Ore_algebra[Ore_to_diff] - convert a differential operator to a differential equation
Ore_algebra[Ore_to_shift] - convert a shift operator to a recurrence equation
Ore_algebra[Ore_to_DESol] - convert a differential operator to a DESol structure
Ore_algebra[Ore_to_RESol] - convert a shift operator to an RESol structure
|
Calling Sequence
|
|
Ore_to_diff(G, f, A)
Ore_to_diff(G, f, A, 'D')
Ore_to_shift(G, u, A)
Ore_to_shift(G, u, A, 'indexed')
Ore_to_DESol(P, f, A)
Ore_to_RESol(P, u, A)
|
|
Parameters
|
|
G
|
-
|
list of operators of the Ore algebra A
|
P
|
-
|
operator of the Ore algebra A
|
f
|
-
|
expression denoting a mathematical function
|
A
|
-
|
Ore algebra table
|
|
|
|
|
Description
|
|
•
|
The Ore_to_diff command converts a differential operator or a list of differential operators of the skew algebra A into a differential equation or a list of differential equations in the function f. The output is expressed in terms of the diff function by default, or in terms of the D function when the optional parameter is set.
|
•
|
The Ore_to_DESol command converts a single differential operator of the skew algebra A into a DESol structure in the function f.
|
•
|
The Ore_to_shift command converts a shift operator or a list of shift operators of the skew algebra A into a recurrence equation or a list of recurrence equations in the sequence u. The output is expressed in functional notation ( ) by default, or in the indexed notation ( ) when the optional argument is set.
|
•
|
The Ore_to_RESol command converts a single recurrence operator of the skew algebra A into an RESol structure in the sequence u.
|
|
|
Examples
|
|
>
|
|
Differential case.
>
|
|
>
|
|
>
|
|
| (1) |
>
|
|
| (2) |
>
|
|
| (3) |
>
|
|
| (4) |
Euler case.
>
|
|
>
|
|
>
|
|
| (5) |
Recurrence case.
>
|
|
>
|
|
>
|
|
| (6) |
>
|
|
| (7) |
>
|
|
| (8) |
Multivariate differential case.
>
|
|
>
|
![G := [-2*x*Dx+Dy*y, -(4*(mu-x*y^2))*(mu+x*y^2)+2*x*Dx+y^2*Dy^2, -(2*(mu-x*y^2))*(mu+x*y^2)+Dy*Dx*y*x, -(mu-x*y^2)*(mu+x*y^2)+x*Dx+x^2*Dx^2]](/support/helpjp/helpview.aspx?si=7356/file02458/math266.png)
|
These are operators for BesselJ(mu,x*y^2).
>
|
|
![[-2*x*(diff(f(x, y), x))+y*(diff(f(x, y), y)), -4*(mu-x*y^2)*(mu+x*y^2)*f(x, y)+2*x*(diff(f(x, y), x))+y^2*(diff(f(x, y), `$`(y, 2))), -2*(mu-x*y^2)*(mu+x*y^2)*f(x, y)+y*x*(diff(f(x, y), x, y)), -(mu-x*y^2)*(mu+x*y^2)*f(x, y)+x*(diff(f(x, y), x))+x^2*(diff(f(x, y), `$`(x, 2)))]](/support/helpjp/helpview.aspx?si=7356/file02458/math275.png)
| (9) |
>
|
|
)(x, y)+y*(D[2](f))(x, y), -4*(mu-x*y^2)*(mu+x*y^2)*f(x, y)+2*x*(D[1](f))(x, y)+y^2*(D[2, 2](f))(x, y), -2*(mu-x*y^2)*(mu+x*y^2)*f(x, y)+y*x*(D[1, 2](f))(x, y), -(mu-x*y^2)*(mu+x*y^2)*f(x, y)+x*(D[1](f))(x, y)+x^2*(D[1, 1](f))(x, y)]](/support/helpjp/helpview.aspx?si=7356/file02458/math282.png)
| (10) |
No conversion is available to a multivariate DESol.
>
|
|
|
|