Sponsored links: Algebra eBooks
 

Related

product

product(e**2, i, 1, n);

Calculate

product

product(e**2, i, 1, n);

2*4;

Calculate

product-taylor

taylor(product((1/(1-...

Calculate

product-sum

product(1/(sigma[i] +...

Calculate

product-sum

sum((product(k+1+sum(...

Calculate

product-taylor

taylor(product(1/(1-x...

Calculate

product-taylor

taylor(product((1/(1-...

Calculate

product-sum

sum((product(k+1+sum(...

Calculate

product

product(i,i,1,5);

Calculate

product

product (i, i, 1, 5);

Calculate

product

Run Example
(%i1)I: matrix([1,0],[0,1]);
                                   [ 1  0 ]
(%o1)                              [      ]
                                   [ 0  1 ]
(%i2) S_z: matrix([1,0],[0,-1]);
                                  [ 1   0  ]
(%o2)                             [        ]
                                  [ 0  - 1 ]
(%i3) S_x: matrix([0,1],[1,0]);
                                   [ 0  1 ]
(%o3)                              [      ]
                                   [ 1  0 ]
(%i4) S_y: matrix([0,-%i],[%i,0]);
                                 [ 0   - %i ]
(%o4)                            [          ]
                                 [ %i   0   ]
(%i5) [vals,vecs]:eigenvectors(kronecker_product(S_x,S_y));
(%o5) [[[- 1, 1], [2, 2]], [[[1, 0, 0, - %i], [0, 1, %i, 0]], 
                                             [[1, 0, 0, %i], [0, 1, - %i, 0]]]]
(%i6) 
Run Example
load(draw);
(%o1)            /usr/share/maxima/5.21.1/share/draw/draw.lisp
(%i2) coord: setify(makelist(k,k,-4,4));
(%o2)                 {- 4, - 3, - 2, - 1, 0, 1, 2, 3, 4}
(%i3) points2d: listify(cartesian_product (coord ,coord ));
(%o3) [[- 4, - 4], [- 4, - 3], [- 4, - 2], [- 4, - 1], [- 4, 0], [- 4, 1], 
[- 4, 2], [- 4, 3], [- 4, 4], [- 3, - 4], [- 3, - 3], [- 3, - 2], [- 3, - 1], 
[- 3, 0], [- 3, 1], [- 3, 2], [- 3, 3], [- 3, 4], [- 2, - 4], [- 2, - 3], 
[- 2, - 2], [- 2, - 1], [- 2, 0], [- 2, 1], [- 2, 2], [- 2, 3], [- 2, 4], 
[- 1, - 4], [- 1, - 3], [- 1, - 2], [- 1, - 1], [- 1, 0], [- 1, 1], [- 1, 2], 
[- 1, 3], [- 1, 4], [0, - 4], [0, - 3], [0, - 2], [0, - 1], [0, 0], [0, 1], 
[0, 2], [0, 3], [0, 4], [1, - 4], [1, - 3], [1, - 2], [1, - 1], [1, 0], 
[1, 1], [1, 2], [1, 3], [1, 4], [2, - 4], [2, - 3], [2, - 2], [2, - 1], 
[2, 0], [2, 1], [2, 2], [2, 3], [2, 4], [3, - 4], [3, - 3], [3, - 2], 
[3, - 1], [3, 0], [3, 1], [3, 2], [3, 3], [3, 4], [4, - 4], [4, - 3], 
[4, - 2], [4, - 1], [4, 0], [4, 1], [4, 2], [4, 3], [4, 4]]
(%i4) vf2d(x,y):=  vector ([x,y],[cos(y),x]/6);
                                                [cos(y), x]
(%o4)              vf2d(x, y) := vector([x, y], -----------)
                                                     6
(%i5) vect2: makelist(vf2d(k[1],k[2]),k,points2d );
                           cos(4)    2                        cos(3)    2
(%o5) [vector([- 4, - 4], [------, - -]), vector([- 4, - 3], [------, - -]), 
                             6       3                          6       3
                    cos(2)    2                        cos(1)    2
vector([- 4, - 2], [------, - -]), vector([- 4, - 1], [------, - -]), 
                      6       3                          6       3
                  1    2                      cos(1)    2
vector([- 4, 0], [-, - -]), vector([- 4, 1], [------, - -]), 
                  6    3                        6       3
                  cos(2)    2                      cos(3)    2
vector([- 4, 2], [------, - -]), vector([- 4, 3], [------, - -]), 
                    6       3                        6       3
                  cos(4)    2                        cos(4)    1
vector([- 4, 4], [------, - -]), vector([- 3, - 4], [------, - -]), 
                    6       3                          6       2
                    cos(3)    1                        cos(2)    1
vector([- 3, - 3], [------, - -]), vector([- 3, - 2], [------, - -]), 
                      6       2                          6       2
                    cos(1)    1                      1    1
vector([- 3, - 1], [------, - -]), vector([- 3, 0], [-, - -]), 
                      6       2                      6    2
                  cos(1)    1                      cos(2)    1
vector([- 3, 1], [------, - -]), vector([- 3, 2], [------, - -]), 
                    6       2                        6       2
