5.14.1 Xcas operators: $ %
-
$ is the infixed version of seq (see
Section 5.39.2).
Example
Input:
(2^k)$(k=0..3)
(do not forget to put parenthesis around the arguments)
or:
seq(2^k,k=0..3)
Output:
- mod or % defines a modular number; a mod n is
the equivalence class of a in ℤ/nℤ.
Example
Input:
5 % 7
or:
5 mod 7
Output:
- @ is used to compose functions; (f@g)(x)=f(g(x)).
Example
Input:
(sin@exp)(x)
Output:
- @@ is used to compose a function with itself many times (like
a power, replacing multiplication by composition); for example,
(f@@3)(x)=f(f(f(x))).
Example
Input:
(sin@@4)(x)
Output:
sin | ⎛
⎝ | sin | ⎛
⎝ | sin | ⎛
⎝ | sinx | ⎞
⎠ | ⎞
⎠ | ⎞
⎠ |
- minus, union and intersect return the difference, the union and the
intersection of two sets, respectively. (See Section 4.3.2).
Example
Input:
A := set[1,2,3,4]; |
B := set[3,4,5,6];
|
then:
A minus B
Output:
Input:
A union B
Output:
then:
A intersect B
Output:
- -> is used to define a function, which can be assigned a name.
Example
Input:
(x->x^2)(3)
Output:
Input:
f := x -> x^2
then:
f(3)
Output:
- => is the infixed version of sto (see
Section 4.4.2) and so is used to store an expression in a
variable.
Example
Input:
2 => a
then:
a
Output:
- := is used to store an expression in a variable, but the
variable comes first (the argument order is switched from =>).
Example
Input:
a := 2
then:
a
Output:
- =< to store an expression in a variable, but the storage is
done by reference if the target is a matrix element or a list element.
This is faster if you modify objects inside an existing list or matrix
of large size, because no copy is made, the change is done in place.
Use with care, all objects pointing to this matrix or list will
be modified.
Example
Input:
then:
L[0] =< 5
and:
L
Output:
Input:
L2
Output: