%pi SciMax Toolbox %rnum_list

SciMax Toolbox >> %piargs

%piargs

Option variable

%piargs

Description

Default value: true

When %piargs is true, trigonometric functions are simplified to algebraic constants when the argument is an integer multiple of %pi, %pi/2, %pi/3, %pi/4, or %pi/6

Maxima knows some identities which can be applied when %pi, etc., are multiplied by an integer variable (that is, a symbol declared to be integer).

Examples:

(%i1) %piargs : false;
(%o1)                         false
(%i2) [sin (%pi), sin (%pi/2), sin (%pi/3)];
                                %pi       %pi
(%o2)            [sin(%pi), sin(---), sin(---)]
                                 2         3
(%i3) [sin (%pi/4), sin (%pi/5), sin (%pi/6)];
                      %pi       %pi       %pi
(%o3)            [sin(---), sin(---), sin(---)]
                       4         5         6
(%i4) %piargs : true;
(%o4)                         true
(%i5) [sin (%pi), sin (%pi/2), sin (%pi/3)];
                                sqrt(3)
(%o5)                    [0, 1, -------]
                                   2
(%i6) [sin (%pi/4), sin (%pi/5), sin (%pi/6)];
                         1         %pi   1
(%o6)                [-------, sin(---), -]
                      sqrt(2)       5    2
(%i7) [cos (%pi/3), cos (10*%pi/3), tan (10*%pi/3), cos (sqrt(2)*%pi/3)];
                1    1               sqrt(2) %pi
(%o7)          [-, - -, sqrt(3), cos(-----------)]
                2    2                    3

Some identities are applied when %pi and %pi/2 are multiplied by an integer variable.

(%i1) declare (n, integer, m, even);
(%o1)                         done
(%i2) [sin (%pi * n), cos (%pi * m), sin (%pi/2 * m), cos (%pi/2 * m)];
                                      m/2
(%o2)                  [0, 1, 0, (- 1)   ]
%pi SciMax Toolbox %rnum_list