Reduce¶

Simplifies a logical condition, e.g. a polynomial equation, to an equivalent form describing all solutions.

$ wo 'Reduce[x^2 == 4, x]'
x == -2 || x == 2

Woxi keeps specialized built-in paths for polynomial equations, integer intervals, complex algebra, and common transcendental forms. Exact linear formulas over the reals and rationals use Woxi's self-contained exact Fourier-Motzkin engine, including nested quantifiers:

$ wo 'Reduce[Exists[y, x < y && y < 1], x, Reals]'
x < 1

Exact linear integer formulas use Woxi's self-contained Presburger engine. Unbounded solution sets are represented symbolically rather than searched up to an arbitrary cap, and a residue class is reported as a parametrization:

$ wo 'Reduce[Exists[y, x == 2 y + 1], x, Integers]'
Element[C[1], Integers] && x == 1 + 2*C[1]

A bound on the variable becomes a bound on the parameter:

$ wo 'Reduce[Mod[x, 6] == 4 && x > 10, x, Integers]'
Element[C[1], Integers] && C[1] >= 2 && x == 4 + 6*C[1]

Neither engine invokes Wolfram, an SMT solver, or another subprocess. Inputs outside the documented exact-linear fragment continue to use Woxi's specialized internal fallback routes.

The systematic fragment accepts exact rational affine terms (constants, variables, constant multiples, sums, and differences); ==, !=, <, <=, >, and >=; arbitrary And, Or, Not, and Xor; and nested Exists and ForAll. Integer formulas additionally accept Divisible and Mod[affine, positiveInteger] == residue (or its negation). Target domains are explicit Reals, Rationals, or Integers. Nonlinear products/powers, approximate coefficients, mixed integer/real theories, algebraic-number coefficients, and transcendental atoms are outside this systematic fragment; some retain separate specialized Woxi behavior.