MrvLimitPackage

mrv_limit.spad line 26 [edit on github]

Compute limits using Gruntz-Gonnet MRV algorithm

expr_to_series: (Expression Integer, Kernel Expression Integer, Record(tan_syms: List Symbol, atan_syms: List Symbol, tan_kers: List Kernel Expression Integer, atan_kers: List Kernel Expression Integer)) -> Union(Record(degree: OrderedExpression, coeff: Expression Integer), failed)

expr_to_series computes degree and leading coefficinet of series expansion.

mrv_cmp: (Kernel Expression Integer, Kernel Expression Integer, Symbol, Record(tan_syms: List Symbol, atan_syms: List Symbol, tan_kers: List Kernel Expression Integer, atan_kers: List Kernel Expression Integer)) -> Union(Record(sign: Integer, coeff: Expression Integer), failed)

mrv_cmp compare kernels.

mrv_limit1: (Expression Integer, Symbol) -> Union(OrderedCompletion Expression Integer, failed)

mrv_limit1(f, x) normalizes and computes limit.

mrv_limit: (Expression Integer, Equation Expression Integer, String) -> Union(OrderedCompletion Expression Integer, failed)

mrv_limit(f, x = a, str) computes limit(f(x), x=a) for a strictly finite limit point a. This function computes one-sided limits from the left or right.

mrv_limit: (Expression Integer, Equation OrderedCompletion Expression Integer) -> Union(OrderedCompletion Expression Integer, Record(leftHandLimit: Union(OrderedCompletion Expression Integer, failed), rightHandLimit: Union(OrderedCompletion Expression Integer, failed)), failed)

mrv_limit(f, x=a) computes limit(f(x), x=a) for a finite or infinite limit point a.

mrv_limit: (Expression Integer, Symbol, Expression Integer, String) -> Union(OrderedCompletion Expression Integer, failed)

mrv_limit(f, x, a, str) is like mrv_limit(f, x = a, str).

mrv_limit: (Expression Integer, Symbol, OrderedCompletion Expression Integer) -> Union(OrderedCompletion Expression Integer, Record(leftHandLimit: Union(OrderedCompletion Expression Integer, failed), rightHandLimit: Union(OrderedCompletion Expression Integer, failed)), failed)

mrv_limit(f, x, a) is like mrv_limit(f, x = a).

mrv_limit: (Expression Integer, Symbol, Record(tan_syms: List Symbol, atan_syms: List Symbol, tan_kers: List Kernel Expression Integer, atan_kers: List Kernel Expression Integer)) -> Union(OrderedCompletion Expression Integer, failed)

mrv_limit(f, x, s) computes limit.

mrv_normalize: (Expression Integer, Symbol, Record(tan_syms: List Symbol, atan_syms: List Symbol, tan_kers: List Kernel Expression Integer, atan_kers: List Kernel Expression Integer)) -> Expression Integer

mrv_normalize(f, x, s) transform f to the form acceptable by core variant of mrv_limit.

mrv_rewrite0: (Expression Integer, List Kernel Expression Integer, List Expression Integer, Expression Integer) -> Expression Integer

mrv_rewrite0 rewrites comparable kernels in terms of a single one.

mrv_rewrite: (Expression Integer, List Kernel Expression Integer, List Expression Integer, Symbol, Record(tan_syms: List Symbol, atan_syms: List Symbol, tan_kers: List Kernel Expression Integer, atan_kers: List Kernel Expression Integer)) -> Union(Record(degree: OrderedExpression, coeff: Expression Integer), failed)

mrv_rewrite rewrites comparable kernels and computes leading term of series expansion.

mrv_set: (Expression Integer, Symbol, Record(tan_syms: List Symbol, atan_syms: List Symbol, tan_kers: List Kernel Expression Integer, atan_kers: List Kernel Expression Integer)) -> Union(Record(lk: List Kernel Expression Integer, lc: List Expression Integer), failed)

mrv_set compute MRV set.

mrv_sign: (Expression Integer, Symbol, Record(tan_syms: List Symbol, atan_syms: List Symbol, tan_kers: List Kernel Expression Integer, atan_kers: List Kernel Expression Integer)) -> Union(Integer, failed)

mrv_sign(f, x, s) computes sign of f near x.