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Short-weierstrass

Short-weierstrass-p

Recognizer for short-weierstrass structures.

Signature
(short-weierstrass-p x) → *

Definitions and Theorems

Function: short-weierstrass-p

(defun short-weierstrass-p (x)
  (declare (xargs :guard t))
  (let ((acl2::__function__ 'short-weierstrass-p))
    (declare (ignorable acl2::__function__))
    (and (mbe :logic (and (alistp x)
                          (equal (strip-cars x) '(p a b)))
              :exec (fty::alist-with-carsp x '(p a b)))
         (b* ((p (cdr (std::da-nth 0 x)))
              (a (cdr (std::da-nth 1 x)))
              (b (cdr (std::da-nth 2 x))))
           (and (natp p)
                (natp a)
                (natp b)
                (> p 3)
                (fep a p)
                (fep b p)
                (posp (mod (+ (* 4 a a a) (* 27 b b)) p)))))))

Theorem: consp-when-short-weierstrass-p

(defthm consp-when-short-weierstrass-p
  (implies (short-weierstrass-p x)
           (consp x))
  :rule-classes :compound-recognizer)