diffalg[field_extension] - define a field extension of the field of the rational numbers
|
Calling Sequence
|
|
field_extension (transcendental_elements = L, base_field = G)
field_extension (relations = J, base_field = G)
field_extension (prime_ideal = P)
|
|
Parameters
|
|
L
|
-
|
list or set of names
|
G
|
-
|
(optional) ground field
|
J
|
-
|
list or set of polynomials
|
P
|
-
|
characterizable differential ideal
|
|
|
|
|
Description
|
|
•
|
The function field_extension returns a table representing a field extension of the field of the rational numbers. This field can be used as a field of constants for differential polynomial rings.
|
•
|
For all the forms of field_extension, the parameter base_field = G can be omitted. In that case, it is taken as the field of the rational numbers.
|
•
|
The first form of field_extension returns the purely transcendental field extension of G.
|
•
|
The second form of field_extension returns the field of the fractions of the quotient ring G [X1 ... Xn] / (J) where the Xi are the names that appear in the polynomials of R and do not belong to G and (J) denotes the ideal generated by J in the polynomial ring G [X1 ... Xn].
|
|
You must ensure that the ideal (J) is prime, field_extension does not check this.
|
•
|
The third form of field_extension returns the field of fractions of R / P where P is a characterizable differential ideal in the differential polynomial ring R.
|
|
You must ensure that the characterizable differential ideal P is prime. The function field_extension does not check this.
|
|
The embedding differential polynomial ring of P must be endowed with a jet notation.
|
|
|
Examples
|
|
Important: The diffalg package has been deprecated. Use the superseding package DifferentialAlgebra instead.
>
|
|
>
|
|
| (1) |
>
|
|
| (2) |
>
|
|
| (3) |
>
|
|
| (4) |
>
|
|
| (5) |
>
|
|
| (6) |
>
|
|
| (7) |
>
|
|
| (8) |
>
|
|
| (9) |
>
|
|
| (10) |
>
|
|
| (11) |
>
|
|
| (12) |
|
|
Download Help Document
Was this information helpful?