William Stein wrote:
> Before voting, may I register some concerns?
>
> 1. Recall your example:
>
> sage: t = var('t')
> sage: r=vector([t,t^2])
> sage: f(x,y)=x^2+y
> sage: f(r)
> boom.
>
> If we make f(r) work (as you propose), note that the following will
> still not work, and can never ever be made to work:
>
> sage: t = var('t')
> sage: r=vector([t,t^2])
> sage: f=lambda x,y: x^2+y
> sage: f(r)
> boom!
>
> and equally:
>
> sage: def f(x,y): return x^2+y
> sage: f(r)
> boom.
>
> There is already a lot of confusion that results from the difference
> between callable symbolic expressions ("symbolic functions") and
> Python functions. I'm worried that Jason's proposal would add yet
> another point of confusion.
These are great examples. Given these two examples, I think Nick (and
you?) are right that the resulting confusion would be worse than
teaching students that to pass a vector, they need to either "dismantle"
the vector into components f(*r), or define the function to actually
take a vector like f(v)=v[0]*2+v[1]^2 (once we have the necessary
changes; see below).
So I officially withdraw my proposal. Thanks for the discussion.
> 2. A second concern is that at some point we will enhance symbolic
> expressions to more naturally take vectors as input (I played with
> Bill Furnish's symbolics rewrite and remember it being good at this
> sort of thing, and it being natural for expressing certain things).
> Then the following will work:
>
> sage: t=var('t')
> sage: f(x,y) = 2*x + 3*y
> sage: r=vector([t,t^2]); s = vector([t,sin(t)])
> sage: f(r,r)
> (5*t, 2*t^2 + 3*sin(t))
You can sort of manipulate this to get it to work, since you can convert
a matrix to a symbolic expression:
sage: f(x,y) = 2*x + 3*y
sage: r=matrix([[t,t^2]]); s = matrix([[t,sin(t)]])
sage: f(SR(r), SR(r))
[ 5*t 5*t^2]
sage: f(SR(r), SR(s))
[ 5*t 2*t^2 + 3*sin(t)]
so it looks like all you need to do is
* Make vectors behave like matrices, so that SR(vector([1,2])) works
* automatically cast symbolic function arguments to SR
Thanks,
Jason
--
Jason Grout
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