JP5286890B2 - Formula arithmetic device and formula calculation processing program - Google Patents

Description

  The present invention relates to a mathematical expression calculation apparatus and a mathematical expression calculation processing program for performing an identity calculation.

  Conventionally, in scientific calculators, many proposals have been made to enhance the learning effect when finding the solution of the variables in the equation. As an example, an equation processing apparatus has been proposed for performing numerical analysis of higher-order differential equations in a manner that is easy for the user to understand (see, for example, Patent Document 1).

On the other hand, when an equation including an unknown constant is an identity with respect to a variable x, it is unknown by comparing coefficients for each order of x (coefficient comparison method) or by substituting an arbitrary numerical value for x (numerical value substitution method). Finding a constant is done in school education. It is very important to learn how to solve such identities, which is the basis for advanced numerical analysis.
JP 2003-108535 A

  However, in the conventional scientific calculator, no proposal has been made to increase the learning effect for finding unknown constants in the identity.

  The present invention has been made in view of such a problem, and an object of the present invention is to provide a mathematical expression calculation apparatus and a mathematical expression processing program that can effectively learn about solving an unknown constant in an identity.

The mathematical expression calculation apparatus according to claim 1 is a mathematical expression display unit that displays a mathematical expression including a character input in response to a user operation, and an arbitrary one type of character included in the mathematical expression displayed by the mathematical expression display unit. Variable designation means for designating as a variable in response to a user operation, and a variable designated by the variable designation means when the mathematical formula displayed by the mathematical formula display means is an equation including a plurality of types of characters. A constant solution calculating means for obtaining a numerical value corresponding to the character other than the variable by solving an equation for each coefficient corresponding to the order of the variable included in the equation, and the constant solution calculating means and a constant value displaying means for displaying together with the corresponding character of the numerical value obtained by, when mathematical expression displayed by the mathematical expression display means is equality, including a plurality of types of characters, the user Misao In accordance with the numerical value substituting means for substituting an arbitrary numerical value for the variable included in the equation, the numerical value substituting means calculates the equation in which the numerical value is assigned to the variable, and displays the calculation result. And a substitution calculation result display means .

The mathematical expression calculation apparatus according to claim 2 is a mathematical expression display unit that displays a mathematical expression including a character input in response to a user operation, and an arbitrary one type of character included in the mathematical expression displayed by the mathematical expression display unit. Variable designation means for designating as a variable in response to a user operation, and a variable designated by the variable designation means when the mathematical formula displayed by the mathematical formula display means is an equation including a plurality of types of characters. A constant solution calculating means for obtaining a numerical value corresponding to the character other than the variable by solving an equation for each coefficient corresponding to the order of the variable included in the equation, and the constant solution calculating means and a constant value displaying means for displaying together with the corresponding character of the numerical value obtained by, when mathematical expression displayed by the mathematical expression display means is equality, including a plurality of types of characters, the user Misao In accordance with the calculation formula input means for inputting arbitrary formulas to be subjected to four arithmetic operations on both sides of the equation, and four arithmetic operations on both sides of the equation based on the formulas input by the calculation formula input means, and the calculation result It is characterized in that example Bei and a four arithmetic operation result display means for displaying.

A mathematical expression calculation apparatus according to claim 3 is a mathematical expression display means for displaying a mathematical expression including a character input in response to a user operation, and an arbitrary one type of character included in the mathematical expression displayed by the mathematical expression display means. Variable designation means for designating as a variable in response to a user operation, and a variable designated by the variable designation means when the mathematical formula displayed by the mathematical formula display means is an equation including a plurality of types of characters. A constant solution calculating means for obtaining a numerical value corresponding to the character other than the variable by solving an equation for each coefficient corresponding to the order of the variable included in the equation, and the constant solution calculating means and a constant value displaying means for displaying together with the corresponding character of the numerical value obtained by, when mathematical expression displayed by the mathematical expression display means is equality, including a plurality of types of characters, the user Misao It is characterized in that there was Bei ETae and a equation display means for displaying respective equations for each coefficient corresponding to the degree of the variables included in the equation depending on.

