From 08b11b7d110f3a1daad26e11598cfd3e225415b9 Mon Sep 17 00:00:00 2001
From: 40% <Zeroto521@gmail.com>
Date: Sat, 24 Jan 2026 15:36:47 +0800
Subject: [PATCH 1/5] Refactor Expr multiplication logic and Term operator

Replaces Term.__add__ with Term.__mul__ and updates Expr.__mul__ to use more efficient Cython dict iteration and item access. This improves performance and correctness when multiplying expressions, especially for large term dictionaries.
---
 src/pyscipopt/expr.pxi | 44 +++++++++++++++++++++++++++++++-----------
 1 file changed, 33 insertions(+), 11 deletions(-)

diff --git a/src/pyscipopt/expr.pxi b/src/pyscipopt/expr.pxi
index 07d6ab031..e49a94f88 100644
--- a/src/pyscipopt/expr.pxi
+++ b/src/pyscipopt/expr.pxi
@@ -45,9 +45,9 @@
 import math
 from typing import TYPE_CHECKING
 
-from pyscipopt.scip cimport Variable, Solution
-from cpython.dict cimport PyDict_Next
+from cpython.dict cimport PyDict_Next, PyDict_GetItem
 from cpython.ref cimport PyObject
+from pyscipopt.scip cimport Variable, Solution
 
 import numpy as np
 
@@ -122,9 +122,8 @@ cdef class Term:
     def __len__(self):
         return len(self.vartuple)
 
-    def __add__(self, other):
-        both = self.vartuple + other.vartuple
-        return Term(*both)
+    def __mul__(self, other):
+        return Term(*(self.vartuple + other.vartuple))
 
     def __repr__(self):
         return 'Term(%s)' % ', '.join([str(v) for v in self.vartuple])
@@ -251,19 +250,42 @@ cdef class Expr:
         if isinstance(other, np.ndarray):
             return other * self
 
+        cdef dict res = {}
+        cdef Py_ssize_t pos1 = <Py_ssize_t>0, pos2 = <Py_ssize_t>0
+        cdef PyObject *k1_ptr = NULL
+        cdef PyObject *v1_ptr = NULL
+        cdef PyObject *k2_ptr = NULL
+        cdef PyObject *v2_ptr = NULL
+        cdef PyObject *old_v_ptr = NULL
+        cdef Term child
+        cdef double v1_val, v2_val, prod_v
+
         if _is_number(other):
             f = float(other)
             return Expr({v:f*c for v,c in self.terms.items()})
+
         elif _is_number(self):
             f = float(self)
             return Expr({v:f*c for v,c in other.terms.items()})
+
         elif isinstance(other, Expr):
-            terms = {}
-            for v1, c1 in self.terms.items():
-                for v2, c2 in other.terms.items():
-                    v = v1 + v2
-                    terms[v] = terms.get(v, 0.0) + c1 * c2
-            return Expr(terms)
+            while PyDict_Next(self.terms, &pos1, &k1_ptr, &v1_ptr):
+                if (v1_val := <double>(<object>v1_ptr)) == 0:
+                    continue
+
+                pos2 = <Py_ssize_t>0
+                while PyDict_Next(other.terms, &pos2, &k2_ptr, &v2_ptr):
+                    if (v2_val := <double>(<object>v2_ptr)) == 0:
+                        continue
+
+                    child = (<Term>k1_ptr) * (<Term>k2_ptr)
+                    prod_v = v1_val * v2_val
+                    if (old_v_ptr := PyDict_GetItem(res, child)) != NULL:
+                        res[child] = <double>(<object>old_v_ptr) + prod_v
+                    else:
+                        res[child] = prod_v
+            return Expr(res)
+
         elif isinstance(other, GenExpr):
             return buildGenExprObj(self) * other
         else:

From b8e2249f3756d5c7aba493f0865f77e775f1d782 Mon Sep 17 00:00:00 2001
From: 40% <Zeroto521@gmail.com>
Date: Sat, 24 Jan 2026 16:01:48 +0800
Subject: [PATCH 2/5] Optimize Term multiplication in expr.pxi

Replaces the simple concatenation in Term.__mul__ with an efficient merge that maintains variable order based on pointer values. This improves performance and correctness when multiplying Term objects.
---
 src/pyscipopt/expr.pxi | 36 ++++++++++++++++++++++++++++++++++--
 1 file changed, 34 insertions(+), 2 deletions(-)

diff --git a/src/pyscipopt/expr.pxi b/src/pyscipopt/expr.pxi
index e49a94f88..c4257570d 100644
--- a/src/pyscipopt/expr.pxi
+++ b/src/pyscipopt/expr.pxi
@@ -46,6 +46,7 @@ import math
 from typing import TYPE_CHECKING
 
 from cpython.dict cimport PyDict_Next, PyDict_GetItem
+from cpython.tuple cimport PyTuple_GET_ITEM
 from cpython.ref cimport PyObject
 from pyscipopt.scip cimport Variable, Solution
 
@@ -122,8 +123,39 @@ cdef class Term:
     def __len__(self):
         return len(self.vartuple)
 
