-from sage.functions.other import sqrt
-from sage.matrix.constructor import matrix
-from sage.modules.free_module_element import vector
-
-def _charpoly_sage_input(s):
- r"""
- Helper function that you can use on the string output from sage
- to convert a charpoly coefficient into the corresponding input
- to be cached.
-
- SETUP::
-
- sage: from mjo.eja.eja_utils import _charpoly_sage_input
-
- EXAMPLES::
-
- sage: J = JordanSpinEJA(4,QQ)
- sage: J._charpoly_coefficients()[0]
- X1^2 - X2^2 - X3^2 - X4^2
- sage: _charpoly_sage_input("X1^2 - X2^2 - X3^2 - X4^2")
- 'X[0]**2 - X[1]**2 - X[2]**2 - X[3]**2'
-
- """
- import re
-
- exponent_out = r"\^"
- exponent_in = r"**"
-
- digit_out = r"X([0-9]+)"
-
- def replace_digit(m):
- # m is a match object
- return "X[" + str(int(m.group(1)) - 1) + "]"
-
- s = re.sub(exponent_out, exponent_in, s)
- return re.sub(digit_out, replace_digit, s)
-
+from sage.structure.element import is_Matrix
def _scale(x, alpha):
r"""
# first needing to convert them to a list of octonions and
# then recursing down into the list. It also avoids the wonky
# list(x) when x is an element of a CFM. I don't know what it
- # returns but it aint the coordinates. This will fall through
- # to the iterable case the next time around.
- return _all2list(x.to_vector())
+ # returns but it aint the coordinates. We don't recurse
+ # because vectors can only contain ring elements as entries.
+ return x.to_vector().list()
+
+ if is_Matrix(x):
+ # This sucks, but for performance reasons we don't want to
+ # call _all2list recursively on the contents of a matrix
+ # when we don't have to (they only contain ring elements
+ # as entries)
+ return x.list()
try:
xl = list(x)
# Avoid the retardation of list(QQ(1)) == [1].
return [x]
- return sum(list( map(_all2list, xl) ), [])
-
-
+ return sum( map(_all2list, xl) , [])
-def _mat2vec(m):
- return vector(m.base_ring(), m.list())
-
-def _vec2mat(v):
- return matrix(v.base_ring(), sqrt(v.degree()), v.list())
def gram_schmidt(v, inner_product=None):
"""
# cool
return v
- R = v[0].base_ring()
-
# Our "zero" needs to belong to the right space for sum() to work.
zero = v[0].parent().zero()