schubmult.symbolic.functions

SymEngine-first wrappers (expand, symbols, sympify) that fall back to SymPy, plus small helpers.

expand

def expand(obj, **kwargs)

Expand with SymEngine; use SymPy if keyword options are given or SymEngine fails.

symbols

def symbols(*args, **kwargs)

SymEngine symbols.

sympify

def sympify(val)

SymEngine sympify, falling back to SymPy for objects SymEngine cannot convert.

is_of_func_type

def is_of_func_type(elem, typ)

isinstance that also sees through SymEngine PyFunction wrappers around SymPy functions.

expand_seq

def expand_seq(seq, genset)

The monomial genset[1]**seq[0] * genset[2]**seq[1] * ... (1-indexed generators).

prod

def prod(a, start=1)

Product of the elements of a times start (same as sympy.prod).

efficient_subs

def efficient_subs(expr, subs_dict)

expr.subs restricted to the entries of subs_dict that actually occur in expr.

vanish_at_random_points

def vanish_at_random_points(exprs, trials=2, seed=1, bound=10**6)

For each expression, whether it evaluates to zero at trials random integer points (exact arithmetic).

A polynomial that is identically zero always does; a nonzero one of modest degree vanishes at a random point of [-bound, bound]^n with negligible probability, so this is a fast surrogate for expand(e) == 0 that never touches the (possibly enormous) expanded form. Values of shared subtrees are memoized across the whole batch, which is what makes it cheap: the coefficients of one Schubert product reuse the same (y_i - z_j) factors and partial products over and over.

Expressions containing nodes other than numbers, symbols, Add, Mul and integer Pow fall back to expand(e) == 0.