EJEMPLOS

RESOLUCIÓN DE ECUACIONES LINEALES

2%3

2

x, y = var('x, y') 
solve([x + y == 5, x - y == 4], x, y)

[[x == (9/2), y == (1/2)]]

x, y, z, t = var('x, y, z, t') 
solve([x + y + 4*z == 11, 2*x + 3*z - t == 11, 4*x + 2*y + 6*z - 2*t == 1, x -y + 5*z -2*t == 0], x, y, z, t)

[[x == (217/22), y == (-21/2), z == (32/11), t == (192/11)]]

M1 = Matrix([[1.0, 1.0, 4.0, 0.0],[2, 0, 0, -1], [0, 2, 6, -2], [1, -1, 5, -2]]) 
v1 = vector([1, 11, 1, 0]) 
X2 = M1.solve_right(v1) 
X2

(4.29310344827586, 2.22413793103448, -1.37931034482759, -2.41379310344828)

a = var('a')
S = solve(x^2 + 2*x == 3+a,x); S

[x == -sqrt(a + 4) - 1, x == sqrt(a + 4) - 1]

#más numeros grandes
factorial(100)

93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000

#digitos de pi
N(pi, digits=150)

3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172535940813

FACTORIZACIÓN DE POLINOMIOS

R.<x,y> = QQ[]
F = factor(x^99 + y^99)
F

(x + y) * (x^2 - x*y + y^2) * (x^6 - x^3*y^3 + y^6) * (x^10 - x^9*y + x^8*y^2 - x^7*y^3 + x^6*y^4 - x^5*y^5 + x^4*y^6 - x^3*y^7 + x^2*y^8 - x*y^9 + y^10) * (x^20 + x^19*y - x^17*y^3 - x^16*y^4 + x^14*y^6 + x^13*y^7 - x^11*y^9 - x^10*y^10 - x^9*y^11 + x^7*y^13 + x^6*y^14 - x^4*y^16 - x^3*y^17 + x*y^19 + y^20) * (x^60 + x^57*y^3 - x^51*y^9 - x^48*y^12 + x^42*y^18 + x^39*y^21 - x^33*y^27 - x^30*y^30 - x^27*y^33 + x^21*y^39 + x^18*y^42 - x^12*y^48 - x^9*y^51 + x^3*y^57 + y^60)

F.expand()

x^99 + y^99

EXPRESIONES SIMBÓLICAS

x = var('x') 
f = sin(3*x)*x+log(x) + 1/(x+1)^2 
show(f)

\newcommand{\Bold}[1]{\mathbf{#1}}x \sin\left(3 \, x\right) + \frac{1}{{\left(x + 1\right)}^{2}} + \log\left(x\right)

plot(f,(0.01,2))

GRÁFICOS

x=var('x') 
parametric_plot((x,1/x),(0.1,10))

#gráficos y programación
lista = [] 
for k in range(-10, 10): 
    f = sin(k*x**2 - k*x)
    lista.append(f) 
plot(lista)

t=var('t')
parametric_plot((t*cos(t),t*sin(t)),0,16*pi)

/sagenb/sage_install/sage-5.0-boxen-x86_64-Linux/local/lib/python2.7/site-packages/sage/misc/decorators.py:534: DeprecationWarning: variable ranges to parametric_plot must be given as tuples, like (2,4) or (t,2,3)
  return func(*args, **options)

#graficos 3D 
r=var('r')
parametric_plot3d([r,cos(r),sin(r)],(r,0,16*pi))

u,v=var('u,v') 
fx=(3+sin(v)+cos(u))*cos(2*v)
fy=(3+sin(v)+cos(u))*sin(2*v) 
fz=sin(u)+2*cos(v)
parametric_plot3d([fx,fy,fz],(u,0,4*pi),(v,0,4*pi),color="red")

#Poliedros 
sphere((0,0,0)) + sphere((0,1,0),color='red', opacity=0.5) + icosahedron((1,1,0), color='orange')