According to a fourth aspect of the present invention, there is provided a mathematical expression calculation device that displays a mathematical expression including a character input in response to a user operation, and an arbitrary one type of character included in the mathematical expression displayed by the mathematical expression display means. Variable designation means for designating as a variable in response to a user operation, and a variable designated by the variable designation means when the mathematical formula displayed by the mathematical formula display means is an equation including a plurality of types of characters. A constant solution calculating means for obtaining a numerical value corresponding to the character other than the variable by solving an equation for each coefficient corresponding to the order of the variable included in the equation, and the constant solution calculating means identities of storing a plurality of kinds of the constant value displaying means for displaying together with the corresponding character of the numerical value obtained, the identity data of the formulas associated with identities that do not contain equal signs and inequality by It comprises a chromatography data storage means, the said equation display means, when the formula that contains a character that is input in response to a user operation does not include an equal sign and inequality, identity is the identity data store corresponding to the formula When stored by means, the identity is read and displayed.

  ADVANTAGE OF THE INVENTION According to this invention, the numerical formula calculating apparatus and mathematical formula calculation processing program which can learn effectively about the solution of the unknown constant in an identity can be provided.

  Embodiments of the present invention will be described below with reference to the drawings.

  FIG. 1 is a block diagram showing a configuration of an electronic circuit of an electronic calculator (scientific calculator) 10 according to an embodiment of a mathematical formula calculation apparatus of the present invention.

  The electronic calculator 10 includes a control unit (CPU) 11 that is a computer.

  The control unit (CPU) 11 is a computer program read into the ROM 12 via the storage medium reading unit 14 from a system program stored in a ROM (storage area: flash ROM) 12 or an external storage medium 13 such as a memory card. In accordance with a control program or a computer control program downloaded from the Web server (program server) 15 on the communication network N via the communication control unit 16 and read into the ROM 12, the operation of each part of the circuit is controlled using the RAM 17 as a working memory. . The system program and computer control program stored in advance in the ROM 12 are activated in response to a key input signal from the key input unit 18.

  In addition to the ROM 12, the storage medium reading unit 14, the communication control unit 16, the RAM 17, and the key input unit 18, a liquid crystal display unit (LCD) 19 is connected to the control unit (CPU) 11.

  The ROM 12 stores in advance a computer control program that controls the overall operation of the electronic computer 10, and performs arithmetic processing according to various equations such as various equations and inequalities arbitrarily input by the user, Various arithmetic processing programs 12a for displaying the mathematical expression H1, the designated variable display H2, the command display H3, and the processing result display H4 are stored for the calculation process and calculation result. . The ROM 12 previously stores an identity database 12b having contents as shown in FIG.

  In this electronic calculator 10, problem data Dq for learning to calculate various mathematical formulas is read from the external storage medium 13 and stored in the ROM 12 or used, or stored in advance in the ROM 12. Used.

  FIG. 2 is a diagram showing the contents of the identity database 12b stored in advance in the ROM 12 of the electronic calculator 10. As shown in FIG.

  In this identity database 12b, a fractional expression that is associated with model expressions (fractional expressions in the figure) of various patterns that do not include an equal sign or an inequality sign, and an expression obtained by partial fractional decomposition of the fractional expression. The identity model data consisting of the following equations is stored in advance. Partial fraction decomposition is a calculation necessary for advanced mathematical operations such as Laplace transform, and is highly important learning content.

  In the electronic calculator 10, in the identity mode in which the identity equation is calculated, when a user input an expression that does not include an equal sign or an inequality sign, it is equal to the model expression of any pattern stored in the identity database 12b. (Including the case where the constants a, b, c,... Are replaced with numerical values). When a model expression equal to the input expression is determined, the identity associated with the model expression is read, and constants a, b, c,... In the identity are replaced with the corresponding numerical values described in the input expression. Displayed.

  Thus, when an expression that does not include an equal sign or an inequality sign is input by the user, the identity corresponding to the input expression is automatically input based on the identity database 12b.

  The key input unit 18 includes “various function keys (including Fn key)” 18a operated when designating functions of various calculation modes mounted on the electronic calculator 10, and various characters provided in the scientific calculator.・ "Character / symbol / numeric key" 18b operated when inputting symbol / numeric data, the input position indicated by the cursor C or item on the display screen is moved and displayed, or the display range is scrolled. "↑", "↓", "←", "→" cursor keys 18c that are operated at the time of execution, "decision key" 18d that is operated at the time of instructing determination of input data or execution of calculation, and the process input this time A “return key” 18e that is operated when canceling the step and returning to the immediately preceding processing state is provided.

  The RAM 17 has a work area (work memory) for temporarily storing various data input / output to / from the control unit 11 in accordance with various calculation processes. As a work area required at least in the identity mode, a mathematical expression memory 17a, a variable memory 17b, a solution command (Fn) memory 17c, an arithmetic memory 17d, and a processing result memory 17e are secured.

  The mathematical formula memory 17a stores a mathematical formula input in response to a user operation of the input unit 18, or an identity read from the identity database 12b corresponding to the input formula.

