Feature/asymptotics by RotemKalisch · Pull Request #150 · RamanujanMachine/ramanujantools

RotemKalisch · 2026-03-06T20:42:43Z

Birkhoff-Trjitzinsky Asymptotics

Classes

SeriesMatrix

Introduced SeriesMatrix, a formal Puiseux Series Ring, to handle formal power series expansions in terms of a ramified local parameter t = n^{-1/p}. It supports exact Cauchy multiplication, formal inversion, and generalized binomial discrete shifts (n -> n+1).

GrowthRate

Implements a Tropical Semiring to track and compare asymptotic hierarchies (factorials, exponentials, sub-exponentials, polynomials, and logarithms). Overloads + to act as an L_infinity max-filter (safely isolating dominant terms without SymPy relational crashes) and * for asymptotic term multiplication and degree shifting.

Reducer

The core Birkhoff-Trjitzinsky algebraic solver. Iteratively applies gauge transformations (shears) and series ramification to deflate the Poincaré rank of formal difference systems until they completely decouple into scalar equations. Outputs the mathematically pure Canonical Fundamental Matrix (CFM).

Usage

Extracts a formal basis of asymptotic solutions for scalar linear difference equations. Because a linear recurrence is inherently solved as a companion matrix, the gauge transformation to physical space is the identity matrix (U = I). The formal BT solutions map strictly 1:1 to the sequence bounds.

from ramanujantools import LinearRecurrence, Matrix
import sympy as sp
from sympy.abc import n

M = Matrix([
    [1, n**3, (n - 1)*(3*n + 3)*(n**2 + n + 1)],
    [2, 1 - 3*n**2, (-n - 1)*(8*n**2 + n + 5)],
    [1, 3*n + 2, 6*n*(n + 1)]
])

# Convert the coupled system into a scalar sequence
lr = LinearRecurrence(M)

# Extract the pure formal asymptotic basis
lr_bounds = lr.asymptotics()

Copilot

Pull request overview

This PR introduces a Birkhoff–Trjitzinsky-based asymptotics engine for linear difference systems/recurrences, adding core algebra types (formal series ring + tropical growth comparisons) and wiring them into LinearRecurrence.asymptotics() with accompanying unit tests.

Changes:

Added new asymptotics subsystem (SeriesMatrix, GrowthRate, Reducer) and extensive test coverage for reduction/growth extraction.
Extended Matrix utilities (degrees, Jordan form block sorting, infinity-limit helper) and added tests for degree extraction.
Added LinearRecurrence.asymptotics() plus tests (including MeijerG-derived regressions).

Reviewed changes

Copilot reviewed 12 out of 12 changed files in this pull request and generated 9 comments.

Show a summary per file

File	Description
`ramanujantools/matrix.py`	Adds caching to companion coboundary matrix; adds degree extraction, Jordan block sorting, and an infinity-limit helper.
`ramanujantools/matrix_test.py`	Adds unit test for new `Matrix.degrees()`.
`ramanujantools/linear_recurrence.py`	Adds hashing + asymptotics extraction via the new reduction engine, with precision backoff.
`ramanujantools/linear_recurrence_test.py`	Updates existing tests and adds Fibonacci asymptotics test (but introduces global test state).
`ramanujantools/cmf/meijer_g_test.py`	Adds asymptotics regression tests via `LinearRecurrence`.
`ramanujantools/asymptotics/series_matrix.py`	New formal Puiseux/Taylor series matrix ring implementation.
`ramanujantools/asymptotics/series_matrix_test.py`	New unit tests for `SeriesMatrix` operations.
`ramanujantools/asymptotics/reducer.py`	New BT reduction engine and canonical growth/fundamental matrix extraction.
`ramanujantools/asymptotics/reducer_test.py`	New reducer correctness and guardrail tests.
`ramanujantools/asymptotics/growth_rate.py`	New tropical growth semiring/comparator implementation.
`ramanujantools/asymptotics/growth_rate_test.py`	New unit tests for growth comparisons and operations.
`ramanujantools/asymptotics/__init__.py`	Exports the new asymptotics API surface.

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ramanujantools/matrix.py

ramanujantools/asymptotics/reducer.py

ramanujantools/linear_recurrence_test.py

ramanujantools/linear_recurrence.py

ramanujantools/asymptotics/series_matrix.py

ramanujantools/asymptotics/reducer_test.py

ramanujantools/linear_recurrence.py

Copilot

Pull request overview

Copilot reviewed 12 out of 12 changed files in this pull request and generated 3 comments.

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ramanujantools/asymptotics/series_matrix.py

ramanujantools/asymptotics/reducer.py

ramanujantools/asymptotics/series_matrix_test.py

Copilot

Pull request overview

Copilot reviewed 12 out of 12 changed files in this pull request and generated 3 comments.

