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2.3 Rational Expression ¶

Command: num expr ¶

The function num takes a rational expression as input and returns a numerator of the expression.

(%0013) num((x^2+y^2)/(x^2-y^2));
          2    2
%0013: - x  - y
(%0014) num(7/4);
%0014: 7
(%0015) num(7/(4/3));
%0015: 21

Operator: denom rational-expression ¶

The Jacal command denom is used to obtain the denominator of a rational expression.

(%0016) denom(4/5);
%0016: 5
(%0017) denom((x^2+y^2)/(x^2-y^2));
          2    2
%0017: - x  + y

Command: listofvars expr ¶

The command listofvars takes as input a rational expression and returns a list of the variables that occur in that expression.

(%0018) listofvars(x^2+y^3);
%0018: [x, y]
(%0019) listofvars((x^2+y^3)/(2*x^7+y*x+z));
%0019: [x, y, z]

Command: imagpart z ¶

Returns the coefficient of %i in expression z;

Command: realpart z ¶

Returns all but the coefficient of %i in expression z;

Command: abs z ¶

Command: cabs z ¶

| z |

Returns the square root of the sum of the squares of the realpart and the imagpart of z.

(%0020) abs(z);
%0020: |z|
(%0021) abs(-z);
%0021: |- z|
(%0022) abs(-3);
%0022: 3
(%0023) abs(1/%i);
%0023: 1
(%0024) realpart(1/%i);
%0024: 0
(%0025) imagpart(1/%i);
%0025: -1
(%0026) imagpart(3/%i);
%0026: -3