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QDifferenceEquations[IsSolution] - test the solution of a linear q-difference equation
QDifferenceEquations[AreSameSolution] - test if solutions of a linear q-difference equation are equivalent
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Calling Sequence
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IsSolution(sol, eq, var, ['certificates'])
AreSameSolution(sol, sol1, x)
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Parameters
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sol
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solution to be checked, or a certificate (set or list of certificates) for q-hypergeometric solution
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eq
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q-difference equation or list of such equations (for the system case)
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var
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function variable to solve for, such as  , or a list of such function variables (for the system case)
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'certificates'
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(optional) if given sol then treated as certificate for q-hypergeometric solution
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sol1
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solution to be compared with
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x
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independent variable in the solutions given
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Description
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The IsSolution(sol,eq,var) calling sequence returns true if eq is a linear q-difference equation with polynomial coefficients (or a system of such equations) and sol is its solution. Otherwise, false is returned for q-hypergeometric solution (that is, if 'certificates' option is specified) and the degree of the result of substitution is returned for other types of solutions to be checked.
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The IsSolution command substitutes sol for the function variables and checks the result.
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The AreSameSolution(sol, sol1, x) calling sequence returns true if the solutions sol and sol1 are equivalent. Otherwise, false is returned.
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The command checks that the numbers of linear independent solutions in sol and sol1 are the same, as well as the degrees in x.
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Examples
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![sol1 := PolynomialSolution(eq, y(x), {}, output = basis[_K])](/support/helpjp/helpview.aspx?si=8733/file02640/math163.png)
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![sol1 := _K[1]*x^10+_K[2]*x+1-_K[2]](/support/helpjp/helpview.aspx?si=8733/file02640/math166.png)
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![sol2 := _K[1]*x^10+_K[2]*x+1-_K[2]-x^5](/support/helpjp/helpview.aspx?si=8733/file02640/math180.png)
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![sol3 := _K[1]*x^10+_K[2]*x+1-_K[2]-x^10](/support/helpjp/helpview.aspx?si=8733/file02640/math194.png)
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![sol4 := sol1-_K[1]*x^10](/support/helpjp/helpview.aspx?si=8733/file02640/math212.png)
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![sol4 := _K[2]*x+1-_K[2]](/support/helpjp/helpview.aspx?si=8733/file02640/math215.png)
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| (10) |
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| (11) |
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