Merge pull request #94 from 1e9abhi1e10/subresultant

Add benchmarks for subresultants PRS method

benchmarks/polys.py

@@ -1,4 +1,4 @@
-from sympy import symbols, prod, prem, rem, degree, LC
+from sympy import symbols, prod, prem, rem, degree, LC, subresultants
 from sympy.polys import QQ, Poly
 
 
@@ -52,7 +52,27 @@ def as_ring(self):
 
 
 class _LinearDenseQuadraticGCD(_GCDExample):
-    """A pair of linearly dense quartic inputs with quadratic GCDs"""
+    """A pair of linearly dense quartic inputs with quadratic GCDs.
+
+    This class generates benchmark examples with two polynomials, ``f`` and
+    ``g``, that are linearly dense quartic polynomials with quadratic GCDs. The
+    polynomials are constructed based on the input parameter ``n`.
+
+    Examples
+    ========
+
+    >>> example = _LinearDenseQuadraticGCD(3)
+    >>> f, g, d, syms = example.as_expr()
+    >>> f
+    (x - y1 - y2 - y3 - 2)**2*(x + y1 + y2 + y3 + 1)**2
+    >>> g
+    (x + y1 + y2 + y3 + 1)**2*(x + y1 + y2 + y3 + 2)**2
+    >>> d
+    (x + y1 + y2 + y3 + 1)**2
+    >>> syms
+    (x, y1, y2, y3)
+
+    """
 
     def make_poly(self, n):
         x, *y = syms = symbols("x, y1:{}".format(n+1))
@@ -61,8 +81,29 @@ def make_poly(self, n):
         g = d * (2 + x + sum(y[:n])) ** 2
         return f, g, d, syms
 
+
 class _SparseGCDHighDegree(_GCDExample):
-    """A pair of polynomials in n symbols with a high degree sparse GCD."""
+    """A pair of polynomials in n symbols with a high degree sparse GCD.
+
+    This class generates benchmark examples with two polynomials, ``f`` and
+    ``g``, that have a high degree sparse GCD. The polynomials are constructed
+    based on the input parameter ``n``.
+
+    Examples
+    ========
+
+    >>> example = _SparseGCDHighDegree(3)
+    >>> f, g, d, syms = example.as_expr()
+    >>> f
+    (x**4 + y1**4 + y2**4 + y3**4 - 2)*(x**4 + y1**4 + y2**4 + y3**4 + 1)
+    >>> g
+    (x**4 + y1**4 + y2**4 + y3**4 + 1)*(x**4 + y1**4 + y2**4 + y3**4 + 2)
+    >>> d
+    x**4 + y1**4 + y2**4 + y3**4 + 1
+    >>> syms
+    (x, y1, y2, y3)
+
+    """
 
     def make_poly(self, n):
         x, *y = syms = symbols("x, y1:{}".format(n+1))
@@ -73,7 +114,27 @@ def make_poly(self, n):
 
 
 class _QuadraticNonMonicGCD(_GCDExample):
-    """A pair of quadratic polynomials with a non-monic GCD."""
+    """A pair of quadratic polynomials with a non-monic GCD.
+
+    This class generates benchmark examples with two quadratic polynomials,
+    ``f`` and ``g``, that have a non-monic GCD. The polynomials are constructed
+    based on the input parameter ``n``.
+
+    Examples
+    ========
+
+    >>> example = _QuadraticNonMonicGCD(3)
+    >>> f, g, d, syms = example.as_expr()
+    >>> f
+    (x**2*y1**2 + y2**2 + y3**2 + 1)*(x**2 - y1**2 + y2**2 + y3**2 - 1)
+    >>> g
+    (x*y1 + y2 + y3 + 2)**2*(x**2*y1**2 + y2**2 + y3**2 + 1)
+    >>> d
+    x**2*y1**2 + y2**2 + y3**2 + 1
+    >>> syms
+    (x, y1, y2, y3)
+
+    """
 
     def make_poly(self, n):
         x, *y = syms = symbols("x, y1:{}".format(n+1))
@@ -84,7 +145,27 @@ def make_poly(self, n):
 
 
 class _SparseNonMonicQuadratic(_GCDExample):
-    """A pair of sparse non-monic quadratic polynomials with linear GCDs."""
+    """A pair of sparse non-monic quadratic polynomials with linear GCDs.
+
+    This class generates benchmark examples with two sparse non-monic quadratic
+    polynomials, ``f`` and ``g``, that have a linear GCD. The polynomials are
+    constructed based on the input parameter ``n``.
+
+    Examples
+    ========
+
+    >>> example = _SparseNonMonicQuadratic(3)
+    >>> f, g, d, syms = example.as_expr()
+    >>> f
+    (x*y1*y2*y3 - 1)*(x*y1*y2*y3 + 3)
+    >>> g
+    (x*y1*y2*y3 - 3)*(x*y1*y2*y3 - 1)
+    >>> d
+    x*y1*y2*y3 - 1
+    >>> syms
+    (x, y1, y2, y3)
+
+    """
 
     def make_poly(self, n):
         x, *y = syms = symbols("x, y1:{}".format(n+1))
@@ -93,6 +174,7 @@ def make_poly(self, n):
         g = d * (-3 + x * prod(y[:n]))
         return f, g, d, syms
 
