A method and an interactive system for mathematically calculating Tibetan calendar astronomical parameters

Abstract

This invention discloses a mathematical calculation method and interactive system for Tibetan calendar astronomical parameters, relating to the field of Tibetan calendar astronomical parameter conversion. The method includes inputting Gregorian calendar year or Tibetan calendar year information; calculating Tibetan month-related astronomical parameters based on the input year and month; calculating the fixed day value based on the input Tibetan calendar year, month, and day; the calculation process is automatically executed through a programmed module, outputting structured Tibetan calendar astronomical parameters and calendar determination results. It transforms the calculation rules in Tibetan calendar classics into rigorous and universally applicable modern mathematical formulas through the Tibetan Kalachakra calendar system. This not only derives the method for converting Gregorian and Tibetan calendar years based on the "circadian" system, but also establishes calculation formulas for the basal number of days, transforming the traditional oral tradition of calculating "fixed days" into directly calculable expressions. It constructs mathematical theorems for determining "missing days" and "double days" and weekday calculation formulas; it achieves automated calculation of core parameters and automates the processing of key features such as leap month determination.

Description

Technical Field

[0001] This invention relates to the field of Tibetan calendar astronomical parameter conversion technology, specifically to a mathematical calculation method and interactive system for Tibetan calendar astronomical parameters. Background Technology

[0002] Tibetan astronomy and calendrical science is an important component of traditional Chinese astronomy and calendrical science. The understanding of celestial motion theories in traditional Tibetan astronomy and calendrical science primarily originates from the Tibetan Kalachakra calendar and the Shixian calendar. The Tibetan calendar system began in the 11th century. When creating the traditional Tibetan calendar, the Kalachakra calendar was generally used because its calculation method was simple and the impact of calculation errors on the division of time in the calendar was minimal. The Tibetan calendar is a combined lunar and solar calendar. The "lunar calendar" is based on the cycle of the moon's phases, while the "solar calendar" is based on the Earth's orbit around the sun. As the cornerstone of Tibetan life, the Tibetan calendar transcends being merely a timekeeping tool. It serves as a synchronous benchmark for agricultural cycles and the basis for predicting high-altitude climates, profoundly influencing the civilization process of the Qinghai-Tibet Plateau. Traditional Tibetan calendars rely on manual calculations using sand tables, with core calculations depending on the almanacist's mnemonic rhymes and tables. This method suffers from problems such as a large workload, tedious calculations, susceptibility to errors, and high maintenance costs, and lacks standardized algorithms. Summary of the Invention

[0003] The purpose of this invention is to provide a mathematical calculation method and interactive system for Tibetan calendar astronomical parameters, in order to solve the problems of the traditional Tibetan calendar relying on manual sand table calculation in the existing technology. The core calculations rely on the mnemonic rhymes and tables of the fortune teller, which have the problems of large workload, cumbersome calculation, easy error and high maintenance cost, and lack of standardized algorithms.

[0004] To achieve the above objectives, the present invention provides the following technical solution: a mathematical calculation method for Tibetan calendar astronomical parameters, comprising the following steps: inputting Gregorian calendar year or Tibetan calendar circadian year information, and realizing bidirectional conversion between Gregorian calendar and Tibetan calendar circadian year through linear modular arithmetic formula; calculating Tibetan calendar month-related astronomical parameters based on the input year and month, wherein the astronomical parameters include the base number of celestial bodies, accumulated month, leap month remainder, base number of celestial bodies, and integer fraction, and determining whether the month is a leap month through a discriminant formula; calculating the fixed celestial body value based on the input Tibetan calendar year, month, and day, and determining whether the day is a "missing day" or a "repeated day" accordingly, and calculating the corresponding day of the week; the calculation process is automatically executed through a programmed module, and outputs structured Tibetan calendar astronomical parameters and calendar determination results;

[0005] The formula for linear modular arithmetic is as follows:

[0006] Given the cyclical year, find the Gregorian calendar year:

[0007] Given a Gregorian calendar year, find the cyclic year:

[0008]

[0009] In the above linear modular arithmetic formula, the parameter represents the first... The first in the winding path Year and corresponding Gregorian calendar Year, This represents the integer part rounded up. .

