diff -r 6a696ae732ab sage/rings/polynomial/multi_polynomial_ideal.py --- a/sage/rings/polynomial/multi_polynomial_ideal.py Fri Jul 23 06:39:05 2010 +0200 +++ b/sage/rings/polynomial/multi_polynomial_ideal.py Fri Jul 23 07:59:19 2010 +0200 @@ -604,7 +604,7 @@ return S -class MPolynomialIdeal_singular_commutative_repr( +class MPolynomialIdeal_singular_repr( MPolynomialIdeal_singular_base_repr): """ An ideal in a multivariate polynomial ring, which has an @@ -1349,6 +1349,7 @@ False """ R = self.ring() + if not isinstance(other, MPolynomialIdeal_singular_repr) or other.ring() != R: raise ValueError, "other must be an ideal in the ring of self, but it isn't." @@ -2274,8 +2275,20 @@ R = self.ring() return R(k) -class NCPolynomialIdeal(MPolynomialIdeal_singular_base_repr, Ideal_generic): +class NCPolynomialIdeal(MPolynomialIdeal_singular_repr, Ideal_generic): def __init__(self, ring, gens, coerce=True): + r""" + Computes a non-commutative ideal. + + EXAMPLES:: + + sage: A. = FreeAlgebra(QQ, 3) + sage: H = A.g_algebra({y*x:x*y-z, z*x:x*z+2*x, z*y:y*z-2*y}) + sage: H.inject_variables() + Defining x, y, z + + sage: I = H.ideal([y^2, x^2, z^2-H.one_element()],coerce=False) # indirect doctest + """ Ideal_generic.__init__(self, ring, gens, coerce=coerce) def __call_singular(self, cmd, arg = None): @@ -2290,11 +2303,12 @@ r""" Computes a left GB of the ideal. - EXAMPLE:: + EXAMPLES:: sage: A. = FreeAlgebra(QQ, 3) sage: H = A.g_algebra({y*x:x*y-z, z*x:x*z+2*x, z*y:y*z-2*y}) sage: H.inject_variables() + Defining x, y, z sage: I = H.ideal([y^2, x^2, z^2-H.one_element()],coerce=False) sage: I.std() Ideal (z^2 - 1, y*z - y, x*z + x, y^2, 2*x*y - z - 1, x^2) of Noncommutative Multivariate Polynomial Ring in x, y, z over Rational Field... @@ -2308,11 +2322,12 @@ r""" Computes a two-sided GB of the ideal. - EXAMPLE:: + EXAMPLES:: sage: A. = FreeAlgebra(QQ, 3) sage: H = A.g_algebra({y*x:x*y-z, z*x:x*z+2*x, z*y:y*z-2*y}) sage: H.inject_variables() + Defining x, y, z sage: I = H.ideal([y^2, x^2, z^2-H.one_element()],coerce=False) sage: I.twostd() Ideal (z^2 - 1, y*z - y, x*z + x, y^2, 2*x*y - z - 1, x^2) of Noncommutative Multivariate Polynomial Ring in x, y, z over Rational Field... @@ -2336,14 +2351,28 @@ sage: A. = FreeAlgebra(QQ, 3) sage: H = A.g_algebra({y*x:x*y-z, z*x:x*z+2*x, z*y:y*z-2*y}) sage: H.inject_variables() + Defining x, y, z sage: I = H.ideal([y^2, x^2, z^2-H.one_element()],coerce=False) - sage: G = vector(I.gens()); G - ... + sage: G = vector(I.gens()); G + doctest:357: UserWarning: You are constructing a free module over a noncommutative ring. Sage does + not have a concept of left/right and both sided modules be careful. It's also + not guarantied that all multiplications are done from the right side. + doctest:573: UserWarning: You are constructing a free module over a noncommutative ring. Sage does not have a concept of left/right and both sided modules be careful. It's also not guarantied that all multiplications are done from the right side. (y^2, x^2, z^2 - 1) sage: M = I.syzygy_module(); M - ... - sage: (G.transpose() * M.transpose()).transpose() - (0, 0) + [ -z^2 - 8*z - 15 0 y^2] + [ 0 -z^2 + 8*z - 15 x^2] + [ x^2*z^2 + 8*x^2*z + 15*x^2 -y^2*z^2 + 8*y^2*z - 15*y^2 -4*x*y*z + 2*z^2 + 2*z] + [ x^2*y*z^2 + 9*x^2*y*z - 6*x*z^3 + 20*x^2*y - 72*x*z^2 - 282*x*z - 360*x -y^3*z^2 + 7*y^3*z - 12*y^3 6*y*z^2] + [ x^3*z^2 + 7*x^3*z + 12*x^3 -x*y^2*z^2 + 9*x*y^2*z - 4*y*z^3 - 20*x*y^2 + 52*y*z^2 - 224*y*z + 320*y -6*x*z^2] + [ x^2*y^2*z + 4*x^2*y^2 - 8*x*y*z^2 - 48*x*y*z + 12*z^3 - 64*x*y + 108*z^2 + 312*z + 288 -y^4*z + 4*y^4 0] + [ 2*x^3*y*z + 8*x^3*y + 9*x^2*z + 27*x^2 -2*x*y^3*z + 8*x*y^3 - 12*y^2*z^2 + 99*y^2*z - 195*y^2 -36*x*y*z + 24*z^2 + 18*z] + [ 2*x^3*y*z + 8*x^3*y + 9*x^2*z + 27*x^2 -2*x*y^3*z + 8*x*y^3 - 12*y^2*z^2 + 99*y^2*z - 195*y^2 -36*x*y*z + 24*z^2 + 18*z] + [ x^4*z + 4*x^4 -x^2*y^2*z + 4*x^2*y^2 - 4*x*y*z^2 + 32*x*y*z - 6*z^3 - 64*x*y + 66*z^2 - 240*z + 288 0] + [x^3*y^2*z + 4*x^3*y^2 + 18*x^2*y*z - 36*x*z^3 + 66*x^2*y - 432*x*z^2 - 1656*x*z - 2052*x -x*y^4*z + 4*x*y^4 - 8*y^3*z^2 + 62*y^3*z - 114*y^3 48*y*z^2 - 36*y*z] + + sage: M*G + (0, 0, 0, 0, 0, 0, 0, 0, 0, 0) ALGORITHM: Uses Singular's syz command """ @@ -2360,7 +2389,7 @@ return self.__call_singular('res', length) -class MPolynomialIdeal( MPolynomialIdeal_singular_commutative_repr, \ +class MPolynomialIdeal( MPolynomialIdeal_singular_repr, \ MPolynomialIdeal_macaulay2_repr, \ MPolynomialIdeal_magma_repr, \ Ideal_generic ):