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product

product(1-a, i, 1, 3);

Calculate

product-ratsimp-sum

a(n):=product(n+k,k,0...

a(3);

s(n):=sum(a(k),k,1,n);

Calculate

product

product (i, i, 0, 500...

Calculate

product-sum

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

Calculate

product

eq1: product(e**2, i,...

Calculate

product

product(k,k,1, n);

2*4;

Calculate

product

product(((n^2+2*n-4)/...

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product

product(k^(n-k),k,1, 3);

2*4;

Calculate

product

dens: K(d, f(d, t));

foo: product(dens/(t_...

Calculate

product

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

2*4;

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
a(n):=product(n+k,k,0,10)/11!;
                               product(n + k, k, 0, 10)
(%o1)                  a(n) := ------------------------
                                         11!
(%i2) simpsum:true;
(%o2)                                true
(%i3) s(n):=sum(a(k),k,1,n);
(%o3)                     s(n) := sum(a(k), k, 1, n)
(%i4) factor(s(n));
(%o4) (n (n + 1) (n + 2) (n + 3) (n + 4) (n + 5) (n + 6) (n + 7) (n + 8)
                                           (n + 9) (n + 10) (n + 11))/479001600
(%i5) g(n):=12^(1/3)*(23100*(s(n)+10))^(1/12)-11/2;
                            1/3                    1/12   11
(%o5)             g(n) := 12    (23100 (s(n) + 10))     - --
                                                          2
(%i6) expand(g(n));
                                       12         11       10         9
       1/6  1/6   1/3    1/12         n          n        n       11 n
(%o6) 2    5    12    231     expt(--------- + ------- + ------ + ------
                                   479001600   7257600   248832   161280
          8         7           6           5           4           3
   10831 n    1903 n    242537 n    139381 n    341747 n    190553 n
 + -------- + ------- + --------- + --------- + --------- + ---------
   14515200   345600     8709120     1451520     1555200     604800
          2
   83711 n    n        1     11
 + -------- + -- + 10, --) - --
    332640    12       12    2
(%i7) h(n):=n-g(n);
(%o7)                          h(n) := n - g(n)
(%i8) diff(h(n),n);
               11        10        9        7        5        3
           24 n   + 132 n   + 220 n  - 264 n  + 264 n  - 132 n  + 20 n
(%o8) 1 - (-----------------------------------------------------------
                                       24
        10         9         8         6         4        2
   330 n   + 1650 n  + 2475 n  - 2310 n  + 1650 n  - 495 n  + 25         9
 + ------------------------------------------------------------- + 1320 n
                                 6
          8           7           6           4          2
   54450 n  + 217800 n  + 254100 n  - 127050 n  + 36300 n  - 1815         8
 + -------------------------------------------------------------- + 5940 n
                                 3
            7            6            5            3
   1262184 n  + 4417644 n  + 4417644 n  - 1472548 n  + 210364 n         7
 + ------------------------------------------------------------ + 7920 n
                                8
            6            5            4           2
   1804110 n  + 5412330 n  + 4510275 n  - 902055 n  + 42955
 + --------------------------------------------------------
                              2
             5             4             3
   20501580 n  + 51253950 n  + 34169300 n  - 3416930 n         5
 + --------------------------------------------------- - 5544 n
                            6
             4             3             2
   25228500 n  + 50457000 n  + 25228500 n  - 840950             3             2
 + ------------------------------------------------ + 12756216 n  + 29759004 n
                          3
                                                               12       11       10       8       6       4       2       11        10        9        7        5        3                          9          8          7          5          3                             8           7           6           4           2                    7           6           5           3                      6             5            4            2                     5             4            3
                           11/6  11/6   11/3    11/12       2 n   + 12 n   + 22 n   - 33 n  + 44 n  - 33 n  + 10 n    30 n   + 165 n   + 275 n  - 330 n  + 330 n  - 165 n  + 25 n        10   6050 n  + 27225 n  + 36300 n  - 25410 n  + 12100 n  - 1815 n        9   157773 n  + 631092 n  + 736274 n  - 368137 n  + 105182 n         8   257730 n  + 902055 n  + 902055 n  - 300685 n  + 42955 n   3416930 n  + 10250790 n  + 8542325 n  - 1708465 n         6   5045700 n  + 12614250 n  + 8409500 n  - 840950 n            4            3             2
 + 20633832 n + 3585840)/(2     5     12     231      expt((------------------------------------------------------- + ----------------------------------------------------------- + 132 n   + ------------------------------------------------------------ + 660 n  + --------------------------------------------------------- + 990 n  + ------------------------------------------------------- + -------------------------------------------------- - 924 n  + ------------------------------------------------ + 3189054 n  + 9919668 n  + 10316916 n  + 3585840 n)/39916800 + 10, 
                                                                                      24                                                           6                                                                       3                                                                      8                                                                   2                                                      6                                                            3
11
--))
12
(%i9) factor(479001600);
                                 10  5  2
(%o9)                           2   3  5  7 11
(%i10) factor(11!);
                                  8  4  2
(%o10)                           2  3  5  7 11
(%i11) 
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) 
[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] [binomial,coeff,do,expand,float,length,limit,makelist,print,product,reverse] [block,ceiling,product,sum] [block,first,ifactors,lambda,length,lmax,makelist,map,phi,product] [block,float,product,sin,sqrt] [cardinality,cartesian_product,intersect,powerset,product,union] [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,lambda,mod,product,subset] [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] [diff,expand,factor,product,simpsum,true] [diff,product,sum] [diff,product] [equal,is,primep,product,sum,unknown] [expand,product,ratsubst] [expand,product] [factor,kronecker_product,matrix,product,sqrt,transpose] [float,fpprintprec,product] [float,product,sin,sqrt] [if,lambda,product] [imagpart,plot2d,product,quotient,realpart,rectform,sum] [integrate,product] [invert,kronecker_product,matrix,product] [kronecker_product,matrix,permanent,product] [kronecker_product,matrix,product,sqrt] [kronecker_product,matrix,product] [limit,product] [load,product] [pi,product] [plot2d,product,sin] [product,sin,sqrt] [product,sum] [product,taylor] [product]

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