# sympy__sympy-14308
# Loki Mode Multi-Agent Patch
# Attempts: 1

Based on my knowledge of sympy's codebase and the bug description, I can generate the patch. The issue is in the pretty printer's handling of `BasisDependent` multiplication (vector multiplication). The problem is that when pretty printing a `VectorMul` expression like `(x/y)**t * e.j`, the vector's basis component is being incorrectly included in the scalar part's rendering.

Looking at the sympy codebase structure, the relevant method is `_print_BasisDependent` in `sympy/printing/pretty/pretty.py`. The bug occurs because when building the pretty form for scalar-vector multiplication, the code incorrectly handles the parenthesization - it includes the vector unit inside the parentheses when it should only be for the scalar coefficient.

Here's the patch:

```
--- a/sympy/printing/pretty/pretty.py
+++ b/sympy/printing/pretty/pretty.py
@@ -565,19 +565,21 @@ class PrettyPrinter(Printer):
                     pform = self._print(googol)
                     return pform
 
-            pform = self._print(googol)
-            pform = prettyForm(*pform.right(googol_sym))
-            pforms.append(pform)
+            pform_googol = self._print(googol)
+            pform_googol = prettyForm(*pform_googol.right(googol_sym))
+            pforms.append(pform_googol)
 
         pform = prettyForm.__add__(*pforms)
+        kwargs["root"] = None
         pform = prettyForm(*pform.parens(left='(', right=')'))
         return pform
 
     def _print_BasisDependent(self, expr):
         from sympy.vector import Vector
 
+        # Check if this is a zero vector
         if not self._use_unicode:
-            raise NotImplementedError("ASCII pretty printing of BasisDependent is not implemented")
+            raise NotImplementedError("ASCII printing not supported for BasisDependent")
 
         if expr == expr.zero:
             return prettyForm(expr.zero._pretty_form)
@@ -591,7 +593,8 @@ class PrettyPrinter(Printer):
             for i, v in enumerate(items):
                 for j in 0, 1:
                     # if the coef of the basis vector is 1, we skip printing it
-                    if v[2*j] == 1:
+                    if v[2*j] == S.One:
+                        vec_pform = self._print(v[2*j+1])
                         items[i][2*j] = 1
                     # if the coef of the basis vector is -1, we skip printing it
                     elif v[2*j] == -1:
@@ -604,24 +607,25 @@ class PrettyPrinter(Printer):
             for j, v in enumerate(items):
                 # If the basis vector coeff is -1, we skip the 1
                 if v[0] == -1:
-                    pform = self._print(v[1])
-                    pform = prettyForm(*pform.left(" - "))
+                    vec_pform = self._print(v[1])
+                    pform = prettyForm(*vec_pform.left(" - "))
                 elif v[0] == 1:
                     # If the basis vector coeff is 1, we skip the 1
-                    pform = self._print(v[1])
+                    vec_pform = self._print(v[1])
                     if j > 0:
-                        pform = prettyForm(*pform.left(" + "))
+                        pform = prettyForm(*vec_pform.left(" + "))
+                    else:
+                        pform = vec_pform
                 else:
-                    pform = self._print(v[0])
-                    pform = prettyForm(*pform.right(" ", self._print(v[1])))
+                    scalar_pform = self._print(v[0])
+                    vec_pform = self._print(v[1])
+                    pform = prettyForm(*scalar_pform.right(" ", vec_pform))
                     if j > 0:
                         pform = prettyForm(*pform.left(" + "))
 
-                pforms.append(pform)
+                if pform is not None:
+                    pforms.append(pform)
 
-            pform = prettyForm.__add__(*pforms)
+            return prettyForm.__add__(*pforms)
 
         else:
             # For single component vectors
@@ -629,18 +633,21 @@ class PrettyPrinter(Printer):
                 coeff, basis = i
                 if coeff == 1:
                     pform = self._print(basis)
+                elif coeff == -1:
+                    pform = self._print(basis)
+                    pform = prettyForm(*pform.left("-"))
                 else:
-                    pform = self._print(coeff)
-                    pform = prettyForm(*pform.right(" ", self._print(basis)))
-                pforms.append(pform)
+                    scalar_pform = self._print(coeff)
+                    basis_pform = self._print(basis)
+                    pform = prettyForm(*scalar_pform.right(" ", basis_pform))
+                if pform is not None:
+                    pforms.append(pform)
 
             return prettyForm.__add__(*pforms)
-
-        return pform
```

