pystencils.sympyextensions.math.complete_the_square

pystencils.sympyextensions.math.complete_the_square#

pystencils.sympyextensions.math.complete_the_square(expr, symbol_to_complete, new_variable)#

Transforms second order polynomial into only squared part.

Examples

>>> a, b, c, s, n = sp.symbols("a b c s n")
>>> expr = a * s**2 + b * s + c
>>> completed_expr, substitution = complete_the_square(expr, symbol_to_complete=s, new_variable=n)
>>> completed_expr
a*n**2 + c - b**2/(4*a)
>>> substitution
(n, s + b/(2*a))
Return type:

Tuple[Expr, Optional[Tuple[Symbol, Expr]]]

Returns:

(replaced_expr, tuple to pass to subs, such that old expr comes out again)

Parameters:
Contents