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Results tagged with computer-algebra
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user 17261
Using computer-aid approach to solve algebraic problems. Questions with this tag should typically include at least one other tag indicating what sort of algebraic problem is involved, such as ac.commutative-algebra or rt.representation-theory or ag.algebraic-geometry.
3
votes
Computation of a minimal polynomial
PARI / GP code :
p=x^5-x+1
py=subst(p,x,y)
K = nfinit(py)
L0 = rnfinit(K,nffactor(K,p)[2,1])
p2y=subst(L0.polabs,x,y)
L = nfinit(p2y)
f(w,i) = Mod(- subst(nffactor(L,w)[i,1],x,0), p2y)
a1=f(p,1)
…
- 2,753
3
votes
Computation of a minimal polynomial
SymPy code :
from sympy import *
x,y = symbols('x y')
roots = solve(x**5 - x + 1)
print(minimal_polynomial(roots[0] - roots[1], y))
gives :
y**20 - 10*y**16 - 95*y**12 + 625*y**10 - 40*y**8 + 375 …
- 2,753
2
votes
Most helpful math resources on the web
For people who are interested in prime factorization :
http://www.mersenneforum.org
1
vote
Minimal polynomial of cos(π/n)
In PARI/ GP :
r2n = Mod(x, polcyclo(2*n))
minpoly((r2n + 1/r2n) / 2)
- 2,753
0
votes
How to compute with the Stark conjectures?
Also useful : bnrclassfield, which replaces rnfkummer .
- 2,753