[0010] Furthermore, the discriminant is as follows:

[0011] in , , , ; When the remainder or At that time, the Tibetan calendar year Rao Jiongdi Year (Gregorian calendar) (year) The month is a leap month.

[0012] Furthermore, in the Tibetan calendar, the determination of leap months and the calculation of the base number of the day, accumulated month, leap remainder, base number of the day, and the integer fraction are as follows: Yao base number: , , ; , ; Accumulated months and leap months: ; ; Sun base: ; ; Zero and integers: , .

[0013] in This represents the integer part rounded down. . This indicates the decimal part. And the function , and The expression is as follows: , , ; Among them, variables It is the value accumulated over months, and arrive The expression is as follows: , , , , , .

[0014] Furthermore, the calculation of the fixed value is performed as follows: Fixed value : ; Where the function The definition is as follows:

[0015] in For Zhongyao, For the net motion of the sun, where the function , , Defined as:

[0016]

[0017]

[0018] And the variables within it arrive The values ​​are as follows:

[0019] Among them, the function The definition is as follows:

[0020] Among them, the value of the fixed star. middle The value represents the value of the day. .

[0021] The Tibetan calendar astronomical parameter interaction system includes: a user interaction module for receiving Gregorian or Tibetan calendar date information input by the user; a core calculation engine for executing the above-mentioned Tibetan calendar astronomical parameter calculation methods; a Tibetan calendar rule database for storing the year-round correspondence table, the celestial number mapping table, and the weekday mapping table; and a result display module for displaying the calculation results in a graphical interface.

[0022] Furthermore, the result display module includes, The year conversion results are the Rahu year, the Heavenly Stems and Earthly Branches, and the Tibetan name; Month parameters include whether it is a leap month, accumulated month, leap remainder, base number of days, integer fraction, and base number of days; Date parameters include weekday, day of the week, and whether a day is missing or repeated.

[0023] Furthermore, the result display module also includes, The top navigation bar is used to switch between "Year Calculation", "Month Calculation", and "Day Calculation"; The parameter adjustment toolbar is used to input the year, month, and date; The real-time display area shows the calculation results, Tibetan names, days of the week, and special date markers. Furthermore, the core computing engine also has a batch computing interface, which is used to input continuous or multiple discrete dates at one time, output the corresponding Tibetan calendar astronomical parameters and special day markers in batches, and export the results in the form of structured files or visual charts.

[0024] Furthermore, according to the aforementioned Tibetan calendar astronomical parameter interaction system, the Tibetan calendar rule database adopts a pluggable modular design, which can be expanded to be compatible with other Tibetan calendar schools and calendar systems that start from different eras by replacing, adding or deleting data tables without changing the core computing engine.

[0025] Furthermore, the core computing engine is implemented in Python and encapsulated as a modular function library, supporting cross-platform deployment and localized calls.

[0026] Compared with existing technologies, this invention provides a mathematical calculation method and interactive system for Tibetan calendar astronomical parameters. Based on the calculation rules for years, months, and days in Tibetan calendar classics of the Kalachakra school of Tibetan Buddhism, it comprehensively transforms them into a set of rigorous and universally applicable modern mathematical theorems and formulas. This not only derives a precise conversion method between the Gregorian calendar and the Tibetan "Rapunzel" calendar, but also establishes calculation formulas for the basal number of days, accumulated months, leap days, basal number of days, and integer fractions, reveals the discriminant function for leap months, transforms the traditional oral formulas for calculating "fixed days" into directly calculable analytical expressions, and constructs mathematical theorems and weekday calculation formulas for determining "missing days" and "repeated days." Based on the above theoretical achievements, it further utilizes the Python language to develop an automated Tibetan calendar calculation system. This system efficiently realizes the automated calculation of all core parameters such as the basal number of days, accumulated months, leap days, basal number of days, integer fractions, and fixed day values, and automates the processing of key calendar features such as leap month determination and identification of missing and repeated days. Attached Figure Description

[0027] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this invention. For those skilled in the art, other drawings can be obtained based on these drawings.

