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args-determinant-expand-factor-ident-matrix-solve-transpose

A:matrix([1,-1],[-4,4]);

B:A-t*ident(2);

C:determinant(B);

Calculate

args-cos-load-matrix-plot2d-sin-sqrt
plot2d(A(a), [a, -12, 12]);

l1:105.005;

l2:107.011;

Hx:1114.34;

Calculate

args-genmatrix-kill-powerdisp-transpose-true

""/* MATRIZENMULTIPLI...

kill(all);

powerdisp:true;

Calculate

args-determinant-expand-factor-ident-invert-matrix-solve-sqrt-transpose

A: matrix([1,1],[1,1]);

B:A-t*ident(2);

C:determinant(B);

Calculate

args-isolate

eq: x!*(x-y)!/(y-1)!;

isolate(eq,x);

isolate(eq,y);

Calculate

args-cos-determinant-diff-ev-flatten-float-matrix-sin-sqrt-transpose

Rx(t) := matrix ([1, ...

Ry(t) := matrix ([cos...

Rz(t) := matrix ([cos...

Calculate

args

args(a+b*c+d^2+2);

args(a*b);

Calculate

args-inpart-op

f(x):= x^2;

op(f(x));

args(f(x));

Calculate

args

Run Example
(%i1)modulus:2;
(%o1)                                  2
(%i2)  N:2;
(%o2)                                  2
(%i3)   block( P:0, Vars:[], Sol:zeromatrix(N,N), for i: 1 thru N do ( for j: 1 thru N do ( S:zeromatrix(N+2,N+2), S[i ][j ]:1, S[i ][j+1]:1,  S[i ][j+2]:1, S[i+1][j ]:1, S[i+1][j+2]:1, S[i+2][j ]:1, S[i+2][j+1]:1, S[i+2][j+2]:1, S:submatrix (1,N+2,S,1,N+2), P:P+V[i*N+j]*S, Vars: append(Vars, [V[i*N+j]]), Sol[i][j]:V[i*N+j]) ) );
(%o3)                                done
(%i4)  P;
                        [ V  + V  + V   V  + V  + V  ]
                        [  6    5    4   6    5    3 ]
(%o4)                   [                            ]
                        [ V  + V  + V   V  + V  + V  ]
                        [  6    4    3   5    4    3 ]
(%i5)  Vars;
(%o5)                          [V , V , V , V ]
                                 3   4   5   6
(%i6)  R:zeromatrix(N,N)+1;
                                   [ 1  1 ]
(%o6)                              [      ]
                                   [ 1  1 ]
(%i7)  LGS:xreduce('append ,args(P-R));
(%o7) [V  + V  + V  - 1, V  + V  + V  - 1, V  + V  + V  - 1, V  + V  + V  - 1]
        6    5    4       6    5    3       6    4    3       5    4    3
(%i8)  Res:algsys(LGS, Vars);
(%o8)                 [[V  = 1, V  = 1, V  = 1, V  = 1]]
                         3       4       5       6
(%i9)  append([l=Sol],Res[1]);
                    [ V   V  ]
                    [  3   4 ]
(%o9)          [l = [        ], V  = 1, V  = 1, V  = 1, V  = 1]
                    [ V   V  ]   3       4       5       6
                    [  5   6 ]
(%i10) 
Run Example
Rx(t) := matrix ([1, 0, 0], [0, cos(t), -sin(t)], [0, sin(t), cos(t)]);
(%o1) Rx(t) := matrix([1, 0, 0], [0, cos(t), - sin(t)], [0, sin(t), cos(t)])
(%i2) Ry(t) := matrix ([cos(t), 0, sin(t)], [0, 1, 0], [-sin(t), 0, cos(t)]);
(%o2) Ry(t) := matrix([cos(t), 0, sin(t)], [0, 1, 0], [- sin(t), 0, cos(t)])
(%i3) Rz(t) := matrix ([cos(t), -sin(t), 0], [sin(t), cos(t), 0], [0, 0, 1]);
(%o3) Rz(t) := matrix([cos(t), - sin(t), 0], [sin(t), cos(t), 0], [0, 0, 1])
(%i4) Rxyz(a, b, c) := Rx(a) . Ry(b) . Rz(c);
(%o4)              Rxyz(a, b, c) := Rx(a) . (Ry(b) . Rz(c))
(%i5) x:float([3, 4, 2]/sqrt(9 + 16 + 4));
(%o5)        [0.55708601453116, 0.74278135270821, 0.3713906763541]
(%i6) y:flatten(args(Rz(0.1) . x));
(%o6)        [0.48014850461422, 0.79468634003232, 0.3713906763541]
(%i7) F : flatten (args (Rxyz(a,b,c).x - y));
(%o7) [- 0.74278135270821 cos(b) sin(c) + 0.55708601453116 cos(b) cos(c)
 + 0.3713906763541 sin(b) - 0.48014850461422, 
0.74278135270821 (cos(a) cos(c) - sin(a) sin(b) sin(c))
 + 0.55708601453116 (cos(a) sin(c) + sin(a) sin(b) cos(c))
 - 0.3713906763541 sin(a) cos(b) - 0.79468634003232, 
0.74278135270821 (cos(a) sin(b) sin(c) + sin(a) cos(c))
 + 0.55708601453116 (sin(a) sin(c) - cos(a) sin(b) cos(c))
 + 0.3713906763541 cos(a) cos(b) - 0.3713906763541]
(%i8) ev(F, a=0, b=0, c=0.1);
(%o8)                 [1.3877787807814457E-17, 0.0, 0.0]
(%i9) DF : transpose (matrix (diff(F, a), diff(F, b), diff(F, c)));
(%o9) matrix([0, 0.74278135270821 sin(b) sin(c)
 - 0.55708601453116 sin(b) cos(c) + 0.3713906763541 cos(b), 
- 0.55708601453116 cos(b) sin(c) - 0.74278135270821 cos(b) cos(c)], 
