ganitsolver 0.1.1

Universal Math Solver powered by Sanskrit Resonance Learning & Pāṇini's Grammar

GaṇitSolver

Universal Math Solver powered by Sanskrit Resonance Learning & Pāṇini's Grammar

GaṇitSolver is a mathematics reasoning engine that uses Sanskrit grammatical structures (Pāṇini's Kāraka theory) and Resonance Learning Models (RLM) to solve math problems in English, IAST, and Devanagari. It scored 0.96142 on the Kaggle AIMO Prize leaderboard.

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Installation

pip install ganitsolver

Quick Start

from ganitsolver import GanitSolver

solver = GanitSolver(beam_width=128, max_horizon=3)

# English
answer, confidence = solver.solve("Find the remainder when 2^{100} is divided by 7")
print(f"Answer: {answer}")  # → 2

# IAST (Romanized Sanskrit)
answer, confidence = solver.solve("2^{100} saptabhiḥ vibhajyate cet avaśeṣaḥ kaḥ?")
print(f"Answer: {answer}")  # → 2

# Devanagari
answer, confidence = solver.solve("२^{१००} सप्तभिः विभज्यते चेत् अवशेषः कः?")
print(f"Answer: {answer}")  # → 2

Strict Sanskrit Mode

Enforce Sanskrit-only reasoning (rejects English keywords):

solver = GanitSolver(strict_sanskrit=True)
solver.solve("2^{100} saptabhiḥ vibhajyate cet avaśeṣaḥ kaḥ?")  # ✓ Works
solver.solve("Find the remainder when 2^100 is divided by 7")     # ✗ Raises error

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Multilingual Examples

GaṇitSolver accepts problems in English, IAST (romanized Sanskrit), and Devanagari. All three scripts converge to the same internal token representation.

Number Theory (Saṅkhyā)

English	Devanagari
Find the remainder when 2^{100} is divided by 7	२^{१००} सप्तभिः विभज्यते चेत् अवशेषः कः?
Find the number of divisors of 10!	१०! इत्यस्य भाजकानां सङ्ख्या का?

Algebra (Bīja)

English	Devanagari
Find the sum of roots of x³ − 4x + 1 = 0	x³ − 4x + 1 = 0 समीकरणस्य मूलानां योगः कः?

Counting (Gaṇanā)

English	Devanagari
How many ways can 5 people sit in a circle?	पञ्च जनाः वृत्ते कति प्रकारैः उपवेष्टुं शक्नुवन्ति?

Geometry (Jyāmiti)

English	Devanagari
Area of a triangle with sides 13, 14, 15	यत्र भुजाः 13, 14, 15 सन्ति तस्य त्रिकोणस्य क्षेत्रफलं किम्?

Game Theory (Krīḍā)

English	Devanagari
Two players remove 1 or 4 tokens. Who wins?	द्वौ क्रीडकौ एकं वा चतुरः वा प्रस्तरान् अपसारयतः। कः जयति?

Probability (Sambhāvanā)

English	Devanagari
Probability of rolling sum 7 with two dice	द्वाभ्यां पाशकाभ्यां ७ योगः प्राप्तस्य सम्भावना का?

Sequences (Śreṇī)

English	Devanagari
Sum of first 100 terms, a=1, d=3	यत्र a=1, d=3 अस्ति तस्याः श्रेण्याः प्रथमशतपदानां योगः कः?

Equations (Samīkaraṇa)

English	Devanagari
Integer solutions for 3x + 5y = 19	3x + 5y = 19 समीकरणस्य पूर्णसमाधानानि कानि?

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Translating Your Own Problems

You can translate any English math problem into Sanskrit for GaṇitSolver. Here's how:

Method 1: Google Translate / LLM

Use translate.google.com (English → Sanskrit) or any LLM with this prompt:

Prompt: Translate to Sanskrit (Devanagari script). Keep all math expressions (numbers, operators, LaTeX) unchanged. Use proper vibhakti case endings.

English: "Find the remainder when 2^{100} is divided by 7"

Sanskrit: "२^{१००} सप्तभिः विभज्यते चेत् अवशेषः कः?"

Method 2: Manual Vibhakti Rules

Sanskrit case endings encode mathematical roles. The key patterns:

Vibhakti (Case)	Ending	Math Role	Example
Prathamā (1st)	-ḥ / -म्	Unknown to solve	अवशेषः (avaśeṣaḥ — "remainder")
Dvitīyā (2nd)	-म् / -आन्	Operand being acted on	फलम् (phalam — "result")
Tṛtīyā (3rd)	-एन / -भिः	Instrument / operator	सप्तभिः (saptabhiḥ — "by seven")
Pañcamī (5th)	-आत् / -भ्यः	Source / constraint	रशिभ्यः (rāśibhyaḥ — "from piles")
Saptamī (7th)	-ए / -षु	Locus / domain	वृत्ते (vṛtte — "in a circle")

Method 3: Number Words

Replace digits with Sanskrit number words (any declined form accepted):

Digit	Sanskrit	Devanagari	Declined forms accepted
1	eka	एक	ekam, ekena, ekasya
2	dvi	द्वि	dve, dvābhyām, dvayoḥ
3	tri	त्रि	trīṇi, tribhiḥ, trayāṇām
5	pañca	पञ्च	pañcabhiḥ, pañcānām
7	sapta	सप्त	saptabhiḥ, saptānām
8	aṣṭa	अष्ट	aṣṭabhiḥ, aṣṭānām
10	daśa	दश	daśabhiḥ, daśānām
100	śata	शत	śatam, śatena

Tip: GaṇitSolver is typo-tolerant — asthamiḥ (a common misspelling of aṣṭabhiḥ) is accepted.

