Inverse Number Theoretic Transform is a Fast Fourier transform theorem generalization. It is obtained by the replacement of e^(-2piik/N) with an nth primitive unity root. So this means, instead of the complex numbers C, use transform over the quotient ring Z/pZ. The theory is based on and uses the concepts of finite fields and number theory.
Inverse Number Theoretic Transform modulus needs to be prime necessarily. But if it is prime, it makes things simpler. One can perform the Inverse NTT with a composite modulus. For modulus :
- nth root of unity existence
- multiplicative inverse of n
A number-theoretic transform is basically a Fourier transform. Also, suppose that a Normal Discrete Fourier Transform is given and it can be done in matrix form by multiplying the data with a Fourier Matrix. Let us suppose N = 4. Then, the matrix can be –
[ 1 1 1 1 ] [ 1 w w^2 w^3 ] [ 1 w^2 w^4 w^6 ] [ 1 w^3 w^6 w^9 ]
sympy.discrete.transforms.intt( ) :
It can Inverse Number Theoretic Transform (NTT) of the sequence. It specializes over the Discrete Fourier Transform (DFT) quotient ring with Z/pZ for prime number instead of acomplex numbers.
Automatically the sequence is padded with zero to the right because the radix-2 FFT requires the sample point number as a power of 2.
Parameters : -> seq : [iterable] sequence on which DFT is to be applied. -> prime no. : [Integer] prime modulus for INTT to perform on. Returns : Number Theoretic Transform
Example #1 :
Inverse NTT : [600, 357, 183, 413]
Example #2 :
Inverse NTT : [355, 710, 557, 69]
- Python | Number Theoretic Transformation
- Python | Inverse Fast Fourier Transformation
- Python | Inverse Fast Walsh Hadamard Transformation
- Python | Fast Fourier Transformation
- Python | Intensity Transformation Operations on Images
- Inverse Gamma Distribution in Python
- Python | Inverse Sorting String
- NLP | Chunk Tree to Text and Chaining Chunk Transformation
- Python | Find the Number Occurring Odd Number of Times using Lambda expression and reduce function
- Python | Superfactorial of a number.
- 21 Number game in Python
- Python | Number to Words using num2words
- Python Number | fabs() method
- Python | First occurrence of True number
- Python Number | uniform() method
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to firstname.lastname@example.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.