ToFiniteField

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`ToFiniteField`

New in 14

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ToFiniteField[k,ff]

converts the integer k to an element of the prime subfield of the finite field ff.

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ToFiniteField[expr,ff]

converts the coefficients of the rational expression expr to elements of the finite field ff.

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ToFiniteField[expr,ff,t]

converts the coefficients of the rational expression expr to elements of the finite field ff, with t representing the field generator.

Details

ToFiniteField replaces integers k with elements ff[{k}] of the prime subfield of ff and replaces t with the field generator ff[{0,1}].
ToFiniteField goes inside List, Plus, Times and integer Power in expr.

Examples

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Basic Examples (4)Summary of the most common use cases

Convert an integer to an element of the prime subfield of a finite field:

In[1]:=1

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https://wolfram.com/xid/01yxj57iz4u-783jpd

Out[1]=1

Use t to represent the field generator:

In[1]:=1

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https://wolfram.com/xid/01yxj57iz4u-z40b4g

Out[1]=1

Convert the coefficients of a rational expression to elements in the prime subfield of a finite field:

In[1]:=1

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https://wolfram.com/xid/01yxj57iz4u-2p95dg

Out[1]=1

Use t to represent the field generator:

In[1]:=1

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https://wolfram.com/xid/01yxj57iz4u-g9epn8

Out[1]=1

Scope (4)Survey of the scope of standard use cases

Convert integers and rational numbers to elements of the prime subfield of a finite field:

In[1]:=1

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https://wolfram.com/xid/01yxj57iz4u-gwbyiv

Out[1]=1

In[2]:=2

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https://wolfram.com/xid/01yxj57iz4u-bew2ed

Out[2]=2

Convert a polynomial in t to a a polynomial in the field generator:

In[1]:=1

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https://wolfram.com/xid/01yxj57iz4u-g7w3f1

Out[1]=1

In[2]:=2

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https://wolfram.com/xid/01yxj57iz4u-h6eu0o

Out[2]=2

In[3]:=3

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https://wolfram.com/xid/01yxj57iz4u-c2bkmj

Out[3]=3

Convert the coefficients of a polynomial to elements in the prime subfield of a finite field:

In[1]:=1

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https://wolfram.com/xid/01yxj57iz4u-d8iv40

Out[1]=1

Convert the coefficients of a rational function, with t used to represent the field generator:

In[1]:=1

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https://wolfram.com/xid/01yxj57iz4u-b63lb

Out[1]=1

In[2]:=2

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https://wolfram.com/xid/01yxj57iz4u-dress

Out[2]=2

In[3]:=3

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https://wolfram.com/xid/01yxj57iz4u-gx3iyr

Out[3]=3

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

FromFiniteField converts finite field elements to polynomials in the field generator:

In[1]:=1

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https://wolfram.com/xid/01yxj57iz4u-fy3fo7

Out[1]=1

In[2]:=2

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https://wolfram.com/xid/01yxj57iz4u-ogsqa5

Out[2]=2

FromFiniteFieldIndex gives finite field elements with specified indices:

In[1]:=1

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https://wolfram.com/xid/01yxj57iz4u-dgxqzq

Out[1]=1

ToFiniteField converts integers to elements of the prime subfield:

In[2]:=2

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https://wolfram.com/xid/01yxj57iz4u-e36uhj

Out[2]=2

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