improve detection of negative terms

CHANGELOG.md

@@ -2,6 +2,10 @@ To install or update LODA, please follow the [installation instructions](https:/
 
 ## [Unreleased]
 
+### Enhancements
+
+* Simplify generated formulas
+
 ## v24.1.7
 
 ### Bugfixes

src/form/expression_util.cpp

@@ -298,15 +298,20 @@ bool ExpressionUtil::canBeNegative(const Expression& e) {
           std::any_of(e.children.begin(), e.children.end(),
                       [](const Expression& c) { return !canBeNegative(c); })) {
         return false;
-      } else if (e.name == "binomial") {
+      } else if (e.name == "binomial" || e.name == "floor" ||
+                 e.name == "truncate") {
         break;  // infer from children
       } else {
         return true;  // unknown function
       }
     case Expression::Type::POWER:
-      if (e.children.size() == 2 &&
-          e.children[1].type == Expression::Type::CONSTANT) {
-        return e.children[1].value.odd();
+      if (e.children.size() == 2) {
+        if (e.children[0].type == Expression::Type::CONSTANT) {
+          return e.children[0].value < Number::ZERO;
+        }
+        if (e.children[1].type == Expression::Type::CONSTANT) {
+          return e.children[1].value.odd();
+        }
       }
     case Expression::Type::SUM:
     case Expression::Type::PRODUCT:

tests/formula/program-formula.txt

@@ -12,7 +12,7 @@ A000073: a(n) = a(n-1)+a(n-2)+a(n-3), a(2) = 1, a(1) = 0, a(0) = 0
 A000096: a(n) = binomial(n+2,2)-1
 A000142: a(n) = n*a(n-1), a(0) = 1
 A000165: a(n) = b(2*n), b(n) = n*b(n-2), b(1) = 1, b(0) = 1
-A000168: a(n) = truncate((2*A151383(n))/(n+2)), A151383(n) = truncate((floor(binomial(2*n,n)/(n+1))*3^(n+1))/3)
+A000168: a(n) = truncate((2*A151383(n))/(n+2)), A151383(n) = floor((floor(binomial(2*n,n)/(n+1))*3^(n+1))/3)
 A000212: a(n) = floor((n^2)/3)
 A000276: a(n) = truncate((2*c(n+1)*(n+3))/2), b(n) = b(n-1)*(n+1), b(2) = 6, b(1) = 2, b(0) = 1, c(n) = c(n-1)*(n+1)+b(n-1), c(2) = 5, c(1) = 1, c(0) = 0
 A000278: a(n) = (-a(n-2))^2+a(n-1), a(1) = 1, a(0) = 0