Bharatiya Bijaganita
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ಪ್ರಾಚೀನ ಭಾರತೀಯ-ಬೀಜಗಣಿತದಲ್ಲಿ ಅನಿರ್ಣೀತ ಸಮೀಕರಣಗಳ ಕುರಿತ ವಿಶ್ಲೇಷಣೆಯು (Indeterminate-analysis) ವಿಶೇಷ ಗಮನಾರ್ಹವಾದ ಸಂಗತಿಯಾಗಿದೆ. ಏಕಘಾತೀಯ ಅನಿರ್ಣೀತ ಸಮೀಕರಣಗಳ ಪರಿಹಾರಕ್ಕೆ ಸಂಬAಧಿಸಿದ ವಿಷಯದ ವಿಶ್ಲೇಷಣೆಯನ್ನು ಭಾರತೀಯ-ಬೀಜಗಣಿತಜ್ಞರು ‘ಕುಟ್ಟಕ’ ಎಂಬ ಪಾರಿಭಾಷಿಕ ಪದದಿಂದ ಸೂಚಿಸಿದರೆ, ಅನಿರ್ಣೀತ ವರ್ಗಸಮೀಕರಣಗಳ ವಿಶ್ಲೇಷಣೆಯನ್ನು ‘ವರ್ಗಪ್ರಕೃತಿ’ ಎಂದು ಕರೆದಿದ್ದಾರೆ. ಎರಡೂ ವಿಷಯಗಳನ್ನು ವಿಶದವಾಗಿ ಚರ್ಚಿಸಿದೆ. ಚಿಹ್ನೆಗಳ-ಬಳಕೆ, ಅವ್ಯಕ್ತಗಳನ್ನು ಸೂಚಿಸುವುದಕ್ಕಾಗಿ ಬಳಸುವ ಅಕ್ಷರಸಂಕೇತಗಳು, ಸಮೀಕರಣಗಳು ಬೀಜಗಣಿತಶಾಸ್ತçದ ಮೂಲಾಧಾರಗಳಾಗಿವೆ. ಅವ್ಯಕ್ತಗಳನ್ನು ಸೂಚಿಸುವುದಕ್ಕಾಗಿ ಶಿಸ್ತುಬದ್ಧವಾಗಿ ಅಕ್ಷರಸಂಕೇತಗಳನ್ನು ಪ್ರಪ್ರಥಮವಾಗಿ ಬಳಸಿದವರು ಭಾರತೀಯರು. ವಿವಿಧ ಬಗೆಯ ಸಮೀಕರಣಗಳನ್ನು ವಿಭಿನ್ನ-ವರ್ಗಗಳಲ್ಲಿ ವಿಂಗಡಿಸಿ, ಅವುಗಳ ವಿಸ್ತöÈತ ಅಧ್ಯಯನವನ್ನು ಪ್ರಪ್ರಥಮವಾಗಿ ಕೈಗೊಂಡವರೂ ಅವರೇ ಆಗಿದ್ದಾರೆ. ಹಾಗಾಗಿ, ಬೀಜಗಣಿತವನ್ನು ಶಾಸ್ತçದ-ಸ್ವರೂಪದಲ್ಲಿ ಹುಟ್ಟುಹಾಕಿ ಮುನ್ನಡಿಸಿದವರೂ ಅವರೇ ಎಂದು ಹೇಳಬಹುದಾಗಿದೆ. ಪ್ರಸ್ತುತ ಕೃತಿಯು ಬೀಜಗಣಿತದ ಸಮೀಕರಣಗಳನ್ನು ಬಿಡಿಸುವುದಕ್ಕೆ ಅವಶ್ಯವಾಗಿರುವ ಪ್ರಕ್ರಿಯೆಗಳನ್ನು ಅಥವಾ ಪರಿಕರ್ಮಗಳನ್ನು ಅರ್ಥಾತ್ “ಬೀಜೋಪಯೋಗಿ-ಗಣಿತ”ವನ್ನು ಮತ್ತು ಬೀಜಗಣಿತೀಯ ಸಮೀಕರಣಗಳ ವಿಶ್ಲೇಷಣೆಯ ಕುರಿತು ಚರ್ಚೆ “ಬೀಜ” ಎರಡನ್ನೂ ಒಳಗೊಂಡಿದೆ. ಪ್ರಾಚೀನ ಆಚಾರ್ಯರು ನಿರೂಪಿಸಿರುವ ನಿಯಮಗಳಿಗೆ ಉಪಪತ್ತಿಯನ್ನು ಒದಗಿಸಿರುವುದು, ಮತ್ತು ಸ್ಪಷ್ಟೀಕರಣಕ್ಕಾಗಿ ಕೊಟ್ಟಿರುವ ಉದಾಹರಣೆ ಲೆಕ್ಕವನ್ನು ಆಯಾ ಗ್ರಂಥಕರ್ತನು ತಿಳಿಸಿರುವ ವಿಧಾನದನ್ವಯವೇ ಆಧುನಿಕ ಗಣಿತೀಯ-ಸಂಕೇತಗಳನ್ನು ಹಾಗೂ ಚಿಹ್ನೆಗಳನ್ನು ಬಳಸಿ ಪೂರ್ತಿಯಾಗಿ ಬಿಡಿಸಿ ತೋರಿಸಿರುವುದು ಈ ಕೃತಿಯ ವಿಶೇಷ ಮಹತ್ವದ ಸಂಗತಿಯಾಗಿವೆ. ಅಲ್ಲಲ್ಲಿ,
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