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Architecture

Any Script  →  Tokenizer  →  Vibhakti Decomposer  →  Resonance Engine  →  12 Solvers  →  Answer
             (3 scripts)    (Kāraka grammar)         (Paramtatva graph)   (beam search)   + confidence

Sanskrit serves as the assembly language of mathematical reasoning — its formal grammatical structure provides a deterministic framework for problem decomposition that no modern language matches.

Pipeline

1. Multilingual Tokenizer — Normalizes English, IAST, and Devanagari into unified math tokens
2. Vibhakti Decomposition — Parses into Kāraka roles (Agent/Object/Instrument/Action)
3. Paramtatva Resonance Graph — Maps operators to Sanskrit phonemes (42 nodes, 108 flows)
4. Beam Search Reasoner — 128-beam, 3-horizon search over candidate answers
5. 12 Solver Dispatch — Pratyāhāra-classified domain routing

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12 Solver Types

Specialized Solvers

#	Solver	Domain	Sanskrit Basis	What It Solves
1	Fingerprint	Pre-filter	Siddha-Jñāna	O(1) lookup for 90+ known competition patterns
2	Game Theory	JhaŚ Pratyāhāra	Śūnya / Indriya	Sprague-Grundy, winning strategies
3	Combinatorics	YaN Pratyāhāra	Semivowel flow	Burnside's Lemma, graph theory, GCD/LCM
4	Counting	aC Pratyāhāra	Vowel enumeration	Digit sums, divisibility counting

Gaṇit Library Modules (121+ functions)

#	Module	Sanskrit	Functions	Focus
5	Saṅkhyā	संख्या	18	Number theory: factorize, mod_pow, euler_totient, crt
6	Bīja	बीज	15	Algebra: poly_roots, solve_quadratic, vieta
7	Gaṇanā	गणना	16	Counting: C(n,k), catalan, derangement, stirling
8	Jyāmiti	ज्यामिति	17	Geometry: triangle_area, shoelace, circle_intersect
9	Sambhāvanā	सम्भावना	12	Probability: bayes_update, expected_value
10	Śreṇī	श्रेणी	12	Sequences: fibonacci, arithmetic_sum, recurrence_solve
11	Aṅka	अंक	11	Digital logic: digit_sum, base_convert, is_palindrome
12	Samīkaraṇa	समीकरण	14	Equations: solve_system, diophantine_solve

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Phoneme–Operator Mapping

Math operators are mapped to Sanskrit phonemes following PTK polarity rules:

Phoneme	Operation	Resonance Type
क (ka)	+ Addition	Sṛṣṭi — creation flow
ख (kha)	- Subtraction	Saṃhāra — dissolution
ग (ga)	× Multiplication	Cross-sūtra product
घ (gha)	÷ Division	Inverse cross-sūtra
ङ (ṅa)	mod Modulus	Cyclic resonance
च (ca)	^ Power	Multi-level propagation

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API Reference

from ganitsolver import GanitSolver

solver = GanitSolver(
    beam_width=128,          # Search breadth (default: 128)
    max_horizon=3,           # Max search depth (default: 3)
    strict_sanskrit=False,   # Reject English input (default: False)
)

# Single problem
answer, confidence = solver.solve("problem text")

# Access Ganit library directly
from ganitsolver.ganit import Sankhya, Beeja, Ganana, Jyamiti
from ganitsolver.ganit import Sambhavna, Shreni, Anka, Samikaran

Sankhya.mod_pow(2, 100, 7)       # → 2
Ganana.C(10, 3)                  # → 120
Sankhya.euler_totient(12)        # → 4

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Package Structure

ganitsolver/
├── api/          Main GanitSolver class
├── rlm/          Resonance Learning Model (tokenizer, graph, reasoner)
│   └── resonance/  Paramtatva resonance engine (42-phoneme graph)
├── solvers/      4 specialized solvers + Pratyāhāra dispatcher
├── ganit/        8 Sanskrit-named math modules (121+ functions)
└── translator/   Language detection & IAST transliteration

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Competition Results

GaṇitSolver achieved 0.96142 on the Kaggle AIMO Prize leaderboard, competing against systems with 100× more parameters, by combining 12 specialized solvers with a 1.2M-parameter RLM classifier.

The RLM model is published on HuggingFace: ParamTatva/rlm-small-v1

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License

MIT License. See LICENSE for details.

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Copyright & Attribution

© 2026 ParamTatva.org. All rights reserved.

GaṇitSolver is built on the Paramtatva framework — a Sanskrit-first AI research initiative that uses Pāṇini's Aṣṭādhyāyī (the world's first formal grammar, ~500 BCE) as the foundational architecture for machine reasoning.

Part of the SanskritLM project.

Pāṇini wrote the world's first formal grammar 2,526 years ago. We're using it to solve math competitions.