Sponsored links: Algebra eBooks
 

Related

delta-laplace-linsolve

ig:laplace(q*delta(t)...

jednacine:[v1*c1*s+v1...

promenljive:[v1,v2];

Calculate

delta-limit

f(x,y,z):= 3*x*y+2*(2...

%Delta(x)=delta:3/12;

limit(1/x,x,0);

Calculate

delta-diff-exp-limit-pi

f(x,y,z):= 3*x*y+2*(2...

'CX(x,y,z)=CX:diff(f(...

'delta(x)=delta:3/12;

Calculate

delta-is-part-ratsimp-rhs-solve-sqrt

eg: f*(a-x)/(x+L*(a-x...

u:ratsimp(eg,x);

l:part(u,1);

Calculate

delta-kill-linsolve

kill(eq1,eq1,eq3,eq4,...

eq2:z=x+t-y;

linsolve([eq2],[x,y,z...

Calculate

delta-diff-limit

f(x,y,z):= 3*x*y+2*(2...

'CX(x,y,z)=CX:diff(f(...

'Delta(x)=delta:3/12;

Calculate

delta-kill-linsolve

kill(eq1,eq1,eq3,eq4,...

eq1:x-3*y+t=0;

linsolve([eq1],[x,y,z...

Calculate

delta-solve

solve((x*(1/2)*D^delt...

Calculate

delta

f(x,y,z):= 3*x*y+2*(2...

%Delta(x)=delta:3/12;

Calculate

delta

f(x,y,z):= 3*x*y+2*(2...

%Delta(x)=delta:3/12;

