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radnormal

normalize an expression containing radical numbers

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

radnormal(f)

radnormal(f, opts1, opts2, ...)

Parameters

f

-

algebraic expression

opts1, opts2, ...

-

sequence of options

Description

• 

The radnormal function performs normalization of expressions containing algebraic numbers in radical notation (see type/radnum), for example, 2 and 7+521/3. In particular, radnormal simplifies such a number to 0 if and only if it is mathematically equal to 0.

• 

The expression x1n is understood as the principal nth root of the object x (see log).

• 

Note that by default, if f is a number, then the denominator of f is not always rationalized.  To force rationalization of the denominator, use the option 'rationalized'.

• 

For polynomials, radnormal attempts to preserve partial factorizations. Each factor is expanded and its coefficients are normalized. The option 'expanded' causes radnormal to expand all products.

• 

Rational functions are expressed in the form a/b where a and b are normalized polynomials, and gcda,b=1. Again, partial factorizations are preserved and the option 'expanded' applies.

• 

The function radnormal is mapped over sets, lists, and relations.

• 

Note that radnormal does handle expressions involving algebraic numbers in both indexed RootOf and radical notations (see RootOf/indexed).

• 

The function radnormal will sometimes unnest radicals, but will not always find an incidence of unnesting when it exists.

• 

After some preliminary simplifications, a basis (in indexed RootOf notation) for the field generated by the radical numbers occurring in f is constructed and the numbers are expressed in this basis (see radfield). Then, the expression is normalized by evala@Normal and the numbers are converted back to radical notation.

• 

If infolevel[radnormal] is assigned a positive integer, then information about the execution of the program will be displayed.

Examples

a236

a:=236

(1)

radnormala

0

(2)

a7+5213

a:=7+521/3

(3)

radnormala

2+1

(4)

a1212+312+612

a:=12+3+6

(5)

radnormala

12+3+23

(6)

radnormala,'rationalized'

5233123231223+7232

(7)

a214212+28+621212

a:=21/42+28+62

(8)

radnormala

1

(9)

ax2+2x212212x612+52212312x22x312+1

a:=x2+2x22x6+5223x22x3+1

(10)

radnormala

3+2+xx32

(11)

ax612x212312

a:=x6x23

(12)

radnormala

x232

(13)

radnormala,'expanded'

6232x+x2

(14)

a1x+yz

a:=1x+yz

(15)

radnormala

1x+yz

(16)

radnormala,'rationalized'

2xzyx3/2+xy+xz+xyy3/2+zyzxzy+z3/2x22xy2xz+y22yz+z2

(17)

aRootOf_Z2+_Z+1,index=1123

a:=RootOf_Z2+_Z+1,index=112/3

(18)

radnormala

0

(19)

See Also

evala

log

normal

radfield

rationalize

RootOf

simplify/radical

simplify/sqrt

type/radnum

 


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