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SandBoxSqrt

Edit detail for SandBoxSqrt revision 3 of 3

	1 2 3
Editor: Bill Page Time: 2015/02/13 20:31:28 GMT+0
Note: complex roots

added:
Complex roots
\begin{axiom}
complexNumeric(nthRoot(complex(-1,0),2))
nthRoot(%,2)
recip %
complexNumeric(nthRoot(complex(-1,0),3))
recip %
complexNumeric(nthRoot(complex(-1,0),4))
conjugate %
\end{axiom}

Square root

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

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

(1)

Type: Kernel(Expression(Integer))

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name(ksqrt)

$\label{eq2}nthRoot$

(2)

Type: Symbol

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argument(ksqrt)

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

(3)

Type: List(Expression(Integer))

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)di op nthRoot

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

There are 2 unexposed functions called nthRoot :
   [1] (Factored(D4),NonNegativeInteger) -> Record(exponent: 
            NonNegativeInteger,coef: D4,radicand: List(D4))
            from FactoredFunctions(D4) if D4 has INTDOM
   [2] (Integer,((Integer, List(OutputForm)) -> OutputBox),((Integer, 
            List(OutputForm)) -> OutputBox)) -> ((Integer, List(OutputForm))
             -> OutputBox)
            from D if D has FMTCAT

Positive nthRoot is primmitive

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nthRoot(x,3)

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

(4)

Type: Expression(Integer)

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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)

$\label{eq7}\frac{1}{x}$

(7)

Type: Expression(Integer)

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nthRoot(x,-2)

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

(8)

Type: Expression(Integer)

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nthRoot(x,-3)

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

(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))

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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

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

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

(13)

Type: Kernel(Expression(Integer))

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name(psqrt)

$\label{eq14}nthRoot$

(14)

Type: Symbol

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argument(psqrt)

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

(15)

Type: List(Expression(Integer))

Complex roots

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complexNumeric(nthRoot(complex(-1,0),2))

$\label{eq16}i$

(16)

Type: Complex(Float)

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nthRoot(%,2)

$\label{eq17}{0.7071067811 \ 865475244}+{{0.7071067811 \ 865475244}\ i}$

(17)

Type: Complex(Float)

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recip %

$\label{eq18}{0.7071067811 \ 865475244}-{{0.7071067811 \ 865475244}\ i}$

(18)

Type: Union(Complex(Float),...)

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complexNumeric(nthRoot(complex(-1,0),3))

$\label{eq19}{0.5}+{{0.8660254037 \ 8443864676}\ i}$

(19)

Type: Complex(Float)

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recip %

$\label{eq20}{0.5}-{{0.8660254037 \ 8443864676}\ i}$

(20)

Type: Union(Complex(Float),...)

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complexNumeric(nthRoot(complex(-1,0),4))

$\label{eq21}{0.7071067811 \ 865475244}+{{0.7071067811 \ 865475244}\ i}$

(21)

Type: Complex(Float)

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conjugate %

$\label{eq22}{0.7071067811 \ 865475244}-{{0.7071067811 \ 865475244}\ i}$

(22)

Type: Complex(Float)