AlgebraicNumberDenominator

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`AlgebraicNumberDenominator`

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AlgebraicNumberDenominator[a]

gives the smallest positive integer n such that n a is an algebraic integer.

Examples

open allclose all

Basic Examples (2)Summary of the most common use cases

In[1]:=1

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https://wolfram.com/xid/0tqfdc4pygxfvi-449k3

Out[1]=1

In[1]:=1

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https://wolfram.com/xid/0tqfdc4pygxfvi-w2jwc3

Out[1]=1

Scope (3)Survey of the scope of standard use cases

Radical expressions:

In[1]:=1

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https://wolfram.com/xid/0tqfdc4pygxfvi-srk352

Out[1]=1

In[2]:=2

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https://wolfram.com/xid/0tqfdc4pygxfvi-5v0sw1

Out[2]=2

Root and AlgebraicNumber objects:

In[1]:=1

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https://wolfram.com/xid/0tqfdc4pygxfvi-cexgl

Out[1]=1

In[2]:=2

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https://wolfram.com/xid/0tqfdc4pygxfvi-gs8aug

Out[2]=2

AlgebraicNumberDenominator automatically threads over lists:

In[1]:=1

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https://wolfram.com/xid/0tqfdc4pygxfvi-ra3v5n

Out[1]=1

Applications (1)Sample problems that can be solved with this function

Representation of 1/(1+) as a quotient α/n of an algebraic integer α and an integer n:

In[1]:=1

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https://wolfram.com/xid/0tqfdc4pygxfvi-x82csc

Out[1]=1

In[2]:=2

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https://wolfram.com/xid/0tqfdc4pygxfvi-255cfl

Out[2]=2

In[3]:=3

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https://wolfram.com/xid/0tqfdc4pygxfvi-cqku4n

Out[3]=3

Properties & Relations (2)Properties of the function, and connections to other functions

For an algebraic integer n, the denominator is 1:

In[1]:=1

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https://wolfram.com/xid/0tqfdc4pygxfvi-wy56xz

Out[1]=1

Multiplying an algebraic number by its denominator gives an algebraic integer:

In[1]:=1

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https://wolfram.com/xid/0tqfdc4pygxfvi-bvtlvj

In[2]:=2

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https://wolfram.com/xid/0tqfdc4pygxfvi-mxn1ve

Out[2]=2

In[3]:=3

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https://wolfram.com/xid/0tqfdc4pygxfvi-x9oa5

Out[3]=3

Possible Issues (1)Common pitfalls and unexpected behavior

The argument must be an algebraic number:

In[1]:=1

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https://wolfram.com/xid/0tqfdc4pygxfvi-xbjet1

Out[1]=1

In[2]:=2

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https://wolfram.com/xid/0tqfdc4pygxfvi-xiuwef

Out[2]=2

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