Variables in exponent with basis other than e

CHANGELOG.md

@@ -2,6 +2,7 @@
 
 ## Unreleased
 ### Added
+- Added possibility of having variables in exponent.
 - Added basic type stubs to help with IDE autocompletion and type checking.
 ### Fixed
 - Implemented all binary operations between MatrixExpr and GenExpr

src/pyscipopt/expr.pxi

@@ -272,6 +272,19 @@ cdef class Expr:
             res *= self
         return res
 
+    def __rpow__(self, other):
+        """
+        Implements base**x as scip.exp(x * scip.log(base)).
+        Note: base must be positive.
+        """
+        if _is_number(other):
+            base = float(other)
+            if base <= 0.0:
+                raise ValueError("Base of a**x must be positive, as expression is reformulated to scip.exp(x * scip.log(a)); got %g" % base)
+            return exp(self * log(base))
+        else:
+            raise TypeError(f"Unsupported base type {type(other)} for exponentiation.")
+
     def __neg__(self):
         return Expr({v:-c for v,c in self.terms.items()})
 
@@ -544,6 +557,19 @@ cdef class GenExpr:
 
         return ans
 
+    def __rpow__(self, other):
+        """
+        Implements base**x as scip.exp(x * scip.log(base)). 
+        Note: base must be positive.
+        """
+        if _is_number(other):
+            base = float(other)
+            if base <= 0.0:
+                raise ValueError("Base of a**x must be positive, as expression is reformulated to scip.exp(x * scip.log(a)); got %g" % base)
+            return exp(self * log(base))
+        else:
+            raise TypeError(f"Unsupported base type {type(other)} for exponentiation.")
+
     #TODO: ipow, idiv, etc
     def __truediv__(self,other):
         divisor = buildGenExprObj(other)

tests/test_expr.py

@@ -177,3 +177,14 @@ def test_equation(model):
     assert isinstance(equat.expr, GenExpr)
     assert equat._lhs == equat._rhs
     assert equat._lhs == 0.0
+
+def test_rpow_constant_base(model):
+    m, x, y, z = model
+    a = 2**x
+    b = exp(x * log(2.0))
+    assert isinstance(a, GenExpr)
+    assert repr(a) == repr(b) # Structural equality is not implemented; compare strings
+    m.addCons(2**x <= 1)
+
+    with pytest.raises(ValueError):
+        c = (-2)**x