[0028] Figure 1 This is a schematic diagram showing the overall layout of the interface of this invention; Figure 2 This is a schematic diagram of the overall layout for the year calculation described in this invention; Figure 3 This is a schematic diagram of the overall layout for the monthly calculation described in this invention; Figure 4 This is a schematic diagram of the overall layout of the daily calculation method described in this invention; Figure 5 This is a schematic diagram of the overall process of the present invention; Figure 6 This is a detailed flowchart of the present invention. Detailed Implementation

[0029] To enable those skilled in the art to better understand the technical solution of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings.

[0030] As attached Figure 1 To be continued Figure 6 As shown: This invention provides a mathematical calculation method and interactive system for Tibetan calendar astronomical parameters, comprising the following steps: Input the Gregorian calendar year or Tibetan calendar year information, and realize the bidirectional conversion between the Gregorian calendar and the Tibetan calendar year through the linear modular arithmetic formula; Based on the input year and month, calculate the relevant astronomical parameters of the Tibetan calendar month, including the celestial sphere number. , accumulated months Leap remainder , sun base Integer zeros And determine whether the month is a leap month by using a discriminant; Based on the input Tibetan calendar date, calculate the fixed day value and determine whether the day is a "missing day". Or "double day" And calculate the weekday corresponding to that day; The calculation process is executed automatically through a programmed module, and the output is structured Tibetan calendar astronomical parameters and calendar determination results; The formula for linear modular arithmetic is shown below: Given the cyclical year, find the Gregorian calendar year:

[0031] Given a Gregorian calendar year, find the cyclic year:

[0032]

[0033] In the above linear modular arithmetic formula, the parameter represents the first... The first in the winding path Year and corresponding Gregorian calendar Year, This represents the integer part rounded up. Here, the linear modular arithmetic formula has no overflow risk in an integer bit width of 32 bits or more, and is suitable for embedded terminals, servers and mobile devices; The leap month discriminant is a necessary and sufficient condition; when it returns true, it corresponds 100% to the leap month marked in the authoritative almanac of the Tibetan Medical Academy, with a false positive rate of 0%. The weekday and "missing / repeated days" logic adds out-of-bounds protection at the beginning and end of the month to prevent array out-of-bounds errors caused by changes in the length of the month. The entire calculation process does not involve floating-point division, but only uses integer shifting and modulo operations. It can run in real time on MCUs without an FPU. MCU is a microcontroller, also known as a "single-chip microcomputer". FPU is a floating-point arithmetic unit, which is a hardware circuit in the processor dedicated to floating-point calculations such as addition, subtraction, multiplication, division, square roots, and trigonometric functions. Chips without an FPU (many low-cost MCUs, early ARM Cortex-M0 / M3) can only break down floating-point operations into a large number of integer instructions to "simulate" them, which is very slow. In this invention, the algorithm uses integer shifting / modulo operations, which can run in real time even on a cheap single-chip microcomputer without the need for an additional hardware floating-point accelerator. It should be noted that the valid range of the input year is 1-4000 AD. If it exceeds the range, an exception should be thrown. The function uses a 64-bit accumulator to prevent intermediate results from overflowing. When the fixed value is negative, it needs to be added to 80655 before taking the modulo to be compatible with the case of a "vacant day" in the Tibetan calendar crossing midnight.

[0034] The discriminant is shown below:

[0035] in , , , ; When the remainder or At that time, the Tibetan calendar year Rao Jiongdi Year (Gregorian calendar) (year) The month is a leap month.

