X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Fsymbolic.py;h=e2645a30ed7fe33ceb8fb787d51bfaf87305f1ad;hb=3cfc8e228ae337aed975118444a8cbad9a5a7ac3;hp=0afd5a5651ce9dedc3bccab518a6b5f4ec0ee492;hpb=97109030d2075ca8819c72c158285b8f32df4a0d;p=sage.d.git diff --git a/mjo/symbolic.py b/mjo/symbolic.py index 0afd5a5..e2645a3 100644 --- a/mjo/symbolic.py +++ b/mjo/symbolic.py @@ -44,89 +44,3 @@ def safe_simplify(expr): expr = expr.simplify_factorial() expr = expr.simplify_log() return expr - - -def matrix_subs_expr(m, *equations): - """ - 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] - - """ - 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))