elementary_vectors.utility

Utility functions

Functions

is_symbolic(expression)

Return whether this element is a symbolic expression.

kernel_vector_support_given(M, indices)

Return a right kernel vector such that the support is a subset of given indices.
elementary_vectors.utility.is_symbolic(expression)

Return whether this element is a symbolic expression.

If it belongs to the symbolic ring but doesn’t contain any variables it does not count as “symbolic”.

EXAMPLES:

sage: from elementary_vectors.utility import is_symbolic
sage: is_symbolic(5)
False
sage: var('a, b')
(a, b)
sage: is_symbolic(a)
True
sage: is_symbolic(-a)
True
sage: is_symbolic(b^2 - a)
True
sage: is_symbolic(SR(5))
False
elementary_vectors.utility.kernel_vector_support_given(M, indices: list)

Return a right kernel vector such that the support is a subset of given indices.

INPUT:

  • M – a matrix

  • indices – a list of indices

OUTPUT: a vector in the right kernel of M such that the support is a subset of indices.

EXAMPLES:

sage: from elementary_vectors.utility import kernel_vector_support_given
sage: M = matrix([[1, 2, 0, 0], [0, 1, -1, 0]])
sage: v = kernel_vector_support_given(M, [0, 1, 2])
sage: max(v, -v)
(2, -1, -1, 0)
sage: kernel_vector_support_given(M, [3])
(0, 0, 0, 1)
sage: v = kernel_vector_support_given(M, [0, 3]) # (0, 0, 0, 1) or (0, 0, 0, -1) depending on sage version
sage: v.support()
[3]