_Laurent
AST node for laurent(e, v, point, m, n).
Expands e about an isolated singularity as Σ(k = −m to n) c_k·(v − point)ᵏ.
Follows _Taylor's convention that v is the expansion variable rather than a binder — free in the result, but excluded from children so substitute cannot rewrite the variable the expansion is taken in.
m is optional. When absent the pole order is detected with singularitiesOf whose Pole(order) is the length of the principal part. A Removable singularity gives m = 0, which is an ordinary Taylor series — returned rather than refused, since the caller asked a well-formed question that simply has no principal part.
Stays symbolic when the order cannot be determined, when a coefficient does not fold finite, or when the point is an essential singularity: there the principal part is infinite, and a truncation would carry a different contract from the polynomial tiers — the discarded terms blow up near the point instead of becoming small.
Value parameters
- e
-
the expression to expand
- m
-
the pole order, or
Noneto detect it - n
-
the highest non-negative power retained
- point
-
the singularity
- v
-
the expansion variable
Attributes
- Graph
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- Supertypes
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trait Serializabletrait Producttrait Equalsclass _Functionaltrait _Expressionclass Objecttrait Matchableclass Any