<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Deriving di\357\254\200erential consequences</Font></Text-field>

<Text-field style="Heading 2" layout="Heading 2">Example: Symmetries of KdV - again</Text-field>

coordinates([t,x], [u], 9);

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

equation (u_t = u_xxx + 6*u*u_x);

L0kkdV90RzYiLCZJJnVfeHh4R0YkIiIiKiZJInVHRiRGJ0kkdV94R0YkRiciIic=

S := symmetries(u = U);

LCotSSNUREc2IjYkSSJVR0YlSSJ0R0YlIiIiKiZGJ0YpSSR1X3hHRiVGKSEiJyomLUYkNiRGJ0kieEdGJUYpSSJ1R0YlRilGLC1GJDYkRicqJEYwIiIkISIi

dependence(U(x,t,u,u_x,u_xx,u_xxx,u_4x,u_5x));

L0kiVUc2IjwqSSJ0R0YkSSJ1R0YkSSJ4R0YkSSR1X3hHRiRJJXVfeHhHRiRJJnVfeHh4R0YkSSV1XzR4R0YkSSV1XzV4R0Yk

length(S),length(evalTD(S));

NiQiI3UiJilRSQ==

vars(S);

PC1JInRHNiJJInVHRiRJInhHRiRJJHVfeEdGJEkldV94eEdGJEkmdV94eHhHRiRJJXVfNHhHRiRJJXVfNXhHRiRJJXVfNnhHRiRJJXVfN3hHRiRJJXVfOHhHRiQ=

<Text-field style="Heading 3" layout="Heading 3"></Text-field>

Among vars(S), u_8x is of highest order. When differentiating S with respect to u_8x , one may expect that the result will be a rather simple expression:

pd(S,u_8x);

IiIh

T := pd(S,u_7x);

LCQtSSNUREc2IjYkLUkjcGRHRiU2JEkiVUdGJUkldV81eEdGJUkieEdGJSEiJA==

vars(T);

PCtJInRHNiJJInVHRiRJInhHRiRJJHVfeEdGJEkldV94eEdGJEkmdV94eHhHRiRJJXVfNHhHRiRJJXVfNXhHRiRJJXVfNnhHRiQ=

pd(T,u_6x);

LCQtSSNwZEc2IjYkSSJVR0YlKiRJJXVfNXhHRiUiIiMhIiQ=

<Text-field style="Heading 3" layout="Heading 3"></Text-field>

The algorithm to automate derivation of differential consequences is implemented as the procedure derive (which is one of the subroutines called by run):

unknowns(U);

SSJVRzYi

derive(S);

LCQtSSNwZEc2IjYkSSJVR0YlKiRJJXVfNXhHRiUiIiMhIiQ=

To exclude certain \357\254\201bre variables from derivation (along with all jet variables they generate), use noderive(list of \357\254\201bre variables);