GAP Manual: 6.6. Operations for Field Elements

The following operations are always available for field elements. Of course the operands must lie in compatible fields, i.e., the fields must be equal, or at least have a common superfield.

f + g

The operator + evaluates to the sum of the two field elements f and g, which must lie in compatible fields.

f - g

The operator - evaluates to the difference of the two field elements f and g, which must lie in compatible fields.

f * g

The operator * evaluates to the product of the two field elements f and g, which must lie in compatible fields.

f / g

The operator / evaluates to the quotient of the two field elements f and g, which must lie in compatible fields. If the divisor is 0 an error is signalled.

f ^ n

The operator ^ evaluates to the n-th power of the field element f. If n is a positive integer then f^n is f*f*..*f (n factors). If n is a negative integer f^n is defined as 1 / (f^(-n)). If 0 is raised to a negative power an error is signalled. Any field element, even 0, raised to the 0-th power yields 1.

For the precedence of the operators see Operations.