  The variable memory 17b stores a symbol of a variable designated in accordance with a user operation with respect to a mathematical formula (identity) stored in the mathematical formula memory 17a.

  In the solution command (Fn) memory 17c, a command for solving a constant (a, b, c,...) Of the mathematical formula (identity) stored in the mathematical formula memory 17a is [F1; [F2; Numerical value substitution] [F3; Four arithmetic operations] [F4; Coefficient comparison] User selected and stored.

  The calculation memory 17d appropriately stores calculation data that has been input or calculated by the user during the constant solution calculation process of the identity equation.

  The processing result memory 17e stores processing result data that has been subjected to solution calculation processing in accordance with the solution command [F1] [F2] [F3] [F4] selected and stored in the solution command (Fn) memory 17c.

  The display unit 19 is composed of a dot matrix type liquid crystal display unit, and calculation processes and calculation results corresponding to various calculation processes are combined as a mathematical expression display H1, a designated variable display H2, a command display H3, a processing result display H4, and the like. Is displayed.

  Next, an identity solution learning function in the identity mode by the electronic calculator 10 having the above-described configuration will be described.

  FIG. 3 is a flowchart showing identity mode processing by the electronic calculator 10.

Example 1
FIG. 4 is a diagram showing the solution display operation of the first embodiment accompanying the identity mode processing of the electronic calculator 10.

  In accordance with a menu screen Gm (see FIG. 4A) for selecting a calculation mode displayed on the display unit 19 in response to an operation of a menu key (not shown) in the input unit 18, the “identity mode” is set in accordance with a user operation. When selected, the identity mode processing program (12a) stored in the ROM 12 is activated (step S1).

  Then, as shown in FIG. 4B, an “equation” processing screen Gk provided with a formula display H1 area and a designated variable display H2 area for inputting a “formula” as an identity and specifying the “variable”. Is displayed on the display unit 19 (step S2).

In this identity processing screen Gk, as shown in FIG. 4C, a desired mathematical expression “(x + a) (bx−2) = x ² −4” is input and displayed in response to a user operation of the input unit 18. In addition, when the variable “x” is designated and displayed and the “decision key” 18d is operated and input (step S2), the input mathematical formula does not include an equal sign or an inequality sign and includes one or more characters. It is determined whether it is a mathematical expression, that is, whether it is a mathematical expression which is not completed as an identity but is a side of the identity (step S3).

Here, when it is determined that the mathematical expression “(x + a) (bx−2) = x ² −4” input by the user is a mathematical expression including an equal sign (step S3 (NO)), the mathematical expression Is an equation including two or more characters, and it is determined whether or not it is an object of the constant solution calculation as an identity (step S4).

The user-input mathematical expression “(x + a) (bx−2) = x ² −4” is an equation including two or more characters, and is determined to be an object of constant solution calculation as an identity. Then (step S4 (YES)), characters “a” and “b” other than the character “x” designated as a variable in step S2 are designated as constants (step S5).

Then, as shown in FIG. 4D, there are four methods for solving constants “a” and “b” of the identity “(x + a) (bx−2) = x ² −4” input by the user. A command list display H3 for selecting from the solution command [F1; automatic solution] [F2; numerical substitution] [F3; four arithmetic operations] [F4; coefficient comparison] is performed (step S6).

If it is determined that the constant value automatic solution processing is selected in response to the operation input of the “F1 key” on the identity processing screen Gk on which the solution command list display H3 is performed (step S7 (YES)), the coefficient comparison method For the coefficient of the term for each order of the variable “x” in the identity “(x + a) (bx−2) = x ² −4”, the equations “second order: b = 1” and “ The values of constants “a” and “b” that satisfy the first order: ab−2 = 0 and “0th order: −2a = −4” are processed and automatically solved (step S8).

  Then, as shown in FIG. 4E, the character and value of the constant calculated and automatically obtained by the coefficient comparison method are displayed as a processing result H4 as “a = 2” and “b = 1” (step S4). S9).

Therefore, according to the constant value automatic solution processing (F1), the user designates an arbitrary variable “x”, and the identity “(x + a) (bx−2) = x ² −4” is obtained. By doing so, the variable “x” and the unknown constants “a” and “b” can be clearly distinguished and recognized and the solution calculation can be performed.

(Example 2)
FIG. 5 is a diagram showing a solution display operation of the second embodiment accompanying the identity mode processing of the electronic calculator 10.

