JP2019185681A - Data processing method, data processing system and computer program - Google Patents

Abstract

To display a result of calculation of inverse function in an easy-to-understand manner even in the case where an answer cannot be obtained.SOLUTION: A processor 11 is provided which causes a display output unit 16 to display a numerical table indicating a relation between a function and a variable corresponding to an inputted function expression, causes an input unit 14 to accept input of an arbitrary numeric number to a function part in the displayed numerical table, executes calculation of inverse function on the basis of the accepted numeric number inputted to a function, and if a variable being a calculation result thereof can be obtained, causes the obtained variable to be displayed in a variable part in the numerical table while if the variable cannot be obtained, displays an error in the variable part in the numerical table.SELECTED DRAWING: Figure 1

Description

  The present invention relates to a data processing method, a data processing system, and a computer program.

  Graph drawing applications that can be used on a web browser are known. For example, according to Non-Patent Document 1 related to an application that runs on a web browser, an operation is performed based on a mathematical expression input by a user into an expression list, and a graph based on the result of the operation is displayed.

Desmos, desmos User Guide, Translated by Yuri Horikawa [online], [Search April 17, 2018], Internet <URL: http://desmos.s3.amazonaws.com/Desmos_User_Guide_EN.pdf>

  In the graph drawing application as described above, for example, from the state where the function expression represented by “y = f (x)” and the corresponding graph are displayed, the independent variable x of the function expression and the numerical values of the dependent variable y are further displayed. There is known a technique for displaying a numerical table in which the relations are expressed in a tabular form.

  In that case, the numerical value of the dependent variable y of the independent variable x is displayed in the adjacent dependent variable y field by overwriting any numerical value in any of the independent variable x fields in the numerical table. Will be.

  However, in the numerical table, it is not assumed that an arbitrary numerical value is overwritten in the dependent variable y column in the numerical table and the corresponding numerical value is displayed in the adjacent independent variable x column. In addition, there are many cases where the operation of the inverse function cannot uniquely obtain the independent variable x.

  The present invention has been made in view of the above circumstances, and the purpose of the present invention is to execute an inverse function calculation and display the calculation result in an easy-to-understand manner, even when an answer cannot be obtained. The present invention provides a data processing method, a data processing system, and a computer program.

  One aspect of the present invention is a data processing method executed by a control unit of a data processing system, and a numerical table indicating a relationship between an independent variable and a dependent variable associated by a function expression is displayed on a display screen of a display unit. An inverse function of the functional formula obtained by executing and executing a solution processing based on the functional formula, and a numerical value input to the display area of the dependent variable in the numerical table displayed on the display screen of the display unit When only one numerical solution is obtained based on the above, in response to receiving the numerical value input operation, the one numerical solution is notified, and when the obtained numerical solution is not only one, Reporting an error in response to accepting an operation on the display area of the dependent variable in the numerical table.

The figure which shows an example of a structure of the whole system which concerns on one Embodiment of this invention. The sequence diagram which shows the flow of the process from input of a function formula to execution of an inverse function performed between the communication apparatus which concerns on the embodiment, and a server. The flowchart explaining the inverse function calculation process which the server which concerns on the same embodiment performs. The figure which illustrates the menu list display displayed on the display output part concerning the embodiment. The figure which illustrates the formula sticky note in the middle of the function formula displayed on the display output part concerning the embodiment in the middle of input. The figure which illustrates the mathematical formula tag and the graph tag displayed on the display output unit according to the embodiment. The figure which illustrates the number table sticky note, graph sticky note, and number table sticky note displayed on the display output unit according to the embodiment. The figure which illustrates the state which is inputting the numerical value of the dependent variable which concerns on the embodiment. The figure which illustrates the state which is displaying the independent variable corresponding to the numerical value of the dependent variable which concerns on the same embodiment in a number table sticky note. The figure which illustrates the other state which is inputting the numerical value of the dependent variable which concerns on the embodiment. The figure which illustrates the state which is performing error notation without the independent variable corresponding to the numerical value of the dependent variable which concerns on the same embodiment being obtained. The flowchart which shows the other processing content of the inverse function calculation which the server which concerns on the same embodiment performs. The sequence diagram which shows the flow of a process in the modification 2 which performs an inverse function from the input of a function type | formula, and displays an error performed between the communication apparatus and server which concern on the embodiment.

  An embodiment of the present invention will be described in detail with reference to the drawings.

  FIG. 1 is a diagram illustrating an example of a configuration of an entire system including a client device and a server device according to an embodiment of the present invention. The system 1 includes a communication device 10 and a server 20. The communication device 10 is communicably connected to the server 20 via a communication network N such as the Internet. The communication device 10 may be, for example, a tablet terminal, a smartphone, a personal computer (PC), or the like.

  In the system 1, data for graph display / number table creation input to the communication device 10 is transmitted from the communication device 10 to the server 20. The server 20 executes a calculation for graph display / numerical table creation based on the data, and transmits the calculation result to the communication device 10. The communication device 10 executes graph drawing / number table creation based on the result of the calculation.

  The communication device 10 includes a processor 11, a main memory 12, a storage 13, an input unit 14, a communication unit 15, and a display output unit 16. Each of these is connected to each other via a system bus 17.

  The processor 11 may be an integrated circuit such as a CPU (Central Processing Unit). The processor 11 reads out various programs such as a communication device control program stored in advance in the storage 13 and a program that operates on a web browser, expands and stores the programs in the main memory 12, and inputs from the input unit 14. By executing various programs in accordance with signals and signals received by the communication unit 15, the operation of each unit is controlled. Various programs may be downloaded from the web server (not shown) on the communication network N to the storage 13 via the communication unit 15.

  The input unit 14 assumes that the external input device such as a keyboard or a mouse, or the display output unit 16 of the communication device 10 has a touch panel function, and displays the operation coordinates to the key input unit displayed on the display output unit 16. It may be input. By the operation of the processor 11, an input signal is input from the input interface (I / F) to the processor 11 through the system bus 17.

  The display output unit 16 includes an external display device such as a liquid crystal display or a display unit such as a liquid crystal display of the communication device 10. An output signal is transmitted to the display output unit 16 from the processor 11 via the system bus 17 and the output interface (I / F).

  The server 20 includes a processor 21, a main memory 22, a large capacity storage 23, and a communication unit 24. Each of these is connected to each other via a system bus 25. The server 20 may also be connected to a recognition device or output device (not shown) via its input (I / F) or output (I / F).

  The processor 21 may be an integrated circuit such as a CPU. The processor 21 reads out various programs such as a server control program stored in the mass storage 23 in advance or downloaded and stores them in the main memory 22, and then extracts and decodes the program instructions. The operation of each unit is controlled according to the contents of the command. Further, the processor 21 executes arithmetic processing based on input data from the communication device 10 in accordance with a calculation processing program for graph drawing / number table creation.

  In the present embodiment, the user designates the address of the server 20 in the web browser that operates on the communication device 10, thereby transmitting a request to the server 20. The web browser of the communication device 10 constructs a web application screen for graph display / number table creation based on the response received from the server 20. In addition, the web browser of the communication device 10 issues a request to the server 20 in response to the input of data such as a mathematical expression, and receives the result of the calculation executed by the server 20 according to the calculation processing program as a response from the server 20. To do.

  In other words, in response to a calculation request from the communication device 10, the server 20 transmits the result of the calculation executed by the processor 21 according to the calculation program to the communication device 10 as a response. Further, the communication apparatus 10 uses the received calculation result to generate a graph / numerical table by the processor 11 in accordance with a program operating on the web browser.

  As described above, a function as a web application for drawing a graph and creating a number table is realized by the program operating on the web browser of the communication apparatus 10 and the calculation processing program of the server 20.

Hereinafter, the operation of this embodiment will be described.
In the present embodiment, the client device, that is, the communication device 10 executes only input processing of data such as mathematical formulas and graph drawing / number table creation processing, and does not execute calculation processing for graph drawing / number table creation. The arithmetic processing is executed by a server device connected to the client device via the communication network N, that is, the server 20. Accordingly, it is possible to provide a calculation result from the server apparatus to the client apparatus and to draw a graph / create a number table on the client apparatus without disclosing a highly accurate or complicated calculation algorithm. In addition, this makes it possible to suppress the processing load on the client device by executing a calculation process with a large processing load by the server device.

  Hereinafter, in the present embodiment, in order to unify the description of the operation system, the communication apparatus 10 is configured by, for example, a mobile type PC, and the input unit 14 includes a keyboard and a mouse as a pointing device. I will explain to you.

