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vector constants and vector functions

I'm using sage (through cocalc) with my multivariable calculus class this year. I'm looking for a consistent way to define symbol vector-valued functions and vector constants.

I can define a symbolic vector-valued function like this:

r(t) = [1, t]
r(1) + r(2) # works as expected

I can define constant vectors like this:

a = vector([1, 1])
b = vector([10, 20])
c = a + b # works as expected

But vector does not work for symbolic functions: r(t)=vector([1, t]) throws.


  • vector seems required for constants, else we don't get correct algebraic behavior
  • vector cannot be used with symbolic functions, else sage throws

Question: I'm worried this is going to cause a lot of confusion for my students. Is there a consistent way to define vectors for both constant values and symbolic expressions?