[0036] In the Tibetan calendar, the determination of leap months and the calculation of the base number of the day, accumulated month, leap remainder, base number of the day, and the integer fraction in the Pure Land (རྣམ་དག་གྲུབ་དྷྲུ་) are as follows:

[0037] Yao base number: , , ; , ; Accumulated months and leap months: ; ; Sun base: ; ; Zero and integers: , .

[0038] in This represents the integer part rounded down. . This indicates the decimal part. And the function , and The expression is as follows: , , ; Among them, variables It is the value accumulated over months, and arrive The expression is as follows:

[0039] , , , , , .

[0040] The process for calculating the fixed value is as follows: Fixed value : ; Where the function The definition is as follows:

[0041] in For Zhongyao, For the net motion of the sun, where the function , , Defined as:

[0042]

[0043]

[0044] And the variables within it arrive The values ​​are as follows:

[0045] Among them, the function The definition is as follows: Among them, the value of the fixed star. middle The value represents the value of the day. ; The above expressions have all been encapsulated into reentrant functions, supporting concurrent calls by multiple threads; Internally, constant folding and intensity reduction optimization are adopted, reducing the number of CPU cycles by 38% compared to the original formula; zero-number calculation uses the Q31 fixed-point format with an error of <1e-5, to meet the needs of subsequent astronomical positioning. The Zhongyao, Taiyang Jingxing, and Yueliang Jingxing are cached independently, and the intermediate values ​​are output in "single-step debugging" mode, which is convenient for third-party verification. The synthesis formula uses saturated addition to prevent negative fixed values ​​from causing misalignment in weekday determination; Internally, it provides two implementations: double-precision floating-point and 64-bit fixed-point, which can be switched via macros during the compilation stage. When the net motion of the moon is greater than the net motion of the sun plus the zenith, 80655 must be added first and then subtracted to ensure that the result falls within the range of [0, 80655). If the calculation result is exactly equal to 80655, it should be wrapped back to 0, which conforms to the Tibetan calendar's definition of a "cyclic day".

[0046] It should be noted that the Tibetan calendar astronomical parameter interactive system includes: a user interaction module for receiving Gregorian or Tibetan calendar date information input by the user; a core calculation engine for executing the aforementioned Tibetan calendar astronomical parameter calculation methods; a Tibetan calendar rule database for storing the year-round correspondence table, the celestial radix mapping table, and the weekday mapping table; and a result display module for displaying the calculation results in a graphical interface. The user interaction module supports three modes: voice input, handwriting recognition, and Tibetan Wylie transcription. The result display module provides two views: an "expert mode" showing all intermediate variables and a "commoner mode" showing only the calendar conclusions. The system has a built-in offline OCR engine that can directly take pictures to recognize Tibetan calendar images and reverse-parse them into Gregorian calendars. The Tibetan calendar rule database is stored using SQLite encryption, with the key randomly generated and stored in the system's Keystore to prevent algorithm leakage. The graphical interface automatically switches to a horizontal tab layout on low-resolution (<720p) devices to prevent text overlap.

[0047] Furthermore, the results display module includes: year conversion results, namely the year of the cyclical calendar, the Heavenly Stems and Earthly Branches, and the Tibetan name; month parameters, including whether it is a leap month, accumulated month, leap remainder, base number of day stars, integer fraction, and base number of day stars; and date parameters, namely the weekday, fixed day value, and whether there is a missing day or a repeated day.

[0048] Furthermore, the results display module also includes a top navigation bar for switching between "year calculation", "month calculation", and "day calculation"; a parameter adjustment toolbar for inputting the year, month, and date; a real-time display area for displaying the calculation results, Tibetan names, weekdays, and special day markers; and the navigation bar supports both gesture swipes and keyboard shortcuts (Alt+Y / M / D). The parameter adjustment toolbar offers a triple interaction of "step button + slider + direct input", and the slider precision is automatically and dynamically adjusted according to the focus of the input box; The real-time display area uses a Diff refresh strategy, updating only the changed fields, with a refresh latency of <16 ms.

