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coefmatrix-determinant

eq1:x*4-y*2+z=3;

eq2:x+y*3-z*2=1;

eq3:x*2-y-z=-2;

Calculate

coefmatrix-rank

eq1:x+y+t=0;

eq2:x+2*y-z+t=0;

eq3:x-y+z+t=0;

Calculate

coefmatrix

eq1:x=-y-2*z;

eq2:y=-x-2*z;

matrizasociada:coefma...

Calculate

coefmatrix

vf:[z+y,-x+y-z,z];

nf:coefmatrix([z+y,-x...

C:matrix([1,0,0],[0,1...

Calculate

coefmatrix-gamma-lambda-rank-transpose

eq1:x=lambda;

eq2:y=lambda+mu;

eq3:z=gamma;

Calculate

coefmatrix-echelon-kill-lambda-rank

kill(eq1,eq2,eq3,eq,x...

eq1:x=lambda+alpha+beta;

eq2:y=lambda-alpha+3*...

Calculate

coefmatrix

vf:[z+y,-x+y-z,z];

m1:coefmatrix([vf],[x...

Calculate

coefmatrix-if

j1(x,y,z):= 0*x + 0*y...

j2(x,y,z):= 6.5*x + 2...

j3(x,y,z):= 6.5*x - 2...

Calculate

coefmatrix-determinant-echelon-kill-lambda-rank

kill(eq1,eq2,eq3,eq,x...

eq1:x=lambda+alpha+beta;

eq2:y=lambda-alpha+3*...

Calculate

coefmatrix

j1(x,y,z):= 0*x + 0*y...

j2(x,y,z):= 6.5*x + 2...

j3(x,y,z):= 6.5*x - 2...

