ideal.egi

--
-- declare ideal (design/cas-simplification.md G3): Groebner completion
-- at declaration time.  The generated term-level rules are batch-scoped
-- (like declare rule auto), so they apply to every expression in this
-- file -- which is why these tests live apart from the value-level
-- groebner.egi tests.
--

declare symbol s2, s3, s6
declare symbol θ, φ

declare ideal [s2^2 - 2, s3^2 - 3, s6 - s2 * s3]

assertEqual "square" (s2^2) 2
assertEqual "product folds" (s2 * s3) s6
assertEqual "completed rule" (s2 * s6) (2 * s3)
assertEqual "binomial square" ((s2 + s3)^2) (2 * s6 + 5)
assertEqual "conjugate product" ((s2 + s3) * (s2 - s3)) (-1)

-- Pythagorean ideal on the trig atoms; sin θ appears first in the
-- generator, so sin survives (appearance-order priority).
declare ideal [(sin θ)^2 + (cos θ)^2 - 1]

assertEqual "sin^4 - cos^4" ((sin θ)^4 - (cos θ)^4) (2 * (sin θ)^2 - 1)
assertEqual "sin^2 + 2 cos^2" ((sin θ)^2 + 2 * (cos θ)^2) (2 - (sin θ)^2)
assertEqual "other angles untouched"
  (show ((sin φ)^4 - (cos φ)^4)) "('sin φ)^4 - ('cos φ)^4"