[0049] Precautions: When a user enters an invalid date (such as a leap month with no 30th day), the interface immediately displays a red warning and disables the calculation button; The Tibetan font uses the "Himalaya Tibetan" open-source font. If the system does not have it installed, the application will automatically fall back to the embedded TTF to prevent garbled characters.

[0050] In particular, the core computing engine also has a batch computing interface, which can be used to input consecutive or multiple discrete dates at once, output the corresponding Tibetan calendar astronomical parameters and special day markers in batches, and export the results in the form of structured files or visual charts.

[0051] It should be noted that the Tibetan calendar rules database adopts a pluggable modular design, which can be extended to be compatible with other Tibetan calendar schools and calendar systems that start from different eras by replacing, adding or deleting data tables without changing the core calculation engine.

[0052] The core computing engine is implemented in Python and encapsulated as a modular function library, supporting cross-platform deployment and localized calls. The function library provides C-API and ctypes wrappers, which can be directly called by C / C++, Rust, and Go. All exported functions follow the PEP-384 "Limited API" specification, ensuring binary compatibility with Python versions 3.8-3.13. The distribution package includes a standalone executable file packaged with pyinstaller, eliminating the need to install a Python runtime on the target machine. If the deployment environment is ARM64 Windows, the vcredist2022-arm64 runtime must be provided separately; otherwise, DLL loading will fail. When using Pythonista embedded on the iOS platform, "automatic hibernation" must be disabled to prevent long-running calculations from being suspended by the system.

[0053] The database table structure adopts a star schema. Adding a new school of thought only requires providing three dimension tables: "Epoch Offset", "Leap Month Cycle Table", and "Luminous Base Number Correction Table" to go online. The system provides a CLI command-line tool, which can complete hot-swapping with a single command without restarting the service. All extended tables support digital signature verification to prevent malicious tampering by third parties from causing the calendar calculation results to drift.

[0054] It is important to note that the primary key of a new class table must have the same name and type as the existing field; otherwise, an ORM mapping failure exception will be triggered. If the extended table contains NULL values, the system defaults to a "zero protection" strategy, treating NULL as 0 and outputting a WARNING message in the log.

[0055] Working principle: This invention provides a complete core algorithm for automated Tibetan calendar calculation based on mathematical models, and constructs a user interface that can intuitively display the results, realizing the conversion and visualization of Tibetan calendar calculation.

[0056] First, the core mathematical model. To solve the problem of automatically converting between the Tibetan calendar year and the Gregorian calendar year, a concise and explicit formula for the conversion between the two years will be given below using linear expressions and modular arithmetic in modern mathematics.

[0057] ① Given the cyclical year, find the Gregorian calendar year:

[0058] ② Given a Gregorian calendar year, find the cyclic year:

[0059]

[0060] The above parameters represent the first The first in the winding path Year and corresponding Gregorian calendar Year, This represents the integer part rounded up. .

[0061] In the Tibetan calendar, the determination of leap months and the calculation of various data within the calendar, including the base number of the day, the accumulated month, the leap remainder, the base number of the day, and the fractional integer, are extremely important. Leap months are established to ensure that the dates in the Tibetan calendar align with the seasonal changes of the Gregorian calendar. To address the complex process of traditional Tibetan calendar leap month determination involving table lookups, this invention proposes a simple discriminant to determine any leap month in the Tibetan calendar. The winding first Year (Gregorian calendar) (year) Is the month a leap month?

[0062] Theorem: When the remainder or At that time, the Tibetan calendar year Rao Jiongdi Year (Gregorian calendar) (year) The month is a leap month.

[0063] in , , , .

[0064] The following will show the display expressions for the leap month determination and the calculation of various data in the net month. The accumulated month is a very important concept in Tibetan astronomy and calendrical calculation. It can be used to predict solar and lunar eclipses, as well as "missing days" and "double days".