Similarly to the above, after the “identity mode” is selected in response to the user operation, the identity mode processing program (12a) is started (step S1), and then the mathematical expression display H1 as shown in FIG. 5B is displayed. In the identity processing screen Gk provided with the region and the region of the designated variable display H2, as shown in FIG. 5C, the desired mathematical expression “3x ² + 2x−3 = a (x−1) (x + 2)” + b (x-1) + c ”is input and displayed, the variable“ x ”is designated and displayed, and the“ decision key ”18d is input (step S2). It is determined that the mathematical expression includes an equal sign (step S3 (NO)). Further, the equation is an equation including two or more characters, and is determined to be an object of constant solution calculation as an identity (step S4 (YES)).

  Then, characters “a”, “b”, and “c” other than the character “x” designated as a variable in step S2 are designated as constants (step S5).

  Thereafter, as shown in FIG. 5D, in the list display H3 of the solution command [F1; automatic solution] [F2; numerical substitution] [F3; four arithmetic operations] [F4; coefficient comparison] (step S6). When it is determined that the numerical value substitution process has been selected in response to the operation input of the “F2 key” (step S10 (YES)), the designated variable display H2 is displayed as shown in FIG. An equality sign “=” and a cursor C are additionally displayed for the variable “x”, and an identity processing screen Gk for prompting the substitution of the numerical value of the variable “x” is displayed (step S11).

Here, in response to a user operation in the designated variable display H2, as shown in FIG. 5F, when “variable: x = 1” is substituted and displayed and the “decision key” 18d is operated, the input is made. And the variable “x = 1” is assigned to “3x ² + 2x-3 = a (x-1) (x + 2) + b (x-1) + c” and the constant “a The calculation process for finding “b” and “c” is executed, and the calculation result is displayed as “ 2 = c” and the process result is displayed H4 (step S11).

  In the identity processing screen Gk (see FIG. 5 (F)) on which the processing result display H4 is performed, when the “decision key” 18a is operated and input is instructed to complete the confirmation, the above FIG. The identity processing screen Gk of the solution command list display H3 shown in (5) is displayed again, and constant solution processing can be performed by selecting a user desired solution command again (steps S11 → S6).

  Therefore, according to the numerical substitution solution process (F2), the user can designate an arbitrary variable “x” and clearly distinguish the variable “x” from the unknown constants “a”, “b”, and “c”. In addition to being able to recognize, by substituting an arbitrary numerical value for the variable “x” of the identity equation, it is possible to solve the problem. Can be effectively recognized by the user. Moreover, by allowing the user to experience the simplification of mathematical expressions by numerical substitution of variables, it is possible to effectively deepen the understanding of the identity.

(Example 3)
FIG. 6 is a diagram showing the solution display operation of the third embodiment accompanying the identity mode processing of the electronic calculator 10.

  Similarly to the above, after the “identity mode” is selected in accordance with the user operation, the identity mode processing program (12a) is started (step S1), and then the mathematical expression display H1 as shown in FIG. 6B is displayed. In the identity processing screen Gk provided with the area and the area of the designated variable display H2, as shown in FIG. 6C, a desired mathematical expression “(x + 2) / (x + 1) x = (a / (x +1)) + b / x ”(which is different from the natural display form shown in the figure due to restrictions on character input) is input and displayed, the variable“ x ”is designated and displayed, and the“ decision key ”18d is input for operation. When it is done (step S2), it is determined that the inputted formula is a formula including an equal sign (step S3 (NO)). Further, the equation is an equation including two or more characters, and is determined to be an object of constant solution calculation as an identity (step S4 (YES)).

  Then, characters “a” and “b” other than the character “x” designated as a variable in step S2 are designated as constants (step S5).

  Thereafter, as shown in FIG. 6D, in the list display H3 of the solution command [F1; automatic solution] [F2; numerical substitution] [F3; four arithmetic operations] [F4; coefficient comparison] (step S6). If it is determined that the four arithmetic operations are selected in response to the operation input of the “F3 key” (step S12 (YES)), as shown in FIG. An identity processing screen Gk having an input area “both sides” H5 for performing solution calculation processing by multiplying or dividing the polynomial is displayed (step S13).

  Here, according to a user operation in the input area “both sides” H5, the calculation target “x” and the calculation content “x (x + 1)” in the mathematical expression are input and displayed, and the “decision key” 18d is operated. And the input operation content “x (x + 1)” is converted into the above-described mathematical expression (identity) “(x + 2) / (x + 1) x = (a / (x + 1)) + b / x” An arithmetic process for multiplying both sides is executed, and the operation result is displayed as a process result H4 as “x + 2 = ax + b (x + 1)” (step S13).

  On the identity processing screen Gk (see FIG. 6 (F)) on which the processing result display H4 is performed, further solution calculation processing for the identity “x + 2 = ax + b (x + 1)” of the calculation result. When the “decision key” 18a is operated and input to perform the above, the inputted formula “(x + 2) / (x + 1) x = (a / (x + 1)) + b / x” is obtained. After the calculation result is replaced with the identity “x + 2 = ax + b (x + 1)” (step S14), the identity processing screen Gk of the solution command list display H3 as shown in FIG. 6D is displayed. Is displayed (step S14 → S6).

  Therefore, according to the four arithmetic calculation solution process (F3), the user can designate an arbitrary variable “x” and can clearly distinguish and recognize the variable “x” and the unknown constants “a” and “b”. In addition to multiplying or dividing an arbitrary polynomial on both sides of the identity, the solution processing is performed so that they are effective as a process for solving unknown constants, and the understanding of the identity is effective. Can be deepened.

Example 4
FIG. 7 is a diagram showing a solution display operation of the fourth embodiment accompanying the identity mode processing of the electronic calculator 10.

Similarly to the above, after the “identity mode” is selected in accordance with the user operation, the identity mode processing program (12a) is started (step S1), and then the mathematical expression display H1 as shown in FIG. 7B is displayed. In the identity processing screen Gk provided with the region and the region of the designated variable display H2, as shown in FIG. 7C, the desired mathematical expression “3x ² + 2x−3 = a (x−1) (x + 2)” + b (x-1) + c ”is input and displayed, the variable“ x ”is designated and displayed, and the“ decision key ”18d is input (step S2). It is determined that the mathematical expression includes an equal sign (step S3 (NO)). Further, the equation is an equation including two or more characters, and is determined to be an object of constant solution calculation as an identity (step S4 (YES)).

  Then, characters “a”, “b”, and “c” other than the character “x” designated as a variable in step S2 are designated as constants (step S5).

Thereafter, as shown in FIG. 7D, in the list display H3 of the solution command [F1; automatic solution] [F2; numerical substitution] [F3; four arithmetic operations] [F4; coefficient comparison] (step S6). If it is determined that the coefficient comparison solution processing has been selected in response to the operation input of the “F4 key” (step S15 (YES)), the inputted identity “3x ² + 2x−3 = a (x−1)” On the coefficient of the term for each degree of the variable “x” in the expression [ax ² + (a + b) x-2a-b + c] obtained by converting (x + 2) + b (x-1) + c ” The equation is obtained, and the processing result is displayed as [coefficient comparison] {“a = 3” “a + b = 2” “−2a-b + c = −3”} as shown in FIG. H4 is performed (step S16).

  In the identity processing screen Gk (see FIG. 7E) on which the processing result display H4 has been performed, when the “enter key” 18a is operated and input is instructed to complete the confirmation, FIG. The identity processing screen Gk of the solution command list display H3 shown in (5) is displayed again, and constant solution processing can be performed by selecting a user desired solution command again (steps S16 → S6).

  Therefore, according to the coefficient comparison solution process (F4), the user can designate an arbitrary variable “x” and clearly distinguish the variable “x” from the unknown constants “a”, “b”, and “c”. In addition to being able to recognize and recognize, it is possible to recognize that the process of solving unknown constants in identities is ultimately accomplished by solving equations for unknowns, which helps to understand identities. Can be deepened.

(Example 5)
FIG. 8 is a diagram showing a solution display operation of the fifth embodiment accompanying the identity mode processing of the electronic calculator 10.

  Similarly to the above, after the “identity mode” is selected in response to the user operation, the identity mode processing program (12a) is started (step S1), and then the mathematical expression display H1 as shown in FIG. 8B is displayed. In the identity processing screen Gk provided with the region and the region of the designated variable display H2, as shown in FIG. 8C, the desired mathematical expression “1 / (x + 1) (x + 2)” (on the character input) When the variable “x” is designated and displayed and the “decision key” 18d is operated and input (step S2), the input mathematical expression is displayed. It is determined that it is a mathematical expression that does not include an equal sign or an inequality sign and includes one or more characters, that is, a mathematical expression that is not completed as an identity but is a side of the identity (step S3 (YES)).

