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 1234567891011121314151617181920212223242526272829303132333435363738394041424344454647484950515253545556575859606162 ``````% Initial load up list off echo\$ lisp(depl!*:=nil)\$ % clearing of all dependences setcrackflags()\$ lisp write "...................................................................", "......."\$ write "An example of the determination of point symmetries for ODEs"\$ depend y,x\$ de := {df(y,x,2) = (df(y,x)*(2*x*y+x**3) - 4*y**2)/x**4, y, x}\$ mo := {0,nil,nil}\$ LIEPDE(de,mo)\$ nodepend y,x\$ lisp write "...................................................................", "......."\$ write "An example of the determination of point symmetries for PDEs"\$ depend u,x,y\$ de := {df(u,x,x)-df(u,y),u,{x,y}}\$ mo := {0,nil,nil}\$ LIEPDE(de,mo)\$ nodepend u,x,y\$ lisp write "...................................................................", "......."\$ write "An example of the determination of first integrals of ODEs"\$ depend y,x\$ de := {df(y,x,2)=x*df(y,x)**2-2*df(y,x)/x-y**2/x, y, x}\$ mo := {0,{},2}\$ FIRINT(de,mo)\$ nodepend y,x\$ lisp write "...................................................................", "......."\$ write "An example of the determination of a Lagrangian for an ODE "\$ depend f,x\$ depend y,x\$ de := {df(y,x,2) = 6*y**2 + x, y, x}\$ mo := {0,{}}\$ LAGRAN(de,mo)\$ nodepend f,x\$ nodepend y,x\$ lisp write "...................................................................", "......."\$ write "An example of the factorization of an ODE " \$ depend f,x\$ depend y,x\$ depend q,x\$ de := {df(y,x,2) = df(y,x)**2/y - f*df(y,x) - y*q, y, x}\$ mo := {2,{}}\$ DECOMP(de,mo)\$ nodepend f,x\$ nodepend y,x\$ nodepend q,x\$ end\$ -- ``````