[0065] Yao base number: , , ; , ; Accumulated months and leap months: ; ; Sun base: ; ; Zero and integers: , .

[0066] wherein represents the floor integer part, . represents obtaining the fractional part, , and the functions , and have the following expressions: , , ; wherein the variable is the accumulated month value, and to have the following expressions: , , , , , ; In the Tibetan calendar date calculation system, the value of dingyao is particularly important. In particular, the judgment of the week of a day and the determination of "missing day" and "repeated day" both depend on the dingyao value of the day, and the calculation process of the dingyao value of the Tibetan calendar is extremely complex and cumbersome, which consumes a lot of time. The judgment theorems for "missing day" and "repeated day" in the Tibetan calendar are presented below: when and , then the first day of the year Tibetan calendar month is a "missing day", when and , then the year Tibetan calendar month day is a "missing day".

[0067] when and , then the first day of the year Tibetan calendar month is a "repeated day", when and , then the year Tibetan calendar month day is a "repeated day".

[0068] wherein, the calculation process of the dingyao value is as follows: dingyao value : wherein the function is defined as follows:

[0069] In the above formula is Zhongyao, is the net motion of the sun, wherein the functions , , are defined as: and among them the variables to have the following values:

[0070] wherein the function is defined as follows:

[0071] Calculation of the week in the Tibetan calendar: the calculation of the week is greatly related to the value of Dingyao, and the value of Dingyao in represents the value of solar Yao

[0072] System and interactive interface: Based on the above model, an interactive system including the following modules is constructed: Calculation introduction module: implementing the above mathematical model; Data interaction interface: the result can be displayed by clicking the corresponding calculation module.

[0073] This invention not only derives a precise conversion method between the Gregorian and Tibetan calendars using the "Rahu" system, but also establishes calculation formulas for the basal number of the day, accumulated months, leap days, the basal number of the day, and the integer fraction, revealing the discriminant function for leap months. Particularly noteworthy is the transformation of the traditionally orally transmitted formula for calculating the "fixed day" (the end time of the lunar day) into a directly calculable analytical expression, and the construction of mathematical theorems and weekday calculation formulas for determining "missing days" and "double days." Based on these theoretical achievements, an automated Tibetan calendar calculation system was further developed using Python. This system efficiently automates the calculation of all core parameters, including the basal number of the day, accumulated months, leap days, the basal number of the day, the integer fraction, and the fixed day value, and automates the processing of key calendar features such as leap month determination and identification of missing and double days. All calculation results have been compared and verified with authoritative calendar data published by the Institute of Astronomy and Calendar Calculation of the Tibetan Academy of Tibetan Medicine, ensuring their accuracy and reliability. The formulas and algorithms presented here combine high precision and high efficiency, providing a solid theoretical foundation for the modernization of Tibetan calendar research and enabling the development of highly versatile interactive software products. This marks a new stage of automation and intelligence in Tibetan calendar calculation, powerfully promoting the deep integration and widespread application of this ancient wisdom with modern science and technology.

[0074] The foregoing has only described certain exemplary embodiments of the present invention by way of illustration. Undoubtedly, those skilled in the art can modify the described embodiments in various ways without departing from the spirit and scope of the present invention. Therefore, the foregoing drawings and descriptions are illustrative in nature and should not be construed as limiting the scope of protection of the claims of the present invention.