  Then, for the inputted mathematical formula “1 / (x + 1) (x + 2)”, the model formula that matches the form of the mathematical formula among the model formulas stored in the identity database 12b (see FIG. 2). [1] “1 / (ax + b) (cx + d)” (different from the natural display form shown in the figure due to restrictions on character input) is determined. Then, the identity “1 / (ax + b) (cx + d) = (A / (ax + b)) + (B / () stored in association with the model expression [1] determined to be coincident is stored. cx + d)) (differing from the natural display form shown in the figure due to restrictions on character input), as shown in FIG. 8D, the identity equation “1 / (x +1) (x + 2) = (a / (x + 1)) + (b / (x + 2)) ”and a message“ prompt the user to confirm whether the identity is OK or not ” OK? "Is displayed (step S17).

  Here, when the displayed identity “1 / (x + 1) (x + 2) = (a / (x + 1)) + (b / (x + 2))” is not the user desired identity When the “return key” 18e is operated (step S18 (NO)), the identity is returned to the original user-input mathematical expression “1 / (x + 1) (x + 2)” (step S19). Then, the screen returns to the identity processing screen Gk immediately after the mathematical expression input by the user as shown in FIG. 8C (step S2).

  On the other hand, “1 / (x + 1) (x + 2) = (a / (x + 1)) + (b / (x + 2)” is an identity represented as shown in FIG. )) ”Is the user-desired identity, and when the“ decision key ”18d is operated and input (step S18 (YES)), as shown in FIG. 8E, the constants“ a ”,“ A command list display H3 for selecting a method for solving “b” from four solution commands [F1; automatic solution] [F2; numerical substitution] [F3; four arithmetic operations] [F4; coefficient comparison] is performed (step S6). ).

  If it is determined that the constant value automatic solution processing is selected in response to the operation input of the “F1 key” on the identity processing screen Gk on which the solution command list display H3 is performed (step S7 (YES)), the coefficient comparison method For each order of the variable `` x '' in the identity `` 1 / (x + 1) (x + 2) = (a / (x + 1)) + (b / (x + 2)) '' The values of constants “a” and “b” that satisfy the equation for the coefficient of the term are calculated and automatically solved (step S8).

  Then, as shown in FIG. 8 (F), the character and value of the constant automatically calculated by the coefficient comparison method are displayed as a processing result H4 as “a = 1” and “b = −1” ( Step S9).

  Therefore, according to the solution processing using the identity database 12b, the identity database 12b can be inputted to the user arbitrarily, does not include the equality / inequality sign, and includes one or more characters so that it can be a side of the identity. From the typical (model) mathematical pattern when calculating the unknown constant stored in the above, the user entered the mathematical formula automatically compensated for the other side of the equal sign to obtain the desired identity. The input labor can be saved greatly. Then, the above-mentioned [F1; constant automatic solution processing] [F2; numerical substitution solution processing] [F3; four arithmetic operation solution processing] [F4; coefficient comparison solution processing] is selectively and easily performed effectively. You can deepen your understanding of identities.

  The operation method in the identity mode by the electronic calculator 10 described in the above embodiment, that is, the method such as the identity mode processing shown in the flowchart of FIG. 3, is a memory card (ROM) as a program that can be executed by the computer. Card, RAM card, etc.), magnetic disk (floppy disk, hard disk, etc.), optical disk (CD-ROM, DVD, etc.), external storage medium (13) such as semiconductor memory, and the like. Then, the computer (11) of the electronic calculator 10 reads the program stored in the external storage medium (13) into the storage device (12) (17), and the operation is controlled by the read program. The identity solution learning function described in the above embodiment can be realized, and the same processing can be executed by the method described above.

  The program data for realizing the above method can be transmitted on a communication network (public line) N in the form of a program code, and the program is connected by the communication device (16) connected to the communication network N. Data can be taken into the computer (11) of the electronic calculator 10 to realize the above-described identity solution learning function.

  Note that the present invention is not limited to the above-described embodiment, and various modifications can be made without departing from the scope of the invention in the implementation stage. Further, the embodiments include inventions at various stages, and various inventions can be extracted by appropriately combining a plurality of disclosed constituent elements. For example, even if some constituent requirements are deleted from all the constituent requirements shown in the embodiment or some constituent requirements are combined in different forms, the problems described in the column of the problem to be solved by the invention are not solved. When the effects described in the column “Effects of the Invention” can be obtained, a configuration in which these constituent requirements are deleted or combined can be extracted as an invention.

