Coercion bug message when working with group algebras

[keirh...@gmail.com]

When I do this:

H = PermutationGroup([ [(1,2), (3,4)], [(5,6,7),(12,14,18)] ])
kH = H.algebra(GF(2))
[a, b] = H.gens()
x = kH(a) + kH(b) + kH.one(); print(x)
x*x

I get an error caused by the last computation: "RuntimeError: There is a bug in the coercion code in Sage." (I was working in Cocalc, but you can cut and paste the code above into a SageMathCell and reproduce the error.)

Is this really a bug, or should I be doing this differently? (I found the problem working with a larger group, but this simpler example above has the same issue.)

Thanks --

Keir

[keirh...@gmail.com]

The Sage version I was using is 9.6.

[Trevor Karn]

I can reproduce this on 9.7.beta7.

The problem is that the parent is not understood to be the same (even though it clearly is). A workaround is:

sage: x = kH(a) + kH(b) + kH(H.one()); x

() + (5,6,7)(12,14,18) + (1,2)(3,4)

sage: x*x

(5,7,6)(12,18,14)

Here H.one() puts the one in the right parent for the coercion framework, but this definitely looks like a bug to me, because

sage: kH(a).parent()

Algebra of Permutation Group with generators [(5,6,7)(12,14,18), (1,2)(3,4)] over Finite Field of size 2

sage: kH.one().parent()

Algebra of Permutation Group with generators [(5,6,7)(12,14,18), (1,2)(3,4)] over Finite Field of size 2

sage: kH(a).parent() is kH.one().parent()

True

Reproducing the bug with messages on 9.7.beta7:

sage: H = PermutationGroup([[(1,2), (3,4)], [(5,6,7),(12,14,18)]])

sage: kH = H.algebra(GF(2))

sage: H.gens()

((5,6,7)(12,14,18), (1,2)(3,4))

sage: a, b = H.gens()

sage: x = kH(a) + kH(b) + kH.one(); x

(5,6,7)(12,14,18) + (1,2)(3,4) + ()

sage: x*x

---------------------------------------------------------------------------

RuntimeError                              Traceback (most recent call last)

Input In [7], in <cell line: 1>()

----> 1 x*x

File ~/Applications/sage/src/sage/structure/element.pyx:1514, in sage.structure.element.Element.__mul__()

   1512 cdef int cl = classify_elements(left, right)

   1513 if HAVE_SAME_PARENT(cl):

-> 1514     return (<Element>left)._mul_(right)

   1515 if BOTH_ARE_ELEMENT(cl):

   1516     return coercion_model.bin_op(left, right, mul)

File ~/Applications/sage/src/sage/structure/element.pyx:1560, in sage.structure.element.Element._mul_()

   1558         raise bin_op_exception('*', self, other)

   1559     else:

-> 1560         return python_op(other)

   1561 

   1562 cdef _mul_long(self, long n):

File ~/Applications/sage/src/sage/categories/coercion_methods.pyx:53, in sage.categories.coercion_methods._mul_parent()

     51     True

     52 """

---> 53 return (<Element>self)._parent.product(self, other)

File ~/Applications/sage/src/sage/categories/magmatic_algebras.py:215, in MagmaticAlgebras.WithBasis.ParentMethods._product_from_product_on_basis_multiply(self, left, right)

    201 def _product_from_product_on_basis_multiply( self, left, right ):

    202     r"""

    203     Compute the product of two elements by extending

    204     bilinearly the method :meth:`product_on_basis`.

   (...)

    213 

    214     """

--> 215     return self.linear_combination((self.product_on_basis(mon_left, mon_right), coeff_left * coeff_right )

    216                                     for (mon_left, coeff_left) in left.monomial_coefficients().items()

    217                                     for (mon_right, coeff_right) in right.monomial_coefficients().items() )

File ~/Applications/sage/src/sage/combinat/free_module.py:969, in CombinatorialFreeModule.linear_combination(self, iter_of_elements_coeff, factor_on_left)

    945 def linear_combination(self, iter_of_elements_coeff, factor_on_left=True):

    946     r"""

    947     Return the linear combination `\lambda_1 v_1 + \cdots +

    948     \lambda_k v_k` (resp.  the linear combination `v_1 \lambda_1 +

   (...)

    967         20*B[1] + 20*B[2]

    968     """

--> 969     return self._from_dict(blas.linear_combination(((element._monomial_coefficients, coeff)

    970                                                     for element, coeff in iter_of_elements_coeff),

    971                                                    factor_on_left=factor_on_left),

    972                            remove_zeros=False)

File ~/Applications/sage/src/sage/data_structures/blas_dict.pyx:313, in sage.data_structures.blas_dict.linear_combination()

    311     return remove_zeros(result)

    312 

--> 313 cpdef dict linear_combination(dict_factor_iter, bint factor_on_left=True):

    314     r"""

    315     Return the pointwise addition of dictionaries with coefficients.

File ~/Applications/sage/src/sage/data_structures/blas_dict.pyx:348, in sage.data_structures.blas_dict.linear_combination()

    346 cdef dict D

    347 

--> 348 for D, a in dict_factor_iter:

    349     if not a: # We multiply by 0, so nothing to do

    350         continue

File ~/Applications/sage/src/sage/combinat/free_module.py:969, in <genexpr>(.0)

    945 def linear_combination(self, iter_of_elements_coeff, factor_on_left=True):

    946     r"""

    947     Return the linear combination `\lambda_1 v_1 + \cdots +

    948     \lambda_k v_k` (resp.  the linear combination `v_1 \lambda_1 +

   (...)

