xmax = 2 ; n = 4
g=plot(x, x, -xmax, xmax)
for d in [1..n]:
    g += plot(x^(2*d+1), x, -xmax, xmax, color=(5*d/(2*n), 1.5*d/(2*n), 1-2*d/(4*n)))
g.show(ymin=-2, ymax=2)

numerical_approx(sin(pi^2)/log(2))

x,y,z=var('x,y,z')
f=x^5*y^7*z^9+1
f(x=25,y=26,z=27)

L=list(filter(is_prime,[1..1000]))
Q=[t^2 for t in L if is_prime(t)]
Q[len(Q):]=['Last']
Q[0:0]=['First']
Q[2:2]=[0]

L=[1,[2,[3]],[4,[[5],6]]]
L[2][1][0]

R=PolynomialRing(QQ,'x,y,z')
x,y,z=R.gens()
f=x*y*z^2+y*z^2+x*z+x+1
f.degree()

R=PolynomialRing(QQ,'x,y,z')
x,y,z=R.gens()
f=x*y*z^2+y*z^2+x*z+x+1
L=f.monomials()
L[0]

R=PolynomialRing(QQ,'x,y,z')
x,y,z=R.gens()
f=x*y*z^2+y*z^2+x*z+x+1
G=f.coefficients()
G[0]

L[0]/G[0]

f=x+2*x^2+3*x^3+4*x^4+5*x^5+6*x^6+7*x^7+8*x^8+9*x^9+10*x^10
g=1+3*x^3+5*x^5+7*x^7+9*x^9
f*g

m,n=var('m,n')
V=500*(1+0.02/(m))^(m*n)
V(m=1)

V(m=2)

V(m=4)

V(m=12)

V(m=365)

i,j=var('i,j')
i=1
j=0
while i<=99:
    j=j+i
    i=i+2
print(i,j)

i,j=var('i,j')
i=200
j=300
if( i<1000 or j<200):
    if(i<100):
        i=i+j
    else:
        if(j<300):
            j=i+2 
        else:
            j=i 
else:
    if(i<100): 
        i=i+j
    else:
        if(j<300):
            j=i+2 
        else:
            j=i+3
print(i,j)

p=var('p')
p=0
for i in range(100,1001):
    p=p+i
p

#Use loop to define functions for (a) t(a,d,n)=a+(a+d)+(a+2d)+...+(a+(n-1)d) and (a) s(a,r,n)=a+(ar)+(ar2)+...+(ar(n-1)) if r≠1.
def f(a,d,n):
    b=1
    s=0
    for i in range(0,n):
        b=a+i*d
        s=s+b
        print(b)
    return s
f(1,2,3)

a,r,n=var('a,r,n')
def S(a,r,n):
    b=0
    s=0
    for i in range(0,n):
        b=a*r^i
        s+=b
        print(b)
    return s
S(1,2,3)