homogeneous poly terms (not adjusted for finite fields).sagews

#How many terms of k degree and v variables
# Let P(k,v) be the homogeneous polynomial of v variables, k degrees, with nonzero coefficients

#i is the sequence length (ie: number of nonzero exponents)
    #l is the max sequence length (defined or defaulted to v
#d is degree, geq 1
#v is number of vari, geq 1

def C(v,d,l= None):
    if l == None:
        l = v
    print(l)
    term = 0
    for i in range(1, min (d,v,l) +1):
	    #z is the number of "0" degrees, for padding purposes
	    z = v-i
	    # first bit is the unpadded, second is multiply by the padding options
	    numiz= binomial (d-1,d-1) *binomial (v,z)
	    #term is number of…terms
	    term=term+numiz
	    print("For", i, "nonzero degrees and", z, "zero degrees, there are", numiz, "terms.")
	    i=i+1
    if i == min(d,v,l)+1:
        print("Using", v, "variables over", d, "degrees and sequence length of", l, ",", term, "is the total number of possible terms using", min(v,l), "variables.")
C(6,3)