-from sage.functions.other import sqrt
-from sage.matrix.constructor import matrix
-from sage.modules.free_module_element import vector
-
-def _change_ring(x, R):
- r"""
- Change the ring of a vector, matrix, or a cartesian product of
- those things.
-
- SETUP::
-
- sage: from mjo.eja.eja_utils import _change_ring
-
- EXAMPLES::
-
- sage: v = vector(QQ, (1,2,3))
- sage: m = matrix(QQ, [[1,2],[3,4]])
- sage: _change_ring(v, RDF)
- (1.0, 2.0, 3.0)
- sage: _change_ring(m, RDF)
- [1.0 2.0]
- [3.0 4.0]
- sage: _change_ring((v,m), RDF)
- (
- [1.0 2.0]
- (1.0, 2.0, 3.0), [3.0 4.0]
- )
- sage: V1 = cartesian_product([v.parent(), v.parent()])
- sage: V = cartesian_product([v.parent(), V1])
- sage: V((v, (v, v)))
- ((1, 2, 3), ((1, 2, 3), (1, 2, 3)))
- sage: _change_ring(V((v, (v, v))), RDF)
- ((1.0, 2.0, 3.0), ((1.0, 2.0, 3.0), (1.0, 2.0, 3.0)))
-
- """
- try:
- return x.change_ring(R)
- except AttributeError:
- try:
- from sage.categories.sets_cat import cartesian_product
- if hasattr(x, 'element_class'):
- # x is a parent and we're in a recursive call.
- return cartesian_product( [_change_ring(x_i, R)
- for x_i in x.cartesian_factors()] )
- else:
- # x is an element, and we want to change the ring
- # of its parent.
- P = x.parent()
- Q = cartesian_product( [_change_ring(P_i, R)
- for P_i in P.cartesian_factors()] )
- return Q(x)
- except AttributeError:
- # No parent for x
- return x.__class__( _change_ring(x_i, R) for x_i in x )