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Reduce

Reduce powers of algebraic numbers and algebraic functions

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

evala(Reduce(a))

evala(Reduce(a), opts)

Parameters

a

-

expression involving algebraic numbers or algebraic functions.

opts

-

(optional) an option name or a set of option names.

 

-

Options currently supported: expanded.

Description

• 

This function reduces powers of algebraic numbers or algebraic functions modulo their defining polynomials.

• 

Algebraic functions and algebraic numbers may be represented by radicals or with the RootOf notation (see type,algnum, type,algfun, type,radnum, type,radfun).

• 

The result will have the form P/Q, where P and Q are polynomials over the extension field. The powers of the RootOfs appearing in the coefficients are positive and lower than the degree of the defining polynomials.

• 

By default, this function attempts to preserve partial factorization of polynomials, but algebraic numbers and functions are always expanded. If the option expanded is specified, then polynomials are also expanded.

• 

Unlike evala@Normal, the function Reduce does not rationalize algebraic numbers and functions and does not rationalize leading coefficients of rational functions and polynomials. It also does not cancel the greatest common divisor of the numerator and the denominator of a rational function.

• 

If the RootOfs appearing in the input are independent, then this function will return 0 if and only if the input is mathematically equal to 0. It may not be so if the RootOfs are dependent or if the polynomial defining a RootOf is reducible.

• 

If a contains functions, their arguments are reduced recursively and the functions are frozen before the computation proceeds.

• 

Since the ordering of objects may vary from a session to another, the result may change accordingly.

• 

Other objects are frozen and considered as variables, except in the cases below.

• 

If a is a set, a list, a range, a relation, or a series, then Reduce is mapped over the object.

Examples

r1RootOf_Z3+_Z+1

r1RootOf_Z3+_Z+1

(1)

p1xr1312r13+1xr12

p1RootOf_Z3+_Z+13+x12RootOf_Z3+_Z+13+1xRootOf_Z3+_Z+12

(2)

evalaReducep1

RootOf_Z3+_Z+1+x2x+RootOf_Z3+_Z+12RootOf_Z3+_Z+1

(3)

evalaReducep1,expanded

RootOf_Z3+_Z+12+2xRootOf_Z3+_Z+1+x2RootOf_Z3+_Z+1+1+2RootOf_Z3+_Z+12xRootOf_Z3+_Z+1x2

(4)

r2RootOf_Z2y

r2RootOf_Z2y

(5)

evalaReducetr2t2y

t+RootOf_Z2yt2y

(6)

r3RootOf_Z24

r3RootOf_Z24

(7)

evalaReducer338

4RootOf_Z248

(8)

aliasseqs||i=RootOf_Z32,index=i,i=1..3

s1,s2,s3

(9)

qs14s23s32

qs14s23s32

(10)

evalaReduceq

4s1s32

(11)

See Also

evala

Expand

Gcd

gcd

normal

Normal

radnormal

RootOf

 


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