集合,等比數列,等差數列,permutation,combination

 集合(Set)
U:{1,2,3,4,5,6,7,8,9,10};
A:{1,2,4,6};B:{1,3,4};

cardinality(U);

cardinality(A);

cardinality(B);

AuB:union(A,B);

AnB:intersect(A,B);

powerset(A);

cardinality(%);

Ap:setdifference(U,A);

Bp:setdifference(U,B);

AminusB:setdifference(A,B);

BminusA:setdifference(B,A);

ApnBp:intersect(Ap,Bp);

ApuBp:union(Ap,Bp);

setequalp (a, b)

Returns true if sets a and b have the same number of elements and is(x = y) is true for x in the elements of a and y in the elements of b, considered in the order determined by listify. Otherwise, setequalp returns false.

setequalp(setdifference(U,AuB),ApnBp);

 setequalp(setdifference(U,AnB),ApuBp);

disjoin(A,B); 

disjoin(B,A); 

 http://maxima.sourceforge.net/docs/manual/maxima_35.html#SEC188

排列(permutation), 組合(combination)

Function: permutation (n, r)

Returns the number of permutations of r objects selected from a set of n objects.
To use this function write first load(functs).

Function: combination (n, r)

Returns the number of combinations of n objects taken r at a time.
To use this function write first load(functs).

Categories:  Package functs · Mathematical functions

 load(functs);
 permutation(5,3);

combination(5,3);

級數和

Function: arithmetic (a, d, n)

Returns the n-th term of the arithmetic series a, a + d, a + 2*d, ..., a + (n - 1)*d.
To use this function write first load(functs).

Categories:  Package functs · Sums and products

Function: geometric (a, r, n)

Returns the n-th term of the geometric series a, a*r, a*r^2, ..., a*r^(n - 1).
To use this function write first load(functs).

Categories:  Package functs · Sums and products

Function: harmonic (a, b, c, n)

Returns the n-th term of the harmonic series a/b, a/(b + c), a/(b + 2*c), ..., a/(b + (n - 1)*c).
To use this function write first load(functs).

Categories:  Package functs · Sums and products

Function: arithsum (a, d, n)

Returns the sum of the arithmetic series from 1 to n.
To use this function write first load(functs).

Categories:  Package functs · Sums and products

Function: geosum (a, r, n)

Returns the sum of the geometric series from 1 to n. If n is infinity (inf) then a sum is finite only if the absolute value of r is less than 1.
To use this function write first load(functs).
  
load(functs);
 a:1;d:2;n:10;
arithmetic(a,d,n); 
/*an=a+(n-1)d*/
a+(n-1)*d;


r:2;n:10;
geometric (a, r, n)  ;
/*an=ar^(n-1)*/
a*r^(n-1);


b:2;c:3;
harmonic (a, b, c, n);

d:2;n:10;
 arithsum (a, d, n);
/*a+(a+d)+(a+2d)+...+(a+(n-1)d) */
/*Sn=n/2(2a+(n-1)d) */
n/2*(2*a+(n-1)*d);

r:2;n:10;
 geosum (a, r, n);
/*a+ar+ar^2+...+ar^(n-1) */ 
/* Sn=a(1-r^n)/(1-r) */
a*(1-r^n)/(1-r);