Add invariant tests and correct doc strings

Author: Jake-Moss

src/flint/test/test_all.py

@@ -3239,14 +3239,24 @@ def quick_poly():
         assert (x0**3 - 6*x0**2 + 11*x0 - 6).discriminant('x0') == 4
         assert (x0**2 + 4*x0*x1 + 4*x1**2 - 1).discriminant('x0') == 4
 
-        res, stride = (3*x0**2*x1**2 + 6*x0*x1**2 + 9*x1**2).deflation()
+        f1 = 3*x0**2*x1**2 + 6*x0*x1**2 + 9*x1**2
+        res, stride = f1.deflation()
         assert res == 3*x0**2 + 6*x0 + 9
         assert tuple(stride) == (1, 0)
 
-        res, stride = ((x0**2 + x1**2)**3 + (x0**2 + x1**2)**2 + 1).deflation()
+        g1 = ((x0**2 + x1**2)**3 + (x0**2 + x1**2)**2 + 1)
+        res, stride = g1.deflation()
         assert res == x0**3 + 3*x0**2*x1 + x0**2 + 3*x0*x1**2 + 2*x0*x1 + x1**3 + x1**2 + 1
         assert tuple(stride) == (2, 2)
 
+        for p in [f1, g1]:
+            n, m = p.deflation_monom()
+            assert m * p.deflate(n).inflate(n) == p
+
+            n, i = p.deflation_index()
+            m = ctx.term(exp_vec=i)
+            assert p.deflate(n).inflate(n) * m == p
+
         if P is flint.fmpz_mpoly:
             assert (x0**2 * x1 + x0 * x1).primitive() == (1, x0**2*x1 + x0*x1)
             assert (4 * x0 + 2 * x0 * x1).primitive() == (2, x0 * x1 + 2 * x0)

src/flint/types/fmpq_mpoly.pyx

@@ -1053,8 +1053,7 @@ cdef class fmpq_mpoly(flint_mpoly):
 
     def deflation(self) -> tuple[fmpq_mpoly, list[int]]:
         """
-        Compute the deflation of ``self``, that is ``p(X^(1/N))`` for maximal
-        N. Returns ``q, N`` such that ``self == q.inflate(N)``.
+        Compute the deflation of ``self``, that is ``p(X^(1/N))`` for maximal N.
 
             >>> from flint import Ordering
             >>> ctx = fmpq_mpoly_ctx.get_context(2, Ordering.lex, nametup=('x', 'y'))

src/flint/types/fmpz_mpoly.pyx

@@ -1149,8 +1149,7 @@ cdef class fmpz_mpoly(flint_mpoly):
 
     def deflation(self) -> tuple[fmpz_mpoly, list[int]]:
         """
-        Compute the deflation of ``self``, that is ``p(X^(1/N))`` for maximal
-        N. Returns ``q, N`` such that ``self == q.inflate(N)``.
+        Compute the deflation of ``self``, that is ``p(X^(1/N))`` for maximal N.
 
             >>> from flint import Ordering
             >>> ctx = fmpz_mpoly_ctx.get_context(2, Ordering.lex, nametup=('x', 'y'))

src/flint/types/nmod_mpoly.pyx

@@ -1102,8 +1102,7 @@ cdef class nmod_mpoly(flint_mpoly):
 
     def deflation(self) -> tuple[nmod_mpoly, list[int]]:
         """
-        Compute the deflation of ``self``, that is ``p(X^(1/N))`` for maximal
-        N. Returns ``q, N`` such that ``self == q.inflate(N)``.
+        Compute the deflation of ``self``, that is ``p(X^(1/N))`` for maximal N.
 
             >>> from flint import Ordering
             >>> ctx = nmod_mpoly_ctx.get_context(2, Ordering.lex, 11, nametup=('x', 'y'))