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trigreduce

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trigreduce

Run Example
(%i1)expr : (x - a)^2*(y - b)*(z - c);
                                  2
(%o1)                      (x - a)  (y - b) (z - c)
(%i2) expand(expr);
       2                    2          2                  2          2
(%o2) x  y z - 2 a x y z + a  y z - b x  z + 2 a b x z - a  b z - c x  y
                                            2            2                2
                             + 2 a c x y - a  c y + b c x  - 2 a b c x + a  b c
(%i3) expr : (y + 1)^3/(y+1)^2;
(%o3)                                y + 1
(%i4) expand(expr);
(%o4)                                y + 1
(%i5) factor(126);
                                       2
(%o5)                               2 3  7
(%i6) factor(x^3 - 1);
                                       2
(%o6)                        (x - 1) (x  + x + 1)
(%i7) factor(2^63 - 1);
                           2
(%o7)                     7  73 127 337 92737 649657
(%i8) factor(-8*y - 4*x + z^2*(2*y + x));
(%o8)                      (2 y + x) (z - 2) (z + 2)
(%i9) ex : (3+x)*(2+2*x)/(1-x^2);
                               (x + 3) (2 x + 2)
(%o9)                          -----------------
                                         2
                                    1 - x
(%i10) fullratsimp(ex);
                                     2 x + 6
(%o10)                             - -------
                                      x - 1
(%i11) ex : ((x^(a/2) - 1)^2*(x^(a/2) + 1)^2)/(x^a - 1);
                              a/2     2   a/2     2
                            (x    - 1)  (x    + 1)
(%o11)                      -----------------------
                                     a
                                    x  - 1
(%i12) fullratsimp(ex);
                                     a
(%o12)                              x  - 1
(%i13) fullratsimp(ex);
                                     a
(%o13)                              x  - 1
(%i14) exp : (sin(x))^2 + 3* (cos(x))^2;
                                 2           2
(%o14)                        sin (x) + 3 cos (x)
(%i15) trigexpand(exp);
                                 2           2
(%o15)                        sin (x) + 3 cos (x)
(%i16) form : (cos(x))^4 + (cos(x))^3 + (cos(x))^2 + cos(x) + 1;
                      4         3         2
(%o16)             cos (x) + cos (x) + cos (x) + cos(x) + 1
(%i17) trigreduce(form);
       cos(4 x) + 4 cos(2 x) + 3   cos(3 x) + 3 cos(x)   cos(2 x) + 1
(%o17) ------------------------- + ------------------- + ------------ + cos(x)
                   8                        4                 2
                                                                            + 1
(%i18) 
Run Example
eq3: Lq*cos(x)^2+Ld*sin(x)^2;
                                  2            2
(%o1)                       Ld sin (x) + Lq cos (x)
(%i2) trigsimp(eq3);
                                         2
(%o2)                       (Lq - Ld) cos (x) + Ld
(%i3) trigreduce(eq3);
                      Lq cos(2 x)   Ld cos(2 x)   Lq   Ld
(%o3)                 ----------- - ----------- + -- + --
                           2             2        2    2
(%i4) T:matrix([cos(x),sin(x),0],[-sin(x),cos(x),0],[0,0,1]);
                            [  cos(x)   sin(x)  0 ]
                            [                     ]
(%o4)                       [ - sin(x)  cos(x)  0 ]
                            [                     ]
                            [    0        0     1 ]
(%i5) Tinv:invert(T);
                 [      cos(x)               sin(x)          ]
                 [ -----------------  - -----------------  0 ]
                 [    2         2          2         2       ]
                 [ sin (x) + cos (x)    sin (x) + cos (x)    ]
                 [                                           ]
