Your matrix is over GF(2) not over the symbolic ring SR:
sage: m1 = SR(GF(2)(1)) * var("m1")
sage: m2 = SR(GF(2)(1)) * var("m2")
sage: m3 = SR(GF(2)(1)) * var("m3")
sage: m4 = SR(GF(2)(1)) * var("m4")
sage: q = Matrix(SR, [
[m1, m2],
[m3, m4],
])
sage: q^2
[ m1^2 + m2*m3 m1*m2 + m2*m4]
[m1*m3 + m3*m4 m2*m3 + m4^2]
On Tuesday 30 Sep 2014 08:46:42 Kim Schoener wrote:
> I'm not sure I understand fully what you're saying. I did
>
> m1 = SR(GF(2)(1)) * var("m1")
> m2 = SR(GF(2)(1)) * var("m2")
> m3 = SR(GF(2)(1)) * var("m3")
> m4 = SR(GF(2)(1)) * var("m4")
>
> but the Matrix definition
>
> q = Matrix(GF(2), [
> [m1, m2],
> [m3, m4],
> ])
>
> still results in the same error: "unable to convert x (=x1) to an integer".
>
> How do I define a variable in the SR that I can work with? I can't seem to
> figure it out from the example you gave me.
>
> Thank you,
> Kim
>
> Am Dienstag, 30. September 2014 17:04:10 UTC+2 schrieb Volker Braun:
> > Anything symbolic is in the symbolic ring SR, finite field elements are in
> > GF(2). You can wrap finite field elements in the symbolic ring if you want
> > to do symbolic computations with finite field coefficients:
> >
> > sage: SR(GF(5)(3)) * x
> > 3*x
> > sage: _ * 2
> > x
> >
> > though the symbolic elemnts still don't know anything about finite fields,
> > they just carry the coefficients along.
> >
> > On Tuesday, September 30, 2014 3:14:03 PM UTC+1, Kim Schoener wrote:
> >> Heya!
> >>
> >> I want to do something relatively easy in Sage but can't figure out how.
> >> Hopefully you can help me. I want to do some symbolic operations
> >> (matrix/vector) in the GF(2). Let's start out with real numbers first:
> >>
> >> (m1, m2, m3, m4) = (var("m1"), var("m2"), var("m3"), var("m4"))
> >> q = Matrix([
> >>
> >> [m1, m2],
> >> [m3, m4],
> >>
> >> ])
> >> print(q)
> >> print(q * q)
> >>
> >> Works pefectly:
> >>
> >> [m1 m2]
> >> [m3 m4]
> >> [ m1^2 + m2*m3 m1*m2 + m2*m4]
> >> [m1*m3 + m3*m4 m2*m3 + m4^2]
> >>
> >> But when I try the same thing in GF(2) by definiing
> >>
> >> q = Matrix(GF(2), [
> >>
> >> [m1, m2],
> >> [m3, m4],
> >>
> >> ])
> >>
> >> I get:
> >>
> >> [...]
> >>
> >> File "parent.pyx", line 1069, in sage.structure.parent.Parent.__call__
> >>
> >> (sage/structure/parent.c:8546)
> >>
> >> File "coerce_maps.pyx", line 156, in
> >>
> >> sage.structure.coerce_maps.NamedConvertMap._call_
> >> (sage/structure/coerce_maps.c:4930)
> >>
> >> File "expression.pyx", line 857, in
> >>
> >> sage.symbolic.expression.Expression._integer_
> >> (sage/symbolic/expression.cpp:5877)
> >> TypeError: unable to convert x (=m1) to an integer
> >>
> >> However, the matrix definition seems to be okay, when I do
> >>
> >> q = Matrix(GF(2), [
> >>
> >> [1, 1 ],
> >> [1, 0],
> >>
> >> ])
> >> print(q * q)
> >>
> >> I get
> >>
> >> [0 1]
> >> [1 1]
> >>
> >> which is what I'd expect. Why does it not work with variables when
> >> working in GF(2) and how can I get this to work the way I want it to?
> >>
> >> Thank you so much,
> >> Regards,
> >> Kim
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