                  cos(3)    1                      cos(4)    1
vector([- 3, 3], [------, - -]), vector([- 3, 4], [------, - -]), 
                    6       2                        6       2
                    cos(4)    1                        cos(3)    1
vector([- 2, - 4], [------, - -]), vector([- 2, - 3], [------, - -]), 
                      6       3                          6       3
                    cos(2)    1                        cos(1)    1
vector([- 2, - 2], [------, - -]), vector([- 2, - 1], [------, - -]), 
                      6       3                          6       3
                  1    1                      cos(1)    1
vector([- 2, 0], [-, - -]), vector([- 2, 1], [------, - -]), 
                  6    3                        6       3
                  cos(2)    1                      cos(3)    1
vector([- 2, 2], [------, - -]), vector([- 2, 3], [------, - -]), 
                    6       3                        6       3
                  cos(4)    1                        cos(4)    1
vector([- 2, 4], [------, - -]), vector([- 1, - 4], [------, - -]), 
                    6       3                          6       6
                    cos(3)    1                        cos(2)    1
vector([- 1, - 3], [------, - -]), vector([- 1, - 2], [------, - -]), 
                      6       6                          6       6
                    cos(1)    1                      1    1
vector([- 1, - 1], [------, - -]), vector([- 1, 0], [-, - -]), 
                      6       6                      6    6
                  cos(1)    1                      cos(2)    1
vector([- 1, 1], [------, - -]), vector([- 1, 2], [------, - -]), 
                    6       6                        6       6
                  cos(3)    1                      cos(4)    1
vector([- 1, 3], [------, - -]), vector([- 1, 4], [------, - -]), 
                    6       6                        6       6
                  cos(4)                         cos(3)
vector([0, - 4], [------, 0]), vector([0, - 3], [------, 0]), 
                    6                              6
                  cos(2)                         cos(1)
vector([0, - 2], [------, 0]), vector([0, - 1], [------, 0]), 
                    6                              6
                1                       cos(1)
vector([0, 0], [-, 0]), vector([0, 1], [------, 0]), 
                6                         6
                cos(2)                       cos(3)
vector([0, 2], [------, 0]), vector([0, 3], [------, 0]), 
                  6                            6
                cos(4)                         cos(4)  1
vector([0, 4], [------, 0]), vector([1, - 4], [------, -]), 
                  6                              6     6
                  cos(3)  1                      cos(2)  1
vector([1, - 3], [------, -]), vector([1, - 2], [------, -]), 
                    6     6                        6     6
                  cos(1)  1                    1  1
vector([1, - 1], [------, -]), vector([1, 0], [-, -]), 
                    6     6                    6  6
                cos(1)  1                    cos(2)  1
vector([1, 1], [------, -]), vector([1, 2], [------, -]), 
                  6     6                      6     6
                cos(3)  1                    cos(4)  1
vector([1, 3], [------, -]), vector([1, 4], [------, -]), 
                  6     6                      6     6
                  cos(4)  1                      cos(3)  1
vector([2, - 4], [------, -]), vector([2, - 3], [------, -]), 
                    6     3                        6     3
                  cos(2)  1                      cos(1)  1
vector([2, - 2], [------, -]), vector([2, - 1], [------, -]), 
                    6     3                        6     3
                1  1                    cos(1)  1
vector([2, 0], [-, -]), vector([2, 1], [------, -]), 
                6  3                      6     3
                cos(2)  1                    cos(3)  1
vector([2, 2], [------, -]), vector([2, 3], [------, -]), 
                  6     3                      6     3
                cos(4)  1                      cos(4)  1
vector([2, 4], [------, -]), vector([3, - 4], [------, -]), 
                  6     3                        6     2
                  cos(3)  1                      cos(2)  1