    967         20*B[1] + 20*B[2]

    968     """

--> 969     return self._from_dict(blas.linear_combination(((element._monomial_coefficients, coeff)

    970                                                     for element, coeff in iter_of_elements_coeff),

    971                                                    factor_on_left=factor_on_left),

    972                            remove_zeros=False)

File ~/Applications/sage/src/sage/categories/magmatic_algebras.py:215, in <genexpr>(.0)

    201 def _product_from_product_on_basis_multiply( self, left, right ):

    202     r"""

    203     Compute the product of two elements by extending

    204     bilinearly the method :meth:`product_on_basis`.

   (...)

    213 

    214     """

--> 215     return self.linear_combination((self.product_on_basis(mon_left, mon_right), coeff_left * coeff_right )

    216                                     for (mon_left, coeff_left) in left.monomial_coefficients().items()

    217                                     for (mon_right, coeff_right) in right.monomial_coefficients().items() )

File ~/Applications/sage/src/sage/categories/semigroups.py:957, in Semigroups.Algebras.ParentMethods.product_on_basis(self, g1, g2)

    939 def product_on_basis(self, g1, g2):

    940     r"""

    941     Product, on basis elements, as per

    942     :meth:`MagmaticAlgebras.WithBasis.ParentMethods.product_on_basis()

   (...)

    955         B['ab'] + B['bdc']

    956     """

--> 957     return self.monomial(g1 * g2)

File ~/Applications/sage/src/sage/groups/perm_gps/permgroup_element.pyx:1295, in sage.groups.perm_gps.permgroup_element.PermutationGroupElement.__mul__()

   1293             return prod

   1294 

-> 1295     return coercion_model.bin_op(left, right, operator.mul)

   1296 

   1297 cpdef _mul_(left, _right):

File ~/Applications/sage/src/sage/structure/coerce.pyx:1200, in sage.structure.coerce.CoercionModel.bin_op()

   1198 # Now coerce to a common parent and do the operation there

   1199 try:

-> 1200     xy = self.canonical_coercion(x, y)

   1201 except TypeError:

   1202     self._record_exception()

File ~/Applications/sage/src/sage/structure/coerce.pyx:1332, in sage.structure.coerce.CoercionModel.canonical_coercion()

   1330         if x_elt._parent is y_elt._parent:

   1331             return x_elt,y_elt

-> 1332     self._coercion_error(x, x_map, x_elt, y, y_map, y_elt)

   1333 

   1334 cdef bint x_numeric = isinstance(x, (int, long, float, complex))

File ~/Applications/sage/src/sage/structure/coerce.pyx:2031, in sage.structure.coerce.CoercionModel._coercion_error()

   2029             <class 'str'> 'g'

   2030         """

-> 2031         raise RuntimeError("""There is a bug in the coercion code in Sage.

   2032 Both x (=%r) and y (=%r) are supposed to have identical parents but they don't.

   2033 In fact, x has parent '%s'

RuntimeError: There is a bug in the coercion code in Sage.

Both x (=()) and y (=(5,6,7)(12,14,18)) are supposed to have identical parents but they don't.

In fact, x has parent 'Permutation Group with generators [(5,6,7)(12,14,18), (1,2)(3,4)]'

whereas y has parent 'Permutation Group with generators [(5,6,7)(12,14,18), (1,2)(3,4)]'

Original elements () (parent Permutation Group with generators [(5,6,7)(12,14,18), (1,2)(3,4)]) and (5,6,7)(12,14,18) (parent Permutation Group with generators [(5,6,7)(12,14,18), (1,2)(3,4)]) and maps

<class 'NoneType'> None

<class 'sage.structure.coerce_maps.DefaultConvertMap_unique'> (map internal to coercion system -- copy before use)

Coercion map:

  From: Permutation Group with generators [(5,6,7)(12,14,18), (1,2)(3,4)]

  To:   Permutation Group with generators [(5,6,7)(12,14,18), (1,2)(3,4)]

[keirh...@gmail.com]

Thanks for this workaround. I was passing the group algebra to a function and then accessing the base group like so:

kH.group()

Both of the following cause the coercion error:

kH.one() * x

kH.group().one() * x

But this works fine:

H.one()*x

I will just have to pass the original group along as well.

--Keir

[Trevor Karn]

Is the x you give in these examples the same x as above? I’m worried (maybe needlessly) about if the x you give includes a summand of kH.one(). If the x you give does not include a summand of one, then the behavior you described is consistent with what I think the problem is. If the x in the new example doesn’t have a summand of kH.one() then I’m misunderstanding something.

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Best,

Trevor

[keirh...@gmail.com]

This code:

H = PermutationGroup([ [(1,2), (3,4)], [(5,6,7),(12,14,18)] ])
kH = H.algebra(GF(2))
[a, b] = H.gens()

# Produces no coercion error
print((kH(a) + kH(b) + H.one())^2)

# Produces a coercion error in all cases below
try:
    print((kH(a) + kH(b) + kH(kH.one()))^2)
except:
    print("Fail 1")
    pass
try:
    print((kH(a) + kH(b) + kH.one())^2)
except:
    print("Fail 2")
    pass
try:
    print((kH(a) + kH(b) + kH.group().one())^2)
except:
    print("Fail 3")
    pass
try:
    print((kH(a) + kH(b) + kH(kH.group().one()))^2)
except:
    print("Fail 4")
    pass

produces the output:

(5,7,6)(12,18,14)

Fail 1

Fail 2

Fail 3

Fail 4

The thing that's irritating is that using H.one() in the sum is fine; using kH.group().one() is not. But I fully admit that I may just not understand what the right behavior should be.

[Trevor Karn]

There is a description/proposed fix of the problem on this trac ticket: https://trac.sagemath.org/ticket/34292

[keirh...@gmail.com]

Ah, thanks!