sagemathgh-38717: NotImplementedError when pow() called with modulus

    
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Many polynomial types silently ignore the modulus (third) argument of
`pow()`.  For example,
```python
sage: R.<x> = PolynomialRing(ZZ)
sage: pow(x, 2, x)
x^2
```
This is true of `LaurentPolynomial`, `LaurentPolynomial_mpair`,
`MPolynomial_libsingular`, `Polynomial_integer_dense_flint`,
`Polynomial_rational_flint`, and `NCPolynomial_plural`.  Ideally these
classes would implement this argument, but at the very least they should
raise `NotImplementedError` instead of giving an incorrect result.
    
URL: sagemath#38717
Reported by: Kyle Hofmann
Reviewer(s): Vincent Macri

src/sage/rings/polynomial/laurent_polynomial.pyx

@@ -1126,7 +1126,7 @@ cdef class LaurentPolynomial_univariate(LaurentPolynomial):
         """
         return self.__u.is_monomial()
 
-    def __pow__(_self, r, dummy):
+    def __pow__(_self, r, mod):
         """
         EXAMPLES::
 
@@ -1145,9 +1145,21 @@ cdef class LaurentPolynomial_univariate(LaurentPolynomial):
             x^-8
             sage: (5*x^-4)^-3
             5*x^12
+
+        Check that using third argument raises an error::
+
+            sage: L.<x> = LaurentPolynomialRing(R)
+            sage: pow(x, 2, x)
+            Traceback (most recent call last):
+            ...
+            NotImplementedError: pow() with a modulus is not implemented for this ring
         """
         cdef LaurentPolynomial_univariate self = _self
         cdef long right = r
+        if mod is not None:
+            raise NotImplementedError(
+                "pow() with a modulus is not implemented for this ring"
+            )
         if right != r:
             raise ValueError("exponent must be an integer")
         try:

src/sage/rings/polynomial/laurent_polynomial_mpair.pyx

@@ -460,7 +460,7 @@ cdef class LaurentPolynomial_mpair(LaurentPolynomial):
             return P({e: c})
         return super().__invert__()
 
-    def __pow__(LaurentPolynomial_mpair self, n, m):
+    def __pow__(LaurentPolynomial_mpair self, n, mod):
         """
         EXAMPLES::
 
@@ -480,8 +480,20 @@ cdef class LaurentPolynomial_mpair(LaurentPolynomial):
             sage: f = (x+y+z^-1)^2
             sage: f.substitute(z=1)
             x^2 + 2*x*y + y^2 + 2*x + 2*y + 1
+
+        Check that using third argument raises an error::
+
+            sage: L.<x,y,z> = LaurentPolynomialRing(R)
+            sage: pow(x + y + z, 2, x)
+            Traceback (most recent call last):
+            ...
+            NotImplementedError: pow() with a modulus is not implemented for this ring
         """
         cdef LaurentPolynomial_mpair ans
+        if mod is not None:
+            raise NotImplementedError(
+                "pow() with a modulus is not implemented for this ring"
+            )
         if n < 0:
             return ~(self ** -n)
         ans = self._new_c()

src/sage/rings/polynomial/multi_polynomial_libsingular.pyx

@@ -2350,7 +2350,7 @@ cdef class MPolynomial_libsingular(MPolynomial_libsingular_base):
         else:
             return (left._parent).fraction_field()(left,right_ringelement)
 
-    def __pow__(MPolynomial_libsingular self, exp, ignored):
+    def __pow__(MPolynomial_libsingular self, exp, mod):
         """
         Return ``self**(exp)``.
 
