This section describes operations on fp-algebras. Most of the operations are very similar to those for noncommutative free algebras; such operations are done by mapping the computation to the preimage ideal and then by mapping the result back into the fp-algebra. See the corresponding functions for the noncommutative free algebras for details.
Given an fp-algebra A, return the i-th indeterminate of A as an element of A.
Return the coefficient ring of the fp-algebra A.
Return the rank of the fp-algebra A (the number of indeterminates of A).
Given an ideal I of an fp-algebra A which is the quotient ring F/J, where F is a free algebra and J an ideal of F, return the ideal J.
Given an ideal I of an fp-algebra A which is the quotient ring F/J, where F is a free algebra and J an ideal of F, return the ideal I' of F such that the image of I' under the natural epimorphism F -> A is I.
Given an fp-algebra A which is the quotient ring F/J, where F is a free algebra and J an ideal of F, return the free algebra F.
Return the generic free algebra F such that A is F/J for some ideal J of F.
Return whether the algebra A is commutative.
Given two ideals I and J of the same fp-algebra A, return true if and only if I and J are equal.
Given two ideals I and J of the same fp-algebra A, return true if and only if I is contained in J.
Given two ideals I and J of the same fp-algebra A, return the sum I + J.
Given two ideals I and J of the same fp-algebra A, return the product I * J.
Given an ideal I of the fp-algebra A, return whether I is proper; that is, whether I is strictly contained in A.
Given an ideal I of the fp-algebra A, return whether I is the zero ideal. Note that this is equivalent to whether the preimage ideal of I is the divisor ideal of A.