Calculate

coefmatrix

Run Example
(%i1)eq1:x=lambda;
(%o1)                             x = lambda
(%i2) eq2:y=lambda+mu;
(%o2)                           y = lambda + mu
(%i3) eq3:z=gamma;
(%o3)                              z = gamma
(%i4) eq4:t=mu;
(%o4)                               t = mu
(%i5) ma:coefmatrix([eq1,eq2,eq3,eq4],[lambda,mu,gamma]);
                               [ - 1   0    0  ]
                               [               ]
                               [ - 1  - 1   0  ]
(%o5)                          [               ]
                               [  0    0   - 1 ]
                               [               ]
                               [  0   - 1   0  ]
(%i6) rank(ma);
(%o6)                                  3
(%i7) transpose(ma);
                            [ - 1  - 1   0    0  ]
                            [                    ]
(%o7)                       [  0   - 1   0   - 1 ]
                            [                    ]
                            [  0    0   - 1   0  ]
(%i8) newma:addcol(ma,[x,y,z,t]);
                             [ - 1   0    0   x ]
                             [                  ]
                             [ - 1  - 1   0   y ]
(%o8)                        [                  ]
                             [  0    0   - 1  z ]
                             [                  ]
                             [  0   - 1   0   t ]
(%i9) determinant:(ma);
                               [ - 1   0    0  ]
                               [               ]
                               [ - 1  - 1   0  ]
(%o9)                          [               ]
                               [  0    0   - 1 ]
                               [               ]
                               [  0   - 1   0  ]
(%i10) 
Run Example
eq1:x:[lambda+alpha+beta];
(%o1)                       [lambda + beta + alpha]
(%i2) eq2:y:[lambda-alpha+3,beta];
(%o2)                     [lambda - alpha + 3, beta]
(%i3) eq3:z:[lambda+2,alpha];
(%o3)                         [lambda + 2, alpha]
(%i4) eq4:t:[2,lambda+3,alpha+beta];
(%o4)                    [2, lambda + 3, beta + alpha]
(%i5) n:matrizasociada:coefmatrix([eq1,eq2,eq3,eq4],[lambda,alpha,beta]);
                                  [ 0  0  0 ]
                                  [         ]
                                  [ 0  0  0 ]
(%o5)                             [         ]
                                  [ 0  0  0 ]
                                  [         ]
                                  [ 0  0  0 ]
(%i6) 
Run Example
coefftheta3(n,k):=(2*n)!/(2^(2*n-2*k)*(2*k)!*(n-k)!)-(-1)^n*kron_delta(n,k);
                                     (2 n)!                  n
(%o1) coefftheta3(n, k) := -------------------------- - (- 1)  kron_delta(n, k)
                            2 n - 2 k
                           2          (2 k)! (n - k)!
(%i2) psi(n):=sum(q[n,ii]*theta3(ii),ii,0,n);
(%o2)             psi(n) := sum(q      theta3(ii), ii, 0, n)
                                 n, ii
(%i3) build_matrices(n):=block(elist: makelist(e(ii),ii,0,n-1),eq: expand(sum(elist[ii+1]*psi(ii),ii,0,n-1)-psi(n)),for i:0 thru n/2 do (eq: subst(0,q[2*i,2*i],eq)),eqlist1: makelist(coeff(eq,theta3(2*ii)),ii,0,floor(n/2)),eqlist1: delete(0,eqlist1),eqlist2: makelist(coeff(eq,theta3(2*ii+1)),ii,0,floor(n/2)),eqlist2: delete(0,eqlist2),return([coefmatrix(eqlist1, elist),coefmatrix(eqlist2, elist)]));
(%o3) build_matrices(n) := block(elist : makelist(e(ii), ii, 0, n - 1), 
eq : expand(sum(elist       psi(ii), ii, 0, n - 1) - psi(n)), 
                     ii + 1
                  n
for i from 0 thru - do eq : subst(0, q        , eq), 
                  2                   2 i, 2 i
                                                         n
eqlist1 : makelist(coeff(eq, theta3(2 ii)), ii, 0, floor(-)), 
                                                         2
eqlist1 : delete(0, eqlist1), eqlist2 : 
                                                   n
makelist(coeff(eq, theta3(2 ii + 1)), ii, 0, floor(-)), 
                                                   2
eqlist2 : delete(0, eqlist2), return([coefmatrix(eqlist1, elist), 
coefmatrix(eqlist2, elist)]))
(%i4) /*slist: makelist(q[2*ii,2*ii]=0,ii,0,n/2),eq: subst(slist,eq),*/build_matrices(3);
                   [ 0  q      q     ]  [ 0  q      q     ]
(%o4)             [[     1, 0   2, 0 ], [     1, 1   2, 1 ]]
                   [                 ]  [                 ]
                   [ 0    0      0   ]  [ 0    0      0   ]
(%i5) build_matrices(5);
       [ 0  q      q      q      q     ]  [ 0  q      q      q      q     ]
       [     1, 0   2, 0   3, 0   4, 0 ]  [     1, 1   2, 1   3, 1   4, 1 ]
       [                               ]  [                               ]
(%o5) [[ 0    0      0    q      q     ], [ 0    0      0    q      q     ]]
       [                   3, 2   4, 2 ]  [                   3, 3   4, 3 ]
       [                               ]  [                               ]
       [ 0    0      0      0      0   ]  [ 0    0      0      0      0   ]
(%i6) 
[addcol,beta,coefmatrix,determinant,echelon,gamma,lambda,rank,row] [addcol,beta,coefmatrix,determinant,echelon,linsolve,rank,transpose] [addcol,beta,coefmatrix,determinant,echelon,rank,row,transpose] [addcol,beta,coefmatrix,determinant,echelon,rank,row] [addcol,beta,coefmatrix,determinant,echelon,rank,transpose] [addcol,beta,coefmatrix,determinant,expand,rank,transpose] [addcol,beta,coefmatrix,determinant,rank,solve,transpose] [addcol,beta,coefmatrix,determinant,rank,transpose] [addcol,beta,coefmatrix,echelon,rank,row,transpose] [addcol,beta,coefmatrix,echelon,rank,transpose] [addcol,beta,coefmatrix,rank,transpose] [addcol,coefmatrix,determinant,echelon,gamma,lambda,matrix,rank,row,transpose] [addcol,coefmatrix,determinant,echelon,gamma,lambda,rank,row] [addcol,coefmatrix,determinant,echelon,gamma,lambda,rank,transpose] [addcol,coefmatrix,determinant,gamma,lambda,rank,transpose] [addcol,coefmatrix,determinant,lambda] [addcol,coefmatrix,determinant,rank,transpose] [addcol,coefmatrix,gamma,lambda,rank,transpose] [addcol,coefmatrix,lambda] [assume,coeff,coefmatrix,determinant,diff,expand,integrate,phi,sin,solve] [assume,coeff,coefmatrix,determinant,diff,integrate,phi,sin,solve] [augcoefmatrix,coefmatrix,col,load,matrix,simpsum,sum] [beta,coefmatrix,determinant,kill,linsolve] [beta,coefmatrix,determinant,kill] [beta,coefmatrix,echelon,rank,row,transpose] [beta,coefmatrix,echelon,rank,row] [beta,coefmatrix,echelon,rank,transpose] [beta,coefmatrix,echelon,rank] [beta,coefmatrix,kill,linsolve,rank] [beta,coefmatrix,kill,rank] [beta,coefmatrix,lambda] [beta,coefmatrix,rank,transpose] [beta,coefmatrix,rank] [beta,coefmatrix] [coefmatrix,determinant,echelon,kill,lambda,rank] [coefmatrix,determinant,linsolve] [coefmatrix,determinant] [coefmatrix,echelon,rank] [coefmatrix,echelon] [coefmatrix,eliminate,length,makelist,rank,triangularize,unique] [coefmatrix,eliminate,length,makelist,rank,triangularize] [coefmatrix,gamma,lambda,rank,transpose] [coefmatrix,gamma,lambda,rank] [coefmatrix,gamma,lambda] [coefmatrix,invert,kill,matrix,transpose] [coefmatrix,invert] [coefmatrix,lambda] [coefmatrix,length,makelist,triangularize] [coefmatrix,rank] [coefmatrix]

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