 |
 |
 |
Constructions in SAGE (How to) |  |
 |
 |
|
|
|
Constructions in SAGE (How to) | |
|
|
To compute
in SAGE, type
sage: R = Integers(97) sage: a = R(51) sage: a^2006 12
Instead of R = Integers(97) you can also type R = IntegerModRing(97).
sage: R = IntegerModRing(51) sage: M = MatrixSpace(R,3,3) sage: A = M([1,2,3, 4,5,6, 7,8,9]) sage: A^2006 [42 0 9] [30 45 9] [18 39 9]
in ![$ GF(97)[x]$](img119.png){kind=small}
,
we create the quotient ring
![$ GF(97)[x]/(x^3+7)$](img115.png){kind=small}
, and compute
in it. As a matter of SAGE notation,
we must distinguish between the 
in
and the
corresponding element (which we denote by 
) in the
quotient ring
.
sage: R = PolynomialRing(GF(97),'x') sage: x = R.gen() sage: S = R.quotient(x^3 + 7, 'a') sage: a = S.gen() sage: S Univariate Quotient Polynomial Ring in a over Finite Field of size 97 with modulus x^3 + 7 sage: a^2006 4*a^2
Another approach to this:
sage: R = PolynomialRing(GF(97),'x')
sage: x = R.gen()
sage: S = R.quotient(x^3 + 7, 'a')
sage: a = S.gen()
sage: time a^20062006
CPU times: user 0.02 s, sys: 0.00 s, total: 0.02 s
Wall time: 0.03
80*a
sage: gap.eval("R:= PolynomialRing( GF(97))")
'PolynomialRing(..., [ x_1 ])'
sage: gap.eval("i:= IndeterminatesOfPolynomialRing(R)")
'[ x_1 ]'
sage: gap.eval("x:= i[1];;")
''
sage: gap.eval("f:= x;;")
''
sage: gap.eval("PowerMod( R, x, 20062006, x^3+7 ); time;")
'Z(97)^41*x_1\n5'
sage: time gap.eval("PowerMod( R, x, 20062006, x^3+7 ); time;")
CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s
Wall time: 0.00
'Z(97)^41*x_1\n0'
sage: gap.eval("PowerMod( R, x, 2006200620062006, x^3+7 ); time;")
'Z(97)^4*x_1^2\n0'
sage: time a^2006200620062006
CPU times: user 0.04 s, sys: 0.00 s, total: 0.05 s
Wall time: 0.06
43*a^2
sage: gap.eval("PowerMod( R, x, 2006200620062006, x^3+7 ); time;")
'Z(97)^4*x_1^2\n0'
|
|
|
Constructions in SAGE (How to) | |
|
|