The block diagram which shows the structure of the electronic circuit of the electronic calculator (functional calculator) 10 which concerns on embodiment of the numerical formula calculation apparatus of this invention. The figure which shows the content of the identity database 12b previously memorize | stored in ROM12 of the said electronic calculator 10. FIG. 5 is a flowchart showing identity mode processing by the electronic calculator 10; The figure which shows the solution display operation | movement of 1st Example accompanying the identity mode process of the said electronic calculator. The figure which shows the solution display operation | movement of 2nd Example accompanying the identity mode process of the said electronic calculator. The figure which shows the solution display operation | movement of 3rd Example accompanying the identity mode process of the said electronic calculator. The figure which shows the solution display operation | movement of 4th Example accompanying the identity mode process of the said electronic calculator. The figure which shows the solution display operation | movement of 5th Example accompanying the identity mode process of the said electronic calculator.

Explanation of symbols

10 ... Electronic calculator (Science calculator)
11: Control unit (CPU)
12… ROM
DESCRIPTION OF SYMBOLS 12a ... Various arithmetic processing programs 12b ... Identity database 13 ... External storage medium 14 ... Storage medium reading part 15 ... Web server 16 ... Communication control part 17 ... RAM
17a ... Numerical memory 17b ... Variable memory 17c ... Solicitation command (Fn) memory 17d ... Calculation memory 17e ... Processing result memory 18 ... Key input unit 18a ... "Various function keys"
18b… “Characters / Symbols / Numeric Keys”
18c ... "Cursor key"
18d ... "OK key"
18e… "Back key"
19 ... Display section H1 ... Numerical expression display H2 ... Designated variable display H3 ... Command display H4 ... Processing result display Dq ... Problem data Gm ... Menu screen Gk ... Identity processing screen N ... Communication network C ... Cursor

Claims (8)

