Thanks Doug. I hadn't realized that the output of mod(m,n) is in the
integers mod n.
On Monday, June 11, 2012 8:26:34 AM UTC-6, D. S. McNeil wrote:
>
> > So is this a bug, or is there some subtle aspect of the set { ... }
> > constuction that I'm misusing?
>
> Oy, that's cute! The second matrix index lives in Zmod(5), and behaves as
> such:
>
> sage: wA = matrix(QuadraticField(2),5,{(j,mod(j+1,5)):1 for j in
> range(5)})
> sage: wA.dict()
> {(0, 1): 1, (1, 2): 1, (3, 4): 1, (2, 3): 1, (4, 0): 1}
> sage: for key in wA.dict():
> ....: print key, map(parent, key)
> ....:
> (0, 1) [<type 'int'>, Ring of integers modulo 5]
> (1, 2) [<type 'int'>, Ring of integers modulo 5]
> (3, 4) [<type 'int'>, Ring of integers modulo 5]
> (2, 3) [<type 'int'>, Ring of integers modulo 5]
> (4, 0) [<type 'int'>, Ring of integers modulo 5]
>
> and so when _list() goes to build the flattened list, its arithmetic
> here doesn't hold:
>
> v[i*self._ncols + j] = x
>
> For example (diagnostic print statements mine):
>
> sage: wA
> nrows 5 ncols 5 with parents <type 'int'> <type 'int'>
> [((0, 1), 1), ((1, 2), 1), ((3, 4), 1), ((2, 3), 1), ((4, 0), 1)]
> i is 0 with parent <type 'int'>
> j is 1 with parent Ring of integers modulo 5
> x is 1 with parent Number Field in a with defining polynomial x^2 - 2
> 0 1 1
> v is now [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
> 0, 0, 0, 0, 0]
> i is 1 with parent <type 'int'>
> j is 2 with parent Ring of integers modulo 5
> x is 1 with parent Number Field in a with defining polynomial x^2 - 2
> 1 2 2
> v is now [0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
> 0, 0, 0, 0, 0]
> i is 3 with parent <type 'int'>
> j is 4 with parent Ring of integers modulo 5
> x is 1 with parent Number Field in a with defining polynomial x^2 - 2
> 3 4 4
> v is now [0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
> 0, 0, 0, 0, 0]
> i is 2 with parent <type 'int'>
> j is 3 with parent Ring of integers modulo 5
> x is 1 with parent Number Field in a with defining polynomial x^2 - 2
> 2 3 3
> v is now [0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
> 0, 0, 0, 0, 0]
> i is 4 with parent <type 'int'>
> j is 0 with parent Ring of integers modulo 5
> x is 1 with parent Number Field in a with defining polynomial x^2 - 2
> 4 0 0
> v is now [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
> 0, 0, 0, 0, 0]
> [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
> 1]
> computing rows: nr 5 nc 5
> [1 1 1 1 1]
> [0 0 0 0 0]
> [0 0 0 0 0]
> [0 0 0 0 0]
> [0 0 0 0 0]
> sage:
>
> I don't know if there's a use case for generic (i.e. non-int) indices
> or not. I've never needed them myself, but maybe there's a reason we
> don't __index__/int the inputs?
>
> In the meantime,
>
> matrix(QuadraticField(2),5,{(j,int(mod(j+1,5))):1 for j in range(5)})
>
> should work.
>
>
>
> Doug
>
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