GuessOption¶

mantepse.spad line 63 [edit on github]

GuessOption is a domain whose elements are various options used by Guess.

=: (%, %) -> Boolean: from BasicType

~=: (%, %) -> Boolean: from BasicType

allDegrees: Boolean -> %: allDegrees(d) specifies whether all possibilities of the degree vector - taking into account maxDegree - should be tried. This is mainly interesting for rational interpolation. This option is expressed in the form allDegrees == d.

check: Union(skip, MonteCarlo, deterministic) -> %: check(d) specifies how we want to check the solution. If the value is “skip”, we return the solutions found by the interpolation routine without checking. If the value is “MonteCarlo”, we use a probabilistic check. This option is expressed in the form check == d

checkExtraValues: Boolean -> %: checkExtraValues(d) specifies whether we want to check the solution beyond the order given by the degree bounds. This option is expressed in the form checkExtraValues == d

coerce: % -> OutputForm: from CoercibleTo OutputForm

debug: Boolean -> %: debug(d) specifies whether we want additional output on the progress. This option is expressed in the form debug == d.

displayKind: Symbol -> %: displayKind(d) specifies kind of the result: generating function, recurrence or equation. This option should not be set by the user, but rather by the HP-specification.

functionName: Symbol -> %: functionName(d) specifies the name of the function given by the algebraic differential equation or recurrence. This option is expressed in the form functionName == d.

functionNames: List Symbol -> %: functionNames(d) specifies the names for the function in algebraic dependence. This option is expressed in the form functionNames == d.

homogeneous: Union(PositiveInteger, Boolean) -> %: homogeneous(d) specifies whether we allow only homogeneous algebraic differential equations. This option is expressed in the form homogeneous == d. If true, then maxPower must be set, too, and ADEs with constant total degree are allowed. If a PositiveInteger is given, only ADE's with this total degree are allowed.

indexName: Symbol -> %: indexName(d) specifies the index variable used for the formulas. This option is expressed in the form indexName == d.

latex: % -> String: from SetCategory

maxDegree: Union(NonNegativeInteger, arbitrary) -> %: maxDegree(d) specifies the maximum degree of the coefficient polynomials in an algebraic differential equation or a recursion with polynomial coefficients. For rational functions with an exponential term, maxDegree bounds the degree of the denominator polynomial. This option is expressed in the form maxDegree == d.

maxDerivative: Union(NonNegativeInteger, arbitrary) -> %: maxDerivative(d) specifies the maximum derivative in an algebraic differential equation. This option is expressed in the form maxDerivative == d.

maxLevel: Union(NonNegativeInteger, arbitrary) -> %: maxLevel(d) specifies the maximum number of recursion levels operators guessProduct and guessSum will be applied. This option is expressed in the form spad{maxLevel == d}.

maxMixedDegree: NonNegativeInteger -> %: maxMixedDegree(d) specifies the maximum q-degree of the coefficient polynomials in a recurrence with polynomial coefficients, in the case of mixed shifts. Although slightly inconsistent, maxMixedDegree(0) specifies that no mixed shifts are allowed. This option is expressed in the form maxMixedDegree == d.

maxPower: Union(PositiveInteger, arbitrary) -> %: maxPower(d) specifies the maximum degree in an algebraic differential equation. For example, the degree of (f'')^3 f' is 4. maxPower(-1) specifies that the maximum exponent can be arbitrary. This option is expressed in the form maxPower == d.

maxShift: Union(NonNegativeInteger, arbitrary) -> %: maxShift(d) specifies the maximum shift in a recurrence equation. This option is expressed in the form maxShift == d.

maxSubst: Union(PositiveInteger, arbitrary) -> %: maxSubst(d) specifies the maximum degree of the monomial substituted into the function we are looking for. That is, if maxSubst == d, we look for polynomials such that $p(f(x), f(x^2), …, f(x^d))=0$. equation. This option is expressed in the form maxSubst == d.

one: Boolean -> %: one(d) specifies whether we are happy with one solution. This option is expressed in the form one == d.

option: (List %, Symbol) -> Union(Any, failed): option(l, option) returns which options are given.

safety: NonNegativeInteger -> %: safety(d) specifies the number of values reserved for testing any solutions found. This option is expressed in the form safety == d.

Somos: Union(PositiveInteger, Boolean) -> %: Somos(d) specifies whether we want that the total degree of the differential operators is constant, and equal to d, or maxDerivative if true. If true, maxDerivative must be set, too.

variableName: Symbol -> %: variableName(d) specifies the variable used in by the algebraic differential equation. This option is expressed in the form variableName == d.

CoercibleTo OutputForm