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[Maxima-commits] [git] Maxima CAS branch master updated. branch-5_49-base-548-g96ea422c6
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From: tomasriker <tom...@us...> - 2026-05-28 22:14:17
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- Log -----------------------------------------------------------------
commit 96ea422c6c5dbf5440ea544500fe8fc885247b64
Author: David Scherfgen <d.s...@go...>
Date: Fri May 29 00:11:25 2026 +0200
SIGNDIFF-SPECIAL: handle sign(abs(a)-b) and sign(a^pos_int-b)
Maxima can now determine more signs without using factoring or when factoring
wouldn't work, for example sign(x^2-2) with -1 < x < 1.
Absolute value handling allows Maxima to, e.g., determine that abs(cos(x)) <= 1.
Also, to make sure that the cases handled by SIGNDIFF-SPECIAL work correctly
regardless of whether XLHS and XRHS are swapped, a simple "swap and flip sign"
logic is introduced.
This fixes bugs #2288 and #3155.
diff --git a/src/compar.lisp b/src/compar.lisp
index 8a5bf0bc6..3e33b3800 100644
--- a/src/compar.lisp
+++ b/src/compar.lisp
@@ -1481,7 +1481,7 @@ TDNEG TDZERO TDPN) to store it, and also sets SIGN."
(defun signdiff-special (xlhs xrhs)
;; xlhs may be a constant
- (let ((sgn nil))
+ (let ((sgn nil) flip-sign)
(when (or (and (realp xrhs) (minusp xrhs)
(not (atom xlhs)) (eq (sign* xlhs) '$pos))
; e.g. sign(a^3+%pi-1) where a>0
@@ -1506,7 +1506,16 @@ TDNEG TDZERO TDPN) to store it, and also sets SIGN."
(eq (sign* (sub (cadr xlhs) 1)) '$pos)
(eq (sign* (sub (caddr xlhs) (caddr xrhs))) '$pos)))
(setq sgn '$pos))
-
+
+ ;; For the following test, swap XLHS and XRHS, if necessary, so that XLHS
+ ;; is one of the operators that we can handle, and remember to flip the result.
+ (let ((operators '(%sin %cos %cosh %sech %signum mabs)))
+ (when (and (not (atom xrhs))
+ (member (caar xrhs) operators :test #'eq)
+ (or (atom xlhs)
+ (not (member (caar xlhs) operators :test #'eq))))
+ (psetq xlhs xrhs xrhs xlhs flip-sign (not flip-sign))))
+
;; sign(sin(x)+c)
(when (and (not (atom xlhs))
(member (caar xlhs) '(%sin %cos))
@@ -1556,10 +1565,46 @@ TDNEG TDZERO TDPN) to store it, and also sets SIGN."
(setq sgn '$pnz))
(t ;; -1 < c < 1, but c # 0
(setq sgn '$pn))))
-
+
+ ;; sign(abs(a) - b) = sign_max(sign(a - b), sign(-a - b)) with real a, b
+ (when (and (null sgn)
+ (not (atom xlhs))
+ (eq (caar xlhs) 'mabs)
+ (zerop1 ($imagpart (cadr xlhs)))
+ (zerop1 ($imagpart xrhs)))
+ (let* ((a (cadr xlhs))
+ (b xrhs)
+ (s1 (sign* (sub a b)))
+ (s2 (sign* (sub (neg a) b)))
+ (max-sign (sminmax '$max s1 s2)))
+ (when (not (eq max-sign '$pnz))
+ (setq sgn max-sign))))
+
+ ;; For the following test, swap XLHS and XRHS, if necessary, so that XRHS is
+ ;; the number, e.g. x^2 - 3 -> 3 - x^2, and remember to flip the result.
