added funcs for analyzing jacobian

# helper functions for analyzing jacobian, rref, etc

import sympy as sy

def make_rhs(jac):

    """ 

    make the rhs for the rref operations. facile way to show the row operations 

    if used with sympy.rref_rhs. 

    """

    syms = []

    for row in range(1, jac.rows+1):

        syms.append(sy.Symbol(f"r{row}"))

    rhs = sy.Matrix(syms)

    return rhs

def exclude_rows(matrix, rows_to_exclude):

    """

    Create new matrix excluding specified rows

    Args:

        matrix: sympy Matrix

        rows_to_exclude: list or set of row indices to exclude

    Returns:

        New sympy Matrix with specified rows removed

    """

    if isinstance(rows_to_exclude, int):

        rows_to_exclude = {rows_to_exclude}

    else:

        rows_to_exclude = set(rows_to_exclude)

    # Validate row indices

    if any(row >= matrix.rows or row < 0 for row in rows_to_exclude):

        raise ValueError("Row index out of bounds")

    kept_rows = [matrix.row(i) for i in range(matrix.rows) 

                 if i not in rows_to_exclude]

    return sy.Matrix(kept_rows) if kept_rows else sy.Matrix(0, matrix.cols, [])

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