This section describes the operations and functions available
for algebra elements. Note that algebra elements may exist
independently of an algebra, e.g., you can write down two
matrices and compute their sum and product without ever defining
an algebra that contains them. Comparisons of Algebra Elements g
= h: trueif the algebra elements g and h are equal and to g < h:
trueif the algebra elements g and h are not equal and to g < h g
<= h g = h true if the algebra element g is strictly less than,
less than or equal to, greater than or equal to and strictly
greater than the algebra element h. There is no general ordering
on all algebra elements, so g and h should lie in the same
parent algebra. Note that for elements of finitely presented
algebra, comparison means comparison with respect to the
underlying free algebra (see Elements of Finitely Presented
Algebras). Arithmetic Operations for Algebra Elements a * b a +
b a - b - evaluate to the product, sum and difference of the two
algebra elements a and b. The