+ (when (and (mnump xlhs) (not (mnump xrhs)))
+ (psetq xlhs xrhs xrhs xlhs flip-sign (not flip-sign)))
+
+ ;; sign(a^pos_int - b) = sign(abs_if_even(a) - b^(1/pos_int))
+ ;; with real a, b >= 0 (for even pos_int), and b^(1/pos_int) being the real root
+ (when (and (null sgn)
+ (mnump xrhs)
+ (mexptp xlhs)
+ (integerp (caddr xlhs))
+ (> (caddr xlhs) 0)
+ (or (oddp (caddr xlhs)) (not (mnegp xrhs)))
+ (zerop1 ($imagpart (cadr xlhs))))
+ (let* ((exponent (caddr xlhs))
+ (root (mul (if (mnegp xrhs) -1 1) (power (ftake 'mabs xrhs) (div 1 exponent))))
+ (base (cadr xlhs))
+ (maybe-abs-base (if (evenp exponent) (ftake 'mabs base) base))
+ (diff-sign (sign* (sub maybe-abs-base root))))
+ (when (not (eq diff-sign '$pnz))
+ (setq sgn diff-sign))))
+
(when (and $useminmax (or (minmaxp xlhs) (minmaxp xrhs)))
(setq sgn (signdiff-minmax xlhs xrhs)))
- (when sgn (setq sign sgn minus nil odds nil evens nil)
+ (when sgn (setq sign (if flip-sign (flip sgn) sgn) minus nil odds nil evens nil)
t)))
;;; Look for symbols with an assumption a > n or a < -n, where n is a number.
diff --git a/tests/rtest_sign.mac b/tests/rtest_sign.mac
index 62f02312f..e83d91993 100644
--- a/tests/rtest_sign.mac
+++ b/tests/rtest_sign.mac
@@ -1606,3 +1606,62 @@ block ([S: make_string_output_stream (), S1],
S1);
"sign: sign undefined for foo
";
+
+/* Bug #2288: "x^2<1 can't get x^2<2, but can get x^2<100" */
+/* and related tests */
+
+assume(x > -1, x < 1);
+[x > -1, x < 1];
+
+[sign(abs(x) - 1), sign(1 - abs(x))];
+[neg, pos];
+
+[sign(abs(x) - 2), sign(2 - abs(x))];
+[neg, pos];
+
+[sign(abs(x) - 1/2), sign(1/2 - abs(x))];
+[pnz, pnz];
+
+[sign(x^2 - 1), sign(1 - x^2)];
+[neg, pos];
+
+[sign(x^2 - 2), sign(2 - x^2)];
+[neg, pos];
+
+[sign(x^2 - 1/2), sign(1/2 - x^2)];
+[pnz, pnz];
+
+[sign(x^2 - 100), sign(100 - x^2)];
+[neg, pos];
+
+[sign(x^2 - 10000), sign(10000 - x^2)];
+[neg, pos];
+
+[sign(x^4 - 2), sign(2 - x^4)];
+[neg, pos];
+
+[sign(x^3 - 1), sign(1 - x^3)];
+[neg, pos];
+
+[sign(x^3 - 2), sign(2 - x^3)];
+[neg, pos];
+
+[sign(x^3 - 1/2), sign(1/2 - x^3)];
+[pnz, pnz];
+
+[sign(x^3 + 1), sign(-1 - x^3)];
+[pos, neg];
+
+[sign(x^3 + 2), sign(-2 - x^3)];
+[pos, neg];
+
+[sign(x^3 + 1/2), sign(-1/2 - x^3)];
+[pnz, pnz];
+
+forget(x > -1, x < 1);
+[x > -1, x < 1];
+
+/* Bug #3155: "is(abs(cos(x))<=1) is unknown, but is(cos(x)<=1) and is(cos(x)>=-1) are true" */
+
+is(abs(cos(x)) <= 1);
+true;
-----------------------------------------------------------------------
Summary of changes:
src/compar.lisp | 53 ++++++++++++++++++++++++++++++++++++++++++----
tests/rtest_sign.mac | 59 ++++++++++++++++++++++++++++++++++++++++++++++++++++
2 files changed, 108 insertions(+), 4 deletions(-)
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