(%o5)            [      sin(x)              cos(x)           ]
                 [ -----------------   -----------------   0 ]
                 [    2         2         2         2        ]
                 [ sin (x) + cos (x)   sin (x) + cos (x)     ]
                 [                                           ]
                 [         0                   0           1 ]
(%i6) L:matrix([Lq,0,0],[0,Ld,0],[0,0,Ls]);
                                [ Lq  0   0  ]
                                [            ]
(%o6)                           [ 0   Ld  0  ]
                                [            ]
                                [ 0   0   Ls ]
(%i7) T*L;
                         [ Lq cos(x)      0      0  ]
                         [                          ]
(%o7)                    [     0      Ld cos(x)  0  ]
                         [                          ]
                         [     0          0      Ls ]
(%i8) T*L*Tinv;
                 [          2                               ]
                 [    Lq cos (x)                            ]
                 [ -----------------          0          0  ]
                 [    2         2                           ]
                 [ sin (x) + cos (x)                        ]
                 [                                          ]
(%o8)            [                             2            ]
                 [                       Ld cos (x)         ]
                 [         0          -----------------  0  ]
                 [                       2         2        ]
                 [                    sin (x) + cos (x)     ]
                 [                                          ]
                 [         0                  0          Ls ]
(%i9) 
Run Example
p: trigreduce(sin(3*x));
(%o1)                              sin(3 x)
(%i2) 
[atan2,collectterms,cos,expand,float,log,plot2d,sin,tan,trigexpand,trigreduce] [block,cos,diff,expand,horner,ratdisrep,subst,sum,taylor,trigreduce] [block,integrate,phi,ratsimp,sin,subst,taylor,trigreduce] [col,cos,matrix,pi,ratsimp,sin,tex,trigreduce] [collectterms,cos,diff,sin,trigreduce] [constant,cos,declare,globalsolve,lhs,multthru,realonly,rhs,sin,trigreduce,true] [cos,cot,diff,expand,ratsimp,sin,sqrt,subst,trigexpand,trigreduce] [cos,diff,divide,ev,first,second,sin,sqrt,third,trigrat,trigreduce] [cos,diff,ev,first,second,sin,sqrt,third,trigrat,trigreduce] [cos,diff,ev,first,second,sqrt,trigrat,trigreduce] [cos,diff,expand,sin,sqrt,subst,tan,trigexpand,trigreduce] [cos,diff,false,sin,trigreduce] [cos,diff,first,second,trigrat,trigreduce] [cos,diff,phi,psi,rhs,sin,solve,subst,trigreduce] [cos,diff,sin,trigreduce,trigsimp] [cos,diff,sin,trigreduce] [cos,display2d,false,sin,solve,trigrat,trigreduce] [cos,display2d,false,sin,solve,trigreduce,trigsimp] [cos,display2d,false,sin,trigexpand,trigreduce,trigsimp] [cos,eliminate,solve,trigreduce] [cos,expand,factor,fullratsimp,sin,trigexpand,trigreduce] [cos,expand,load,sin,trigexpand,trigreduce,trigsimp] [cos,expand,load,sin,trigreduce,trigsimp] [cos,expand,num,trigexpand,trigreduce] [cos,expand,sin,subst,trigexpand,trigreduce] [cos,expand,sin,trigreduce] [cos,expand,trigexpand,trigreduce,trigsimp] [cos,expand,trigreduce] [cos,factor,trigreduce] [cos,load,sin,sqrt,trigexpand,trigrat,trigreduce,trigsimp] [cos,load,sin,sqrt,trigexpand,trigreduce,trigsimp] [cos,matrix,pi,ratsimp,sin,tex,trigreduce] [cos,matrix,sin,trigreduce] [cos,ratsimp,sin,trigreduce] [cos,sin,solve,trigreduce] [cos,sin,sqrt,trigreduce] [cos,sin,trigexpand,trigreduce] [cos,sin,trigreduce] [cos,trigexpand,trigreduce] [cos,trigreduce] [is,trigreduce,trigsimp] [linsolve,rhs,sin,trigreduce] [linsolve,sin,trigexpand,trigreduce] [linsolve,sin,trigreduce] [sin,tan,trigreduce,trigsimp] [sin,tan,trigreduce] [sin,trigexpand,trigreduce,trigsimp] [sin,trigexpand,trigreduce] [sin,trigreduce] [trigreduce]

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