Formula display means for displaying a formula including a character input in response to a user operation;
Variable designation means for designating any one type of character included in the mathematical formula displayed by the mathematical formula display means as a variable in response to a user operation;
When the mathematical formula displayed by the mathematical formula display means is an equation including a plurality of types of characters, the equation is an identity for the variable designated by the variable designation means, and the order of the variable included in the equation Constant solving calculation means for finding a numerical value corresponding to the character other than the variable by solving an equation for each coefficient according to
Constant value display means for displaying the numerical value obtained by the constant solution calculating means together with corresponding characters;
When the mathematical formula displayed by the mathematical formula display means is an equation including a plurality of types of characters, numerical value substitution means for substituting an arbitrary numerical value for the variable included in the equation according to a user operation;
Substitution calculation result display means for calculating the equation in which the numerical value is assigned to the variable by the numerical substitution means and displaying the calculation result;
A mathematical expression arithmetic device comprising: Formula display means for displaying a formula including a character input in response to a user operation;
Variable designation means for designating any one type of character included in the mathematical formula displayed by the mathematical formula display means as a variable in response to a user operation;
When the mathematical formula displayed by the mathematical formula display means is an equation including a plurality of types of characters, the equation is an identity for the variable designated by the variable designation means, and the order of the variable included in the equation Constant solving calculation means for finding a numerical value corresponding to the character other than the variable by solving an equation for each coefficient according to
Constant value display means for displaying the numerical value obtained by the constant solution calculating means together with corresponding characters;
When the mathematical expression displayed by the mathematical expression display means is an equation including a plurality of types of characters, an arithmetic expression input means for inputting an arbitrary mathematical expression to be subjected to four arithmetic operations on both sides of the equation according to a user operation;
Four arithmetic operation result display means for performing arithmetic operations on both sides of the equation based on the mathematical formula input by the arithmetic mathematical formula input means, and displaying the computation results;
The number-equations calculating unit characterized in that example Bei a. Formula display means for displaying a formula including a character input in response to a user operation;
Variable designation means for designating any one type of character included in the mathematical formula displayed by the mathematical formula display means as a variable in response to a user operation;
When the mathematical formula displayed by the mathematical formula display means is an equation including a plurality of types of characters, the equation is an identity for the variable designated by the variable designation means, and the order of the variable included in the equation Constant solving calculation means for finding a numerical value corresponding to the character other than the variable by solving an equation for each coefficient according to
Constant value display means for displaying the numerical value obtained by the constant solution calculating means together with corresponding characters;
When the mathematical formula displayed by the mathematical formula display means is an equation including a plurality of types of characters, an equation for each coefficient corresponding to the order of the variable included in the equation is displayed in response to a user operation. An equation display means ;
The number-equations calculating unit characterized in that example Bei a. Formula display means for displaying a formula including a character input in response to a user operation;
Variable designation means for designating any one type of character included in the mathematical formula displayed by the mathematical formula display means as a variable in response to a user operation;
When the mathematical formula displayed by the mathematical formula display means is an equation including a plurality of types of characters, the equation is an identity for the variable designated by the variable designation means, and the order of the variable included in the equation Constant solving calculation means for finding a numerical value corresponding to the character other than the variable by solving an equation for each coefficient according to
Constant value display means for displaying the numerical value obtained by the constant solution calculating means together with corresponding characters;
An identity data storage means for storing a plurality of types of identity data in which a mathematical expression not including an equal sign and an inequality sign is associated with the identity ;
With
The mathematical expression display means, when an equality and an inequality sign are not included in a mathematical expression including characters input in response to a user operation, and an identity corresponding to the mathematical expression is stored in the identity data storage means , Read and display the identity
The number-equations calculating unit you wherein a. Computer
Formula display control means for causing a display unit to display a formula including characters inputted in response to a user operation,
Variable designation means for designating any one type of character included in the mathematical expression displayed by the mathematical expression display control means as a variable in accordance with a user operation;
When the mathematical expression displayed by the mathematical expression display control means is an equation including a plurality of types of characters, the equation is an identity relating to the variable designated by the variable designation means, and the variable included in the equation Constant solution calculation means for finding a numerical value corresponding to the character other than the variable by solving an equation for each coefficient according to the order,
Constant value display control means for displaying the numerical value obtained by the constant solution calculating means together with the corresponding characters on the display unit;
A numerical value substitution means for assigning an arbitrary numerical value to the variable included in the equation according to a user operation when the mathematical expression displayed by the mathematical expression display means is an equation including a plurality of types of characters;
Substitution calculation result display means for calculating the equation in which the numerical value is assigned to the variable by the numerical substitution means and displaying the calculation result;
A computer-readable mathematical calculation processing program that functions as a computer program. Computer
Formula display control means for causing a display unit to display a formula including characters inputted in response to a user operation,
Variable designation means for designating any one type of character included in the mathematical expression displayed by the mathematical expression display control means as a variable in accordance with a user operation;
When the mathematical expression displayed by the mathematical expression display control means is an equation including a plurality of types of characters, the equation is an identity relating to the variable designated by the variable designation means, and the variable included in the equation Constant solution calculation means for finding a numerical value corresponding to the character other than the variable by solving an equation for each coefficient according to the order,
Constant value display control means for displaying the numerical value obtained by the constant solution calculating means together with the corresponding characters on the display unit;
When the mathematical formula displayed by the mathematical formula display means is an equation including a plurality of types of characters, an arithmetic formula input means for inputting an arbitrary mathematical formula to be subjected to four arithmetic operations on both sides of the formula in accordance with a user operation;
Four arithmetic operation result display means for performing four arithmetic operations on both sides of the equation based on the mathematical formula input by the arithmetic mathematical formula input means, and displaying the arithmetic results;
A computer-readable mathematical calculation processing program that functions as a computer program. Computer
Formula display control means for causing a display unit to display a formula including characters inputted in response to a user operation,
Variable designation means for designating any one type of character included in the mathematical expression displayed by the mathematical expression display control means as a variable in accordance with a user operation;
When the mathematical expression displayed by the mathematical expression display control means is an equation including a plurality of types of characters, the equation is an identity relating to the variable designated by the variable designation means, and the variable included in the equation Constant solution calculation means for finding a numerical value corresponding to the character other than the variable by solving an equation for each coefficient according to the order,
Constant value display control means for displaying the numerical value obtained by the constant solution calculating means together with the corresponding characters on the display unit;
When the mathematical formula displayed by the mathematical formula display means is an equation including a plurality of types of characters, an equation for each coefficient corresponding to the order of the variable included in the equation is displayed in response to a user operation. Equation display means,
A computer-readable mathematical calculation processing program that functions as a computer program. Computer
Formula display control means for causing a display unit to display a formula including characters inputted in response to a user operation,
Variable designation means for designating any one type of character included in the mathematical expression displayed by the mathematical expression display control means as a variable in accordance with a user operation;
When the mathematical expression displayed by the mathematical expression display control means is an equation including a plurality of types of characters, the equation is an identity relating to the variable designated by the variable designation means, and the variable included in the equation Constant solution calculation means for finding a numerical value corresponding to the character other than the variable by solving an equation for each coefficient according to the order,
Constant value display control means for displaying the numerical value obtained by the constant solution calculating means together with the corresponding characters on the display unit;
An identity data storage means for storing a plurality of types of identity data in which a mathematical expression not including an equal sign and an inequality sign is associated with the identity;
Function as
The mathematical expression display means, when an equality and an inequality sign are not included in a mathematical expression including characters input in response to a user operation, and an identity corresponding to the mathematical expression is stored in the identity data storage means , Read and display the identity
A computer-readable mathematical formula processing program.

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