Change lmbda to lambda

src/sage/combinat/designs/block_design.py

@@ -91,23 +91,23 @@ def tdesign_params(t, v, k, L):
     r = integer_floor(L * x/y)
     return (t, v, b, r, k, L)
 
-def are_hyperplanes_in_projective_geometry_parameters(v, k, lmbda, return_parameters=False):
+def are_hyperplanes_in_projective_geometry_parameters(v, k, lambda, return_parameters=False):
     r"""
-    Return ``True`` if the parameters ``(v,k,lmbda)`` are the one of hyperplanes in
+    Return ``True`` if the parameters ``(v,k,lambda)`` are the one of hyperplanes in
     a (finite Desarguesian) projective space.
 
     In other words, test whether there exists a prime power ``q`` and an integer
     ``d`` greater than two such that:
 
     - `v = (q^{d+1}-1)/(q-1) = q^d + q^{d-1} + ... + 1`
     - `k = (q^d - 1)/(q-1) = q^{d-1} + q^{d-2} + ... + 1`
-    - `lmbda = (q^{d-1}-1)/(q-1) = q^{d-2} + q^{d-3} + ... + 1`
+    - `lambda = (q^{d-1}-1)/(q-1) = q^{d-2} + q^{d-3} + ... + 1`
 
     If it exists, such a pair ``(q,d)`` is unique.
 
     INPUT:
 
-    - ``v``, ``k``, ``lmbda`` -- integers
+    - ``v``, ``k``, ``lambda`` -- integers
 
     OUTPUT:
 
@@ -149,9 +149,9 @@ def are_hyperplanes_in_projective_geometry_parameters(v, k, lmbda, return_parame
     import sage.arith.all as arith
 
     q1 = Integer(v - k)
-    q2 = Integer(k - lmbda)
+    q2 = Integer(k - lambda)
 
-    if (lmbda <= 0 or q1 < 4 or q2 < 2 or
+    if (lambda <= 0 or q1 < 4 or q2 < 2 or
         not q1.is_prime_power() or
         not q2.is_prime_power()):
         return (False,(None,None)) if return_parameters else False
@@ -162,7 +162,7 @@ def are_hyperplanes_in_projective_geometry_parameters(v, k, lmbda, return_parame
     k = arith.gcd(e1,e2)
     d = e1//k
     q = p1**k
-    if e2//k != d-1 or lmbda != (q**(d-1)-1)//(q-1):
+    if e2//k != d-1 or lambda != (q**(d-1)-1)//(q-1):
         return (False,(None,None)) if return_parameters else False
 
     return (True, (q,d)) if return_parameters else True

src/sage/combinat/designs/database.py

@@ -2452,14 +2452,14 @@ def QDM_57_9_1_1_8():
 # The syntax of the dictionary is
 #
 # QDM = {
-#     (n+u,lmbda): { # QDM with mu<=lmbda=1 yields a OA(k,n+u)-OA(k,u)
-#         (n,lmbda,mu,u): (k,qdm_constructor),
+#     (n+u,lambda): { # QDM with mu<=lambda=1 yields a OA(k,n+u)-OA(k,u)
+#         (n,lambda,mu,u): (k,qdm_constructor),
 #         }
 # }
 
 
 QDM: dict[tuple[int, int], dict] = {}
-for ((n,k,lmbda,mu,u),f) in [((19,6,1,1,1), QDM_19_6_1_1_1),
+for ((n,k,lambda,mu,u),f) in [((19,6,1,1,1), QDM_19_6_1_1_1),
                              ((21,5,1,1,1), QDM_21_5_1_1_1),
                              ((21,6,1,1,5), QDM_21_6_1_1_5),
                              ((25,6,1,1,5), QDM_25_6_1_1_5),
@@ -2469,15 +2469,15 @@ def QDM_57_9_1_1_8():
                              ((45,7,1,1,9), QDM_45_7_1_1_9),
                              ((54,7,1,1,8), QDM_54_7_1_1_8),
                              ((57,9,1,1,8), QDM_57_9_1_1_8)]:
-    if (n+u,lmbda) not in QDM:
-        QDM[n+u,lmbda] = {}
-    QDM[n+u,lmbda][n,lmbda,mu,u] = (k,f)
+    if (n+u,lambda) not in QDM:
+        QDM[n+u,lambda] = {}
+    QDM[n+u,lambda][n,lambda,mu,u] = (k,f)
 
