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asked 11 years ago

Johan gravatar image

Symbolic computions in a finite field

Hallo

I am interested in symbolic computations in a file field. Working in the field GF(28) with x as a generator and a variable y, also there is a function f:GF(28)GF(28) of which the exact definition is not given. Can sage do the following:

(x+y)281x+y

(x+y)26x26+y26

f(y)+f(y)0x

Regards

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No.2 Revision

Symbolic computions in a finite field

Hallo

I am interested in symbolic computations in a file field. Working in the field GF(28) with x as a generator and a variable y, also there is a function f:GF(28)GF(28) of which the exact definition is not given. Can sage do the following:

(x+y)281x+y

(x+y)26x26+y26

f(y)+f(y)0x

If sage cannot do it does there exist another program which can?

Regards

click to hide/show revision 3
No.3 Revision

Symbolic computions in a finite field

Hallo

I am interested in symbolic computations in a file field. Working in the field GF(28) with x as a generator and a variable y, also there is a function f:GF(28)GF(28) of which the exact definition is not given. Can sage do the following:

(x+y)281x+y

(x+y)26x26+y26

f(y)+f(y)0x

If sage cannot do it does there exist another program which can?


Below is my question updated:

For the function I have a partial solution but I cannot mix it with an element of an finite field


import sympy
f = sympy.Function('f')
y = var('y')
sympy.expand((f(y)+f(y)), modulus=2)
 

When I want to add an element of a finite field


import sympy
f = sympy.Function('f')
x = GF(2^8,'x').gen()
f(x)
f(x) + x
 

the statement f(x)+x give me an error that makes sense ... TypeError: unsupported operand parent(s) for '+': 'f' and 'Finite Field in g of size 2^8'

To create a variable in a finite field I decided to use a Polynomial ring


import sympy
f = sympy.Function('f')
R.< x > = PolynomialRing(GF(2))
f(x)
f(x) + x
 

both f(x) and f(x)+x fails with a very long Trace message.

Regards

click to hide/show revision 4
No.4 Revision

Symbolic computions in a finite field

Hallo

I am interested in symbolic computations in a file field. Working in the field GF(28) with x as a generator and a variable y, also there is a function f:GF(28)GF(28) of which the exact definition is not given. Can sage do the following:

$(x + y) ^ {2^8-1} {2^8} \mapsto x + y$

(x+y)26x26+y26

f(y)+f(y)0x

If sage cannot do it does there exist another program which can?


Below is my question updated:

For the function I have a partial solution but I cannot mix it with an element of an finite field


import sympy
f = sympy.Function('f')
y = var('y')
sympy.expand((f(y)+f(y)), modulus=2)
 

When I want to add an element of a finite field


import sympy
f = sympy.Function('f')
x = GF(2^8,'x').gen()
f(x)
f(x) + x
 

the statement f(x)+x give me an error that makes sense ... TypeError: unsupported operand parent(s) for '+': 'f' and 'Finite Field in g of size 2^8'

To create a variable in a finite field I decided to use a Polynomial ring


import sympy
f = sympy.Function('f')
R.< x > = PolynomialRing(GF(2))
f(x)
f(x) + x
 

both f(x) and f(x)+x fails with a very long Trace message.

Regards

click to hide/show revision 5
None

updated 6 years ago

FrédéricC gravatar image

Symbolic computions in a finite field

Hallo

I am interested in symbolic computations in a file field. Working in the field GF(28) with x as a generator and a variable y, also there is a function f:GF(28)GF(28) of which the exact definition is not given. Can sage do the following:

(x+y)28x+y

(x+y)26x26+y26

f(y)+f(y)0x

If sage cannot do it does there exist another program which can?


Below is my question updated:

For the function I have a partial solution but I cannot mix it with an element of an finite field


import sympy
f = sympy.Function('f')
y = var('y')
sympy.expand((f(y)+f(y)), modulus=2)
 

When I want to add an element of a finite field


import sympy
f = sympy.Function('f')
x = GF(2^8,'x').gen()
f(x)
f(x) + x
 

the statement f(x)+x give me an error that makes sense ... TypeError: unsupported operand parent(s) for '+': 'f' and 'Finite Field in g of size 2^8'

To create a variable in a finite field I decided to use a Polynomial ring


import sympy
f = sympy.Function('f')
R.< x > = PolynomialRing(GF(2))
f(x)
f(x) + x
 

both f(x) and f(x)+x fails with a very long Trace message.

Regards

click to hide/show revision 6
None

updated 6 years ago

FrédéricC gravatar image

Symbolic computions in a finite field

Hallo

I am interested in symbolic computations in a file field. Working in the field GF(28) with x as a generator and a variable y, also there is a function f:GF(28)GF(28) of which the exact definition is not given. Can sage do the following:

(x+y)28x+y

(x+y)26x26+y26

f(y)+f(y)0x

If sage cannot do it does there exist another program which can?


Below is my question updated:

For the function I have a partial solution but I cannot mix it with an element of an finite field


import sympy
f = sympy.Function('f')
y = var('y')
sympy.expand((f(y)+f(y)), modulus=2)
 

When I want to add an element of a finite field


import sympy
f = sympy.Function('f')
x = GF(2^8,'x').gen()
f(x)
f(x) + x
 

the statement f(x)+x give me an error that makes sense ... TypeError: unsupported operand parent(s) for '+': 'f' and 'Finite Field in g of size 2^8'

To create a variable in a finite field I decided to use a Polynomial ring


import sympy
f = sympy.Function('f')
R.< x > = PolynomialRing(GF(2))
f(x)
f(x) + x
 

both f(x) and f(x)+x fails with a very long Trace message.

Regards