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 1 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. $x^{m} \partial_{x}^{n} \partial_{y}^{r} \cdot f = x^{m} \frac{partial^{n+r} f}{\partial x^{n} \partial y^{r}}$