 # Create the list of QDM matrices for the doc
-LIST_OF_QDM = ", ".join("`({},{};{},{};{})`".format(n,k,lmbda,mu,u)
-                         for n,k,lmbda,mu,u in
-                          sorted((n,k,lmbda,mu,u) for entry in QDM.values()
-                            for (n,lmbda,mu,u),(k,_) in sorted(entry.items())))
+LIST_OF_QDM = ", ".join("`({},{};{},{};{})`".format(n,k,lambda,mu,u)
+                         for n,k,lambda,mu,u in
+                          sorted((n,k,lambda,mu,u) for entry in QDM.values()
+                            for (n,lambda,mu,u),(k,_) in sorted(entry.items())))
 
 _ref_Handbook = """Handbook of Combinatorial Designs (2ed),
     C. Colbourn, J. Dinitz, 2010 CRC Press"""
@@ -2700,10 +2700,10 @@ def QDM_57_9_1_1_8():
 }
 # Translate all V(m,t) into (mt+1,m+2;1,0;t)-QDM constructors
 for (m,t),(vec,source) in Vmt_vectors.items():
-    n,k,lmbda,mu,u = (m*t+1,m+2,1,0,t)
-    if (n+u,lmbda) not in QDM:
-        QDM[n+u,lmbda] = {}
-    QDM[n+u,lmbda][n,lmbda,mu,u] = (k,lambda m=m,t=t,vec=vec:QDM_from_Vmt(m,t,vec))
+    n,k,lambda,mu,u = (m*t+1,m+2,1,0,t)
+    if (n+u,lambda) not in QDM:
+        QDM[n+u,lambda] = {}
+    QDM[n+u,lambda][n,lambda,mu,u] = (k,lambda m=m,t=t,vec=vec:QDM_from_Vmt(m,t,vec))
 
 # Create the list of V(m,t) vectors for the doc
 _all_m = sorted(set(m for m,_ in Vmt_vectors.keys()))

src/sage/combinat/designs/designs_pyx.pyx

@@ -665,7 +665,7 @@ def is_projective_plane(blocks, verbose=False):
                                      verbose=verbose)
 
 
-def is_difference_matrix(M,G,k,lmbda=1,verbose=False):
+def is_difference_matrix(M,G,k,lambda=1,verbose=False):
     r"""
     Test if `M` is a `(G,k,\lambda)`-difference matrix.
 
@@ -681,7 +681,7 @@ def is_difference_matrix(M,G,k,lmbda=1,verbose=False):
 
     - ``k`` -- integer
 
-    - ``lmbda`` (integer) -- set to `1` by default.
+    - ``lambda`` (integer) -- set to `1` by default.
 
     - ``verbose`` (boolean) -- whether to print some information when the answer
       is ``False``.
@@ -727,10 +727,10 @@ def is_difference_matrix(M,G,k,lmbda=1,verbose=False):
         The element x appeared 0 times as a difference.
         False
     """
-    return is_quasi_difference_matrix(M,G,k,lmbda=lmbda,mu=lmbda,u=0,verbose=verbose)
+    return is_quasi_difference_matrix(M,G,k,lambda=lambda,mu=lambda,u=0,verbose=verbose)
 
 
-def is_quasi_difference_matrix(M,G,int k,int lmbda,int mu,int u,verbose=False):
+def is_quasi_difference_matrix(M,G,int k,int lambda,int mu,int u,verbose=False):
     r"""
     Test if the matrix is a `(G,k;\lambda,\mu;u)`-quasi-difference matrix
 
@@ -755,7 +755,7 @@ def is_quasi_difference_matrix(M,G,int k,int lmbda,int mu,int u,verbose=False):
 
     - ``G`` -- a group
 
-    - ``k``, ``lmbda``, ``mu``, ``u`` -- integers
+    - ``k``, ``lambda``, ``mu``, ``u`` -- integers
 
     - ``verbose`` (boolean) -- whether to print some information when the answer
       is ``False``.
@@ -783,31 +783,31 @@ def is_quasi_difference_matrix(M,G,int k,int lmbda,int mu,int u,verbose=False):
 
         sage: from sage.combinat.designs.database import QDM
         sage: G,M = QDM[38,1][37,1,1,1][1]()
-        sage: is_quasi_difference_matrix(M,G,k=6,lmbda=1,mu=1,u=1)
+        sage: is_quasi_difference_matrix(M,G,k=6,lambda=1,mu=1,u=1)
         True
 