[0.74278135270821 (- cos(a) sin(b) sin(c) - sin(a) cos(c))
 + 0.55708601453116 (cos(a) sin(b) cos(c) - sin(a) sin(c))
 - 0.3713906763541 cos(a) cos(b), - 0.74278135270821 sin(a) cos(b) sin(c)
 + 0.55708601453116 sin(a) cos(b) cos(c) + 0.3713906763541 sin(a) sin(b), 
0.55708601453116 (cos(a) cos(c) - sin(a) sin(b) sin(c))
 + 0.74278135270821 (- cos(a) sin(c) - sin(a) sin(b) cos(c))], 
[0.74278135270821 (cos(a) cos(c) - sin(a) sin(b) sin(c))
 + 0.55708601453116 (cos(a) sin(c) + sin(a) sin(b) cos(c))
 - 0.3713906763541 sin(a) cos(b), 0.74278135270821 cos(a) cos(b) sin(c)
 - 0.55708601453116 cos(a) cos(b) cos(c) - 0.3713906763541 cos(a) sin(b), 
0.55708601453116 (cos(a) sin(b) sin(c) + sin(a) cos(c))
 + 0.74278135270821 (cos(a) sin(b) cos(c) - sin(a) sin(c))])
(%i10) DF1 :ev (DF, a=0, b=0, c=0.2);
         [         0           0.3713906763541    - 0.83865108413521 ]
         [                                                           ]
(%o10)   [ - 0.3713906763541          0            0.39841350955518  ]
         [                                                           ]
         [ 0.83865108413521   - 0.39841350955518          0          ]
(%i11) determinant (DF1);
(%o11)                      1.3877787807814457E-17
(%i12) 
Run Example
args(1/(x+1)+x+x+x);
                                    1
(%o1)                            [-----, 3 x]
                                  x + 1
(%i2) listp(%);
(%o2)                                false
(%i3) 
[abs,addrow,args,block,copymatrix,disp,do,lambda,length,map,matrix,or,rowswap,while] [algsys,args,invert,matrix] [allroots,args,create_list,diff,ev,exp,log,numer,ratsimp,solve] [append,args,block,first,ifactors,lambda,maplist,rest] [append,args,block,floor,length,load,map,matrix,sum] [append,args,block,globalsolve,modulus,submatrix,true,xreduce] [append,args,block,globalsolve,modulus,submatrix,xreduce] [append,args,block,modulus,solve,submatrix,xreduce] [apply,args,block,col,copymatrix,do,genmatrix,map,mod,quotient,return,transpose] [apply,args,block,copymatrix,do,genmatrix,map,mod,quotient,return,transpose] [apply,args,block,do,genmatrix,if,map,mod,quotient,return,transpose] [apply,args,ceiling,col,do,length,mod,nullspace,print,row] [apply,args,ceiling,col,do,length,mod,nullspace,printf,row] [apply,args,ceiling,do,matrix,mod,nullspace,printf] [apply,args,matrix,nullspace] [apply,args,matrix] [apply1,args,defrule,disprule,matchdeclare,numberp,op,or,ratsimp,symbolp] [args,asin,atan2,block,cos,flatten,float,ident,length,make_random_state,makelist,matrix,set_random_state,sin,sqrt,subst,transpose] [args,asin,atan2,block,cos,flatten,float,ident,length,make_random_state,makelist,matrix,set_random_state,sin,sqrt,transpose] [args,asin,atan2,block,cos,flatten,float,ident,length,make_random_state,makelist,matrix,set_random_state,sin,sqrt] [args,asin,atan2,block,cos,flatten,float,ident,length,make_random_state,makelist,set_random_state,sqrt] [args,asin,atan2,block,cos,flatten,float,length,make_random_state,makelist,set_random_state,sqrt] [args,block,del,length,map,op,part] [args,block,genmatrix,if,map,matrix,mod,quotient,transpose] [args,block,length,op,part] [args,block,modulus,submatrix,xreduce] [args,cos,determinant,diff,ev,flatten,float,matrix,sin,sqrt,transpose] [args,cos,load,matrix,plot2d,sin,sqrt] [args,determinant,expand,factor,fullratsimp,ident,invert,matrix,solve,transpose] [args,determinant,expand,factor,ident,invert,matrix,solve,sqrt,transpose] [args,determinant,expand,factor,ident,invert,matrix,solve,transpose] [args,determinant,expand,factor,ident,matrix,solve,sqrt,transpose] [args,determinant,expand,factor,ident,matrix,solve,transpose] [args,diff,ev,false,length,makelist,map,matrix,numer,ratprint,transpose] [args,diff,false,floor,map,matrix,numer,ratprint,rhs,solve] [args,divisors,lreduce,matrix,subst] [args,expand,op,sqrt] [args,genmatrix,kill,powerdisp,transpose,true] [args,inpart,op] [args,isolate] [args,length,lfreeof,ratexpand] [args,length,makelist,ratexpand] [args,listp] [args,map,matrix,plot2d,rhs,solve,transpose] [args,matrix,nullspace] [args,matrix] [args,op] [args,printf] [args,ratexpand] [args]

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