vector([3, - 3], [------, -]), vector([3, - 2], [------, -]), 
                    6     2                        6     2
                  cos(1)  1                    1  1
vector([3, - 1], [------, -]), vector([3, 0], [-, -]), 
                    6     2                    6  2
                cos(1)  1                    cos(2)  1
vector([3, 1], [------, -]), vector([3, 2], [------, -]), 
                  6     2                      6     2
                cos(3)  1                    cos(4)  1
vector([3, 3], [------, -]), vector([3, 4], [------, -]), 
                  6     2                      6     2
                  cos(4)  2                      cos(3)  2
vector([4, - 4], [------, -]), vector([4, - 3], [------, -]), 
                    6     3                        6     3
                  cos(2)  2                      cos(1)  2
vector([4, - 2], [------, -]), vector([4, - 1], [------, -]), 
                    6     3                        6     3
                1  2                    cos(1)  2
vector([4, 0], [-, -]), vector([4, 1], [------, -]), 
                6  3                      6     3
                cos(2)  2                    cos(3)  2
vector([4, 2], [------, -]), vector([4, 3], [------, -]), 
                  6     3                      6     3
                cos(4)  2
vector([4, 4], [------, -])]
                  6     3
(%i6) apply(draw2d , append ([ color=blue], vect2 ));
(%o6) [gr2d(vector, vector, vector, vector, vector, vector, vector, vector, 
vector, vector, vector, vector, vector, vector, vector, vector, vector, 
vector, vector, vector, vector, vector, vector, vector, vector, vector, 
vector, vector, vector, vector, vector, vector, vector, vector, vector, 
vector, vector, vector, vector, vector, vector, vector, vector, vector, 
vector, vector, vector, vector, vector, vector, vector, vector, vector, 
vector, vector, vector, vector, vector, vector, vector, vector, vector, 
vector, vector, vector, vector, vector, vector, vector, vector, vector, 
vector, vector, vector, vector, vector, vector, vector, vector, vector, 
vector)]
(%i7) 
Run Example
product(sum(f(n,(10*k+1),10*n-(2*k+1))*(is(equal(primep((2*k+1))*primep(2*n-(2*k+1)),true^2))-unknown)/(true-unknown),k, 18000, 19000),n,10^30,10^30);
(%o1) f(1000000000000000000000000000000, 189751, 
9999999999999999999999999962049) + f(1000000000000000000000000000000, 185011, 
9999999999999999999999999962997)
(%i2) 
[append,apply,cartesian_product,cos,draw,listify,load,makelist,product,setify] [append,block,do,expand,hipow,length,makelist,part,print,product,rat,return,sqrt,unique] [append,block,do,integer_partitions,print,product] [append,float,fpprintprec,makelist,phi,plot2d,product,realroots,sum] [append,float,fpprintprec,makelist,plot2d,product,sum] [asin,cos,float,print,product,sin,sqrt] [bfloat,cos,fpprec,pi,product,sqrt] [bfloat,fpprec,product,sin,sqrt] [block,ceiling,product,sum] [block,first,ifactors,lambda,length,lmax,makelist,map,phi,product] [block,first,ifactors,lambda,length,map,phi,product,rest] [block,float,product,sin,sqrt] [cardinality,cartesian_product,product] [cartesian_product,expand,listify,map,powerset,product,transpose] [cartesian_product,full_listify,length,listify,product,setify] [cartesian_product,lambda,makelist,product,setify,subset] [cartesian_product,listify,map,product,reverse,transpose] [cartesian_product,listify,map,product,transpose] [cartesian_product,powerset,product] [cartesian_product,product] [coeff,factor,if,product,ratsimp,sum] [cos,float,product] [cos,numer,product,sqrt] [cos,pi,product,sqrt] [cos,product,sqrt] [determinant,invert,kronecker_product,matrix,product] [determinant,kronecker_product,matrix,product] [diff,product,sum] [diff,product] [equal,is,primep,product,sum,unknown] [expand,factor,product,simpsum,true] [expand,length,product,realroots,solve] [expand,makelist,product,ratsubst] [expand,product,ratsubst] [expand,product] [factor,kronecker_product,matrix,product,sqrt,transpose] [first,ifactors,lambda,map,phi,product,rest] [float,product,sin,sqrt] [integrate,product] [invert,kronecker_product,matrix,product] [kronecker_product,matrix,product,sqrt] [kronecker_product,matrix,product] [load,product] [pi,product] [plot2d,product,sin] [plot2d,product,sum] [product,sin,sqrt] [product,sum] [product,taylor] [product]

Related Help

Help for Product