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Diffstat (limited to 'theta_lib/basis_change/base_change_dim4.py')
| -rw-r--r-- | theta_lib/basis_change/base_change_dim4.py | 152 |
1 files changed, 0 insertions, 152 deletions
diff --git a/theta_lib/basis_change/base_change_dim4.py b/theta_lib/basis_change/base_change_dim4.py deleted file mode 100644 index aaf685f..0000000 --- a/theta_lib/basis_change/base_change_dim4.py +++ /dev/null @@ -1,152 +0,0 @@ -from sage.all import * -import itertools - -from ..theta_structures.theta_helpers_dim4 import multindex_to_index - -def bloc_decomposition(M): - I1=[0,1,2,3] - I2=[4,5,6,7] - - A=M[I1,I1] - B=M[I2,I1] - C=M[I1,I2] - D=M[I2,I2] - - return A,B,C,D - -def mat_prod_vect(A,I): - J=[] - for i in range(4): - J.append(0) - for k in range(4): - J[i]+=A[i,k]*I[k] - return tuple(J) - -def add_tuple(I,J): - K=[] - for k in range(4): - K.append(I[k]+J[k]) - return tuple(K) - -def scal_prod_tuple(I,J): - s=0 - for k in range(4): - s+=I[k]*J[k] - return s - -def red_mod_2(I): - J=[] - for x in I: - J.append(ZZ(x)%2) - return tuple(J) - -def choose_non_vanishing_index(C,D,zeta): - for I0 in itertools.product([0,1],repeat=4): - L=[0 for k in range(16)] - for J in itertools.product([0,1],repeat=4): - CJ=mat_prod_vect(C,J) - DJ=mat_prod_vect(D,J) - e=-scal_prod_tuple(CJ,DJ)-2*scal_prod_tuple(I0,DJ) - - I0pDJ=add_tuple(I0,CJ) - - L[multindex_to_index(red_mod_2(I0pDJ))]+=zeta**(ZZ(e)) - for k in range(16): - if L[k]!=0: - return I0,L - - -def base_change_theta_dim4(M,zeta): - - Z4=Integers(4) - A,B,C,D=bloc_decomposition(M.change_ring(Z4)) - - I0,L0=choose_non_vanishing_index(C,D,zeta) - - - N=[L0]+[[0 for j in range(16)] for i in range(15)] - for I in itertools.product([0,1],repeat=4): - if I!=(0,0,0,0): - AI=mat_prod_vect(A,I) - BI=mat_prod_vect(B,I) - for J in itertools.product([0,1],repeat=4): - CJ=mat_prod_vect(C,J) - DJ=mat_prod_vect(D,J) - - AIpCJ=add_tuple(AI,CJ) - BIpDJ=add_tuple(BI,DJ) - - e=scal_prod_tuple(I,J)-scal_prod_tuple(AIpCJ,BIpDJ)-2*scal_prod_tuple(I0,BIpDJ) - N[multindex_to_index(I)][multindex_to_index(red_mod_2(add_tuple(AIpCJ,I0)))]+=zeta**(ZZ(e)) - - Fp2=zeta.parent() - return matrix(Fp2,N) - -def apply_base_change_theta_dim4(N,P): - Q=[] - for i in range(16): - Q.append(0) - for j in range(16): - Q[i]+=N[i,j]*P[j] - return Q - -def complete_symplectic_matrix_dim4(C,D,n=4): - Zn=Integers(n) - - Col_I4=[matrix(Zn,[[1],[0],[0],[0]]),matrix(Zn,[[0],[1],[0],[0],[0]]), - matrix(Zn,[[0],[0],[1],[0],[0],[0]]),matrix(Zn,[[0],[0],[0],[1],[0],[0],[0]])] - - L_DC=block_matrix([[D.transpose(),-C.transpose()]]) - Col_AB_i=L_DC.solve_right(Col_I4[0]) - A_t=Col_AB_i[[0,1,2,3],0].transpose() - B_t=Col_AB_i[[4,5,6,7],0].transpose() - - for i in range(1,4): - F=block_matrix(2,1,[L_DC,block_matrix(1,2,[B_t,-A_t])]) - Col_AB_i=F.solve_right(Col_I4[i]) - A_t=block_matrix(2,1,[A_t,Col_AB_i[[0,1,2,3],0].transpose()]) - B_t=block_matrix(2,1,[B_t,Col_AB_i[[4,5,6,7],0].transpose()]) - - A=A_t.transpose() - B=B_t.transpose() - - M=block_matrix([[A,C],[B,D]]) - - return M - -def random_symmetric_matrix(n,r): - Zn=Integers(n) - M=zero_matrix(Zn,r,r) - for i in range(r): - M[i,i]=randint(0,n-1) - for i in range(r): - for j in range(i+1,r): - M[i,j]=randint(0,n-1) - M[j,i]=M[i,j] - return M - - -def random_symplectic_matrix(n): - Zn=Integers(n) - - C=random_symmetric_matrix(n,4) - Cp=random_symmetric_matrix(n,4) - - A=random_matrix(Zn,4,4) - while not A.is_invertible(): - A=random_matrix(Zn,4,4) - - tA_inv=A.inverse().transpose() - ACp=A*Cp - return block_matrix([[ACp,A],[C*ACp-tA_inv,C*A]]) - -def is_symplectic_matrix_dim4(M): - A,B,C,D=bloc_decomposition(M) - if B.transpose()*A!=A.transpose()*B: - return False - if C.transpose()*D!=D.transpose()*C: - return False - if A.transpose()*D-B.transpose()*C!=identity_matrix(4): - return False - return True - |