P = 1 + x^2 + 27*x^10 Q = sum(i = 1, 10, (i+1) * x^i) v=[1,2,3,4]; T=Pol(v) U=Polrev(v) polrecip(T)==U f=3*x^2+x*y+4*y; polcoef(f,1) d=poldegree(f);d pollead(f)==polcoef(f,d) polcoef(f,1,y) dy=poldegree(f,y);dy pollead(f,y)==polcoef(f,d,y) P=x^3 - 6*x^2 + 11*x - 6; polroots(P) algdep(3,2) z = 2^(1/6)+3^(1/5); algdep(z, 30) a=[1,2,3];b=[4,0,2]; polinterpolate(a,b) polfromroots(a) f= x^5 + x^4 + 5*x^3 + 3*x^2 + 3*x - 1; factor(f) pol = x^4 - 4*x^2 + 16 polisirreducible(pol) factor(pol) factor(poldisc(pol)) factorpadic(pol, 3, 10) factorpadic(pol, 11, 10) factormod(pol,2) factormod(pol,11) lift(%) g = polcyclo(30) Mod(x,f)^5 lift(Mod(x,g)^15) pol2=x^4 - 4*x^2 + 16 fn = lift( factornf(pol2, t^2 + 1) ) T=(x^2-1)^3-2; polgalois(T) P= x^8-7*x^6+14*x^4-8*x^2+1 polgalois(P) gal=galoisinit(P); gal2=galoissplittinginit(T); poldegree(gal2.pol) gal.pol gal.roots gal.group gal.gen L = galoissubgroups(gal); vector(#L, i, galoisisabelian(L[i],1)) vector(#L, i, galoisidentify(L[i])) [a,b]=%[1]; galoisgetname(a,b) galoisfixedfield(gal,L[1]) galoisfixedfield(gal,L[2]) galoissubfields(gal); vector(#%, i, %[i][1]) p = randomprime(2^100) a = Mod(2,p); type(a) a^(p-1) a.mod == p lift(a) T = x^2+1; b = Mod(x+a, T); type(b) b.pol b.mod == T c = ffgen(3^8,'c) type(c) c.p c.mod polisirreducible(c.mod*Mod(1,3)) c.f d = c^9+1 d.pol type(d.pol) ffinit(3,5) ffgen(x^2+Mod(1,3)) [c,c+1;2*c,1]^-1 d = random(c) issquare(d) trace(d) norm(d) minpoly(d^82) factor(x^5+x^3+c) polrootsmod(x^7+x+c)