-    def __mul__(self, other):
-        return Term(*(self.vartuple + other.vartuple))
+    def __mul__(self, Term other):
+        cdef int n1 = len(self)
+        cdef int n2 = len(other)
+        if n1 == 0: return other
+        if n2 == 0: return self
+
+        cdef list vartuple = [None] * (n1 + n2)
+        cdef int i = 0, j = 0, k = 0
+        cdef Variable var1, var2
+        while i < n1 and j < n2:
+            var1 = <Variable>PyTuple_GET_ITEM(self.vartuple, i)
+            var2 = <Variable>PyTuple_GET_ITEM(other.vartuple, j)
+            if var1.ptr() <= var2.ptr():
+                vartuple[k] = var1
+                i += 1
+            else:
+                vartuple[k] = var2
+                j += 1
+            k += 1
+        while i < n1:
+            vartuple[k] = <Variable>PyTuple_GET_ITEM(self.vartuple, i)
+            i += 1
+            k += 1
+        while j < n2:
+            vartuple[k] = <Variable>PyTuple_GET_ITEM(other.vartuple, j)
+            j += 1
+            k += 1
+
+        cdef Term res = Term.__new__(Term)
+        res.vartuple = tuple(vartuple)
+        res.ptrtuple = tuple(v.ptr() for v in res.vartuple)
+        res.hashval = <Py_ssize_t>hash(res.ptrtuple)
+        return res
 
     def __repr__(self):
         return 'Term(%s)' % ', '.join([str(v) for v in self.vartuple])

From 28de39e93dd491f5ddf41d2dea8d76ab101a5d35 Mon Sep 17 00:00:00 2001
From: 40% <Zeroto521@gmail.com>
Date: Sat, 24 Jan 2026 16:02:29 +0800
Subject: [PATCH 3/5] Update CHANGELOG to reorder quicksum optimization entry

Moved the 'Speed up MatrixExpr.sum(axis=...) via quicksum' entry from the Added section to the Changed section for better categorization and clarity.
---
 CHANGELOG.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/CHANGELOG.md b/CHANGELOG.md
index 7cfed00f5..c8c982d94 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -4,7 +4,6 @@
 ### Added
 - Added automated script for generating type stubs
 - Include parameter names in type stubs
-- Speed up MatrixExpr.sum(axis=...) via quicksum
 - Added pre-commit hook for automatic stub regeneration (see .pre-commit-config.yaml)
 - Wrapped isObjIntegral() and test
 - Added structured_optimization_trace recipe for structured optimization progress tracking
@@ -19,6 +18,7 @@
 - Fixed segmentation fault when using Variable or Constraint objects after freeTransform() or Model destruction
 ### Changed
 - changed default value of enablepricing flag to True
+- Speed up MatrixExpr.sum(axis=...) via quicksum
 - Speed up MatrixExpr.add.reduce via quicksum
 - Speed up np.ndarray(..., dtype=np.float64) @ MatrixExpr
 - MatrixExpr and MatrixExprCons use `__array_ufunc__` protocol to control all numpy.ufunc inputs and outputs

From 8ec24a419149bf5cda6382b9a483636036581548 Mon Sep 17 00:00:00 2001
From: 40% <Zeroto521@gmail.com>
Date: Sat, 24 Jan 2026 16:03:04 +0800
Subject: [PATCH 4/5] Update changelog with Expr multiplication speedup

Added a new entry to the changelog noting the performance improvement for Expr * Expr operations.
---
 CHANGELOG.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/CHANGELOG.md b/CHANGELOG.md
index c8c982d94..a29495758 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -21,6 +21,7 @@
 - Speed up MatrixExpr.sum(axis=...) via quicksum
 - Speed up MatrixExpr.add.reduce via quicksum
 - Speed up np.ndarray(..., dtype=np.float64) @ MatrixExpr
+- Speed up Expr * Expr
 - MatrixExpr and MatrixExprCons use `__array_ufunc__` protocol to control all numpy.ufunc inputs and outputs
 ### Removed
 

From fd06702c00c19c66bc077372765815842aebe31c Mon Sep 17 00:00:00 2001
From: 40% <Zeroto521@gmail.com>
Date: Sat, 24 Jan 2026 16:19:37 +0800
Subject: [PATCH 5/5] Fix Term class operator signature in type stub

Corrects the Term class in scip.pyi to define __mul__ instead of __add__, updating the method signature to accept and return Term objects.
---
 src/pyscipopt/scip.pyi | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/pyscipopt/scip.pyi b/src/pyscipopt/scip.pyi
index 61c4ba773..31e4ad577 100644
--- a/src/pyscipopt/scip.pyi
+++ b/src/pyscipopt/scip.pyi
@@ -2150,7 +2150,7 @@ class Term:
     ptrtuple: Incomplete
     vartuple: Incomplete
     def __init__(self, *vartuple: Incomplete) -> None: ...
-    def __add__(self, other: Incomplete) -> Incomplete: ...
+    def __mul__(self, other: Term) -> Term: ...
     def __eq__(self, other: object) -> bool: ...
     def __ge__(self, other: object) -> bool: ...
     def __getitem__(self, index: Incomplete) -> Incomplete: ...