Matroid Union working

#!/usr/bin/env sage -python

import sys
from sage.all import *


#Let Mi = (Si,Ii)
#Matroid Union M = M1 v M2 v M3 v ... v Mk is defined as (S1 U S2 U S3 U ... U Sk,I1 v I2 v I3 v ... v Ik )
#where I1 v I2 v I3 v ... v Ik = {i1 U i2 U i3 U ... U ik | ij \in Ij }

def MatroidUnion(*matroids):

    #Checking if the arguments given are valid

    if len(matroids) < 2:
        raise ValueError("Atleast two arguments expected")

    for i in range(len(matroids)):
        if not (isinstance(matroids[i],sage.matroids.matroid.Matroid) and matroids[i].is_valid()):
            raise ValueError("Argument "+str(i+1)+" doesn't seem to be a matroid")
        # if not (matroids[i].base_ring == ZZ or matroids[i].base_ring().is_field()):
        #   raise NotImplementedError("MatroidUnion is only implemented for fields or integer ring")

    #Creating a matroid using the independent sets

    prev_ind_sets = set([])

    prev_matroid = matroids[0]
    rank = prev_matroid.rank()


    for r in range(rank+1):
        for it in prev_matroid.independent_r_sets(r):
            prev_ind_sets.add(it)  #Adding bases of first matroid


    temp_ind_sets = set([]) #Using Set to eliminate duplicates


    index=1

    while index < len(matroids):
        curr_matroid = matroids[index]
        rank = curr_matroid.rank()
        for r in range(rank+1):
            for it in curr_matroid.independent_r_sets(r):
                for s in prev_ind_sets:
                    n = frozenset(set(s).union(it))
                    temp_ind_sets.add(n)


        prev_ind_sets=prev_ind_sets.union(temp_ind_sets)


        index = index + 1

    M = Matroid(independent_sets=prev_ind_sets)
    return M

##Testing
# M1=matroids.named_matroids.Fano()
# M2=matroids.named_matroids.Vamos()
# M=MatroidUnion(M1,M2)