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Trace

trace of an algebraic number (or function)

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

Trace(a, L, K)

Parameters

a

-

any expression

L

-

(optional) set of RootOfs

K

-

(optional) set of RootOfs

Description

• 

The Trace function is a placeholder for representing the trace of an algebraic number (or function), that is the sum of its conjugates. It is used in conjunction with evala.

• 

The call evala(Trace(a, L, K)) computes the trace of a over the algebraic number (or function) field represented by K. In case K is not specified and a is an algebraic number, the trace over the rational is computed. In case K is not specified and a is an algebraic function, the smallest possible transcendental extension of the rational numbers is chosen. The expression a is viewed as an element of the smallest field containing a and the RootOfs in L.

• 

The RootOfs in K must form a subset of the RootOfs occurring in L and in a. In other words, K must be a 'syntactic' subfield of the field generated  by L and the RootOfs in a.

Examples

aliassqrt2=RootOfx22:

aliasα=RootOfy2x+RootOfx22y,y:

evalaTraceα

0

(1)

evalaTraceα,,sqrt2

sqrt2

(2)

evalaTracezαz

4z

(3)

See Also

evala

mod

RootOf

sum

trace

 


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