Wed Oct 24
18:23:14 2007 -0400
@@ -453,23 +453,31 @@ cdef class MPolynomialRing_generic(sage.
sage: R.random_element(41) # random
-4*x^6*y^4*z^4*a^6*b^3*c^6*d^5 + 1/2*x^4*y^3*z^5*a^4*c^5*d^6 -
5*x^3*z^3*a^6*b^4*c*d^5 + 10*x^2*y*z^5*a^4*b^2*c^3*d^4 - 5*x^3*y^5*z*b^2*c^5*d
-
+ sage: f=ZZ['q,w,e,r,t,y'].random_element(degree=200,terms=19)
+ sage: f.degree() <= 200
+ True
+
AUTHOR:
-- didier deshommes
"""
- # General strategy:
- # generate n-tuples of numbers with each element in the tuple
- # not greater than (degree/n) so that the degree
- # (ie, the sum of the elements in the tuple) does not exceed
- # their total degree
-
+
n = self.__ngens # length of the n-tuple
- max_deg = int(degree/n) # max degree for each term
R = self.base_ring()
- # restrict exponents to positive integers only
- exponents = [ tuple([ZZ.random_element(0,max_deg+1) for _ in range(n)])
- for _ in range(terms) ]
+ exponents = []
+ for i in range(terms):
+ exps = []
+ deg = degree
+ for i in range(n):
+ exp = ZZ.random_element(0,deg+1)
+ if exp <= deg:
+ exps.append(exp)
+ deg -= exp
+ else:
+ exps.append(0)
+
+ exponents.append(tuple(exps))
+
coeffs = []
for _ in range(terms):
c = R.random_element(*args,**kwds)
