JP3567292B2 - Electronic computer and factorization display processing method - Google Patents

Description

[0001]
[Industrial applications]
The present invention particularly relates to a computer for factorizing and displaying an input expression and a factorized display processing method .
[0002]
[Prior art]
2. Description of the Related Art Conventionally, in a computer having a factoring function, for example, when an equation such as X ² + AX + B is input and displayed, and a factoring of the input equation is instructed, a prime factor is automatically obtained inside the computer. The factorization formulas (X + a) and (X + b) are immediately displayed.
[0003]
[Problems to be solved by the invention]
However, if the equation obtained by factoring the input equation is immediately obtained and displayed as in the conventional computer, the process cannot be known.In particular, when this computer is used for education, However, there is a problem that is not suitable for deepening the user's understanding of the factorization.
The present invention has been made in view of the above problems, and has as its object to provide an electronic computer and a factorization display processing method that enable a user to deepen understanding of factorization .
[0004]
[Means for Solving the Problems]
That is, the computer according to the present invention described in claim 1 is:
In a computer that displays data related to factorization on a display unit,
Expression input means for inputting an expression to be factored;
Prime factorization means for factorizing the numerical value of the constant term constituting the expression input by the expression input means,
Based on the result obtained by the prime factorization unit, a numerical value that is a factorization candidate of the expression input by the expression input unit is calculated, and a plurality of the numerical values that are the calculated factorization candidates are displayed on the display unit. Candidate display control means,
Selecting means for the user to select and operate an arbitrary numerical value from among numerical values serving as factorization candidates displayed under the control of the candidate display control means;
Determining means for determining whether a number is selection operation by the selection means is input by said formula input means wherein a numerical value for factoring,
It is characterized by having.
The computer according to the present invention described in claim 2 is:
The computer according to claim 1, further comprising:
When the input expression by the formula input means is determined to be a value for factoring a number that the selected operation by the selection means the determination unit, the factorization type of the input expression on the display unit It is characterized by comprising a disassembled display control means for displaying.
[0005]
[Action]
According to the computer according to the first aspect of the present invention, a plurality of numerical values that are candidates when the input expression is factorized are displayed based on the prime factors of the numerical values constituting the input expression obtained by the prime factorization. When any number is selected by the user from the value to be used as the displayed plurality of factored candidate, determines whether the selected manipulated value is a numerical value for factoring said input expression be able to.
According to the computer according to the second aspect of the invention, it is determined the input by the formula input means by the numerical said determining means that the selected operation by the selection means wherein a is a numerical value for factoring At this time, a factorization formula of the input formula can be displayed on the display unit. Thus, the process of factorizing the input expression is displayed.
[0006]
【Example】
An embodiment of the present invention will be described below with reference to the drawings.
FIG. 1 is a block diagram showing the configuration of an electronic computer having a factor decomposition function.
This computer includes a central processing unit (CPU) 11.
[0007]
The CPU 11 activates a system program stored in the ROM 13 in advance in accordance with a key operation signal from the key input unit 12 and controls the operation of each unit of the computer. In addition to the ROM 13, a RAM 14 is connected, and a liquid crystal display unit 16 is connected via a display drive circuit 15.
[0008]
The key input unit 12 includes a numeric keypad 12a and a function key 12b for inputting an arbitrary numerical value or a calculation formula, and is operated when the input formula is registered in the registration area 14a in the RAM 14. Key 12c, an "execute" key 12d operated when executing the factorization process of the registration formula, and a numerical value which is a candidate for factorization displayed on the liquid crystal display unit 16 with the execution of the factorization process Up and down cursor keys 12e and 12f operated when selecting data, and a "confirm" key 12g operated when fixing the numerical data selected by the cursor as a factorization solution.
[0009]
FIG. 2 is a diagram showing the contents of each data storage area provided in the RAM 14 of the computer.
