mathematica('N[Gamma[Pi + I]]')       # optional 
G = mathematica('Plot3D[Sin[x]*Cos[y],{x,2,10},{y,2,10}]');
_ = G.show()
gp.zeta(2)       # number theory
gp.factor(2006)
f = maxima('x*sin(x)^2').integral('x'); f    # calculus
maple.eval('solve({ 2*x + 3*y = 1, 3*x + 5*y = 1 })')
A = MatrixSpace(QQ,3)([1,2,3, 4,5,6, 8,10,12]); A
A.charpoly().factor()
V = QQ^3
E = End(V); t = E(A); t
print latex(A)
P.<x,y,z,w> = ProjectiveSpace(3,QQ)
C = P.subscheme([y^2-x*z, z^2-y*w, x*w-y*z])  
len(C.irreducible_components())   # twisted cubic
J = C.defining_ideal()
G = J.groebner_fan()
len(G.reduced_groebner_bases())
G.fvector()
f = prod(J.gens())     # \/-- newton polytope 
NP = polymake.convex_hull(f.exponents())  
NP.facets()
R.<t> = PowerSeriesRing(QQ, 't')
f = 1/(1-t)
f
print latex(f)
view(f) 
E = EllipticCurve('37a')
v = E.Lseries_values_along_line(1, 1+10*I, 300)
w = [(z[1].real(), z[1].imag()) for z in v]
L = line(w, rgbcolor=(0.5,0,0))
L.save('line.png')
V = VectorSpace(QQ, 5)
W = V.submodule([[1,2,3,4,5],[2,3,4,5,3]]); W
W.save('W')
load('W')