Suppose A is an fp-algebra for which generators have already been defined. A word is defined inductively as follows:
If the underlying monoid has an identity algorithm, construct the element e * ( Id)(M), where e is an element of the coefficient ring R and M is the monoid.
The word operations defined here may be applied either to the
words of a free algebra or the words of a algebra with non-trivial
relations.
u + v : AlgFPElt, AlgFPElt -> AlgFPElt
Given words u and v belonging to the same fp-algebra A, return the sum of u and v.
Given words u and v belonging to the same fp-algebra A, return the difference of u and v.
Given words u and v belonging to the same fp-algebra A, return the product of u and v.
The n-th power of the word u, where n is a positive integer.
The words of an fp-algebra A are ordered first by length and then
lexicographically.
The lexicographic ordering is determined by the ordering on the
coefficient ring and the monoid.
Here, u and v are words belonging to some common
fp-algebra.
u eq v : AlgFPElt, AlgFPElt -> BoolElt
True if the words u and v are identical (as elements of the appropriate free algebra), false otherwise.
True if the words u and v are not identical (as elements of the appropriate free algebra), false otherwise.
True if the word u precedes the word v, with respect to the ordering defined above for elements of an fp-algebra, false otherwise.
True if the word u either precedes, or is equal to, the word v, with respect to the ordering defined above for elements of an fp-algebra, false otherwise.
True if the word u either follows, or is equal to, the word v, with respect to the ordering defined above for elements of an fp-algebra, false otherwise.
True if the word u follows the word v, with respect to the ordering defined above for elements of an fp-algebra.
True if u is zero (the empty word), false otherwise.
True if u is a scalar, that is, an element of the underlying ring, false otherwise.
The length of the word u.
Returns the sequence of words whose coefficients in u are non-zero.
Returns the coefficient of the highest occurring power of the most principal monoid generator (where M.i is more principal than M.j if and only if i>j).
Returns the coefficient of the monoid element m in u.[Next] [Prev] [Right] [Left] [Up] [Index] [Root]