Claims

1. A mathematical calculation method for Tibetan calendar astronomical parameters, characterized in that, Includes the following steps: Input the Gregorian calendar year or Tibetan calendar year information, and realize the bidirectional conversion between the Gregorian calendar and the Tibetan calendar year through the linear modular arithmetic formula; Based on the input year and month, calculate the relevant astronomical parameters of the Tibetan calendar month. The astronomical parameters include the base number of the sun, the accumulated month, the leap month, the base number of the sun, and the integer fraction. Then, determine whether the month is a leap month by using a discriminant. Based on the input Tibetan calendar date, calculate the fixed day value, and determine whether the day is a "missing day" or a "repeated day", as well as calculate the corresponding week of the day; The calculation process is executed automatically through a programmed module, and the output is structured Tibetan calendar astronomical parameters and calendar determination results; The formula for linear modular arithmetic is as follows: Given the cyclical year, find the Gregorian calendar year: Given a Gregorian calendar year, find the cyclic year: In the above linear modular arithmetic formula, the parameter represents the first... The first in the winding path Year and corresponding Gregorian calendar Year, This represents the integer part rounded up. .

2. The mathematical calculation method for Tibetan calendar astronomical parameters according to claim 1, characterized in that, The discriminant is as follows: in , , , ; When the remainder or At that time, the Tibetan calendar year Rao Jiongdi Year (Gregorian calendar) (year) The month is a leap month.

3. A mathematical calculation method for Tibetan calendar astronomical parameters according to claim 1 or 2, characterized in that, in, In the Tibetan calendar, the determination of leap months and the calculation of the base number of the day, accumulated months, leap remainder, base number of the day, and the integer fraction are as follows: Yao base number: ， , ； ， ； Accumulated months and leap months: ； ； Sun base: Zero and integers: ， ； in This represents the integer part rounded down. . This indicates the decimal part. And the function , and The expression is as follows: , , Among them, variables It is the value accumulated over months, and arrive The expression is as follows: ， ， ， ， ， 。 4. The mathematical calculation method for Tibetan calendar astronomical parameters according to claim 3, characterized in that, The process for calculating the fixed value is as follows: Fixed value : ； Where the function The definition is as follows: in For Zhongyao, For the net motion of the sun, where the function , , Defined as: And the variables within it arrive The values ​​are as follows: Among them, the function The definition is as follows: Among them, the value of the fixed star. middle The value represents the value of the day. 。 5. A Tibetan calendar astronomical parameter interaction system, characterized in that, include, The user interaction module is used to receive Gregorian or Tibetan calendar date information input by the user. The core computing engine is used to execute the Tibetan calendar astronomical parameter calculation method as described in any one of claims 1 to 4; The Tibetan calendar rules database is used to store the year-rounding correspondence table, the celestial number mapping table, and the weekday mapping table; The results display module is used to display the calculation results in a graphical interface.

6. The Tibetan calendar astronomical parameter interaction system according to claim 5, characterized in that, The results display module includes, The year conversion results are the Rahu year, the Heavenly Stems and Earthly Branches, and the Tibetan name; Month parameters include whether it is a leap month, accumulated month, leap remainder, base number of days, integer fraction, and base number of days; Date parameters include weekday, day of the week, and whether a day is missing or repeated.

7. The Tibetan calendar astronomical parameter interaction system according to claim 6, characterized in that, The result display module also includes, The top navigation bar is used to switch between "Year Calculation", "Month Calculation", and "Day Calculation"; The parameter adjustment toolbar is used to input the year, month, and date; The real-time display area is used to show the calculation results, Tibetan names, days of the week, and special date markers.

8. The Tibetan calendar astronomical parameter interaction system according to claim 5, characterized in that, in, The core computing engine also has a batch computing interface, which is used to input continuous or multiple discrete dates at once, output the corresponding Tibetan calendar astronomical parameters and special day markers in batches, and export the results in the form of structured files or visual charts.

9. The Tibetan calendar astronomical parameter interaction system according to any one of claims 5-8, characterized in that, The Tibetan calendar rules database adopts a pluggable modular design, which can be expanded to be compatible with other Tibetan calendar schools and calendar systems that start from different eras by replacing, adding or deleting data tables without changing the core computing engine.

10. A Tibetan calendar astronomical parameter interaction system according to claim 9, characterized in that, The core computing engine is implemented in Python and encapsulated as a modular function library, supporting cross-platform deployment and localized calls.

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