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map-solve

solutions: solve(x^2=9);

xvals: map(rhs, map(f...

xvals[1];

Calculate

map-print-solve

f(x) := 3*x^2 + 1...

lx : map (rhs, (s...

Sx : mean (lx);

Calculate

map-matrix

Aufgabe:matrix([1000,...

Z(x):=x[1]*x[2]*x[3]/...

K(x):=x[4]*36000.0/(x...

Calculate

map-plot2d
plot2d([map,x],[x,-5,5]);

map:if x<=-1 then ...

plot2d([map,x],[x,-5,...

map2:map,x=map;

Calculate

map

Schularbeitsergebnis:...

X(x):=x[1];

H(x):=x[2];

Calculate

map-print-solve

f(x) := 3*x^2 + 12*x ...

lx : map (rhs, (solve...

Sx : mean (lx);

Calculate

map

Gesamtkaufpreis:[1500...

berechnung(x):=if x &...

Mindestanzahlung:map(...

Calculate

map-op

map(op(a-b), [0, 1, 2...

Calculate

map-matrix-solve

P:matrix([0.59,1.76,2...

V:matrix([X],[10],[10]);

Q:P . V;

Calculate

map

map (euler, [1, 0, 1,...

Calculate

map

Run Example
(%i1)load (eigen);
(%o1)           /usr/share/maxima/5.21.1/share/matrix/eigen.mac
(%i2)  x: matrix ([1, 2, 2, -1], [1, 1, -5, 3], [3, 2, 8, -7]);
                              [ 1  2   2   - 1 ]
                              [                ]
(%o2)                         [ 1  1  - 5   3  ]
                              [                ]
                              [ 3  2   8   - 7 ]
(%i3)  y: gramschmidt (x);
(%o3)        [[1, 2, 2, - 1], [2, 3, - 3, 2], [2, - 1, - 1, - 2]]
(%i4)  map (innerproduct, [y[1], y[2], y[3]], [y[2], y[3], y[1]]);
(%o4)                              [0, 0, 0]
(%i5)  load (eigen);
(%o5)           /usr/share/maxima/5.21.1/share/matrix/eigen.mac
(%i6)  ip (f, g) := integrate (f * g, u, a, b);
(%o6)                 ip(f, g) := integrate(f g, u, a, b)
(%i7)  y : gramschmidt ([1, sin(u), cos(u)], ip), a= -%pi/2, b=%pi/2;
                                      %pi cos(u) - 2
(%o7)                     [1, sin(u), --------------]
                                           %pi
(%i8)  map (ip, [y[1], y[2], y[3]], [y[2], y[3], y[1]]), a= -%pi/2, b=%pi/2;
(%o8)                              [0, 0, 0]
(%i9) 
Run Example
eq:x^8-x^7+x^5-x^4+x^3-x+1;
                         8    7    5    4    3
(%o1)                   x  - x  + x  - x  + x  - x + 1
(%i2) eq2:ev(eq,x=x-4);
                     8          7          5          4          3
(%o2)   - x + (x - 4)  - (x - 4)  + (x - 4)  - (x - 4)  + (x - 4)  + 5
(%i3) eq3:expand(eq2);
       8       7        6         5          4          3           2
(%o3) x  - 33 x  + 476 x  - 3919 x  + 20139 x  - 66127 x  + 135444 x
                                                             - 158161 x + 80581
(%i4) eq4:create_list(coeff(eq3,x,i),i,0,7);
(%o4)    [80581, - 158161, 135444, - 66127, 20139, - 3919, 476, - 33]
(%i5) map(gcd,eq4);
(%o5) [spmod(80581), spmod(- 158161), spmod(135444), spmod(- 66127), 
                          spmod(20139), spmod(- 3919), spmod(476), spmod(- 33)]
(%i6) 
Run Example
kill(all);
(%o0)                                done
(%i1) Punkt:[[5,12],[10,27],[20,94],[30,209],[40,426],[50,870]];
(%o1)   [[5, 12], [10, 27], [20, 94], [30, 209], [40, 426], [50, 870]]
(%i2) n:length(Punkt);
(%o2)                                  6
(%i3) Grad:n-1;
(%o3)                                  5
(%i4) g(x):=x[2]=sum(a[i]*x[1]^(n-i),i,1,Grad)+a[n];
                                      n - i
(%o4)            g(x) := x  = sum(a  x     , i, 1, Grad) + a
                          2        i  1                     n
(%i5) Gleichungen:map(g,Punkt);
(%o5) [12 = a  + 5 a  + 25 a  + 125 a  + 625 a  + 3125 a , 
             6      5       4        3        2         1
27 = a  + 10 a  + 100 a  + 1000 a  + 10000 a  + 100000 a , 
      6       5        4         3          2           1
94 = a  + 20 a  + 400 a  + 8000 a  + 160000 a  + 3200000 a , 
      6       5        4         3           2            1
209 = a  + 30 a  + 900 a  + 27000 a  + 810000 a  + 24300000 a , 
