gh-35305: `sage.quadratic_forms`: Modularization fixes for imports
    
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### 📚 Description
We make `sage.quadratic_forms` ready for modularized distributions by:
- moving imports from some packages, such as
`sage.rings.padics.factory`, into methods
- using `lazy_import` to provide the methods of `QuadraticForm`
implemented in separate modules
- adding `# optional` annotations to doctests

Also some improvements to the code style of doctests and the Sphinx
markup of some docstrings have been made.

This has been and can be tested by merging into:
- #35095
**sagemath-polyhedra** ships vector spaces etc. and now also portions of
`sage.quadratic_forms` – see #35095
/files#diff-
f4c7c1beea87ae44c426de0a55459daef63b75b701b72bc136d88f4e7c9285cfR104

Resolves #35243

Part of:
- #29705

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### 📝 Checklist

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### ⌛ Dependencies
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- Depends on #35248
- Depends on #35166
    
URL: #35305
Reported by: Matthias Köppe
Reviewer(s): Kwankyu Lee, Matthias Köppe

Author: Release Manager

src/sage/dynamics/arithmetic_dynamics/berkovich_ds.py

@@ -926,7 +926,7 @@ def __call__(self, x, type_3_pole_check=True):
         variable = nth_derivative.parent().gens()[0]
         a = x.center()[0]
         Taylor_expansion = []
-        from sage.functions.other import factorial
+        from sage.arith.misc import factorial
         for i in range(f.degree() + 1):
             Taylor_expansion.append(nth_derivative(a) * 1/factorial(i))
             nth_derivative = nth_derivative.derivative(variable)

src/sage/groups/misc_gps/argument_groups.py

@@ -1192,7 +1192,7 @@ def __pow__(self, exponent):
             sage: a.parent()
             Symbolic Ring
         """
-        from sage.symbolic.ring import SymbolicRing
+        from sage.rings.abc import SymbolicRing
 
         element = self._element_ ** exponent
         parent = element.parent()

src/sage/modular/arithgroup/congroup_gamma0.py

@@ -593,8 +593,6 @@ def dimension_new_cusp_forms(self, k=2, p=0):
              sage: all(Gamma0(N).dimension_new_cusp_forms(2)==100 for N in L)
              True
         """
-        from sage.functions.other import floor
-
         N = self.level()
         k = ZZ(k)
 
@@ -669,8 +667,8 @@ def v3(q, a):
 
         res = (k - 1) / 12 * N * prod(s0(q, a) for q, a in factors)
         res -= prod(vinf(q, a) for q, a in factors) / ZZ(2)
-        res += ((1 - k)/4 + floor(k/4)) * prod(v2(q, a) for q, a in factors)
-        res += ((1 - k)/3 + floor(k/3)) * prod(v3(q, a) for q, a in factors)
+        res += ((1 - k)/4 + k//4) * prod(v2(q, a) for q, a in factors)
+        res += ((1 - k)/3 + k//3) * prod(v3(q, a) for q, a in factors)
         if k == 2:
             res += moebius(N)
         return res