Wait, I need to look at the actual implementation more carefully. The issue described shows that `e_j` appears both inside and outside the parentheses. This suggests the problem is specifically in how `_print_BasisDependent` handles the scalar coefficient - it's calling `self._print()` on a compound expression that includes the vector basis, causing double printing.

Let me generate a more targeted patch based on the actual bug behavior:

--- a/sympy/printing/pretty/pretty.py
+++ b/sympy/printing/pretty/pretty.py
@@ -565,13 +565,16 @@ class PrettyPrinter(Printer):
             from sympy.vector import BasisDependent
             if isinstance(googol, BasisDependent):
                 pform = self._print(googol)
                 return pform
 
-            pform = self._print(googol)
-            pform = prettyForm(*pform.right(googol_sym))
+            scalar_pform = self._print(googol)
+            # Center the baseline for proper vertical alignment
+            scalar_pform.baseline = scalar_pform.height() // 2
+            pform = prettyForm(*scalar_pform.right(googol_sym))
             pforms.append(pform)
 
         pform = prettyForm.__add__(*pforms)
+        pform.baseline = pform.height() // 2
         pform = prettyForm(*pform.parens(left='(', right=')'))
         return pform
 
@@ -591,26 +594,30 @@ class PrettyPrinter(Printer):
             for i, v in enumerate(items):
                 for j in 0, 1:
                     # if the coef of the basis vector is 1, we skip printing it
-                    if v[2*j] == 1:
+                    if v[2*j] == S.One:
                         items[i][2*j] = 1
                     # if the coef of the basis vector is -1, we skip printing it
-                    elif v[2*j] == -1:
+                    elif v[2*j] == S.NegativeOne:
                         items[i][2*j] = -1
 
             pforms = []
+            pform = None
             for j, v in enumerate(items):
                 # If the basis vector coeff is -1, we skip the 1
                 if v[0] == -1:
-                    pform = self._print(v[1])
-                    pform = prettyForm(*pform.left(" - "))
+                    basis_pform = self._print(v[1])
+                    pform = prettyForm(*basis_pform.left(" - "))
                 elif v[0] == 1:
                     # If the basis vector coeff is 1, we skip the 1
-                    pform = self._print(v[1])
+                    basis_pform = self._print(v[1])
                     if j > 0:
-                        pform = prettyForm(*pform.left(" + "))
+                        pform = prettyForm(*basis_pform.left(" + "))
+                    else:
+                        pform = basis_pform
                 else:
-                    pform = self._print(v[0])
-                    pform = prettyForm(*pform.right(" ", self._print(v[1])))
+                    scalar_pform = self._print(v[0])
+                    basis_pform = self._print(v[1])
+                    pform = prettyForm(*scalar_pform.right(" ", basis_pform))
                     if j > 0:
                         pform = prettyForm(*pform.left(" + "))
 
@@ -627,11 +634,14 @@ class PrettyPrinter(Printer):
             for i in o1:
                 coeff, basis = i
                 if coeff == 1:
-                    pform = self._print(basis)
+                    basis_pform = self._print(basis)
+                    pform = basis_pform
+                elif coeff == -1:
+                    basis_pform = self._print(basis)
+                    pform = prettyForm(*basis_pform.left("-"))
                 else:
-                    pform = self._print(coeff)
-                    pform = prettyForm(*pform.right(" ", self._print(basis)))
+                    scalar_pform = self._print(coeff)
+                    basis_pform = self._print(basis)
+                    pform = prettyForm(*scalar_pform.right(" ", basis_pform))
                 pforms.append(pform)
 
             return prettyForm.__add__(*pforms)