In the RAM 14, an input expression input by a key through the key input unit 12 and displayed on the liquid crystal display unit 16 is registered in response to the operation of the "register" key 12c, for example, as shown in FIG. In the factor registration process according to the operation of the expression registration area 14a and the "execute" key 12d, the numerical values constituting the input expression registered in the expression registration area 14a are decomposed into prime factors, for example, as shown in FIG. As shown in FIG. 2 (C), for example, according to the prime factor decomposition area 14b in which the prime factors (except 1) decomposed as shown and their numbers are stored in association with each other, and the prime factors stored in the prime factor decomposition area 14b. A factorization candidate area 14c is provided for storing numerical data that is candidates when the input expression is factorized.
[0010]
Here, in the factorization candidate area 14c, when the input expression is, for example, “X ² + AX + B”, the prime factor of the numerical value B constituting the input expression is stored as one candidate numerical value a of the factorization. A first area A1, a second area A2 in which a division value of the numerical value B by one of the candidate numerical values a of the factorization stored in the first area A1 is stored as the other candidate numerical value b, and a first area A1 A third area A3 in which an addition value of one of the stored candidate factor values a of the factorization and the other candidate value b stored in the second area A2 is stored as a candidate value of the value A constituting the input expression Be provided.
[0011]
The one and other factorization candidate values a and b stored in the factorization candidate area 14c in the RAM 14 and the candidate value of the numerical value A constituting the input expression corresponding to the factorization candidate values a and b are Are arranged and displayed on the liquid crystal display unit 16. At this time, by operating the "cursor" keys 12e and 12f and the "confirm" key 12g, the candidate values of the numerical value A constituting the input expression are displayed. Is selected and determined, the factorization expression “(X + a) (X + b)” of the input expression “X ² + AX + B” is determined according to the one and other factorization candidate values a and b corresponding to the determined candidate value of the numerical value A. Is displayed.
[0012]
Next, the operation of the computer having the factor decomposition function according to the above configuration will be described.
FIG. 3 is a flowchart showing the factorization process in the computer.
[0013]
FIG. 4 is a diagram showing a process of storing each candidate numerical value in the factorization candidate area 14c in the RAM 14 accompanying the factorization processing of the computer.
FIG. 5 is a diagram showing the key input operation and the display state associated with the factor decomposition processing of the computer in association with each other.
[0014]
That is, when the ten-key pad 12a and the function key 12b of the key input unit 12 are operated to input, for example, a quadratic expression “X ² + 11X + 30” composed of “X ² + AX + B”, the input expression “X ² + 11X + 30” As shown in FIG. 5A, the image is displayed on the liquid crystal display unit 16 (step S1).
[0015]
Here, when the "registration" key 12c of the key input unit 12 is operated, the input expression "X ² + 11X + 30" displayed on the liquid crystal display unit 16 is registered in the expression registration area 14a in the RAM 14 {FIG. Reference｝, when the “execute” key 12d is operated, first, the constant value B (= 30) is decomposed into prime factors in the registered input expression “X ² + 11X + 30” (steps S2 → S3, S4 → S5). .
[0016]
In this case, the prime factors of the constant value B (= 30) are obtained as “1, 2, 3, 5”, and the prime factors “2, 3, 5” excluding “1” are represented by the respective numbers “1, 1, 5”. 1 is stored in the prime factor decomposition area 14b in the RAM 14 (see FIG. 2B) (step S6).
[0017]
Then, in each of the prime factors stored in the prime factorization area 14b, the prime factors “1, 2, 3, 5” smaller than √ · B are all considered as one candidate numeric value a of the factorization in FIG. As shown, it is stored in the first area A1 of the factorization candidate area 14c in the RAM 14 (step S7).
[0018]
In this manner, when one of the candidate numerical values a “1, 2, 3, 5” of the factorization for the input expression “X ² + 11X + 30” is stored in the first area A1 of the factorization storage area 14, the constant value B (= 30) is divided by one candidate numerical value a “1, 2, 3, 5”, and the corresponding division results “30, 15, 10, 6” are all the other candidate numerical values b of the factorization. 4B, is stored in the second area A2 of the factorization candidate area 14c (step S8).
[0019]
At this time, as shown in FIG. 4C, one factorization candidate numerical value a “1, 2, 3, 5” stored in the first area A1 of the factorization candidate area 14 and stored in the second area A2. Of the other factorization candidate numerical value b “30, 15, 10, 6” to be processed, one candidate numerical value a “−1, −2, −3, −5” and the sign of all the numerical values are inverted. The other candidate numerical value b “−30, −15, −10, −6” is additionally stored.
[0020]
In this way, for the first area A1 and the second area A2 of the factorization candidate area 14c, all the factorization candidate numerical values a “1,2” based on the constant value B (= 30) of the input expression “X ² + 11X + 30”. , 3, 5, -1, -2, -3, -5 "and b" 30, 15, 10, 6, -30, -15, -10, -6 ", the first areas A1 and The corresponding one and other candidate numerical values a and b stored in the second area A2 are respectively added, and as shown in FIG. 4D, the respective addition results “31, 17, 13, 11, 11, −31, −17, −13, and −11 ”are stored in the third area A3 as candidate values of the numerical value A (= 11) in the input expression“ X ² + 11X + 30 ”(step S9).
[0021]
Then, one and the other factorization candidate numerical values a and b stored in the first area A1 and the second area A2 of the factorization candidate area 14c are the candidate values of the numerical value A stored in the third area A3, respectively. The data is sorted in ascending order {see FIG. 2 (C)}. As a result, as shown in FIG. 5 (B), the liquid crystal display unit 16 displays the input expression “X ² + 11X + 30” together with the sorting process. The factorization candidate numerical values a and b in the factorization candidate area 14c and the candidate value of the numerical value A are displayed from the top thereof (steps S10 and S11).
[0022]
Here, the user refers to the candidate value of the numerical value A displayed on the liquid crystal display unit 16 and operates the cursor key 12e or 12f to determine one or the other of the input expression “X ² + 11X + 30” which seems to be correct. In FIG. 5C, for example, as shown in FIG. 5C, one factorized candidate numerical value a (= 5) corresponding to the candidate value “11” of the numerical value A and the other When the cursor is selected for the factorization candidate numerical value b (= 6) and the “Enter” key 12g is operated, the candidate value “11” of the numerical value A in the selected third area A3 and the actual value in the input expression “X ² + 11X + 30” are obtained. It is determined whether or not the numerical value A (= 11) matches, that is, whether or not each of the factorized candidate numerical values a (= 5) and b (= 6) determined and determined is correct (step S12 → S13, S14 → S15).
[0023]
"YES" in step S15, i.e., the candidate value of a number A of the third area A3, which is selected cursor "11" on the display unit 16, the actual numbers A in the input formula ^"X 2 + 11X + 30" (= 11) is determined to be the same, and when it is determined that the corresponding factorization candidate numerical values a (= 5) and b (= 6) are correct numerical values, as shown in FIG. The expression “(X + 5) (X + 6)” of the factorization according to the factorization candidate numerical values a (= 5) and b (= 6) is displayed in correspondence with the input expression “X ² + 11X + 30” ( Step S15 → S16).
[0024]
On the other hand, if "NO" in the step S15, that is, if it is determined that the candidate value of the numerical value A selected by the cursor on the display unit 16 does not match the actual numerical value A in the input expression, Each of the selected factorization candidate numerical values a and b is determined to be erroneous, and an error message is displayed on the liquid crystal display unit 16 (steps S15 to S17).
[0025]
Therefore, according to the computer having the above-described factoring function, when the quadratic expression “X ² + AX + B” is input and the “Execute” key 12 d is operated by the key input unit 12, the constant B is factorized. The factorization candidate numerical values a and b and the candidate value of the numerical value A, which are stored in the prime factorization area 14b in the RAM 14 when the input expression obtained based on the respective prime factors are factorized, are respectively stored in the RAM 14 as factors. The factor decomposition candidate values a and b and the numerical value A, which are stored in association with the first to third areas A1 to A3 of the decomposition candidate area 14c and are arranged and displayed on the liquid crystal display unit 16, and are considered to be correct for the input expression. Is selected by the user and determined, the correct answer of the corresponding candidate numerical values a and b is determined based on the coincidence between the selected numerical value A and the numerical value A in the input expression, and the factorized expression “ (X + a) (X + b) "is displayed, so that the process of factorizing the input expression is displayed. In particular, when this computer is used for educational purposes, the user understands the factorization. Can be further deepened.
[0026]
Note that, in the above-described embodiment, for the input expression “X ² + AX + B”, first, the prime factor of the constant B is obtained and the factorization procedure is displayed. However, the factorization candidate values a, A procedure for obtaining b may be displayed.
[0027]
Further, in the above embodiment, the quadratic expression to be input is in the form of “X ² + AX + B”. However, even in the form of “AX ² + BX + C”, the number of combinations of candidate numerical values increases, The process can be displayed by the disassembly process.
Further, the present invention can of course be applied to a multi-term equation or a cubic equation.
[0028]
【The invention's effect】
As described above, according to the present invention, based on the prime factors of the numerical values constituting the input expression obtained by the prime factorization, a plurality of numerical values that are candidates when the input expression is factorized are displayed. the numerical values a plurality of factored candidates the user selects, it is possible to the selected numerical value to determine whether the input expression is a numeric value for factoring.
Also, when the numerical value selected by the selecting means is determined by the determining means to be a numerical value for factorizing the expression input by the expression inputting means, the factorizing expression of the input expression is displayed on the display unit. Can be displayed. Therefore, the process of factorizing the input expression is displayed, and it becomes possible for the user to deepen the understanding of the factorization.
[Brief description of the drawings]
FIG. 1 is a block diagram showing a configuration of an electronic computer having a factor decomposition function according to an embodiment of the present invention.
FIG. 2 is a view showing contents of respective data storage areas provided in a RAM of the computer.
FIG. 3 is a flowchart showing a factorization process in the computer.
FIG. 4 is an exemplary view showing a process of storing each candidate numerical value in a factorization candidate area in a RAM accompanying the factorization processing of the computer.
FIG. 5 is an exemplary diagram showing a key input operation and a display state associated with the factor decomposition process of the computer in association with each other.
[Explanation of symbols]
11: Central processing unit (CPU), 12: Key input unit, 12a: Numeric keypad, 12b: Function key, 12c: "Registration" key, 12d: "Execute" key, 12e, 12f: Cursor key, 12g: "Confirm" Keys, 13 ROM, 14 RAM, 14a registration area, 14b prime factor decomposition area, 14c factor decomposition candidate area, A1 to A3 ... first to third areas, 15 display drive circuit, 16 liquid crystal display unit .

Claims (4)

In a computer that displays data related to factorization on a display unit,
Expression input means for inputting an expression to be factored;
Prime factorization means for factorizing the numerical value of the constant term constituting the expression input by the expression input means,
Based on the result obtained by the prime factorization unit, a numerical value that is a factorization candidate of the expression input by the expression input unit is calculated, and a plurality of the numerical values that are the calculated factorization candidates are displayed on the display unit. Candidate display control means,
Selecting means for the user to select and operate an arbitrary numerical value from among numerical values that are displayed as factorization candidates under the control of the candidate display control means;
Determining means for determining whether the numerical value selected and operated by the selecting means is a numerical value for factorizing the expression input by the expression inputting means,
An electronic computer comprising: The computer according to claim 1, further comprising:
When the numerical value selected and operated by the selecting means is judged by the judging means to be a numerical value for factoring the expression input by the expression inputting means, the factoring expression of the input expression is displayed on the display section. An electronic computer comprising disassembled display control means for displaying. In a factorization display processing method of displaying data relating to factorization on a display unit,
When an expression to be factored is input, a prime factorization step of performing a prime factorization on a numerical value of a constant term constituting the input expression,
Based on the result obtained by the prime factorization step, a numerical value that is a factorization candidate of the expression input in the expression input step is calculated, and a plurality of the calculated numerical values that are candidate factorizations are displayed on the display unit. A candidate display control step;
When an arbitrary numerical value is selected by the user from among the numerical values of the factor decomposition candidates displayed by the control of the candidate display control step, the selected numerical value is converted into the factor input by the expression input step. A judging step of judging whether it is a numerical value for decomposing,
And a factorization display processing method. The method of claim 3, further comprising:
When the numerical values set selection operation by the selection step is the input formula by the formula input step is determined to be a value for factoring by the determining step, the factorization type of the input expression on the display unit A factor decomposition display processing method, comprising a decomposition display control step of displaying.

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