modulo operation for polynomials?

[smslca]

I know , how to calculate " x mod p " for a given very large "x" value and some p value. Here , x and p are integers

But how can we calculate f(x) mod g(x) , for which f(x) has higher degree(or order) than g(x).
And that degree turns out to be a very large number.

Ex:[ (x+1)^1729 mod ((x^5)-1) ] or [ (x+1)^1729 mod (1729,((x^5)-1)) ]

Is there any method or algorithm to calculate it at faster speeds

 

[lostinxlation]

What you are asking is exactly how to run a CRC. With a hardware, CRC is performed by shift registers, a few tappings with XORs and divisor's bit pattern shifted into the shift register, and the bit pattern left in the shift registers at the end represents the remainder. You can easily implement it with software as well.
Google CRC and you'll be able to make a script based on that.

 

[zorro]

Agree with lostinxlation.
Let me add this:
For integers, (x mod p) is the remainder of the integer division of x by p. It is an integer less than p (between 0 and p-1).
For polynomials, [f(x) mod g(x)] is the remainder of the polynomial division f(x)/g(x). It is a poynomial of degree less than the degree of g(x) (or the null polynomial).
Regards

Z