# Running a for cycle in parallel

I have an algorithm that I need to speed up. I would like to parallelize computations

the main part I need to speed up is the following

`for r2 in Subsets(V2,k-4): check2(fuse(v,r2),k)`

this gives as output three values b1, b2, b3 that are global and for any input check2 can either leave them unchanged or increase them by 1. I tried looking into @parallel but it doens't seem to fit my requirements.

How can I parallelize that (I can use up to 16 cores)?

This is the whole code (minus all the parts that do, I can't publish it all):

```
P2=[]
def P_2(q,n,S): %creates the set P2
I2R=[]
I2S=[]
I3=[]
I3R=[]
I6=[]
I8=[]
def IG(k): %creates a set of indeces vectors
def coll(x,y,z): %checks if 3 given tuples are collinear
A=[x,y,z]
M = matrix(A)
if M.determinant()==0:
return 'true'
def cone(v): %defines a function to be used in conic()
def conic(x1,x2,x3,x4,x5,x6): %checks if 6 given tuples are on a conic
A=[cone(x1),cone(x2),cone(x3),cone(x4),cone(x5),cone(x6)]
M = matrix(A)
if M.determinant()==0:
return 'true'
def cube(v): %defines a function to be used in SIcubic()
def dxcube(v): %defines a function to be used in SIcubic()
def dycube(v): %defines a function to be used in SIcubic()
def dzcube(v): %defines a function to be used in SIcubic()
def SIcubic(x1,x2,x3,x4,x5,x6,x7,x8): %checks if 8 given tuples are on a special cubic
v1='false'
v=[x1,x2,x3,x4,x5,x6,x7,x8]
for a in range(8):
x=v[a]
A=[]
A.append(dxcube(x))
A.append(dycube(x))
A.append(dzcube(x))
for t in range(8):
if t!=a:
y=v[t]
A.append(cube(y))
M = matrix(A)
if M.determinant()==0:
v1='true'
return v1
b1=0
b2=0
b3=0
def check(s,k): %checks a vector s of lenght k
global b1
global b2
global b3
IG(k)
q1=0
q2=0
q3=0
for i3 in I3:
a0=i3[0]
a1=i3[1]
a2=i3[2]
if coll(s[a0],s[a1],s[a2])=='true':
q1=1
q2=1
q3=1
break
if q2==0:
if k>5:
if q==0:
for i6 in I6:
a0=i6[0]
a1=i6[1]
a2=i6[2]
a3=i6[3]
a4=i6[4]
a5=i6[5]
if conic(s[a0],s[a1],s[a2],s[a3],s[a4],s[a5])=='true':
q2=1
q3=1
break
if q3==0:
if k>7:
for i8 in I8:
a0=i8[0]
a1=i8[1]
a2=i8[2]
a3=i8[3]
a4=i8[4]
a5=i8[5]
a6=i8[6]
a7=i8[7]
if SIcubic(s[a0],s[a1],s[a2],s[a3],s[a4],s[a5],s[a6],s[a7])=='true':
q3=1
break
b1=b1+q1
b2=b2+q2
b3=b3+q3
return b1
return b2
return b3
b1=0
def check1(s,a): %checks a vector s and an element a
global b1
q1=0
for i2 in I2S:
a0=i2[0]
a1=i2[1]
if coll(s[a0],s[a1],a)=='true':
q1=1
break
b1=b1+q1
return b1
b1=0
b2=0
b3=0
def check2(s,k): %checks a vector s of lenght k
global b1
global b2
global b3
q1=0
q2=0
q3=0
for i3 in I3R:
a0=i3[0]
a1=i3[1]
a2=i3[2]
if coll(s[a0],s[a1],s[a2])=='true':
q1=1
q2=1
q3=1
break
if q2==0:
if k>5:
for i6 in I6:
a0=i6[0]
a1=i6[1]
a2=i6[2]
a3=i6[3]
a4=i6[4]
a5=i6[5]
if conic(s[a0],s[a1],s[a2],s[a3],s[a4],s[a5])=='true':
q2=1
q3=1
break
if q3==0:
if k>7:
for i8 in I8:
a0=i8[0]
a1=i8[1]
a2=i8[2]
a3=i8[3]
a4=i8[4]
a5=i8[5]
a6=i8[6]
a7=i8[7]
if SIcubic(s[a0],s[a1],s[a2],s[a3],s[a4],s[a5],s[a6],s[a7])=='true':
q3=1
break
b1=b1+q1
b2=b2+q2
b3=b3+q3
return b1
return b2
return b3
t=1
def TOT(P,q,n,k): %computes a polynomial depending on q,n,k,P
def fuse(s,t): %fuses two vectors into 1 (see repsonse to answere)
sn=[]
def Count(S,q,n,k): %main function
IG(k)
global b1
global b2
global b3
l1=0
l2=0
l3=0
y=q^n
s=len(S)
v=[(0,0,1),(0,1,0),(1,0,0),(1,1,1)]
V1=copy(S)
V1.remove((1,0,0))
V1.remove((0,1,0))
V1.remove((0,0,1))
V1.remove((1,1,1))
if k<4:
b1=0
for s in Subsets(S,k):
check(s,k)
l1=b1*factorial(k)
if k>4:
V2=copy(V1)
for r1 in V1:
b1=0
b2=0
b3=0
check1(v,r1)
if b1==1:
V2.remove(r1)
s2=len(V2)
l1=l1+binomial(s-4,k-4)-binomial(s2,k-4)
l2=l2+binomial(s-4,k-4)-binomial(s2,k-4)
l3=l3+binomial(s-4,k-4)-binomial(s2,k-4)
b1=0
b2=0
b3=0
for r2 in Subsets(V2,k-4):
check2(fuse(v,r2),k)
l1=l1+b1
l2=l2+b2
l3=l3+b3
l1=l1*(y^2+y+1)*(y^3-y)*(y^3-y^2)*factorial(k-4)
l2=l2*(y^2+y+1)*(y^3-y)*(y^3-y^2)*factorial(k-4)
l3=l3*(y^2+y+1)*(y^3-y)*(y^3-y^2)*factorial(k-4)
g1=t-l1
g2=t-l2
g3=t-l3
print('There are ', g1/factorial(k) , ' unordered', k,'-tuples in general linear position')
print('There are ', g1 , ' ordered', k ,'-tuples in general linear position')
print('There are ', g2/factorial(k) , ' unordered', k,'-tuples in general linear and conic position')
print('There are ', g2 , ' ordered', k ,'-tuples in general linear and conic position')
print('There are ', g3/factorial(k) , ' unordered', k,'-tuples in general position')
print('There are ', g3 , ' ordered', k ,'-tuples in general position')
def Active(q,n,k): %every fucntion I need to run reduced into 1
P2=[]
P_2(q,n,P2)
TOT(P2,q,n,k)
Count(P2,q,n,k)
```

Why do you think that parallelization will provide a speed up? Writing parallel code is extremy delicate

unlessit is embarassingly parallel (that is independent programs being run in parallel). If you want help to speed up your code, provide the full code of your program.Because all the operations in this key passage are independent (I need to check if any given element has a property), therefore I can do several of them at the same time