  FIG. 2 illustrates a graph drawing, a number table creation, and a number table created from input of a function expression executed between the communication device 10 as a client device and the server 20 as a server device based on a web application. It is a sequence diagram which shows the flow of a process until it performs an inverse function by.

  In the communication device 10, after the graph drawing / number table creation application is launched, the menu list display MD is displayed at an arbitrary position on the screen of the display output unit 16 by, for example, a double tap operation or a right click operation of the mouse. Is displayed (step C101), a function formula icon is selected and designated (step C102).

(If only one value is available)
4 to 9 show a series of display states on the display screen of the display output unit 16 when only one answer is obtained by the inverse function shown in FIG.
FIG. 4 illustrates a menu list display MD displayed at an arbitrary position of the display output unit 16 of the communication device 10, for example, a position close to the upper left side. Here, it is assumed that the menu list display MD includes a calculation sticky note icon IC1, a mathematical formula sticky note icon IC2, a graph sticky note icon IC3, a number table sticky note icon IC4, a geometric sticky note icon IC5, and a memo sticky note icon IC6.

  The calculation sticky note icon IC1 is an operation icon for displaying a display area called “sticky note” in the present embodiment as indicated by the symbol “√α”. By selecting this calculation sticky note icon IC1, four arithmetic operations are performed. Calculation sticky notes for executing calculations such as and various functions are displayed.

  The mathematical formula tag icon IC2 is an operation icon for inputting a function formula and displaying a formula sticky note to be described later, as indicated by the symbol “f (x)”.

  The graph sticky note icon IC3 is an operation icon for displaying a graph sticky note corresponding to the input function formula, plot coordinate value, etc., as indicated by a simple quadratic curve on the x and y coordinate axes.

The number table tag icon IC4 is an operation icon for displaying a number table tag indicating the correspondence between the value of the independent variable and the value of the dependent variable in the function expression. When the functional expression is “y = x ³ ”, the independent variable is x and the dependent variable is y.

  The geometric tag icon IC5 is an operation icon for causing the display output unit 16 to display a geometric tag for displaying an arbitrary geometric figure.

  The memo sticky note icon IC6 is an operation icon for displaying a memo sticky note that accepts any handwritten input or character input that is not particularly related to other sticky notes.

  When the mathematical formula tag icon IC2 is operated from the menu list display MD, the menu list display MD is hidden, and instead, the mathematical formula tag MP10 is displayed on the display output unit 16 (step C102). In the display area, nothing is input except that the cursor C is displayed at the head position.

From this state, when an arbitrary function expression, for example, “y = x ³ ” is input through the input unit 14 of the communication device 10, these inputs are received by the processor 11 (step C103).

FIG. 5 illustrates the state of the mathematical formula tag MP10 immediately after the function formula “y = x ³ ” is input. The cursor C is displayed at a subsequent position in the formula of the formula tag MP10 to prompt further input.

Thereafter, as an operation to confirm the function expression “y = x ³ ” input to the mathematical formula tag MP10, for example, by pressing the “Enter” key on the keyboard of the input unit 14, “y = x” input to the mathematical formula tag MP10. ³ ”is accepted by the processor 11 as a confirmed function expression, and the function expression input from the communication device 10 to the server 20 and data specifying the graph display area request creation of graph data. Sent with instructions.

  The display area of the graph can be arbitrarily input and set by the user, but can be determined only by inputting a function expression without specifying the display area. In this way, especially when the user does not designate a graph display area, a value prepared in advance as a default value in the program on the communication device 10 side, for example, data of “−7 ≦ x, y ≦ 7” It is automatically associated with the data of the function formula and transmitted to the server 20 together.

  When the server 20 receives the function formula and the graph area data from the communication device 10 together with the request information, the coordinate data string of the plot point positions within the graph area range according to the corresponding function formula is displayed as graph data for graph drawing. (Step S101).

  In this case, the server 20 automatically sets the x-coordinate sampling interval, the y-coordinate calculation accuracy, and the like of the plot point position to be created according to the set graph area and the display resolution in the display output unit 16.

  The server 20 returns the graph data formed of the coordinate data string of the created plot point positions to the communication device 10 as a response to the request from the communication device 10 (step S102).

  In the communication device 10, the processor 11 newly creates a graph tag MP 20 based on the graph data returned from the server 20 and associates it with the mathematical formula tag MP 10 on the display screen of the display output unit 16. The graph tag MP20 is displayed (step C104).

