Using diff/derivative
it does not seem easily possible to specify derivatives of variable order, e.g., to define a function P(m,n)
that applies the diff
m+n
times to a polynomial:
sage: x=var('x')
sage: P(m,n)=derivative((1-x^2)^n,x,m+n)
...
TypeError: argument symb must be a symbol
sage: R.<x> = PolynomialRing(QQ, 'x')
sage: p=(1-x^2)^11
sage: P(m,n)=derivative(p,x,m+n)
...
ValueError: Cannot differentiate with respect to m + n
This is obviously because diff
supports such syntactic sugar like diff(p,x,x,x)
. So how to differentiate to a variable order?