# Polynomial multiplication using the DFT?

How to do polynomial multiplication using the discrete Fourier transform in SageMath?

Polynomial multiplication using the DFT?

How to do polynomial multiplication using the discrete Fourier transform in SageMath?

1

Here is the example from the article in SageMath:

```
sage: R.<x> = PolynomialRing(QQ)
sage: f = 1 + x
sage: g = 1 + x + x^2
sage: fg_deg = f.degree() + g.degree()
sage: I_f = IndexedSequence([f.monomial_coefficient(x^d) for d in range(fg_deg+1)], list(range(fg_deg+1)))
sage: I_g = IndexedSequence([g.monomial_coefficient(x^d) for d in range(fg_deg+1)], list(range(fg_deg+1)))
sage: I_fg = IndexedSequence(list(vector(I_f.dft().list()).pairwise_product(vector(I_g.dft().list()))), list(range(fg_deg+1))).idft()
sage: fg = sum(c*x^k for k,c in I_fg.dict().items())
sage: fg == f*g
True
```

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Asked: ** 2022-03-02 14:47:10 +0200 **

Seen: **290 times**

Last updated: **Mar 02 '22**

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