Codex/find and fix a bug (#12782)

* Fix enumeration order in FFT string representation

* updating DIRECTORY.md

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* Update radix2_fft.py

* [pre-commit.ci] auto fixes from pre-commit.com hooks

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---------

Co-authored-by: alejandroaldas <alejandroaldas@users.noreply.github.com>
Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Maxim Smolskiy <mithridatus@mail.ru>

Author: 3 people

maths/radix2_fft.py

@@ -39,14 +39,14 @@ class FFT:
     >>> x = FFT(A, B)
 
     Print product
-    >>> x.product  # 2x + 3x^2 + 8x^3 + 4x^4 + 6x^5
+    >>> x.product  # 2x + 3x^2 + 8x^3 + 6x^4 + 8x^5
     [(-0-0j), (2+0j), (3-0j), (8-0j), (6+0j), (8+0j)]
 
     __str__ test
     >>> print(x)
-    A = 0*x^0 + 1*x^1 + 2*x^0 + 3*x^2
-    B = 0*x^2 + 1*x^3 + 2*x^4
-    A*B = 0*x^(-0-0j) + 1*x^(2+0j) + 2*x^(3-0j) + 3*x^(8-0j) + 4*x^(6+0j) + 5*x^(8+0j)
+    A = 0*x^0 + 1*x^1 + 0*x^2 + 2*x^3
+    B = 2*x^0 + 3*x^1 + 4*x^2
+    A*B = (-0-0j)*x^0 + (2+0j)*x^1 + (3-0j)*x^2 + (8-0j)*x^3 + (6+0j)*x^4 + (8+0j)*x^5
     """
 
     def __init__(self, poly_a=None, poly_b=None):
@@ -159,13 +159,13 @@ def __multiply(self):
     # Overwrite __str__ for print(); Shows A, B and A*B
     def __str__(self):
         a = "A = " + " + ".join(
-            f"{coef}*x^{i}" for coef, i in enumerate(self.polyA[: self.len_A])
+            f"{coef}*x^{i}" for i, coef in enumerate(self.polyA[: self.len_A])
         )
         b = "B = " + " + ".join(
-            f"{coef}*x^{i}" for coef, i in enumerate(self.polyB[: self.len_B])
+            f"{coef}*x^{i}" for i, coef in enumerate(self.polyB[: self.len_B])
         )
         c = "A*B = " + " + ".join(
-            f"{coef}*x^{i}" for coef, i in enumerate(self.product)
+            f"{coef}*x^{i}" for i, coef in enumerate(self.product)
         )
 
         return f"{a}\n{b}\n{c}"