Factor out the is_full_space() function.

[sage.d.git] / mjo / symbolic.py

diff --git a/mjo/symbolic.py b/mjo/symbolic.py
index e4c6d23faef7117bcd7807da3d95d84a39fd18ad..0afd5a5651ce9dedc3bccab518a6b5f4ec0ee492 100644 (file)
--- a/mjo/symbolic.py
+++ b/mjo/symbolic.py
@@ -9,7 +9,23 @@ def set_simplification_domain(d):
 
     INPUT:
 
-      - d -- The domain, either 'real' or 'complex'.
+      - ``d`` -- The domain, either 'real' or 'complex'.
+
+    TESTS:
+
+    With the default 'complex' domain, we don't simplify this::
+
+        sage: (abs(x)^2).simplify()
+        abs(x)^2
+
+    But in the 'real' domain, we do::
+
+        sage: set_simplification_domain('real')
+        'real'
+        sage: (abs(x)^2).simplify()
+        x^2
+        sage: set_simplification_domain('complex')
+        'complex'
 
     """
     cmd = 'domain: %s;' % d
@@ -30,16 +46,87 @@ def safe_simplify(expr):
     return expr
 
 
-def medium_simplify(expr):
+def matrix_subs_expr(m, *equations):
     """
-    A reasonably-safe set of simplifications, much better than
-    simplify() and safer than simplify_full()
+    Symbolic matrices have a `subs()` method, but no `subs_expr()`.
+    This makes it diffucult to substitute in a list of solutions obtained
+    with `solve()`.
+
+    INPUT:
+
+      - ``m`` -- A symbolic matrix.
+
+      - ``equations`` - One or more symbolic equations, presumably for
+        the entries of `m`.
+
+    OUTPUT:
+
+    The result of substituting each equation into `m`, one after another.
+
+    EXAMPLES::
+
+    sage: w,x,y,z = SR.var('w,x,y,z')
+    sage: A = matrix(SR, [[w,x],[y,z]])
+    sage: matrix_subs_expr(A, w == 1, x == 2, y == 3, z == 4)
+    [1 2]
+    [3 4]
 
-    Uses a top-level function because we can't monkey-patch Cython
-    classes.
     """
-    expr = expr.simplify_factorial()
-    expr = expr.simplify_trig()
-    expr = expr.simplify_rational()
-    expr = expr.simplify_log()
-    return expr
+    from sage.symbolic.expression import is_SymbolicEquation
+
+    if not m.base_ring() == SR:
+        raise TypeError, 'the matrix "m" must be symbolic'
+
+    if isinstance(equations[0], dict):
+        eq_dict = equations[0]
+        equations = [ x == eq_dict[x] for x in eq_dict.keys() ]
+
+    if not all([is_SymbolicEquation(eq) for eq in equations]):
+            raise TypeError, "each expression must be an equation"
+
+    d = dict([(eq.lhs(), eq.rhs()) for eq in equations])
+    return m.subs(d)
+
+
+def matrix_simplify_full(A):
+    """
+    Simplify each entry of a symbolic matrix using the
+    Expression.simplify_full() method.
+
+    INPUT:
+
+      - ``A`` - The matrix whose entries we should simplify.
+
+    OUTPUT:
+
+    A copy of ``A`` with all of its entries simplified.
+
+    EXAMPLES:
+
+    Symbolic matrices (examples stolen from Expression.simplify_full())
+    will have their entries simplified::
+
+        sage: a,n,k = SR.var('a,n,k')
+        sage: f1 = sin(x)^2 + cos(x)^2
+        sage: f2 = sin(x/(x^2 + x))
+        sage: f3 = binomial(n,k)*factorial(k)*factorial(n-k)
+        sage: f4 = x*sin(2)/(x^a)
+        sage: A = matrix(SR, [[f1,f2],[f3,f4]])
+        sage: matrix_simplify_full(A)
+        [                1    sin(1/(x + 1))]
+        [     factorial(n) x^(-a + 1)*sin(2)]
+
+    But an exception will be raised if ``A`` is not symbolic::
+
+        sage: A = matrix(QQ, [[1,2],[3,4]])
+        sage: matrix_simplify_full(A)
+        Traceback (most recent call last):
+        ...
+        ValueError: The base ring of `A` must be the Symbolic Ring.
+
+    """
+    if not A.base_ring() == SR:
+        raise ValueError('The base ring of `A` must be the Symbolic Ring.')
+
+    M = A.matrix_space()
+    return M(map(lambda x: x.simplify_full(), A))