       6       5        4          3           2             1
426 = a  + 40 a  + 1600 a  + 64000 a  + 2560000 a  + 102400000 a , 
       6       5         4          3            2              1
870 = a  + 50 a  + 2500 a  + 125000 a  + 6250000 a  + 312500000 a ]
       6       5         4           3            2              1
(%i6) Unbekannte:makelist(a[i],i,1,n);
(%o6)                      [a , a , a , a , a , a ]
                             1   2   3   4   5   6
(%i7) l:solve(Gleichungen,Unbekannte);
                29            323           103        1949         14699
(%o7) [[a  = --------, a  = -------, a  = - ----, a  = ----, a  = - -----, 
         1   42000000   2   1680000   3     7000   4   3360   5     4200
                                                                          117
                                                                     a  = ---]]
                                                                      6    7
(%i8) y=Unbekannte.makelist(x^(n-i),i,1,n),l;
                    5          4         3         2
                29 x      323 x     103 x    1949 x    14699 x   117
(%o8)      y = -------- + ------- - ------ + ------- - ------- + ---
               42000000   1680000    7000     3360      4200      7
(%i9) 
[abs,do,if,is,length,map,ratsimp,realroots,solve] [alphacharp,ascii,delete,if,length,makelist,map,string] [and,apply,cardinality,every,integer_partitions,integerp,lambda,map,subset] [append,atom,block,delete,do,emptyp,freeof,if,indices,lambda,length,lmax,lmin,makelist,map,member,not,sublist_indices,subst] [append,atom,block,delete,flatten,if,lambda,load,map,return] [append,block,delete,do,emptyp,if,lambda,length,makelist,map,not,subst] [append,block,delete,flatten,lambda,length,makelist,map,return] [append,block,floor,makelist,map,mod,reverse] [append,build_info,map,plot2d,rat,resultant,solve,sqrt] [append,map,plot2d,resultant,solve,sqrt] [apply,args,block,col,copymatrix,do,genmatrix,map,mod,quotient,return,transpose] [assume,cons,eliminate,ev,fpprintprec,map,plot2d,solve] [atvalue,diff,ilt,lambda,laplace,map,solve] [bftorat,block,cons,delete,do,emptyp,first,float2bf,fpprec,lambda,last,listp,map,mod,ratepsilon,ratprint,rest,return] [bftorat,block,cons,delete,emptyp,false,first,float2bf,fpprec,if,integerp,kill,lambda,listp,map,mod,ratdenom,ratepsilon,ratprint,rest,return] [block,buildq,indices,lambda,macroexpand,map,sublist_indices] [block,cos,flatten,if,li,load,makelist,map,numer,outermap,plot2d,sin,sort,unique] [block,delete,emptyp,if,lambda,length,makelist,map,not,subst] [block,do,indices,lambda,makelist,map,mod,print,sublist_indices] [block,length,map,matrix,print,return] [cos,flatten,li,load,makelist,map,numer,outermap,plot2d,sin,sort,unique] [cos,gramschmidt,integrate,load,map,matrix,sin] [diff,float,is,lambda,load,map,plot2d,rhs] [disjoin,first,if,lambda,listify,makelist,map,mod,setify,subset] [disprule,false,grind,map,partfrac,properties,radexpand,rat,simp,tellsimp] [do,evenp,first,if,lambda,makelist,map,return,setify,subset] [do,evenp,first,if,lambda,makelist,map,setify,subset] [do,if,is,length,map,ratsimp,realroots,solve,subst] [ev,map,numer,pi,solve] [evenp,first,if,lambda,makelist,map,setify,subset] [evenp,if,lambda,makelist,map,setify,subset] [expand,factor,map,plot2d,rat,realroots,resultant,solve] [factor,kill,length,makelist,map,plot2d,rhs,solve,sum] [first,if,lambda,makelist,map,mod,setify,subset] [floor,map] [gcdex,genmatrix,load,map] [gramschmidt,integrate,load,map,matrix] [gramschmidt,load,map,matrix] [jacobi,lambda,map] [kill,length,makelist,map,solve,sum] [lambda,makelist,map,numer] [lambda,makelist,map,setify] [lambda,map] [length,listify,makelist,map,powerset,setify,sort,sqrt] [length,map,realroots,solve] [map,mod] [map,plot2d,solve] [map,plot2d] [map,solve] [map]

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