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ramanujantools/asymptotics/growth_rate.py

ramanujantools/asymptotics/series_matrix.py

ramanujantools/linear_recurrence.py

…e conjugates of each other

Copilot

Pull request overview

Copilot reviewed 12 out of 12 changed files in this pull request and generated 4 comments.

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ramanujantools/asymptotics/series_matrix.py

ramanujantools/asymptotics/series_matrix_test.py

ramanujantools/linear_recurrence.py

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Pull request overview

Copilot reviewed 12 out of 12 changed files in this pull request and generated 3 comments.

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ramanujantools/asymptotics/series_matrix_test.py

ramanujantools/linear_recurrence.py

ramanujantools/asymptotics/series_matrix.py

RotemKalisch added 15 commits February 18, 2026 19:16

Implement degrees and poincare_poly

a3ef99d

Implement SeriesMatrix

2575354

Implement exponential separation

a853fc4

Implement newton polygon shearing

94e230f

Implement ramification

f4f2870

All tests pass (except for block sylvester)

d78fc44

Support asymptotic expressions for ramified processes

8a5c031

Simplify interface, add gauge equivalence

cf3323c

Simplify jordan_form

ccc222b

Fix more tests

b16d683

Wrap asymptotics to Matrix and LinearRecurrence

c44f98d

Make GrowthRate class act as a ring

629d34b

Move exceptions to a separate file

92eb4cd

Review code and add docstrings

92d9856

Finalize Matrix asymptotics methods

0ef5ccd

RotemKalisch self-assigned this Mar 6, 2026

RotemKalisch force-pushed the feature/asymptotics branch from d13deb6 to a18539f Compare March 21, 2026 22:04

Passing tests with new trajectory case

d22e353

RotemKalisch force-pushed the feature/asymptotics branch from a18539f to d22e353 Compare March 22, 2026 19:16

RotemKalisch added 6 commits March 22, 2026 21:28

Remove redundant exception hirearchy

64b0943

Code cleanup

4b7ec5a

Replace all prints with logs

578ac4b

Simplify precision backoff logic

6e0bd2b

Make BT only support LinearRecurrence, simplify code

98a79f9

Simplify code

a235c7d

RotemKalisch force-pushed the feature/asymptotics branch from 4d01b7d to a235c7d Compare April 2, 2026 13:52

RotemKalisch requested a review from Copilot April 2, 2026 13:53

Copilot started reviewing on behalf of RotemKalisch April 2, 2026 13:54 View session

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Remove stale function

b1c4618

RotemKalisch added 2 commits April 2, 2026 20:05

sp.eye -> Matrix.eye

9aa3d21

Remove redundat safety checks in Matrix.degrees

900d20b

RotemKalisch force-pushed the feature/asymptotics branch from ece31b4 to 900d20b Compare April 2, 2026 17:09

RotemKalisch requested a review from Copilot April 2, 2026 17:09

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RotemKalisch added 3 commits April 2, 2026 20:28

Remove anti-pattern lru_cache on Reducer.reduce

9052ef0

Add validations to SeriesMatrix.__mul__

844b2d5

Remove wrong assertion message

47edfdc

RotemKalisch requested a review from Copilot April 2, 2026 17:34

Copilot started reviewing on behalf of RotemKalisch April 2, 2026 17:35 View session

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RotemKalisch added 2 commits April 2, 2026 20:51

Fix typo

43aba3e

Make GrowthRate.__gt__ fall back to a default sorting key, if they ar…

7b9ed5d

…e conjugates of each other

RotemKalisch force-pushed the feature/asymptotics branch from c067e52 to 74cfc8d Compare April 2, 2026 20:12

RotemKalisch requested a review from Copilot April 2, 2026 20:13

Copilot started reviewing on behalf of RotemKalisch April 2, 2026 20:13 View session

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Rename confusing variables

805a667

RotemKalisch force-pushed the feature/asymptotics branch from 74cfc8d to 805a667 Compare April 2, 2026 20:18

RotemKalisch added 3 commits April 2, 2026 23:19

Fix type hint

50d4016

Make type checking in shear_coboundary more explicit

60f5461

Move parameter declaration inside the test

cd0a0dc

RotemKalisch requested a review from Copilot April 2, 2026 20:25

Copilot started reviewing on behalf of RotemKalisch April 2, 2026 20:26 View session

Remove leftover debug assertion

ac455a0

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ramanujantools/asymptotics/series_matrix.py Outdated Show resolved Hide resolved

Remove redundant check

897a239

RotemKalisch merged commit f3bb146 into master Apr 2, 2026
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RotemKalisch deleted the feature/asymptotics branch April 2, 2026 20:38

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Birkhoff-Trjitzinsky Asymptotics

Classes

SeriesMatrix

GrowthRate

Reducer

Usage

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RotemKalisch commented Mar 6, 2026 •

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