It seems that Integer Programs solved with CPLEX sometimes have the wrong
bounds on binary variables. For instance,
p=MixedIntegerLinearProgram(solver=CPLEX)
x=p.new_variable(dim=1) #,binary=True)
p.add_constraint(x[0]+x[1]==2)
p.set_objective(None)
p.set_binary(x)
p.show()
p.solve()
print
Curious. The polynomial does not seem particularly ill-conditioned, in the
sense that its discriminat is roughly what one might expect (unlike, say,
Wilkinson's). Maple gives 50 roots with |f(x)|10^{-12}, and one with f(x)=,
i.e. much larger.
On Thursday, 12 December 2013 15:35:53 UTC, AWWQUB
Apparently you need about 65 bits of accuracy, presumably maxima uses
doubles (=53 bits). Compare:
sage: eq = (I*x^51+sum(x^k,k,0,50)).subs(x=x-1-I)
sage: var('x, k')
(x, k)
sage: eq = (I*x^51+sum(x^k,k,0,50)).subs(x=x-1-I)
sage: sol = eq.polynomial(ComplexField(65)).roots()
sage:
Sorry - I was looking at the original *(I*x^51+sum(x^k,k,0,50))==0.* Note
that if you make the x-x-1 substitution, the polynomial now has
coefficient as large as 10^18. The discriminant is unchanged, but the value
you would expect it to be, given the size of the coefficient, is
roughly10^800
The function delsarte_bound_hamming_space(n, d, q, isinteger=False,
return_data=False, solver='PPL') offers the option isinteger=True. As the
doc doesn't tell it, I got a little curious what is assumed to be integral.
Looking at the implementation it turns out that the distance distribution
is
On 12/15/2013 06:46 AM, Peter Mueller wrote:
The function delsarte_bound_hamming_space(n, d, q, isinteger=False,
return_data=False, solver='PPL') offers the option isinteger=True. As
the doc doesn't tell it, I got a little curious what is assumed to be
integral. Looking at the implementation it