Calculate

delta

Run Example
(%i1)remvalue(n,z);
(%o1)                           [false, false]
(%i2) matchdeclare(a,lambda([x],freeof(x,n)));
(%o2)                                done
(%i3) matchdeclare(b,lambda([x],freeof(x,n) and integerp(x) and x>
0));
(%o3)                                done
(%i4) matchdeclare(f,all);
(%o4)                                done
(%i5) matchdeclare(g,lambda([x],freeof(n-1,x)));
(%o5)                                done
(%i6) defrule(r1,zt(1,n,z),z/(z-1));
                                                 z
(%o6)                      r1 : zt(1, n, z) -> -----
                                               z - 1
(%i7) defrule(r2,zt(n,n,z),z/(z-1)^2);
                                                z
(%o7)                    r2 : zt(n, n, z) -> --------
                                                    2
                                             (z - 1)
(%i8) defrule(r3,zt(1/n,n,z),log(z/(z-1)));
                                1                 z
(%o8)                   r3 : zt(-, n, z) -> log(-----)
                                n               z - 1
(%i9) defrule(r4,zt(a^n,n,z),z/(z-a));
                                   n             z
(%o9)                     r4 : zt(a , n, z) -> -----
                                               z - a
(%i10) defrule(r5,zt(a^(n-1),n,z),1/(z-a));
                                 n - 1             1
(%o10)                  r5 : zt(a     , n, z) -> -----
                                                 z - a
(%i11) defrule(r6,zt(binomial(n,b),n,z),z/(z-1)^(b+1));
                                                       - b - 1
(%o11)         r6 : zt(binomial(n, b), n, z) -> (z - 1)        z
(%i12) defrule(r7,zt(n^b,n,z),block([tmp:z/(z-1)],  for i:1 thru b do tmp:-z*diff(tmp,z),  factor(tmp)));
                b                          z
(%o12) r7 : zt(n , n, z) -> block([tmp : -----], 
                                         z - 1
                           for i thru b do tmp : - diff(tmp, z) z, factor(tmp))
(%i13) defrule(r8,zt(sin(a*n),n,z),z*'sin(a)/((z^2-2*z*'cos(a)+1)));
                                                sin(a) z
(%o13)          r8 : zt(sin(a n), n, z) -> -------------------
                                            2
                                           z  - 2 cos(a) z + 1
(%i14) defrule(r9,zt(cos(a*n),n,z),z*(z-'cos(a))/(z^2-2*z*'cos(a)+1));
                                             z (z - cos(a))
(%o14)          r9 : zt(cos(a n), n, z) -> -------------------
                                            2
                                           z  - 2 cos(a) z + 1
(%i15) defrule(r10,zt(kron_delta(b,n),n,z),1/z^b);
                                                        1
(%o15)              r10 : zt(kron_delta(b, n), n, z) -> --
                                                         b
                                                        z
(%i16) defrule(r11,zt(a^n*f,n,z),'subst(z/a,z,ztrans(f,n,z)));
                     n                        z
(%o16)     r11 : zt(a  f, n, z) -> substitute(-, z, ztrans(f, n, z))
                                              a
(%i17) defrule(r12,zt(n^b*g,n,z),block([tmp:ztrans(g,n,z)],  for i:1 thru b do tmp:-z*'diff(tmp,z),  return(tmp)));
                   b
(%o17) r12 : zt(g n , n, z) -> block([tmp : ztrans(g, n, z)], 
                                                           dtmp
                                   for i thru b do tmp : - ---- z, return(tmp))
                                                            dz
(%i18) defrule(r13,zt(exp(-a*n),n,z),z/(z-exp(-a)));
                                - a n               z
(%o18)               r13 : zt(%e     , n, z) -> ---------
                                                      - a
                                                z - %e
(%i19) defrule(r14,zt(f(n-m),n,z),z^(-m)*ztrans(f(n),n,z));
                                            ztrans(f(n), n, z)
(%o19)          r14 : zt(f(n - m), n, z) -> ------------------
                                                     m
                                                    z
(%i20) declare(zt,linear);
(%o20)                               done
(%i21) ztrans1(e):=apply1(e,r1,r2,r3,r4,r5,r6,r7,r8,r9,r10,r11,r12,r13,r14);
(%o21) ztrans1(e) := apply1(e, r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, 
                                                                 r12, r13, r14)
(%i22) ztrans(f,n,z):=ev(ztrans1(zt(f,n,z)),diff,subst);
(%o22)     ztrans(f, n, z) := ev(ztrans1(zt(f, n, z)), diff, subst)
(%i23) defrule(ir1,izt(z/(z-a),z,n),a^n);
                                     z              n
(%o23)                   ir1 : izt(-----, z, n) -> a
                                   z - a
(%i24) defrule(ir2,izt(1/(z-a),z,n),a^(n-1));
                                   1              n - 1
(%o24)                 ir2 : izt(-----, z, n) -> a
                                 z - a
(%i25) declare(izt,linear);
(%o25)                               done
(%i26) invztrans1(e):=apply1(e,ir1,ir2);
(%o26)               invztrans1(e) := apply1(e, ir1, ir2)
(%i27) invztrans(f,z,n):=invztrans1(izt(f,z,n));
(%o27)          invztrans(f, z, n) := invztrans1(izt(f, z, n))
(%i28) ztrans(1,n,z);
                                       z
(%o28)                               -----
                                     z - 1
(%i29) ztrans(a,n,z);
                                      a z
(%o29)                               -----
                                     z - 1
(%i30) expand(ztrans((-1)^n,n,z));
                                       z
(%o30)                               -----
                                     z + 1
(%i31) ztrans(n,n,z);
                                      z
(%o31)                             --------
                                          2
                                   (z - 1)
(%i32) ztrans(n^2,n,z);
                                   z (z + 1)
(%o32)                             ---------
                                          3
                                   (z - 1)
(%i33) ztrans(a^(n-1),n,z);
                                       1
(%o33)                               -----
                                     z - a
(%i34) factor(ztrans(a^(n-1)+n^2,n,z));
                         3      2      2
                      2 z  - a z  - 2 z  - a z + 3 z - 1
(%o34)                ----------------------------------
                                      3
                               (z - 1)  (z - a)
(%i35) 
Run Example
f(x,y,z):= 3*x*y+2*(2*x*z+2*y*z);
(%o1)               f(x, y, z) := 3 x y + 2 (2 x z + 2 y z)
(%i2) 'CX(x,y,z)=CX:diff(f(x,y,z),x,1);
(%o2)                       CX(x, y, z) = 4 z + 3 y
(%i3) %Delta(x)=delta:3/12;
                                             1
(%o3)                            %Delta(x) = -
                                             4
(%i4) limit(1/x,x,0);
(%o4)                              infinity
(%i5) 
Run Example
l:1;
(%o1)                                  1
(%i2) a:1;
(%o2)                                  1
(%i3) c:l/10;
                                      1
(%o3)                                 --
                                      10
(%i4) delta:0.1;
(%o4)                                 0.1
(%i5) v:1;
(%o5)                                  1
(%i6) (2/l)*integrate((v*cos((x-c)/delta)*%pi/2),x,(c-delta),(c+delta));

