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2.9 Referencing results and special numbers

An @ used for an escape character; rules currently in force are as follows.

@n

The evaluated result of n-th input command

@@

The evaluated result of the last command

@i

The unit of imaginary number, square root of -1.

@pi

The number pi, the ratio of a circumference of the circle and its diameter.

@e

Napier’s number, the base of natural logarithm.

@

A generator of GF(2^m), a finite field of characteristic 2, over GF(2). It is a root of an irreducible univariate polynomial over GF(2) which is set as the defining polynomial of GF(2^m).

@>, @<, @>=, @<=, @==, @&&, @||

Fist order logical operators. They are used in quantifier elimination.

[0] fctr(x^10-1);     
[[1,1],[x-1,1],[x+1,1],[x^4+x^3+x^2+x+1,1],[x^4-x^3+x^2-x+1,1]]
[1] @@[3];            
[x^4+x^3+x^2+x+1,1]
[2] eval(sin(@pi/2)); 
1.000000000000000000000000000000000000000000000000000000000
[3] eval(log(@e),20);
0.99999999999999999999999999998
[4] @0[4][0];
x^4-x^3+x^2-x+1
[5] (1+@i)^5;
(-4-4*@i)
[6] eval(exp(@pi*@i));
-1.0000000000000000000000000000
[7] (@+1)^9;
(@^9+@^8+@+1)

As you can see in the above example, results of toplevel computation can be referred to by @ convention. This is convenient for users, while it sometimes imposes a heavy burden to the garbage collector. It may happen that GC time will rapidly increase after computing a very large expression at the toplevel. In such cases delete_history() (see section delete_history) takes effect.


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