1mathematica('N[Gamma[Pi + I]]')       # optional
2G = mathematica('Plot3D[Sin[x]*Cos[y],{x,2,10},{y,2,10}]');
3_ = G.show()
4gp.zeta(2)       # number theory
5gp.factor(2006)
6
7f = maxima('x*sin(x)^2').integral('x'); f    # calculus
8
9maple.eval('solve({ 2*x + 3*y = 1, 3*x + 5*y = 1 })')
10
11A = MatrixSpace(QQ,3)([1,2,3, 4,5,6, 8,10,12]); A
12A.charpoly().factor()
13V = QQ^3
14E = End(V); t = E(A); t
15print latex(A)
16
17
18P.<x,y,z,w> = ProjectiveSpace(3,QQ)
19C = P.subscheme([y^2-x*z, z^2-y*w, x*w-y*z])
20len(C.irreducible_components())   # twisted cubic
21J = C.defining_ideal()
22G = J.groebner_fan()
23len(G.reduced_groebner_bases())
24G.fvector()
25
26
27f = prod(J.gens())     # \/-- newton polytope
28NP = polymake.convex_hull(f.exponents())
29NP.facets()
30
31
32R.<t> = PowerSeriesRing(QQ, 't')
33f = 1/(1-t)
34f
35print latex(f)
36view(f)
37
38
39E = EllipticCurve('37a')
40v = E.Lseries_values_along_line(1, 1+10*I, 300)
41w = [(z[1].real(), z[1].imag()) for z in v]
42L = line(w, rgbcolor=(0.5,0,0))
43L.show()
44
45V = VectorSpace(QQ, 5)
46W = V.submodule([[1,2,3,4,5],[2,3,4,5,3]]); W
47W.save('W')
48load('W')
49