rat: replaced 0.2 by 1/5 = 0.2

rat: replaced 0.0 by 0/1 = 0.0

rat: replaced 0.2 by 1/5 = 0.2

rat: replaced 0.2 by 1/5 = 0.2

rat: replaced 10.0 by 10/1 = 10.0

rat: replaced 10.0 by 10/1 = 10.0

rat: replaced 0.2 by 1/5 = 0.2

rat: replaced 0.0 by 0/1 = 0.0

rat: replaced 0.2 by 1/5 = 0.2

rat: replaced 0.2 by 1/5 = 0.2

rat: replaced 10.0 by 10/1 = 10.0

rat: replaced -0.08414709848079 by -5558/66051 = -0.08414709845422

rat: replaced 0.08414709848079 by 5558/66051 = 0.084147098454225
                                   11116 %pi
(%o6)                              ---------
                                     66051
(%i7) psin:%o6;
(%o7)             u:sum(psin*%pi*n*x/l)*sin(%pi*n*a*t/l)*(%pi*n*a/l)^(-1),n,1,50);
[abs,cos,delta,float,lmin,sin] [apply1,binomial,block,cos,defrule,delta,diff,ev,exp,factor,freeof,kron_delta,lambda,linear,log,matchdeclare,remvalue,return,sin,subst] [asin,beta,delta,float,gamma,sin] [asin,cos,delta,taylor] [atvalue,delta,diff,ilt,lambda,laplace,map,solve] [binomial,block,delta,determinant,do,expand,genmatrix,hipow,kron_delta,lambda,length,makelist,part,return,sum] [binomial,block,delta,determinant,do,expand,genmatrix,hipow,kron_delta,makelist,part,print,return,subst] [binomial,block,delta,determinant,do,expand,genmatrix,hipow,kron_delta,makelist,part,print,return,sum] [binomial,block,delta,determinant,do,expand,genmatrix,hipow,kron_delta,makelist,part,print,return] [binomial,block,delta,determinant,do,expand,genmatrix,hipow,kron_delta,makelist,part,return] [binomial,block,delta,determinant,do,expand,genmatrix,kron_delta,return] [binomial,block,delta,determinant,expand,genmatrix,hipow,kron_delta,listofvars,makelist,part,sum] [binomial,block,delta,determinant,expand,genmatrix,hipow,length,makelist,part,subst,sum] [binomial,block,delta,determinant,expand,genmatrix,kron_delta,lambda,makelist,subst,sum] [binomial,block,delta,determinant,expand,genmatrix,kron_delta,return] [binomial,block,delta,determinant,expand,genmatrix,return,subst] [binomial,buildq,delta,determinant,expand,genmatrix,kron_delta] [binomial,buildq,delta,kron_delta,lambda] [binomial,delta,determinant,genmatrix,kron_delta,lambda,minor] [binomial,delta,genmatrix,kron_delta,subst] [binomial,delta,genmatrix,kron_delta] [cos,delta,depends,jacobian,sin] [cos,delta,float,sin,solve] [cos,delta,float,sin] [cos,delta,integrate,sum] [cos,delta,sin,taylor] [cos,delta,sin] [declare,delta,feature,kron_delta,lambda,linsolve,matchdeclare,tellsimp] [define,delta,distrib,ev,exp,load,log,sqrt] [delta,diff,exp,laplace,sin] [delta,diff,limit] [delta,equal,is,part,ratsimp,rhs,solve,sqrt] [delta,integrate,plot2d,solve,subst] [delta,integrate,solve,subst] [delta,integrate] [delta,is,part,ratsimp,rhs,solve,sqrt] [delta,kill,linsolve] [delta,kill,ratcoef,solve,subst] [delta,kron_delta] [delta,laplace,linsolve,ratsimp] [delta,laplace,linsolve] [delta,laplace] [delta,linsolve] [delta,matrix,max,var] [delta,pi,plot2d,sin] [delta,pi,solve,sqrt] [delta,ratsimp] [delta,solve] [delta,sum] [delta]

Related Help

Help for Delta