     Bad input::
 
-        sage: is_quasi_difference_matrix(M,G,k=6,lmbda=1,mu=1,u=3,verbose=1)
+        sage: is_quasi_difference_matrix(M,G,k=6,lambda=1,mu=1,u=3,verbose=1)
         The matrix has 39 rows instead of lambda(|G|-1+2u)+mu=1(37-1+2.3)+1=43
         False
-        sage: is_quasi_difference_matrix(M,G,k=6,lmbda=1,mu=2,u=1,verbose=1)
+        sage: is_quasi_difference_matrix(M,G,k=6,lambda=1,mu=2,u=1,verbose=1)
         The matrix has 39 rows instead of lambda(|G|-1+2u)+mu=1(37-1+2.1)+2=40
         False
         sage: M[3][1] = None
-        sage: is_quasi_difference_matrix(M,G,k=6,lmbda=1,mu=1,u=1,verbose=1)
+        sage: is_quasi_difference_matrix(M,G,k=6,lambda=1,mu=1,u=1,verbose=1)
         Row 3 contains more than one empty entry
         False
         sage: M[3][1] = 1
         sage: M[6][1] = None
-        sage: is_quasi_difference_matrix(M,G,k=6,lmbda=1,mu=1,u=1,verbose=1)
+        sage: is_quasi_difference_matrix(M,G,k=6,lambda=1,mu=1,u=1,verbose=1)
         Column 1 contains 2 empty entries instead of the expected lambda.u=1.1=1
         False
     """
     from sage.combinat.designs.difference_family import group_law
 
     assert k>=2
-    assert lmbda >=1
+    assert lambda >=1
     assert mu>=0
     assert u>=0
 
@@ -817,9 +817,9 @@ def is_quasi_difference_matrix(M,G,int k,int lmbda,int mu,int u,verbose=False):
     cdef bint bit
 
     # Height of the matrix
-    if lmbda*(n-1+2*u)+mu != M_nrows:
+    if lambda*(n-1+2*u)+mu != M_nrows:
         if verbose:
-            print("The matrix has {} rows instead of lambda(|G|-1+2u)+mu={}({}-1+2.{})+{}={}".format(M_nrows,lmbda,n,u,mu,lmbda*(n-1+2*u)+mu))
+            print("The matrix has {} rows instead of lambda(|G|-1+2u)+mu={}({}-1+2.{})+{}={}".format(M_nrows,lambda,n,u,mu,lambda*(n-1+2*u)+mu))
         return False
 
     # Width of the matrix
@@ -892,16 +892,16 @@ def is_quasi_difference_matrix(M,G,int k,int lmbda,int mu,int u,verbose=False):
                         return False
                     bit = True
 
-    # Each column contains lmbda*u empty entries
+    # Each column contains lambda*u empty entries
         for j in range(k):
             ii = 0
             for i in range(M_nrows):
                 if M_c[i*k+j] == n:
                     ii += 1
-            if ii!=lmbda*u:
+            if ii!=lambda*u:
                 if verbose:
                     print("Column {} contains {} empty entries instead of the expected "
-                          "lambda.u={}.{}={}".format(j, ii, lmbda, u, lmbda*u))
+                          "lambda.u={}.{}={}".format(j, ii, lambda, u, lambda*u))
                 sig_free(x_minus_y_data)
                 sig_free(x_minus_y)
                 sig_free(G_seen)
@@ -926,11 +926,11 @@ def is_quasi_difference_matrix(M,G,int k,int lmbda,int mu,int u,verbose=False):
                 return False
 
             for ii in range(1,n): # bad number of g_ii\in G
-                if G_seen[ii] != lmbda:
+                if G_seen[ii] != lambda:
                     if verbose:
                         print("Columns {} and {} do not generate all elements of G "
                          "exactly lambda(={}) times. The element {} appeared {} "
-                         "times as a difference.".format(i,j,lmbda,int_to_group[ii],G_seen[ii]))
+                         "times as a difference.".format(i,j,lambda,int_to_group[ii],G_seen[ii]))
                     sig_free(x_minus_y_data)
                     sig_free(x_minus_y)
                     sig_free(G_seen)