weylalgebra1
http://www.math.kobe-u.ac.jp/OCD/weylalgebra1.tfb
2003-08-07
experimental
2002-08-07, 2003-11-28 revised to 1.1
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1
freealg1
arith1
list1
relation1
This CD defines elements of the ring of differential operators
with coefficients in the polynomial ring.
diffop
constructor of a differential operator from a polynomial or
from an element of the finitely generated free algebra.
The inverse of gr.
d/dq q = q d/dq + 1
1
gr
the symbol polynomial of a given differential operator.
The inverse of diffop.
$\gr( q \partial_{q} + 1) = q p + 1 $
1
1
diff
Differentiation of a given function in one variable.
$\frac{d x^2}{dx} = 2 x$
2
2
partialdiff
partial differentiation of a given function.
$\frac{\partial^{2} x^{2} y}{\partial x^{2}} = 2 y $
2
2
times
multiplication in D
$\partial_{q} q = \partial{q} q + 1 $
1
act
action of a differential operator to a function.
$ x^{m} \partial_{x}^{n} \partial_{y}^{r} \cdot f
= x^{m} \frac{partial^{n+r} f}{\partial x^{n} \partial y^{r}}
$
act_of_poly
action of a polynomial as a differential operator to a function.
act_of_poly is equivalent to the composition of act and diffop.
$ x^{m} \partial_{x}^{n} \partial_{y}^{r} \cdot f
= x^{m} \frac{partial^{n+r} f}{\partial x^{n} \partial y^{r}}
$