On Friday, November 30, 2018 at 1:59:40 PM UTC-8, saad khalid wrote:
>
> However, when I try to compute this h(.1), the function doesn't plug in .1
> in for s in the function, and it returns:
>
> [ s + 1 0]
> [ 0 -s + 1]
>
>
> What exactly is happening?
>
> The problem is that a matrix over SR is not a symbolic expression itself:
sage: parent(M1+s*Mx)
Full MatrixSpace of 2 by 2 dense matrices over Symbolic Ring
The effect of "h(s)=..." is (you can check by calling
'preparse("h(s)=...")'):
h = symbolic_expression(M1+s*Mx).function(s)
which "forces" the sage object M1+s*Mx into the symbolic ring. Nearly
everything can be stuffed into the symbolic ring, but in this case it
basically becomes a constant:
sage: symbolic_expression(M1+s*Mx).variables()
()
sage: symbolic_expression(M1+s*Mx).is_constant()
True
Once stuffed into SR, it's an opaque entity, and the occurrence of s in it
is not visible. So turning it into a function of s is straightforward: it's
a constant function!
The solution here is to use that matrices over symbolic rings do inherit
some properties of symbolic expressions. One is substitution, so
sage: h=M1+s*Mx
sage: h(s=1.0)
[ 2.00000000000000 0]
[ 0 0.000000000000000]
works just fine.
If you want to turn it into something for which h(1.0) works, you can do
h=lambda s0: (M1+s*Mx)(s=s0)
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