+
 class _TimeOP:
     """
     Benchmarks comparing Poly implementations of a given operation.
@@ -111,12 +193,22 @@ def setup(self, n, impl):
         if impl == 'expr':
             func = self.get_func_expr(*examples.as_expr())
             expected = examples.to_expr(expected)
+
         elif impl == 'dense':
             func = self.get_func_poly(*examples.as_poly())
-            expected = examples.to_poly(expected)
+            if isinstance(expected, list):
+                # some methods output a list of polynomials
+                expected = [examples.to_poly(p) for p in expected]
+            else:
+                # others output only a single polynomial.
+                expected = examples.to_poly(expected)
+
         elif impl == 'sparse':
             func = self.get_func_sparse(*examples.as_ring())
-            expected = examples.to_ring(expected)
+            if isinstance(expected, list):
+                expected = [examples.to_ring(p) for p in expected]
+            else:
+                expected = examples.to_ring(expected)
 
         self.func = func
         self.expected_result = expected
@@ -147,20 +239,64 @@ def get_func_sparse(self, f, g, d, ring):
 
 
 class TimePREM_LinearDenseQuadraticGCD(_TimePREM):
+    """This case involves linearly dense quartic inputs with quadratic GCDs.
+    The quadratic GCD suggests that the pseudo remainder method could be
+    applicable and potentially efficient for computing the GCD of these
+    polynomials."""
+
+    GCDExampleCLS = _LinearDenseQuadraticGCD
+    # This case is slow for n>5.
+    params = [(1, 3, 5), ('expr', 'dense', 'sparse')]
+
+
+class TimePREM_QuadraticNonMonicGCD(_TimePREM):
+    """This case deals with quadratic polynomials having a non-monic GCD. The
+    non-monic aspect may introduce additional complexities, but the quadratic
+    nature suggests that the pseudo remainder method could be useful.
+    """
+
+    GCDExampleCLS = _QuadraticNonMonicGCD
+    # This case is slow for n>5.
+    params = [(1, 3, 5), ('expr', 'dense', 'sparse')]
+
+
+class _TimeSUBRESULTANTS(_TimeOP):
+    """Benchmarks for subresultants PRS method"""
+
+    def expected(self, f, g, d, syms):
+        x = syms[0]
+        subresultant = subresultants(f, g, x)
+
+        return subresultant
+
+    def get_func_expr(self, f, g, d, syms):
+        x = syms[0]
+        return lambda: subresultants(f, g, x)
+
+    def get_func_poly(self, f, g, d):
+        return lambda: f.subresultants(g)
+
+    def get_func_sparse(self, f, g, d, ring):
+        return lambda: f.subresultants(g)
+
+
+class TimeSUBRESULTANTS_LinearDenseQuadraticGCD(_TimeSUBRESULTANTS):
     GCDExampleCLS = _LinearDenseQuadraticGCD
-    params = [(1, 3, 5), ('expr', 'dense', 'sparse')] # This case is slow for n=8.
+    # This case is slow for n>3.
+    params = [(1, 2, 3), ('expr', 'dense', 'sparse')]
 
 
-class TimePREM_SparseGCDHighDegree(_TimePREM):
+class TimeSUBRESULTANTS_SparseGCDHighDegree(_TimeSUBRESULTANTS):
     GCDExampleCLS = _SparseGCDHighDegree
-    params = [(1, 3, 5, 8), ('expr', 'dense', 'sparse')]
+    params = [(1, 3, 5), ('expr', 'dense', 'sparse')]
 
 
-class TimePREM_QuadraticNonMonicGCD(_TimePREM):
+class TimeSUBRESULTANTS_QuadraticNonMonicGCD(_TimeSUBRESULTANTS):
     GCDExampleCLS = _QuadraticNonMonicGCD
-    params = [(1, 3, 5), ('expr', 'dense', 'sparse')] # This case is slow for n=8.
+    # This case is slow for n>3.
+    params = [(1, 2, 3), ('expr', 'dense', 'sparse')]
 
 
-class TimePREM_SparseNonMonicQuadratic(_TimePREM):
+class TimeSUBRESULTANTS_SparseNonMonicQuadratic(_TimeSUBRESULTANTS):
     GCDExampleCLS = _SparseNonMonicQuadratic
-    params = [(1, 3, 5, 8), ('expr', 'dense', 'sparse')]
+    params = [(1, 3, 5), ('expr', 'dense', 'sparse')]