mjo/symbolic.py

   1 from sage.all import *
   2 from sage.interfaces.maxima_lib import maxima_lib
   3 from sage.symbolic.expression import Expression
   4
   5
   6 def set_simplification_domain(d):
   7     """
   8     Set Maxima's simplification domain.
   9
  10     INPUT:
  11
  12       - ``d`` -- The domain, either 'real' or 'complex'.
  13
  14     TESTS:
  15
  16     With the default 'complex' domain, we don't simplify this::
  17
  18         sage: (abs(x)^2).simplify()
  19         abs(x)^2
  20
  21     But in the 'real' domain, we do::
  22
  23         sage: set_simplification_domain('real')
  24         'real'
  25         sage: (abs(x)^2).simplify()
  26         x^2
  27         sage: set_simplification_domain('complex')
  28         'complex'
  29
  30     """
  31     cmd = 'domain: %s;' % d
  32     result = maxima_lib._eval_line(cmd)
  33     return result
  34
  35
  36 def safe_simplify(expr):
  37     """
  38     What should be a totally safe simplification operation that works
  39     a little better than the plain simplify().
  40
  41     Uses a top-level function because we can't monkey-patch Cython
  42     classes.
  43     """
  44     expr = expr.simplify_factorial()
  45     expr = expr.simplify_log()
  46     return expr
  47
  48
  49 def matrix_simplify_full(A):
  50     """
  51     Simplify each entry of a symbolic matrix using the
  52     Expression.simplify_full() method.
  53
  54     INPUT:
  55
  56       - ``A`` - The matrix whose entries we should simplify.
  57
  58     OUTPUT:
  59
  60     A copy of ``A`` with all of its entries simplified.
  61
  62     EXAMPLES:
  63
  64     Symbolic matrices (examples stolen from Expression.simplify_full())
  65     will have their entries simplified::
  66
  67         sage: a,n,k = SR.var('a,n,k')
  68         sage: f1 = sin(x)^2 + cos(x)^2
  69         sage: f2 = sin(x/(x^2 + x))
  70         sage: f3 = binomial(n,k)*factorial(k)*factorial(n-k)
  71         sage: f4 = x*sin(2)/(x^a)
  72         sage: A = matrix(SR, [[f1,f2],[f3,f4]])
  73         sage: matrix_simplify_full(A)
  74         [                1    sin(1/(x + 1))]
  75         [     factorial(n) x^(-a + 1)*sin(2)]
  76
  77     But an exception will be raised if ``A`` is not symbolic::
  78
  79         sage: A = matrix(QQ, [[1,2],[3,4]])
  80         sage: matrix_simplify_full(A)
  81         Traceback (most recent call last):
  82         ...
  83         ValueError: The base ring of `A` must be the Symbolic Ring.
  84
  85     """
  86     if not A.base_ring() == SR:
  87         raise ValueError('The base ring of `A` must be the Symbolic Ring.')
  88
  89     M = A.matrix_space()
  90     return M(map(lambda x: x.simplify_full(), A))