  FIG. 6 is a diagram exemplifying a state in which the function formula is determined from the state of FIG. 5 and the corresponding graph tag MP20 is displayed. A graph sticky note MP20 is newly displayed corresponding to the mathematical formula sticky note MP10, and a state where the graph sticky note MP20 is connected by a thick line link LK using a spline curve, for example, is displayed. .

  The graph sticky note MP20 plots points based on the coordinate data string of a plurality of plot point positions on the xy coordinate plane based on the graph data received by the processor 11 from the server 20 side, and plots the points between the plotted points as necessary. In this case, a graph with a three-dimensional curve can be obtained by linear interpolation.

  In the communication device 10, the graph sticky note icon IC 3 in the menu list display MD of FIG. 4 is attached to the mathematical formula sticky note MP 10 by further performing a right click operation of the mouse with the pointer positioned on the mathematical formula sticky note MP 10, and An icon similar to the number table sticky note icon IC4 is displayed.

  Here, when an icon corresponding to the number table sticky note icon IC4 is designated and the mouse is clicked, the input function formula and an instruction to request creation of number table data are transmitted to the server 20 (step C105). ).

  In the server 20, for example, the value of the dependent variable y in the case of the independent variable x = 1, 2, 3, 4, 5 is calculated as an initial value, respectively, and numerical table data in which the independent variable and the dependent variable are associated is created. (Step S103), the created number table data is returned to the communication device 10 (Step S105).

  In the communication apparatus 10 that has received the number table data from the server 20, the processor 11 newly creates a number table tag MP30 based on the obtained number table data, and the above formula tag MP10 is displayed on the display screen of the display output unit 16. Then, the created number table tag MP30 is displayed so as to be associated with the graph tag MP20 (step C106).

FIG. 7 is a diagram illustrating a state in which the number table sticky note MP30 is further displayed from the state of FIG. A numerical table sticky note MP30 is newly displayed corresponding to the mathematical formula sticky note MP10 and the graph sticky note MP20, and it is assumed that these are associated with each other. For example, a spline curve is used from the mathematical formula sticky note MP10 to the mathematical formula sticky note MP30. The connected state is indicated by the thick line link LK. On the number table sticky note MP30, independent variables are displayed in the left column, and dependent variables are displayed in the right column. Therefore, when the input function expression is “y = x ³ ”, x that is an independent variable is displayed in the first column, and y that is a dependent variable is displayed in the second column.

  In the figure, the pointer PT is positioned in the vicinity of the input column of the second column (column on the dependent variable y side) of the fifth row of the number table tag MP30 in accordance with the operation of the mouse of the input unit 14. Is illustrated.

  From this display state, when the right-click operation of the mouse of the input unit 14 is performed to input the value of the dependent variable y, the value “125” in the second column of the fifth row of the number table sticky note MP30 is temporarily selected.

  FIG. 8 exemplifies a state where a new numerical value “3.375” is being input to the input column in the second column of the second row of the number table sticky note MP30 using the keyboard of the input unit 14. Immediately after the numerical value “3.375” is input, the operation for confirmation is not yet performed, and a cursor C for prompting further numerical input is displayed in accordance with the next digit position.

  The processor 11 confirms the input by operating the “Enter” key of the keyboard to confirm the input numerical value from this display state. At this time, the processor 11 determines which of the independent variable side and the dependent variable side the column in which the numerical value input is confirmed. When the functional expression is y = f (x), that is, the left side is “y”, the right side is a mathematical expression including the variable x and not including the variable y, x is an independent variable and y is a dependent variable. Make the above judgment. When the functional expression is x = g (y), that is, when the left side is “x”, the right side includes the variable y and does not include the variable x, y is an independent variable and x is a dependent variable. Make the above judgment. In this embodiment, the input numerical value “3.375” and the determination result that the input of the numerical value is confirmed in the column on the dependent variable y side are transmitted to the server 20 (step C107).

In the server 20 that has received the input function expression, the input numerical value, and the determination result that the column in which the input of the numerical value is determined is on the dependent variable side, the processor 21 receives the received function expression (y = x ³ ) is executed with an independent variable x that is not on the side on which the input of the numerical value is determined, and a solution processing for outputting a mathematical expression is executed (step S106).

