Folgen, Mengen und Listen (Einführung)

> restart:

> min(1, sqrt(2), sqrt(2)/2);

> f:=expand((x-2)^3 * (x-3) * (x-1));

> roots(f);

> solve(x^4-10*x^3+35*x^2-50*x+24,x);

> solve( {x^2+y^2=13, x^2-y^2=5},{x,y});

> plot( {sin(x), sin(3*x)/3, sin(5*x)/5}, x=0..Pi);

Folgen

> sq :=a,b,c;

> sq := seq(2^n-2*n, n=0..3);

> seq(i^2,i=1.5..3);

> seq(i^2, i=[1.5, 2, 2.5, 3] );

> seq(i^2, i=seq(j*0.5, j=3..6));

> seq(seq(i,i=1..n),n=1..5);

> sq1:=sq,8;

> sq[4];

> sq[2..4];

> sq1[-2..-1];

> sq[2]:=5;

Error, cannot assign to an expression sequence

> sq1:=op( subsop(2=5,[sq1]) );

> sq1:=op( subsop(4=NULL,[sq1]) );

Listen

> lst := [1,2,3];

> lst := [seq(2^n-2*n,n=0..3)];

> lst[2];

> st:= subsop(2=3,lst);

> lst:= [a,b,op(lst),c,d,x,x^2,x^3];

> sort(lst);

> sort( [e,E,Z,b,a]);

> sort( [e,E,Z,b,a,x,x^2,x^3],lexorder);

Error, invalid arguments to sort

Mengen

> st:={0,1,2};

> {1,2,3} union {3,4,5};

> {1,2,3,4,5} intersect {4,5,6};

> {1,2,3,4} minus {1,2};

Geschachtelte Listen und Mengen

> lst:=[{1,2,3},[a,b,c,d,e],x];

> lst[2];

> lst[2][3];

> lst[2][2..4];

> lst[1..2][1];

> lst:=subsop( 2=subsop(3=x, lst[2]),lst );

member und select

> member( 2, [1,2,3]);

> member( x^3, [x, x^2, x^3], 'pos'):

> pos;

> data:=seq(rand(1..20)(),i=1..10);

> select(isprime, [data]);

> select(type,[data],odd);

> select(has,[data],{12,13,14});

map und zip

> [1,2,3] + [4,5,6];

> [1,2,3] - 2*[4,5,6];

> lst:=[1,2,3]: sqrt(lst);

Error, sqrt expects its 1st argument, x, to be of type algebraic, but received [1, 2, 3]

> map(sqrt, lst);

> map( [sin,cos],1);

> map( [sin,cos], [1,2]);

> map( arctan, x,y);

> map(sqrt, [1,2,[3,4]]);

Error, sqrt expects its 1st argument, x, to be of type algebraic, but received [3, 4]

> map( arctan, [x1,x2], [y1,y2]);

Error, arctan expects its 2nd argument, x, to be of type algebraic, but received [y1, y2]

> zip(arctan, [x1,x2], [y1,y2] );

> zip( irem, [12,15,11], [3,4,5]);

> zip( (x,y)->[x,y], [x1,x2,x3], [y1,y2,y3] );

>