Hello,
in earlier versions of sage this worked:
Omega = Combinations([1, 2, 3, 4, 5, 6], 4)
A1 = Combinations([1], 1)
A2 = Combinations([2, 3, 4, 5, 6], 3)
A = CartesianProduct(A1, A2)
A.cardinality() / Omega.cardinality()
which we used in book for high school students to illustrate basic
probability examples. Now this fails with assertion error (and no
explanation attached). Digging deeper gives:
File
"/usr/local/sage/sage-7.0/local/lib/python2.7/site-packages/sage/combinat/cartesian_product.py",
line 102, in CartesianProduct
return cartesian_product(iters)
File
"/usr/local/sage/sage-7.0/local/lib/python2.7/site-packages/sage/categories/cartesian_product.py",
line 174, in __call__
return super(CartesianProductFunctor, self).__call__(args, **kwds)
File
"/usr/local/sage/sage-7.0/local/lib/python2.7/site-packages/sage/categories/covariant_functorial_construction.py",
line 221, in __call__
assert(all( hasattr(arg, self._functor_name) for arg in args))
AssertionError
Simply making A1 and A2 list fails as well, because Combinations
iterates over lists, so list(A1) is list of lists.
TypeError: unhashable type: 'list'
Easiest way I found around this is:
A = cartesian_product([[tuple(a1) for a1 in A1], [tuple(a2) for a2 in A2]])
there is a LOT of syntax noise compared to simply:
A = CartesianProduct(A1, A2)
And the meaning is slightly different (in A there are tuples, in Omega
there are lists, so we are not comparing same objects).
Is there any simpler way to product output of Combinations? Limiting
syntax noise is very important for making mathematical packages
approachable to young students, and this change is definiately not
along the lines. Also, it is important that most use cases are with
same syntax, so if we have
A1 = [1,2,3]
A2 = [4,5,6]
A = cartesian_product([A1, A2])
it would be good if the syntax was same for Combinations and other objects.
Is the current behaviour designed or bug?
Regards,
Andrzej.
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