12/25/2023 0 Comments Icq number generatorΗ u x, t, u, v − ξ x x, t, u, v u x − ξ t x, t, u, v u t This resulting characteristic is a function that can then be applied to an integer as large as the number of dependent variables of the problem, in this case two Q ≔ m :: satisfies m ↦ m :: Typesetting :- _Hold ' posint ' and m ≤ 2 ↦ η m − add ξ j ⋅ diff y m, X j, j = 1. S ≔ ξ x x, t, u, v, ξ t x, t, u, v, η u x, t, u, v, η v x, t, u, vīy default CharacteristicQ returns, fast, an operator in its most abstract form, with a test-type for the value of m and not expanded essentially, nothing is actually computed until you need it S ≔ seq ξ j x, t, u, v, j = x, t, seq η j x, t, u, v, j = u, v With PDEtools, CharacteristicQ, InfinitesimalGeneratorĬharacteristicQ, InfinitesimalGeneratorĬonsider a problem in two independent and two dependent variables u( x, t ), v( x, t ), and the generic form of infinitesimals for this type of problemį ≔ u x, t, v x, t To avoid having to remember the optional keywords, if you misspell a keyword, or a portion of it, a matching against the correct keywords is performed, and when there is only one match, the input is automatically corrected. Also, jetnotation is used in this operator and a check-of-type for the value of m is automatically inserted unless explicitly requested otherwise with the optional arguments jetnotation = false and/or checktype = false - see the examples below. The sum in the body of this operator returned by CharacteristicQ is not expanded unless explicitly requested using the optional argument expanded. M → η m − ∑ j = 1 n x i j &DifferentialD u m &DifferentialD x j , η m, CharacteristicQ computes the procedure That is, for a PDE problem with n independent and m dependent variables, given a related list of infinitesimals ξ 1. The CharacteristicQ command computes the characteristic of a point symmetry represented by its infinitesimals or the corresponding infinitesimal generator operator. (optional) can be true (default, the notation found in S ), false, jetvariables, jetvariableswithbrackets, jetnumbers or jetODE to respectively return or not using the different jet notations available Optional - can be true or false (default), to have or have not expanded the sums entering the body of the output procedure ![]() Optional - can be true (default) or false, to have or have not inserted a check-of-type for the arguments of the output procedure ![]() Compute the characteristic of a point symmetry represented by its infinitesimalsĬharacteristicQ(S, DepVars, 'options'='value')Ī list with the infinitesimals of a symmetry generator or the corresponding infinitesimal generator operatorĪ function or a list of them indicating the dependent variables of the problem
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