Hi,
On Mon, Apr 19, 2010 at 08:28:21AM -0700, Ben Goodrich wrote:
> Hi,
>
> Okay, I got the domain thing figured out, but now I am running into a
> separate problem when the polynomial in sdp form is inside of a
> matrix.
>
> All this is fine:
>
> from sympy.polys.monomialtools import monomial_lex_key as O_lex
> from sympy.polys.groebnertools import *
> from sympy.polys.polytools import basic_from_dict
> gens = symbols('xyz')
> f = x**3 + 2 * y**2 - z
> F = Poly(f, *gens)
The following line needs a few words of comment.
> FF = sdp_from_dict(F.as_dict(), O_lex)
F.as_dict() returns { M_i: c_i } representation where M_i are tuples
with exponents of type int and c_i are coefficients of type Integer.
> Poly(dict(FF), *gens) == F # True
If you create a Poly of FF as above, then there is no problem. If you
would specify the domain via domain='ZZ', then you can run into trouble
because ZZ.dtype won't match c_i type (e.g. it might be mpz v.s. Integer).
Secondly, if you will use FF for computations then F.as_dict() shouldn't
be used. Probably I used as_dict() improperly earlier in this thread. So,
F.as_dict() should be replaced with F.rep.to_dict() which return a dict
as as_dict() does, but c_i type will match ZZ.dtype.
>
> But not this:
>
> M = Matrix(1, 1, [FF])
> Poly(dict(M[0,0]), *gens) == F # False
>
> because the left-hand side becomes the zero polynomial for some reason
>
> In [45]: Poly(dict(M[0,0]), *gens)
> Out[45]: Poly(0, x, y, z, domain='ZZ')
>
> It appears to be something related to the coercion to a dictionary
>
> M[0,0] == FF # True
> dict(M[0,0]) == dict(FF) # False
>
> even though they look identical
>
> In [50]: dict(M[0,0])
> Out[50]: {(0, 0, 1): -1, (0, 2, 0): 2, (3, 0, 0): 1}
>
> In [51]: dict(FF)
> Out[51]: {(0, 0, 1): -1, (0, 2, 0): 2, (3, 0, 0): 1}
>
> Any ideas?
>
They look identical, but they're not. As you use F.as_dict(), then in
both cases c_i are of type Integer. However, keys of _50 and _51 are
different. In _50 M_i are tuples of Integer instances and in _51 they
are tuples of ints. When you created a Matrix of FF then FF got sympified
and all ints were converted to Integers. Poly, however, expects M_i to
have int exponents. To solve this problem you can replace dict(M[0,0])
with:
dict([ (map(int, monom), coeff) for monom, coeff in M[0,0] ])
> Thanks,
> Ben
>
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Mateusz
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