Fangchengshu, an ancient Chinese algorithm, refers to an elimination method for solving linear equations proposed in Nine Chapters of Arithmetic. Today's examples are as follows: the first question of "equation" in Chapter 8: "Today, there are three strokes of Shanghe, two strokes of Zhonghe, one stroke of Xiahe, and thirty-nine strokes; two strokes of Shanghe, three strokes of Zhonghe, one stroke of Xiahe, and thirty-four strokes; One stroke of the upper grain, two strokes of the middle grain, three strokes of the lower grain, and twenty-six strokes of the grain. How about each stroke of the upper grain, the middle grain, and the lower grain? " According to the text, the equation is as follows:
Equation technique [1]
The elimination process is as follows:
1. "Multiply the right row with the middle row and divide it directly", that is, multiply the right row with the middle row three times, and then subtract the right row twice from the middle row
Equation technique 2. "Multiply by the next, and divide by the straight", that is, multiply the right row by the left row three times, and then subtract the right row from the left row
Equation technique 3. "However, if the middle row is full, multiply it by the left row and divide it by the straight", that is, multiply the middle row by the left row five times, and then subtract the middle row from the left row
Equation technique 4. "If the left side can not get enough grain, the upper part is the law, and the lower part is the purchase. The purchase is the real thing to get the grain." 99 is the real thing to get the grain
5. "Seeking the middle grain is to multiply the middle grain by the law, and then eliminate the reality of the lower grain. The rest is just like the number of the middle grain, that is, the reality of the middle grain." The reality of the middle grain is
Equation technique Among them, "direct division" is to subtract two lines of corresponding numbers to eliminate one of the numbers. Liu Hui explained that "if you want to subtract more lines from fewer lines, the first digit must be exhausted after repeated subtraction"
