On 4/4/07, Kyle Schalm <[EMAIL PROTECTED]> wrote:
> perhaps there's been a discussion about this that i didn't pay attention
> to, but i just realized that equality (==) is not always transitive:
>
> In [109]: mod(2,5)==mod(2,10)
> Out[109]: True
>
> In [110]: mod(2,5)==mod(7,10)
> Out[110]: True
>
> In [111]: mod(2,10)==mod(7,10)
> Out[111]: False
>
> what is the rationale for this?
I'm not sure what to say except:
(1) the definition of equality in SAGE is "equal images under a
canonical map",
(2) both MAGMA and PARI are the same way regarding equality not
being transitive:
sage: magma.eval('Integers(5)!2 eq 2')
'true'
sage: magma.eval('Integers(10)!2 eq 2')
'true'
sage: magma.eval('Integers(5)!2 eq 7')
'true'
sage: magma.eval('2 eq 7')
'false'
sage: gp.eval('Mod(2,5) == 2')
'1'
sage: gp.eval('Mod(2,5) == 7')
'1'
sage: gp.eval('2 == 7')
'0'
William
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