Important: The diffalg package has been deprecated. Use the superseding package DifferentialAlgebra instead.

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.