Trouble with Sage assumptions

[David White]

Hello,

I am trying to use Sage in my class with some basic problems about matrices. Several of the problems in the book are of the form “find all values of k such that … is consistent” where the … is some linear system where k appears. If doing these problems by hand, one would take the determinant and solve for the values of k where the determinant is not zero. Sometimes the linear system is large, so I want to be able to use the .determinant() command (or .echelon_form() for similar problems) on a matrix where k is an element. However, Sage is not letting me create such a matrix object, because it does not recognize my assume() command telling it that the variable k is rational (or real, for that matter; neither works).

I’m trying to mimic what is going on here:
http://doc.sagemath.org/html/en/reference/calculus/sage/symbolic/assumptions.html

When I type the following code, I get an error saying Sage is "unable to convert k to an element of a rational field" (I get this error with and without the assume())

var('k')
assume(k,'rational')
v = vec(QQ,[k,k,k])

Can someone please tell me how to make variables and matrices play nicely together?

[David Joyner]

On Mon, Apr 17, 2017 at 7:53 PM, David White <dav...@gmail.com> wrote:
> Hello,
>
> I am trying to use Sage in my class with some basic problems about matrices.
> Several of the problems in the book are of the form “find all values of k
> such that … is consistent” where the … is some linear system where k
> appears. If doing these problems by hand, one would take the determinant and
> solve for the values of k where the determinant is not zero. Sometimes the
> linear system is large, so I want to be able to use the .determinant()
> command (or .echelon_form() for similar problems) on a matrix where k is an

Is this an example of what you want?

sage: k = var("k")
sage: A = matrix(SR, [[-1,20],[20,k]])
sage: det(A)
-k - 400
sage: solve(det(A)==0,k)
[k == -400]

> element. However, Sage is not letting me create such a matrix object,
> because it does not recognize my assume() command telling it that the
> variable k is rational (or real, for that matter; neither works).
>
> I’m trying to mimic what is going on here:
> http://doc.sagemath.org/html/en/reference/calculus/sage/symbolic/assumptions.html
>
> When I type the following code, I get an error saying Sage is "unable to
> convert k to an element of a rational field" (I get this error with and
> without the assume())
>
> var('k')
> assume(k,'rational')
> v = vec(QQ,[k,k,k])
>
> Can someone please tell me how to make variables and matrices play nicely
> together?
>

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[David White]

Yes, this completely solves my issue. Thanks!