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SandBoxSqrt

Edit detail for SandBoxSqrt revision 2 of 3

	1 2 3
Editor: Bill Page Time: 2015/02/13 19:03:34 GMT+0
Note:

added:
Square root

added:
Positive nthRoot is primmitive

added:
\end{axiom}

Strange library message
\begin{axiom}
nthRoot(x,0)
\end{axiom}

Negative nthRoot is not primitive
\begin{axiom}

added:
msqrt:=kernels(nthRoot(x,-3))(1)
name(msqrt)
argument(msqrt)

added:
Powers are roots

changed:
-nthRoot(x,0)
psqrt:=kernels(x^(1/2))(1)
name(psqrt)
argument(psqrt)

Square root

fricas

ksqrt:=kernels(sqrt(x))(1)

$\label{eq1}\sqrt{x}$

(1)

Type: Kernel(Expression(Integer))

fricas

name(ksqrt)

$\label{eq2}nthRoot$

(2)

Type: Symbol

fricas

argument(ksqrt)

$\label{eq3}\left[ x , \: 2 \right]$

(3)

Type: List(Expression(Integer))

fricas

)di op nthRoot

There is one exposed function called nthRoot :
   [1] (D,Integer) -> D from D if D has RADCAT

There is one unexposed function called nthRoot :
   [1] (Factored(D4),NonNegativeInteger) -> Record(exponent: 
            NonNegativeInteger,coef: D4,radicand: List(D4))
            from FactoredFunctions(D4) if D4 has INTDOM

Positive nthRoot is primmitive

fricas

nthRoot(x,3)

$\label{eq4}\root{3}\of{x}$

(4)

Type: Expression(Integer)

fricas

nthRoot(x,2)

$\label{eq5}\sqrt{x}$

(5)

Type: Expression(Integer)

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nthRoot(x,1)

$\label{eq6}x$

(6)

Type: Expression(Integer)

Strange library message

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nthRoot(x,0)

   >> Error detected within library code:
   not invertible

Negative nthRoot is not primitive

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nthRoot(x,-1)

$\label{eq7}1 \over x$

(7)

Type: Expression(Integer)

fricas

nthRoot(x,-2)

$\label{eq8}1 \over{\sqrt{x}}$

(8)

Type: Expression(Integer)

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nthRoot(x,-3)

$\label{eq9}1 \over{\root{3}\of{x}}$

(9)

Type: Expression(Integer)

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msqrt:=kernels(nthRoot(x,-3))(1)

$\label{eq10}\root{3}\of{x}$

(10)

Type: Kernel(Expression(Integer))

fricas

name(msqrt)

$\label{eq11}nthRoot$

(11)

Type: Symbol

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argument(msqrt)

$\label{eq12}\left[ x , \: 3 \right]$

(12)

Type: List(Expression(Integer))

Powers are roots

fricas

psqrt:=kernels(x^(1/2))(1)

$\label{eq13}\sqrt{x}$

(13)

Type: Kernel(Expression(Integer))

fricas

name(psqrt)

$\label{eq14}nthRoot$

(14)

Type: Symbol

fricas

argument(psqrt)

$\label{eq15}\left[ x , \: 2 \right]$

(15)

Type: List(Expression(Integer))