@@ -2413,7 +2413,20 @@ cdef class MPolynomial_libsingular(MPolynomial_libsingular_base):
             Traceback (most recent call last):
             ...
             TypeError: R is neither an integer nor a rational
+
+        Check that using third argument raises an error::
+
+            sage: R.<x,y,z> = PolynomialRing(ZZ)
+            sage: pow(x + y + z, 2, x)
+            Traceback (most recent call last):
+            ...
+            NotImplementedError: pow() with a modulus is not implemented for this ring
         """
+        if mod is not None:
+            raise NotImplementedError(
+                "pow() with a modulus is not implemented for this ring"
+            )
+
         if type(exp) is not Integer:
             try:
                 exp = Integer(exp)

src/sage/rings/polynomial/plural.pyx

@@ -1671,7 +1671,7 @@ cdef class NCPolynomial_plural(RingElement):
         else:
             return (<NCPolynomialRing_plural>left._parent).fraction_field()(left,right)
 
-    def __pow__(NCPolynomial_plural self, exp, ignored):
+    def __pow__(NCPolynomial_plural self, exp, mod):
         """
         Return ``self**(exp)``.
 
@@ -1697,7 +1697,22 @@ cdef class NCPolynomial_plural(RingElement):
             Traceback (most recent call last):
             ....
             OverflowError: exponent overflow (2147483648)
+
+        Check that using third argument raises an error::
+
+            sage: A.<x,z,y> = FreeAlgebra(QQ, 3)
+            sage: P = A.g_algebra(relations={y*x:-x*y + z},  order='lex')
+            sage: P.inject_variables()
+            Defining x, z, y
+            sage: pow(x + y + z, 2, x)
+            Traceback (most recent call last):
+            ...
+            NotImplementedError: pow() with a modulus is not implemented for this ring
         """
+        if mod is not None:
+            raise NotImplementedError(
+                "pow() with a modulus is not implemented for this ring"
+            )
         if type(exp) is not Integer:
             try:
                 exp = Integer(exp)

src/sage/rings/polynomial/polynomial_integer_dense_flint.pyx

@@ -1035,7 +1035,7 @@ cdef class Polynomial_integer_dense_flint(Polynomial):
         sig_off()
         return x
 
-    def __pow__(Polynomial_integer_dense_flint self, exp, ignored):
+    def __pow__(Polynomial_integer_dense_flint self, exp, mod):
         """
         EXAMPLES::
 
@@ -1114,10 +1114,23 @@ cdef class Polynomial_integer_dense_flint(Polynomial):
             ...
             TypeError: no canonical coercion from Univariate Polynomial
             Ring in R over Integer Ring to Rational Field
+
+        Check that using third argument raises an error::
+
+            sage: R.<x> = PolynomialRing(ZZ, implementation='FLINT')
+            sage: pow(x, 2, x)
+            Traceback (most recent call last):
+            ...
+            NotImplementedError: pow() with a modulus is not implemented for this ring
         """
         cdef long nn
         cdef Polynomial_integer_dense_flint res
 
+        if mod is not None:
+            raise NotImplementedError(
+                "pow() with a modulus is not implemented for this ring"
+            )
+
         try:
             nn = pyobject_to_long(exp)
         except TypeError:

src/sage/rings/polynomial/polynomial_rational_flint.pyx

@@ -1160,7 +1160,7 @@ cdef class Polynomial_rational_flint(Polynomial):
         if do_sig: sig_off()
         return res
 
-    def __pow__(Polynomial_rational_flint self, exp, ignored):
+    def __pow__(Polynomial_rational_flint self, exp, mod):
         """
         Return ``self`` raised to the power of ``exp``.
 
@@ -1266,10 +1266,23 @@ cdef class Polynomial_rational_flint(Polynomial):
             ...
             TypeError: no canonical coercion from Univariate Polynomial
             Ring in R over Rational Field to Rational Field
+
+        Check that using third argument raises an error::
+
+            sage: R.<x> = PolynomialRing(QQ)
+            sage: pow(x, 2, x)
+            Traceback (most recent call last):
+            ...
+            NotImplementedError: pow() with a modulus is not implemented for this ring
         """
         cdef Polynomial_rational_flint res
         cdef long n
 
+        if mod is not None:
+            raise NotImplementedError(
+                "pow() with a modulus is not implemented for this ring"
+            )
+
         try:
             n = pyobject_to_long(exp)
         except TypeError: