JP5760327B2 - Electronic device and program - Google Patents

Description

  The present invention relates to an electronic device and a program suitable for a scientific calculator as educational equipment.

  Conventionally, when an arbitrary arithmetic expression is input and a key operation for determining a correct answer is performed after inputting a user's own calculation solution, a user input solution and a correct answer calculated from the input arithmetic expression are obtained. A technique for comparing and displaying correct and incorrect is considered. (For example, Patent Document 1)

JP 2000-298423 A

  Although the technique described in the above patent document can know the correctness of the final solution, it cannot determine the correctness or not in the state of the modified expression or the replacement expression in the middle of solving the expression. Therefore, when the user derives an incorrect solution, there is a problem in that the user cannot verify the wrong place from the process of transforming or replacing the formula.

  The present invention has been made in view of the above-described circumstances, and the object of the present invention is to input an arbitrary arithmetic expression and determine whether the expression is correct or not, especially for a substitution expression in the middle of deformation. Providing an electronic device and program.

  The invention described in claim 1 is an equation input means for inputting an equation for the original variable, an original variable solution calculating means for calculating the solution of the original variable input by the equation input means, and the substitution variable as a mathematical expression of the original variable. Substitution expression input means for inputting the described substitution expression, and substitution for calculating the value of the substitution variable by substituting the solution of the original variable calculated by the original variable solution calculation means to the substitution expression input by the substitution expression input means When a variable value calculation means, a deformation expression input means for inputting a deformation expression obtained by modifying the equation for the original variable, and a replacement equation in which the equation is described by a replacement variable are input by the deformation expression input means, the replacement is performed. Whether the substitution variable solution calculation means for calculating the substitution variable solution for the equation, the substitution variable solution calculated by the substitution variable solution calculation means, and the substitution variable value calculated by the substitution variable value calculation means match. The And substitution variable determination means for, characterized by comprising a display control means for performing display in accordance with the determination result in the substitution variable determining means.

  The invention according to claim 5 is a program for controlling a computer incorporated in an electronic device, wherein the computer is input to an equation input means for inputting an equation for the original variable, the original variable input by the equation input means. An original variable solution calculating means for calculating a solution, a replacement expression inputting means for inputting a replacement expression in which a substitution variable is described as a mathematical expression of the original variable, and a replacement expression inputted by the replacement expression inputting means calculated by the original variable solution calculating means. Substitution variable value calculation means for substituting the solution of the original variable to calculate the value of the substitution variable, deformation expression input means for inputting a modified expression obtained by modifying the equation for the original variable, and replacement of the equation by the deformation expression input means When a substitution equation described by a variable is input, a substitution variable solution calculation means for calculating a solution of the substitution variable for the substitution equation, and a substitution variable calculated by the substitution variable solution calculation means. And a replacement variable determining means for determining whether or not the replacement variable value calculated by the replacement variable value calculating means matches, and a display control means for performing display according to the determination result in the replacement variable determining means It is intended to function as.

  According to the present invention, after inputting an arbitrary arithmetic expression, it is possible to determine whether the expression is correct or not, especially for a replacement expression.

1 is a block diagram showing a functional configuration of an electronic device according to an embodiment of the present invention. FIG. 2 is an exemplary plan view showing an external configuration of the electronic apparatus according to the embodiment. The flowchart which shows the content of the input type determination process as a subroutine concerning the embodiment. The flowchart which shows the content of the input type determination process as a subroutine concerning the embodiment. The figure which shows the key operation and transition of a display screen in the 1st operation example which concerns on the embodiment. The figure which shows the key operation and transition of a display screen in the 1st operation example which concerns on the embodiment. The figure which shows the key operation and transition of a display screen in the 1st operation example which concerns on the embodiment. The figure which shows the key operation and transition of a display screen in the 2nd operation example which concerns on the embodiment. The figure which shows the key operation and transition of a display screen in the 2nd operation example which concerns on the embodiment. The figure which shows the key operation and transition of a display screen in the 2nd operation example which concerns on the embodiment. The figure which shows the key operation and transition of a display screen in the 2nd operation example which concerns on the embodiment. The figure which shows the key operation and transition of a display screen in the 2nd operation example which concerns on the embodiment. The figure which shows the key operation and transition of a display screen in the 2nd operation example which concerns on the embodiment.

Hereinafter, an embodiment of the present invention will be described with reference to the drawings.
In the present embodiment, mathematics education in the secondary education program is targeted, and the concepts of imaginary numbers and complex numbers used in mathematics education in the later secondary education program are not included in the range of numbers. Therefore, when the final solution of the equation includes the square root sign “√ (n)” (n is a real number), “n ≧ 0” and “√ (n) ≧ 0”.

(Configuration of the embodiment)
FIG. 1 is a block diagram showing a functional configuration of an electronic circuit of a scientific calculator 10 according to an embodiment of the present invention.
FIG. 2 is a front view showing an external configuration of the scientific calculator 10.

  The scientific calculator 10 includes a control unit (CPU) 11 that is a main component of the computer.

The control unit (CPU) 11 controls the operation of the scientific calculator 10 as a working memory (work memory) according to a system program and a computer control program stored in advance in a ROM 12 constituted by a flash memory. ,
The computer control program stored in the system area of the ROM 12 is input from the memory card 13 which is an external storage medium via the I / O port 14 or from the I / O port 14 to an external personal computer (PC) 15. Also included are those downloaded and input from a Web server (program server) 16 on the communication network N connected via the Internet.

  The system program stored in the ROM 12 and the computer control program stored in the system area are activated in response to a key input signal from the keyboard 18 or a touch input signal from the touch input unit 21 described later.

  Note that the computer control program stored in the ROM 12 includes a basic processing program for controlling the calculation and display operations over the entire operation of the scientific calculator 10. Symbols, calculation formula display, calculation formula calculation, calculation result display, graph drawing display, and cursor (pointer) display are controlled.

  The computer control program includes an input type determination processing program 12a (see FIGS. 3 and 4), which will be described later, as one subroutine.

  The RAM 17 stores the formula data storage unit 17a, the target equation storage unit 17b, the target equation solve result storage unit 17c, the substitution formula storage unit 17d, the substitution formula when the control unit (CPU) 11 executes the input formula determination processing program 12a. Each storage unit includes a value storage unit 17e, a mixed equation value storage unit 17f, and a modified equation solve result storage unit 17g.

The expression data storage unit 17a stores data relating to an expression in the middle of input, such as an arbitrary equation to be verified, which is input by the user, and a modified expression for the equation.
The target equation storage unit 17b stores an arbitrary equation to be verified.
The target equation solve result storage unit 17c stores the value of the solution of the target equation.
The substitution expression storage unit 17d stores a substitution expression described by the user as a mathematical expression of the original variable of the target equation, which is input by the user.
The replacement formula value storage unit 17e stores the value of the provisional solution of the replacement formula.

  The mixed equation value storage unit 17f stores a value of a provisional solution of a mixed equation in which the target equation is described with substitution variables and original variables.

  The modified equation solve result storage unit 17g stores the value of the modified equation solution.

  In addition to the ROM 12, the memory card 13, the I / O port 14, the RAM 17, and the keyboard 18, the control unit (CPU) 11 is connected to a liquid crystal display unit (LCD) 20 through a liquid crystal driving circuit 19. Is done.

  The liquid crystal display unit (LCD) 20 includes, for example, a dot matrix type transflective liquid crystal display panel having a backlight and a driving circuit thereof, and displays various equations and graphs of functions.

  The liquid crystal display unit (LCD) 20 is integrally formed with a touch input unit 21 using, for example, an electronic transparent touch panel. When the user performs a touch operation on the touch input unit 21 so as to directly indicate the display contents in accordance with the position of the keyboard and various icons displayed on the liquid crystal display unit (LCD) 20, the touch input signal is sent to the coordinate input unit 22. Sent.

  The coordinate input unit 22 converts the touch operation by the user into a time-series two-dimensional coordinate signal by the touch input signal from the touch input unit 21 and outputs the two-dimensional coordinate signal to the control unit (CPU) 11.

  As shown in FIG. 2, the keyboard 18 is provided with various keys such as an operator key, a numeric keypad, and a cursor key, as well as function / function keys for specifying various functions and specifying a calculation format.

Next, the operation of the above embodiment will be described.
(First operation example of embodiment)
FIG. 3 and FIG. 4 are flowcharts of subroutines showing detailed contents of the determination process related to the modification of the input expression, which is also referred to as a verify (Verify) function. The input expression determination processing program 12a stored in the ROM 12 is shown in FIG. This is realized by execution of the control unit (CPU) 11.

  5 to 7 are diagrams showing key operations and display screen transitions in the first operation example.

  Initially, it waits for the user to input an equation to be processed by an operation on the keyboard 18 and the touch input unit 21 (step S101).

FIG. 5A shows a quaternary equation to be processed.
“X ⁴ −5x ² + 6 = 0” (1)
When the “EXE” key of the keyboard 18 is operated to confirm the input, the content displayed on the liquid crystal display unit (LCD) 20 is shown. The liquid crystal display unit (LCD) 20 displays the input equation and a cursor C that prompts further input on the next line.

  In the course of inputting the target equation by the control unit (CPU) 11, input data is sequentially input to the formula data storage unit 17 a, and when the “EXE” key is operated, it is determined that the input is confirmed. The data of the equation stored in is transferred to the target equation storage unit 17b and stored (step S102).

  The control unit (CPU) 11 specifies a variable in the equation stored in the target equation storage unit 17b (here, since there is only x, it becomes x unconditionally), and automatically solves the specified variable. A calculation called a function for obtaining a value of a variable is executed based on a computer control program stored in the ROM 12 (step S103).

  Here, the solution “x = ± √ (2), ± √ (3)” is obtained by solving the above equation (1), and the control unit (CPU) 11 converts the obtained solution into the correct solution of the original variable. Is stored in the target equation solve result storage unit 17c (step S104).

  Next, it is determined whether or not there is an expression including the variable x in the symbol “√” in the equation to be processed stored in the expression data storage unit 17a of the RAM 17 (step S105).

  In the above equation (1), since the variable “x” is not included in the symbol “√”, when this is determined, a modified equation obtained by modifying the equation to be processed by the user or a part of the equation to be processed It waits for a replacement expression in which is replaced with another variable to be input by an operation on the keyboard 18 or the touch input unit 21 (step S107).

FIG. 5 (B) shows that the user replaces the above formula (1).
“#A: = x ² ” (2)
And the “EXE” key of the keyboard 18 is operated to confirm the input. The symbol “#” at the beginning of the formula is a preset symbol that declares that the formula to be input after that is a substitution formula. In the case of the expression (2), it is declared that “x ² ” in the expression (1) is replaced with the variable “a”.

  When the “EXE” key is operated after the expression is input, the control unit (CPU) 11 determines whether or not the input is a replacement expression, depending on whether or not there is a symbol “#” at the beginning of the expression. It discriminate | determines (step S108).

  If it is determined that the input is a replacement formula, the input replacement formula is stored in the replacement formula storage unit 17d of the RAM 17 (step S109).

  At the same time, the solution of the original variable stored in the target equation solve result storage unit 17c is substituted into the replacement formula to calculate the value of the replacement formula, and the calculation result is stored (step S110).

In the case of the above equation (2), the value of the replacement equation corresponding to each solution stored in the target equation solve result storage unit 17c is “a = 2, 3”, and the control unit (CPU) 11 uses this replacement equation value. It is stored in the replacement formula value storage unit 17e.
Thereafter, the process returns to the process from step S107 and waits for further expression input.

As shown in FIG. 5C, an expression using only the variable “a” used by the user in the replacement expression
“A ² + 5a + 6 = 0” (3)
And the “EXE” key on the keyboard 18 is operated to confirm the input.

  When this input is accepted in step S107 and it is determined in step S108 that the input is not a substitution expression, the control unit (CPU) 11 then changes the inputted expression to the equation to be processed using the original variable and the substitution expression. Whether it is a format or not is discriminated based on whether it is an expression described by both the original variable “x” and the variable “a” used in the substitution expression (step S111).

  If it is determined that the above expression (3) is not a modified expression for the equation to be processed using the original variable and the replacement expression, then the input expression is a modified expression for the equation to be processed using the replacement expression. Is determined based on whether or not the expression is described only by the variable “a” used in the substitution expression (step S115).

  Since the variable used in the equation (3) is only the variable “a” used in the substitution equation, the solve function is executed on the substitution variable and the equation (3) is solved. The solution “a = −3, −2” is obtained, and the obtained solution is stored in the modified equation solve result storage unit 17g as a temporary solution of the modified equation (step S116).

  Next, it is determined whether or not the substitution formula includes the symbol “√” (step S117). Since the symbol (√) is not included in the above equation (2), when this is determined, the temporary solution stored in the modified equation solve result storage unit 17g in the above step S116 is next stored in the replacement equation value storage unit 17e. It is determined whether or not the stored replacement expression value matches (step S119).

  Here, the provisional solution “a = −3, −2” stored in the modified equation solve result storage unit 17g does not match the replacement equation value “a = 2, 3” stored in the replacement equation value storage unit 17e. Therefore, assuming that the above equation (3) is not a replacement of the equation to be processed using a replacement equation, an error message is displayed on the liquid crystal display unit (LCD) 20, and an erroneous expression input is awaited for confirmation. After returning the display position of the cursor C to the previous position (step S122), the process returns to step S107.

FIG. 5C shows a state in which an error message window W1 is displayed at the bottom of the equation (3) on the liquid crystal display unit (LCD) 20. In the same figure (B), error message by characters
"ERROR!"
"Sorry, not equivalent"
At the same time, a face symbol F1 that visually indicates that the expression is incorrect and a character “OK?” That prompts confirmation when the user understands that the expression is incorrect are displayed.

  When the user operates the “EXE” key for confirmation on the keyboard 18 as shown in FIG. 5D along with the display in the window W1, the above formula (3) is displayed on the liquid crystal display unit (LCD) 20. After returning the display position of the cursor C to the head position (step S114), the process returns to the process from step S107.

  Next, a modified expression obtained by modifying the equation to be processed by the user or a replacement expression obtained by replacing a part of the equation to be processed with another variable is input by an operation on the keyboard 18 or the touch input unit 21. Wait (step S107).

As shown in FIG. 6 (A), instead of the above (3), the expression using only the variable “a” used in the replacement expression by the user
“A ² −5a + 6 = 0” (4)
Is input again, and the “EXE” key on the keyboard 18 is operated to confirm the input.

  In step S107, this input is accepted, and in the subsequent step S108, it is continuously determined that the input is not a substitution expression and that the input is not a modified expression using the original variable and the substitution expression in step S111. Thereafter, when it is determined in step S115 that the equation is a modified equation using substitution variables, the equation (4) is solved in step S116 to obtain a solution “a = 2, 3”, and the obtained solution is transformed into a modified equation. The result is stored in the solve result storage unit 17g.

  Next, after determining in step S117 that the equation (2) does not include the symbol “√”, the temporary solution stored in the modified equation solve result storage unit 17g in step S119 is the replacement equation value storage unit 17e. It is determined that the value matches the replacement expression value stored in.

  In this case, the control unit (CPU) 11 confirms that the temporary solution is stored in the modified equation solve result storage unit 17g (step S120), and then the temporary solution stored in the modified equation solve result storage unit 17g. It is confirmed again that the solution matches the substitution formula value stored in the substitution formula value storage unit 17e (step S121). Assuming that the input is correct, the processing returns to step S117 and waits for the next input.

  In FIG. 6 (A), it is assumed that the transformation of the formula by the substitution was correct after the input of the formula (4) in the liquid crystal display unit (LCD) 20, and the next line of the formula (4) is urged to prompt the next input. A cursor C is displayed at the position.

Then, as shown in FIG. 6B, the user factored the above equation (4)
(a-2) (a-3) = 0 (5)
Is input again, and the “EXE” key on the keyboard 18 is operated to confirm the input.

  In step S107, this input is accepted, and in the subsequent step S108, it is continuously determined that the input is not a substitution expression and that the input is not a modified expression using the original variable and the substitution expression in step S111. Thereafter, when it is determined in step S115 that the equation is a modified equation using substitution variables, the equation (5) is solved in step S116 to obtain a solution “a = 2, 3”, and the obtained solution is transformed into a modified equation solve. The result is stored in the result storage unit 17g.

  Next, after determining in step S117 that the above equation (2), which is a substitution formula, does not include the symbol “√”, the temporary solution stored in the modified equation solve result storage unit 17g in step S119 is the substitution formula. It is determined that the value matches the replacement expression value stored in the value storage unit 17e.

  In this case, the control unit (CPU) 11 confirms that the temporary solution is stored in the modified equation solve result storage unit 17g (step S120), and then the temporary solution stored in the modified equation solve result storage unit 17g. It is reconfirmed that the solution matches the replacement expression value stored in the replacement expression value storage unit 17e (step S121). Assuming that the input is correct, the processing returns to step S107 and waits for the next input.

  In FIG. 6B, it is assumed that the transformation of the formula by substitution is correct after the input of the formula (5) in the liquid crystal display unit (LCD) 20, and the next line of the formula (5) is urged to prompt the next input. A cursor C is displayed at the position.

Further, as shown in FIG. 6 (C), the solution of the permutation equation derived from the factorization of the above equation (5) by the user is obtained.
a = 2 or a = 3 (6)
The “EXE” key on the keyboard 18 is operated to confirm the input.

  Also in this step S107, this input is accepted, and in the subsequent step S108, it is continuously determined that the input is not a substitution expression and in step S111 that the input is not a modified expression using the original variable and the substitution expression. After that, if it is determined in step S115 that it is a modified expression using a substitution variable, the expression (6) is in the form of the solution “a =” in step S116, and therefore the expression (6) is used as the solve function. Used as a solution and stored in the modified solve result storage unit 17g.

  Next, after determining in step S117 that the above equation (2), which is a substitution formula, does not include the symbol “√”, the temporary solution stored in the modified equation solve result storage unit 17g in step S119 is the substitution formula. It is determined that the value matches the replacement expression value stored in the value storage unit 17e.

  In this case, the control unit (CPU) 11 confirms that the temporary solution is stored in the modified equation solve result storage unit 17g (step S120), and then the temporary solution stored in the modified equation solve result storage unit 17g. It is reconfirmed that the solution matches the replacement expression value stored in the replacement expression value storage unit 17e (step S121). Assuming that the input is correct, the processing returns to step S107 and waits for the next input.

  In FIG. 6C, it is assumed that the solution of the substitution formula is correct after the input of the formula (6) in the liquid crystal display unit (LCD) 20, and the next row position of the formula (6) is urged to prompt the next input. A cursor C is displayed on the screen.

As shown in FIG. 7A, it represents the solution of the substitution variable obtained by substituting the original equation (2) for the substitution variable “a” in the equation (6).
x ² = 2 or x ² = 3 (7)
And the “EXE” key on the keyboard 18 is operated to confirm the input.

  In step S107, this input is accepted, and in the subsequent step S108, it is continuously determined that the input is not a substitution expression and that the input is not a modified expression using the original variable and the substitution expression in step S111. After that, if it is determined in step S115 that it is not a modified expression using a substitution variable, it is next determined whether or not it is a modified expression using the original variable “x” (step S123).

Here, it is determined that it is a modified expression using only original variables. By executing the solve function for “x ² = 2” in the equation (7), a temporary solution “x = ± √ (2)” is obtained, and “x ² = 3” in the equation (7) is obtained. By executing the solve function for, a temporary solution “x = ± √ (3)” is obtained, and these obtained solutions are stored in the modified equation solve result storage unit 17g (step S124).

  Thereafter, it is determined whether or not the provisional solution stored in the modified equation solve result storage unit 17g matches the correct solution of the original variable stored in the target equation solve result storage unit 17c (step S125).

  In this case, the control unit (CPU) 11 determines that the solution of the input transformation equation of the original variable matches the correct solution of the original variable stored in the target equation solve result storage unit 17c, and the above equation (7) Assuming that the input is correct, the process returns to step S107 and waits for the next input.

  In FIG. 7A, it is assumed that the solution of the substitution formula is correct after the input of the formula (7) in the liquid crystal display unit (LCD) 20, and the next row position of the formula (7) is urged to prompt the next input. A cursor C is displayed on the screen.

As shown in FIG. 7B, the user represents the solution of the original variable derived from the equation (7) in response to the input of the equation (7) being correct.
x = √ (2) or x = −√ (2) or
x = √ (3) or x = −√ (3) (8)
And the “EXE” key on the keyboard 18 is operated to confirm the input.

  In step S107, this input is accepted, and in the subsequent step S108, it is continuously determined that the input is not a substitution expression and that the input is not a modified expression using the original variable and the substitution expression in step S111. After that, it is determined in step S115 that it is not a modified expression using a substitution variable, and further in step S123, it is determined that it is not a modified expression using the original variable “x”.

  Next, it is determined whether or not the input expression represents the solution of the original variable, that is, whether or not it is an expression described in the format of “x = (numerical value)” (step S127).

  If it is determined that the equation represents the solution of the original variable, it is determined whether or not the value of the input solution matches the correct solution of the original variable stored in the target equation solve result storage unit 17c (step). S128).

  In this case, the control unit (CPU) 11 determines that the input solution value matches the correct solution value of the original variable stored in the target equation solve result storage unit 17c, and the input of equation (8) is correct. As a result, the correct answer mark and the correct answer message are displayed (step S130), and the process returns to step S107 to wait for the next input.

As shown in FIG. 7B, the liquid crystal display (LCD) 20 exemplifies a correct message window W2 at this time. In this window W2, as shown in FIG.
"Right!"
Is displayed together with a face symbol F2 which visually indicates that the answer is correct.
In this way, when the target equation differs from the substitution formula entered by the user, a message or symbol indicating that fact is displayed, and if a correct substitution formula is entered to derive a solution, the correct answer Therefore, it is possible to increase the user's motivation and enhance the educational effect.

(Second operation example of embodiment)
The description will be made with reference to the flowcharts of FIGS. 3 and 4 as in the first operation example.

8 to 13 are diagrams for explaining key operations and display screen transitions in the second operation example.
Initially, it waits for the user to input an equation to be processed by an operation on the keyboard 18 and the touch input unit 21 (step S101).

FIG. 8A shows an equation to be processed.
“√ (x−1) = x−3” (11)
When the “EXE” key of the keyboard 18 is operated to confirm the input, the content displayed on the liquid crystal display unit (LCD) 20 is shown.

  In the process in which the target equation is input by the control unit (CPU) 11, the input data is sequentially input to the equation data storage unit 17a, and when the “EXE” key is operated, the input is determined to be confirmed. The equation data stored at the time is transferred to and stored in the target equation storage unit 17b (step S102).

  The control unit (CPU) 11 specifies a variable in the equation stored in the target equation storage unit 17b (here, since there is only x, it becomes x unconditionally), and automatically solves the specified variable. A calculation called a function for obtaining a value of a variable is executed based on a computer control program stored in the ROM 12 (step S103).

  Here, the correct solution “x = 5” is obtained by solving the above equation (11), and the control unit (CPU) 11 stores the obtained correct solution in the target equation solve result storage unit 17c (step S104). ).

  Next, it is determined whether or not there is an expression including the variable x in the symbol “√” in the equation to be processed stored in the expression data storage unit 17a of the RAM 17 (step S105).

  Since the variable “x” is included in the symbol “√” in the above equation (11), when this is determined, a modified equation is generated by squaring both sides of the above equation (11) and removing the symbol “√”. Then, the solve function is executed with the equation, and the obtained result is added and stored in the target equation solve result storage unit 17c as a temporary solution (step S106).

When both sides of the above equation (11) are squared, “x−1 = (x−3) ² ” (12)
By solving this equation (12), a temporary solution “x = 2” that is not the correct solution “x = 5” of the temporary solutions “x = 2, 5” is obtained. ) 11 stores the obtained temporary solution in the target equation solve result storage unit 17c in addition to the correct solution stored in step S104.

  Thereafter, a modified expression obtained by modifying the equation to be processed by the user or a replacement expression in which a part of the equation to be processed is replaced with another variable is input by an operation on the keyboard 18 or the touch input unit 21. Wait (step S107).

FIG. 8B shows that the user can replace the above equation (11).
“#A: = √ (x−1)” (13)
And the “EXE” key of the keyboard 18 is operated to confirm the input. The symbol “#” at the beginning of the formula is a preset symbol for declaring that the formula input thereafter is a substitution formula. In the case of the expression (13), it is declared that the entire left side “√ (x−1)” in the expression (11) is replaced with the variable “a”.

  When the “EXE” key is operated after the expression is input, the control unit (CPU) 11 determines whether or not the input is a replacement expression, depending on whether or not there is a symbol “#” at the beginning of the expression. It discriminate | determines (step S108).

  If it is determined that the formula (13) input here is a substitution formula, the substitution formula is then stored in the substitution formula storage unit 17d of the RAM 17 (step S109).

  At the same time, the solution of the original variable stored in the target equation solve result storage unit 17c is substituted into the substitution formula to calculate the value of the substitution formula, and the calculation result is stored in the substitution formula value storage unit 17e (step S110).

  In the case of the above equation (13), the value of the replacement equation corresponding to the correct solution “x = 5” stored in the target equation solve result storage unit 17c is “a = 2”. In addition, the temporary value of the substitution formula corresponding to the temporary solution “x = 2” is “a = −1”. The control unit (CPU) 11 stores the correct value and the temporary value of these substitution formulas in the substitution formula value storage unit 17e, and then returns to the processing from step S107 to wait for further formula input.

  As shown in FIG. 8B, in the liquid crystal display unit (LCD) 20, it is assumed that the substitution formula is correct after the input of the formula (13), and the next line of the formula (13) is urged to prompt the next input. A cursor C is displayed at the position.

As shown in FIG. 8C, the user substitutes the above equation (13) into the above equation (11) and uses both the variable “a” and the original variable “x” used in the substitution equation.
“A = x−3” (14)
And the “EXE” key on the keyboard 18 is operated to confirm the input.

  When this input is accepted in step S107 and it is determined in step S108 that the input is not a substitution expression, the control unit (CPU) 11 then changes the inputted expression to the equation to be processed using the original variable and the substitution expression. Whether it is a format or not is discriminated based on whether it is an expression described by both the original variable “x” and the variable “a” used in the substitution expression (step S111).

  If it is determined that the equation (14) is a modified equation for the equation to be processed using both the original variable and the substitution equation, the control unit (CPU) 11 stores the correct equation stored in the object equation solve result storage unit 17c. The solution “x = 5” and the value “a = 2” of the replacement formula stored in the replacement formula value storage unit 17e corresponding to the solution “x = 5” are read out and substituted into the above formula (14), and the values on the left and right sides are read. Is calculated (step S112).

  As a result, whether or not the above equation (14) is correct as a modified equation is determined based on whether or not the equal sign holds (step S113).

  Here, as a result of substituting “x = 5” and “a = 2” into the above equation (14), both sides become “2” and the equal sign is established. It is determined that it is correct, and the process returns to step S107.

  As shown in FIG. 8C, the liquid crystal display unit (LCD) 20 assumes that the input of the above equation (14), which is a modified equation of the target equation by the substitution equation, is correct, and the above ( 14) A cursor C is displayed at the next line position of the equation.

As shown in FIG. 8D, an expression using both the variable “a” and the original variable “x” used in the replacement expression, which the user may have modified the above expression (14).
“A = (x−1) +2” (15)
And the “EXE” key on the keyboard 18 is operated to confirm the input.

  In step S107, this input is accepted, and it is determined that the expression input in the subsequent step S108 is not a replacement expression. In subsequent step S111, when it is determined that the input formula is a modified formula for the equation to be processed using the original variable and the substitution formula, the control unit (CPU) 11 in step S112, the target equation solve result storage unit. The correct solution “x = 5” stored in 17c and the value “a = 2” of the replacement formula stored in the replacement formula value storage unit 17e corresponding to this are read out and substituted into the above equation (15). Each value of the left side and the right side is calculated.

  Here, as a result of substituting “x = 5” and “a = 2” into the above equation (15), the left side is “2” and the right side is “6”. The above equation (15) is determined to be incorrect as a modified equation, an error message is displayed on the liquid crystal display (LCD) 20, and the display position of the cursor C to the position before the erroneous equation input is waited for confirmation. After returning (step S114), the process returns to the process from step S107.

FIG. 8D shows a state in which an error message window W1 is displayed at the bottom of the equation (15) on the liquid crystal display unit (LCD) 20. In the figure (D), error message by characters
"ERROR!"
"Sorry, not equivalent"
At the same time, a face symbol F1 that visually indicates that the expression is incorrect and a character “OK?” That prompts confirmation when the user understands that the expression is incorrect are displayed.

  When the user operates the “EXE” key for confirmation on the keyboard 18 as shown in FIG. 9A along with the display in the window W1, the above-mentioned formula (115) is displayed on the liquid crystal display (LCD) 20. After returning the display position of the cursor C to the head position (step S114), the process returns to the process from step S107.

As shown in FIG. 9B, an expression using both the variable “a” and the original variable “x” used in the replacement expression, which the user thinks that the above expression (14) is modified again.
“A = (x−1) −2” (16)
And the “EXE” key on the keyboard 18 is operated to confirm the input.

  In step S107, this input is accepted, and it is determined that the expression input in the subsequent step S108 is not a replacement expression. In subsequent step S111, when it is determined that the input formula is a modified formula for the equation to be processed using the original variable and the substitution formula, the control unit (CPU) 11 in step S112, the target equation solve result storage unit. The correct solution “x = 5” stored in 17c and the value “a = 2” of the replacement expression stored in the replacement expression value storage unit 17e corresponding to this are read out and substituted into the above equation (16). Each value of the left side and the right side is calculated.

  Here, as a result of substituting “x = 5” and “a = 2” into the above equation (16), both sides become “2”, and the equal sign is established. Therefore, the above equation (16) is changed in step S113. It is determined that the format is correct, and the process returns to step S107.

  As shown in FIG. 9B, in the liquid crystal display unit (LCD) 20, assuming that the input of the above equation (16), which is a modified equation of the target equation including the substitution equation, is correct, to prompt the next input, The cursor C is displayed at the next line position of the above equation (16).

As shown in FIG. 9C, the user then uses the variable “a” used in the substitution formula.
“A = a ² −2” (17)
And the “EXE” key on the keyboard 18 is operated to confirm the input.

  In step S107, this input is accepted, and it is determined that the expression input in the subsequent step S108 is not a replacement expression. In the subsequent step S111, it is determined that the input expression is not a modified expression using the original variable and the replacement expression, and in the next step S115, it is determined that the input expression is a modified expression using only the replacement variable. Based on this determination, in step S116, the control unit (CPU) 11 executes a solve function on the substitution equation for the substitution variable, calculates the value of the substitution variable, and stores the calculation result in the transformation formula solve result storage unit 17g.

  Here, the solution “a = −1, 2” of the substitution variable is obtained by solving the above equation (17).

  Further, it is determined whether or not the substitution formula stored in the substitution formula storage unit 17d is a formula including the symbol “√” (step S117).

  Here, since the substitution formula of the above formula (13) stored in the substitution formula storage unit 17d includes the symbol “√”, the substitution formula is discriminated in step S117 and deviated from the domain of the substitution variable solution. A process of setting the solution as a temporary solution for the substitution variable is executed (step S118).

  Here, among the substitution variable solutions “a = −1, 2”, the right side of the above equation (13) is the symbol “√ (x−1)”, and therefore the domain of the left side “a” is “a> “A = −1” that is out of the definition range is used as a temporary value.

  Thereafter, it is determined whether or not the value of the substitution variable stored in the modified formula solve result storage unit 17g matches the value of the substitution formula stored in the replacement formula value storage unit 17e (step S119).

  Here, the value of the substitution variable stored in the modified equation solve result storage unit 17g is “a = −1, 2”, and the value of the substitution formula stored in one substitution formula value storage unit 17e is also the correct solution of the original variable. The correct value of the replacement expression corresponding to “x = 5” is “a = 2”, and the temporary value of the replacement expression corresponding to the temporary solution “x = 2” of the original variable is “a = −1”. Then, it is determined that they match each other, and the process returns to the process from step S107 and waits for input of a further expression.

  As shown in FIG. 9C, in the liquid crystal display unit (LCD) 20, assuming that the input of the above formula (17), which is a modification of the substitution formula, is correct, the above formula (17) is used to prompt the next input. The cursor C is displayed at the next line position.

Next, as shown in FIG. 10A, the user uses a variable “a” as a further variation of the above equation (17).
“A ² + a−2 = 0” (18)
And the “EXE” key on the keyboard 18 is operated to confirm the input.

  In step S107, this input is accepted, and it is determined that the expression input in the subsequent step S108 is not a replacement expression. In the subsequent step S111, it is determined that the input expression is not a modified expression using the original variable and the replacement expression, and in the next step S115, it is determined that the input expression is a modified expression using only the replacement variable. Based on this determination, in step S116, the control unit (CPU) 11 executes a solve function on the substitution equation for the substitution variable, calculates the value of the substitution variable, and stores the calculation result in the transformation formula solve result storage unit 17g.

  Here, the solution “a = −2, 1” of the substitution variable is obtained by solving the above equation (18).

  Further, it is determined whether or not the substitution formula stored in the substitution formula storage unit 17d is a formula including the symbol “√” (step S117).

  Here, since the substitution formula of the above formula (13) stored in the substitution formula storage unit 17d includes the symbol “√”, the substitution formula is discriminated in step S117 and deviated from the domain of the substitution variable solution. A process of setting the solution as a temporary solution for the substitution variable is executed (step S118).

  Here, among the substitution variable solutions “a = 1, −2”, the right side of the above equation (13) is the symbol “√ (x−1)”, and therefore the domain of the left side “a” is “a> “A = −2” that is out of the definition range is used as a temporary value.

  Thereafter, it is determined whether or not the value of the substitution variable stored in the modified formula solve result storage unit 17g matches the value of the substitution formula stored in the replacement formula value storage unit 17e (step S119).

  Here, the value of the substitution variable stored in the modified equation solve result storage unit 17g is “a = 1 (positive), −2 (temporary)”, and the value of the substitution formula stored in one substitution formula value storage unit 17e is The correct value of the replacement expression corresponding to the correct solution “x = 5” of the original variable is “a = 2”, and the temporary value of the replacement expression corresponding to the temporary solution “x = 2” of the original variable is “a = -1 ", it is determined that they do not coincide with each other, and an error message is displayed on the liquid crystal display (LCD) 20, and the display position of the cursor C is returned to the position before the erroneous expression input after the confirmation. After that (step S122), the process returns to step S107.

FIG. 10A shows a state in which an error message window W1 is displayed at the bottom of the equation (18) on the liquid crystal display unit (LCD) 20. In the figure (A), the error message is written in characters.
"ERROR!"
"Sorry, not equivalent"
At the same time, a face symbol F1 that visually indicates that the expression is incorrect and a character “OK?” That prompts confirmation when the user understands that the expression is incorrect are displayed.

  When the user operates the “EXE” key for confirmation on the keyboard 18 as shown in FIG. 10B along with the display in the window W1, the above-mentioned formula (18) is displayed on the liquid crystal display (LCD) 20. After returning the display position of the cursor C to the head position, the process returns to step S107.

As shown in FIG. 10C, the user uses a variable “a” as a new modified expression of the above expression (17).
“A ² −a−2 = 0” (19)
And the “EXE” key on the keyboard 18 is operated to confirm the input.

  In step S107, this input is accepted, and it is determined that the expression input in the subsequent step S108 is not a replacement expression. In the subsequent step S111, it is determined that the input expression is not a modified expression using the original variable and the replacement expression, and in the next step S115, it is determined that the input expression is a modified expression using only the replacement variable. Based on this determination, in step S116, the control unit (CPU) 11 executes a solve function on the substitution equation for the substitution variable, calculates the value of the substitution variable, and stores the calculation result in the transformation formula solve result storage unit 17g.

  Here, the solution “a = −1, 2” of the substitution variable is obtained by solving the above equation (19).

  Further, it is determined whether or not the substitution formula stored in the substitution formula storage unit 17d is a formula including the symbol “√” (step S117).

  Here, since the substitution formula of the above formula (13) stored in the substitution formula storage unit 17d includes the symbol “√”, the substitution formula is discriminated in step S117 and deviated from the domain of the substitution variable solution. A process of setting the solution as a temporary solution for the substitution variable is executed (step S118).

  Here, among the substitution variable solutions “a = −1, 2”, the right side of the above equation (13) is the symbol “√ (x−1)”, and therefore the domain of the left side “a” is “a> “A = −1” that is out of the definition range is used as a temporary value.

  Thereafter, it is determined whether or not the value of the substitution variable stored in the modified formula solve result storage unit 17g matches the value of the substitution formula stored in the replacement formula value storage unit 17e (step S119).

  Here, the value of the substitution variable stored in the modified equation solve result storage unit 17g is “a = 2 (positive), −1 (temporary)”, and the value of the substitution formula stored in one substitution formula value storage unit 17e is also The correct value of the replacement expression corresponding to the correct solution “x = 5” of the original variable is “a = 2”, and the temporary value of the replacement expression corresponding to the temporary solution “x = 2” of the original variable is “a = -1 ", it is determined that they match each other, and the process returns to the process from step S107 and waits for further expression input.

  As shown in FIG. 10C, in the liquid crystal display unit (LCD) 20, assuming that the input of the formula (19), which is a modified formula of the substitution formula, is correct, the formula (19) is used to prompt the next input. The cursor C is displayed at the next line position.

As shown in FIG. 11A, the user uses a variable “a” as a modified expression obtained by factoring the expression (19).
“(A + 1) · (a-2) = 0” (20)
And the “EXE” key on the keyboard 18 is operated to confirm the input.

  In step S107, this input is accepted, and it is determined that the expression input in the subsequent step S108 is not a replacement expression. In the subsequent step S111, it is determined that the input expression is not a modified expression using the original variable and the replacement expression, and in the next step S115, it is determined that the input expression is a modified expression using only the replacement variable. Based on this determination, in step S116, the control unit (CPU) 11 executes a solve function on the substitution equation for the substitution variable, calculates the value of the substitution variable, and stores the calculation result in the transformation formula solve result storage unit 17g.

  Here, the solution “a = −1, 2” of the substitution variable is obtained by solving the above equation (20).

  Further, it is determined whether or not the substitution formula stored in the substitution formula storage unit 17d is a formula including the symbol “√” (step S117).

  Here, since the substitution formula of the above formula (13) stored in the substitution formula storage unit 17d includes the symbol “√”, the substitution formula is discriminated in step S117 and deviated from the domain of the substitution variable solution. A process of setting the solution as a temporary solution for the substitution variable is executed (step S118).

  Here, among the substitution variable solutions “a = −1, 2”, the right side of the above equation (13) is the symbol “√ (x−1)”, and therefore the domain of the left side “a” is “a> “A = −1” that is out of the definition range is used as a temporary value.

  Thereafter, it is determined whether or not the value of the substitution variable stored in the modified formula solve result storage unit 17g matches the value of the substitution formula stored in the replacement formula value storage unit 17e (step S119).

  Here, the value of the substitution variable stored in the modified equation solve result storage unit 17g is “a = 2 (positive), −1 (temporary)”, and the value of the substitution formula stored in one substitution formula value storage unit 17e is also The correct value of the replacement expression corresponding to the correct solution “x = 5” of the original variable is “a = 2”, and the temporary value of the replacement expression corresponding to the temporary solution “x = 2” of the original variable is “a = -1 ", it is determined that they match each other, and the process returns to the process from step S107 and waits for further expression input.

  As shown in FIG. 11A, in the liquid crystal display unit (LCD) 20, assuming that the input of the above formula (20), which is a modification of the substitution formula, was correct, the above formula (20) is used to prompt the next input. The cursor C is displayed at the next line position.

As shown in FIG. 11B, the user uses a variable “a” as a modified expression obtained by solving the expression (20).
“A = −1 or a = 2 (21)
And the “EXE” key on the keyboard 18 is operated to confirm the input.

  In step S107, this input is accepted, and it is determined that the expression input in the subsequent step S108 is not a replacement expression. In step S111, the control unit (CPU) determines that the input expression is not a modified expression using the original variable and the replacement expression, and determines that the input expression is a modified expression using only the replacement variable in the next step S115. In step S116, the solve function executes the solve function on the substitution variable, calculates the value of the substitution variable, and stores the calculation result in the transformation formula solve result storage unit 17g.

  Here, since the above equation (21) itself is a description representing the solution of the substitution variable, the solution “a = −1, 2” of the substitution variable is obtained as it is.

  Further, it is determined whether or not the substitution formula stored in the substitution formula storage unit 17d is a formula including the symbol “√” (step S117).

  Here, since the substitution formula of the above formula (13) stored in the substitution formula storage unit 17d includes the symbol “√”, the substitution formula is discriminated in step S117 and deviated from the domain of the substitution variable solution. A process of setting the solution as a temporary solution for the substitution variable is executed (step S118).

  Here, among the substitution variable solutions “a = −1, 2”, the right side of the above equation (13) is the symbol “√ (x−1)”, and therefore the domain of the left side “a” is “a> “A = −1” that is out of the definition range is used as a temporary value.

  Thereafter, it is determined whether or not the value of the substitution variable stored in the modified formula solve result storage unit 17g matches the value of the substitution formula stored in the replacement formula value storage unit 17e (step S119).

  Here, the value of the substitution variable stored in the modified equation solve result storage unit 17g is “a = 2 (positive), −1 (temporary)”, and the value of the substitution formula stored in one substitution formula value storage unit 17e is also The correct value of the replacement expression corresponding to the correct solution “x = 5” of the original variable is “a = 2”, and the temporary value of the replacement expression corresponding to the temporary solution “x = 2” of the original variable is “a = -1 ", it is determined that they match each other, and the process returns to the process from step S107 and waits for further expression input.

  As shown in FIG. 11B, in the liquid crystal display unit (LCD) 20, assuming that the input of the formula (21), which is a modified formula of the substitution formula, is correct, the formula (21) is used to prompt the next input. The cursor C is displayed at the next line position.

As shown in FIG. 12A, the user uses an original variable “x” as a modified expression obtained by removing the substitution from the above expression (21).
“√ (x−1) = − 1 or √ (x−1) = 2 (22)
And the “EXE” key on the keyboard 18 is operated to confirm the input.

  In step S107, this input is accepted, and it is determined that the expression input in the subsequent step S108 is not a replacement expression. In the subsequent step S111, it is determined that the input expression is not a modified expression using the original variable and the replacement expression, and in the next step S115, it is determined that the input expression is not a modified expression using only the replacement variable. In subsequent step S123, the control unit (CPU) 11 determines whether or not it is a modified expression using only the original variable “x”.

  If the control unit (CPU) 11 determines that it is a modified expression using only the original variable, the control unit (CPU) 11 executes a solve function on the original variable, calculates a solution of the original variable, and stores the calculation result as a modified expression solve result. Store in the part 17g (step S124).

  At this time, when the solve function is executed for the expression “√ (x−1) = − 1”, in this embodiment, the concept of an imaginary number is excluded from the solution. Therefore, the solution is not obtained and the result is handled as “No Solution”.

  Further, when the solve function is executed for the expression “√ (x−1) = 2”, the result is “x = 5”. Therefore, only “x = 5” is stored in the modified equation solve result storage unit 17g as a result of calculating the solution.

  In this case, as described above, even if the solve function is executed with a part of the deformation equation and the result is “No Solution”, if the solution can be calculated with another deformation equation, Processing such as error display is not performed.

  The control unit (CPU) 11 determines whether or not the solution of the deformation equation stored in the deformation equation solve result storage unit 17g matches the content stored in the target equation solve result storage unit 17c (step S125).

  Here, since it matches the correct solution “x = 5” stored in the target equation solve result storage unit 17c in step S103, the control unit (CPU) 11 determines it, and returns to the processing from step S107, Wait for further expressions.

  As shown in FIG. 12A, in the liquid crystal display unit (LCD) 20, assuming that the input of the equation (22), which is a modified equation of the original variable, is correct, the equation (22) is used to prompt the next input. The cursor C is displayed at the next line position.

Next, as shown in FIG. 12 (B), the user can use the original variable “x” as a modified equation to eliminate the number “√ (n) <0” (n is a real number) from the above equation (22). Formula using
“√ (x−1) = 2 (23)
And the “EXE” key on the keyboard 18 is operated to confirm the input.

  In step S107, this input is accepted, and it is determined that the expression input in the subsequent step S108 is not a replacement expression. In the subsequent step S111, it is determined that the input expression is not a modified expression using the original variable and the replacement expression, and in the next step S115, it is determined that the input expression is not a modified expression using only the replacement variable.

  If it is determined in step S123 that it is a modified expression using only the original variable “x”, the control unit (CPU) 11 executes a solve function on the original variable to calculate a solution of the original variable, and calculates The result is stored in the modified solve result storage unit 17g (step S124).

  When the solve function is executed for the expression “√ (x−1) = 2”, the result is “x = 5”. Therefore, the solution calculation result “x = 5” is stored in the modified equation solve result storage unit 17g.

  The control unit (CPU) 11 determines whether or not the solution of the deformation equation stored in the deformation equation solve result storage unit 17g matches the content stored in the target equation solve result storage unit 17c (step S125).

  Here, since it matches the correct solution “x = 5” stored in the target equation solve result storage unit 17c in step S103, the control unit (CPU) 11 determines it, and returns to the processing from step S107, Wait for further expressions.

  As shown in FIG. 12B, in the liquid crystal display unit (LCD) 20, assuming that the input of the above equation (23), which is a modified equation of the original variable, is correct, the above equation (23) is used to prompt the next input. The cursor C is displayed at the next line position.

Next, as shown in FIG. 13A, the user uses the original variable “x” as a modified expression based on the theory of a solution that squares both sides of the above equation (23) and removes the symbol “√ ()”. Expression
“X−1 = 4 (24)
And the “EXE” key on the keyboard 18 is operated to confirm the input.

  In step S107, this input is accepted, and it is determined that the expression input in the subsequent step S108 is not a replacement expression. In the subsequent step S111, it is determined that the input expression is not a modified expression using the original variable and the replacement expression, and in the next step S115, it is determined that the input expression is not a modified expression using only the replacement variable.

  If it is determined in step S123 that it is a modified expression using only the original variable “x”, the control unit (CPU) 11 executes a solve function on the original variable to calculate a solution of the original variable, and calculates The result is stored in the modified solve result storage unit 17g (step S124).

  When the solve function is executed for the expression “x−1 = 4”, the result is “x = 5”. Therefore, the solution calculation result “x = 5” is stored in the modified equation solve result storage unit 17g.

  The control unit (CPU) 11 determines whether or not the solution of the deformation equation stored in the deformation equation solve result storage unit 17g matches the content stored in the target equation solve result storage unit 17c (step S125).

  Here, since it matches the correct solution “x = 5” stored in the target equation solve result storage unit 17c in step S103, the control unit (CPU) 11 determines it, and returns to the processing from step S107, Wait for further expressions.

  As shown in FIG. 13A, in the liquid crystal display unit (LCD) 20, assuming that the input of the above equation (24), which is a modified equation of the original variable, is correct, the above equation (24) is used to prompt the next input. The cursor C is displayed at the next line position.

Next, as shown in FIG. 13B, the user moves “-1” on the left side of the above equation (24) to the right side, and uses the equation in the solution description format using the original variable “x”.
“X = 5” (25)
And the “EXE” key on the keyboard 18 is operated to confirm the input.

  In step S107, this input is accepted, and it is determined that the expression input in the subsequent step S108 is not a replacement expression. In the subsequent step S111, it is determined that the input expression is not a modified expression using the original variable and the replacement expression, and in the next step S115, it is determined that the input expression is not a modified expression using only the replacement variable.

  If it is determined in the following step S123 that it is not a modified expression using only the original variable “x”, the control unit (CPU) 11 determines whether or not the next input expression represents the solution of the original variable, that is, “ It is determined whether or not the expression is described in the format of “x = (numerical value)” (step S127).

  If it is determined that it is not an expression describing the solution of the original variable, the control unit (CPU) 11 performs appropriate processing corresponding to the other input contents, but the explanation is given as being unrelated to the present embodiment. Is omitted.

  On the other hand, if it is determined in step S127 that the solution of the original variable is described, the control unit (CPU) 11 matches the input solution with the correct solution of the original variable stored in the target equation solve result storage unit 17c. It is determined whether or not to perform (step S128).

  In this case, the control unit (CPU) 11 determines that the input solution value matches the correct solution value of the original variable stored in the target equation solve result storage unit 17c, and the input of the equation (25) is correct. As a result, the correct answer mark and the correct answer message are displayed (step S130), and the process returns to step S107 to wait for the next input.

As shown in FIG. 13B, the liquid crystal display (LCD) 20 illustrates a correct message window W2 at this time. In this window W2, as shown in FIG.
"Right!"
Is displayed together with a face symbol F2 which visually indicates that the answer is correct.

  In this way, when the target equation differs from the substitution formula entered by the user, a message or symbol indicating that fact is displayed, and if a correct substitution formula is entered to derive a solution, the correct answer Therefore, it is possible to increase the user's motivation and enhance the educational effect.

  If it is determined in step S125 that the solve result of the modified equation using the input original variable does not match the solution of the original variable stored in the target equation solve result storage unit 17c, an error message is displayed on the liquid crystal display. While displaying on the display part (LCD) 20, waiting for the confirmation, the display position of the cursor C is returned to the position before the erroneous expression input (step S126), and the process returns to the process from step S107.

  Similarly, when it is determined in step S128 that the input original variable solution does not match the original variable solution stored in the target equation solve result storage unit 17c, an error message is displayed on the liquid crystal display unit (LCD). In step S129, the display position of the cursor C is returned to the position before the erroneous expression input after waiting for the confirmation (step S129), and the process returns to step S107.

(Effect of embodiment)
As described in detail in the first and second operation examples, according to the present embodiment, it is possible to determine at any time whether an arithmetic expression is input and whether correctness or not with respect to a replacement expression in the middle of deformation of the expression is input at any time. Become. For this reason, when an equation to be processed has various complicated configurations, it is possible to learn and learn how to set a replacement formula so as to simplify it by trial and error.

  Further, as described in detail in the second operation example, when an original variable is included in the square root sign on at least one side in the equation to be processed, a solution is calculated for an equation obtained by squaring both sides of the equation. Thus, since the solution of the equation including the square root sign is obtained, it is possible to cope with the case where the user finds the solution of the equation using the replacement equation.

  In addition, in the above-described embodiment, it is possible to deal with a mixed equation in which substitution variables and original variables are mixed, so that a solution can be derived flexibly by changing the equation.

  In the above embodiment, even when a modified expression using the equation to be processed and the original variable or a final original variable solution is input, the correctness / incorrectness of the modified expression is determined according to the determination result. Since the immediate display is performed, the user can immediately recognize the correctness / incorrectness of the deformation formula or the final solution input by the user, thereby contributing to efficient learning.

  In the above embodiment, when a correct transformation formula or replacement formula is entered, the cursor C is placed at the next line position of the formula entered before that in order to prompt the next input on the screen of the liquid crystal display (LCD) 20. However, the present invention is not limited to this, and simple symbols such as "OK?" For example, it may be displayed for confirmation that the input is correct, such as displaying only for one second.

  In addition, the input type determination processing methods described in the flow charts of FIGS. 3 and 4 of the above-described embodiment are memory cards, magnetic disks (floppy disk (registered trademark) devices, hard disks) as programs that can be executed by a computer. Apparatus), an optical disk (CD-ROM, MO disk, DVD, etc.), an external storage medium such as a semiconductor nonvolatile memory, and the like can be distributed.

  Furthermore, although this embodiment demonstrated the case where this invention was applied to a scientific calculator, this invention is not restricted to it, A small PC, PDA (Personal Digital Assistants: Personal information portable terminal), a mobile telephone terminal, a portable music player By storing the program stored in the external storage medium (13) in the internal memory (12) in a computer terminal which is various electronic devices such as an electronic book, and reading out the stored program to execute the operation. The same process as the input expression determination process described in the above embodiment can be executed.

  Data of a program for realizing the above method can be transmitted on a communication network (Internet) N as a program code form, and a computer terminal (program server) 16 connected to the communication network (Internet) N. The program data can be taken in from the above, and the above-described input type determination process can be realized.

  In addition, the present invention is not limited to the above-described embodiments, and various modifications can be made without departing from the scope of the invention in the implementation stage. Further, the functions executed in the above-described embodiments may be combined as appropriate as possible. The above-described embodiment includes various stages, and various inventions can be extracted by an appropriate combination of a plurality of disclosed constituent elements. For example, even if some constituent requirements are deleted from all the constituent requirements shown in the embodiment, if the effect is obtained, a configuration from which the constituent requirements are deleted can be extracted as an invention.

  DESCRIPTION OF SYMBOLS 10 ... Scientific calculator, 11 ... Control part (CPU), 12 ... ROM, 12a ... Input type determination processing program, 13 ... Memory card, 14 ... I / O port, 15 ... External personal computer (PC), 16 ... Web server , 17 ... RAM, 17a ... Formula data storage unit, 17b ... Target equation storage unit, 17c ... Target equation solve result storage unit, 17d ... Replacement formula storage unit, 17e ... Deformation formula solve result storage unit, 18 ... Keyboard, 19 ... Liquid crystal drive circuit, 20 ... Liquid crystal display unit (LCD), 21 ... Touch input unit, 22 ... Coordinate input unit, N ... Network.

Claims (5)

An equation input means for inputting an equation for the original variable;
Original variable solution calculation means for calculating a solution of the original variable input by the equation input means;
A substitution expression input means for inputting a substitution expression describing the substitution variable as a mathematical expression of the original variable;
Substitution variable value calculation means for substituting the solution of the original variable calculated by the original variable solution calculation means into the replacement expression input by the replacement expression input means, and calculating the value of the substitution variable;
A modified expression input means for inputting a modified expression obtained by modifying the equation for the original variable;
Deformation equation equation input by the deformation-type input means, in the case of the equation for the source variable is a substituted equation that describes substituted variable substitution variables solution calculating means for calculating a solution for the substitution variables for the substituted equation When,
A substitution variable determination means for determining whether or not the solution of the substitution variable calculated by the substitution variable solution calculation means and the value of the substitution variable calculated by the substitution variable value calculation means match;
An electronic apparatus comprising: display control means for performing display in accordance with a result of discrimination by the substitution variable discrimination means. The original variable solution calculation means calculates a solution for an expression in which both sides are squared when either side in the input equation is an expression including the original variable in the square root sign, and a temporary solution of the original variable has a temporary source variable solution calculating means for obtaining,
The substitution variable value calculation means includes provisional substitution variable value calculation means for calculating a provisional solution of the substitution variable by substituting the provisional solution of the original variable into a substitution expression,
Said substituted variable determining means determines substituted and variables of a provisional solution calculated in the temporary replacement variable value calculating means, whether both substituted variable value calculated at replacement variable value calculating means coincides The electronic device according to claim 1, further comprising a provisional replacement variable determination unit. By the deformation type input means, when the mixing equations written in the substitution variables with the original variable deformation formula is entered, the solution of the original variables by the original variables solution calculating unit to the mixing equations, the substitution variable value 2. The electronic apparatus according to claim 1, further comprising a mixing equation determining unit that inputs a value of the substitution variable calculated by the calculating unit and determines whether or not the mixing equation holds. By the deformation type input means, when the modified equation deformed using the original variable deformation expressions of interest is inputted, and deformation equation solution calculating means for calculating a solution of the original variables for the deformation equation,
Deformation expression determining means for determining whether or not the solution of the original variable calculated by the original variable solution calculation means and the solution of the original variable calculated by the deformation expression solution calculation means match;
A deformation equation error display means for displaying that the deformation equation input by the deformation equation input means is incorrect when the deformation equation determination means determines that the solutions of the original variables do not match;
If the solution of the original variable is input by the variable format input means, solutions determination for determining whether or not the original variables solution calculated in the solution and the original variables solution calculating means of the input original variable matches Means,
2. The electronic apparatus according to claim 1, further comprising correct answer display means for displaying that the solution of the input original variable is correct when the answer determining means determines that they match. A program for controlling a computer incorporated in an electronic device,
The above computer
An equation input means for inputting an equation for the original variable,
Original variable solution calculating means for calculating the solution of the original variable input by the equation input means,
A substitution expression input means for inputting a substitution expression describing the substitution variable as a mathematical expression of the original variable,
Substitution variable value calculation means for substituting the solution of the original variable calculated by the original variable solution calculation means to the replacement expression input by the replacement expression input means,
A modified expression input means for inputting a modified expression obtained by modifying the equation for the original variable;
Deformation equation equation input by the deformation-type input means, in the case of the equation for the source variable is a substituted equation that describes substituted variable substitution variables solution calculating means for calculating a solution for the substitution variables for the substituted equation ,
A substitution variable discriminating unit that discriminates whether or not the solution of the substitution variable calculated by the substitution variable solution calculating unit and the value of the substitution variable calculated by the substitution variable value calculating unit match; and the substitution variable discrimination unit display control means for performing a display corresponding to the determination result,
Program to function as.

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