  Further, when the processor 21 can calculate only one numerical calculation result obtained by substituting the received numerical value for the mathematical expression that is the result of solving with the independent variable x, the processor 21 calculates the value as the value corresponding to the received numerical value. The result of the numerical calculation is returned to the communication device 10. In other cases, information for error notation is returned to the communication device 10 (step S107). By performing the above-mentioned solution processing on the server device instead of the client device, it is possible to conceal a complicated calculation algorithm without revealing it.

  FIG. 3 is a flowchart for explaining the processing contents of the inverse function calculation executed on the server 20 side when the numerical value input to the numerical table is confirmed.

  Initially, the processor 21 first determines whether the column for which the input of numerical values is determined is on the independent variable side or the dependent variable side (step S200). If the column in which the input of numerical values is confirmed is not on the dependent variable side, that is, if it is on the independent variable side (No in step S200), the received function expression is not on the side on which the numerical input is confirmed. Since it is not necessary to solve with the dependent variable, the processor 21 directly obtains the result of numerical calculation by substituting the received numerical value into the received function expression, and returns the calculated result to the communication device 10 (step S208).

  If it is determined in step S200 that the column for which the numerical value input has been confirmed is on the dependent variable side (Yes in step S200), the received function expression is solved with the independent variable that is not on the numerical value input side. Since it is necessary, next, the processor 21 determines whether or not the type of the received function expression is y = f (x) (step S201).

  When it is determined that the type of the received function expression is y = f (x) (Yes in step S201), the processor 21 determines the input of the numerical value of the received function expression (y = f (x)). The solution processing for outputting a mathematical expression that is a result of solving with the independent variable (x) that is not the processed side is executed (step S202).

  Further, when it is determined in step S201 that the type of the received function expression is not y = f (x) (No in step S201), the processor 21 determines that the type of the received function expression is x = g (y ) Is determined (step S203).

  When it is determined that the type of the received function expression is x = g (y) (Yes in step S203), the processor 21 determines the input of the numerical value of the received function expression (x = g (y)). A solution finding process is performed to output a mathematical expression that is the result of solving with the independent variable (y) that is not the other side (step S204).

  After executing the processing of step S202 and step S204, the processor 21 determines whether or not a mathematical expression obtained by solving the function expression with variables is obtained as a solution (step S205).

  If it is determined that a mathematical expression as a solution has been obtained (Yes in step S205), the processor 21 determines whether the mathematical expression obtained as a solution is a periodic function (step S206).

  For example, when the solution processing is executed for the functional expression y = sin (x), x = arcsin (y) is obtained as a solution. Since x = arcsin (y) is a periodic function, for example, a plurality of values of y where x = 1 exist periodically. Thus, when the mathematical formula obtained as a solution is a periodic function, it is clear that there is not only one numerical calculation result of the independent variable corresponding to the received numerical value (dependent variable).

  If it is determined that the mathematical expression obtained as a solution is not a periodic function (Yes in step S206), the processor 21 further determines whether or not there is only one mathematical expression for the solution (step S207).

  If it is determined that there is only one solution formula (Yes in step S207), the processor 21 returns the calculated numerical value to the communication device 10 (step S208), and the processing of FIG. Exit.

  Further, when it is determined in step S203 that the type of the received function expression is not x = g (y) (No in step S203), when it is determined in step S205 that a solution expression has not been obtained ( In step S205, if it is determined in step S206 that the mathematical formula obtained as a solution is a periodic function (No in step S206), and in step S207, it is determined that there are a plurality of mathematical formulas instead of only one. If so (No in step S207), the processor 21 returns symbol data for executing error notation to the communication device 10 (step S209), and the processing in FIG.

  In the communication device 10 that has received the numerical value or the error notation symbol data resulting from the inverse function calculation process from the server 20, as shown in FIG. 9, in the number table tag MP 30 displayed on the display output unit 16, The numerical value “1.5” received from the server 20 is displayed at the position (the first column of the second row) of the independent variable x column in the same row corresponding to the dependent variable y column that has received the numerical value input (step C108). ).

(When multiple numbers are available)
Next, referring to FIG. 10 and FIG. 11, an error on the display screen of the display output unit 16 when only one solution formula cannot be obtained by the inverse function calculation process, that is, when a plurality of solution formulas are obtained. A series of display states concerning notation will also be described.

As shown in FIG. 10, in the formula sticky note MP10, the function formula “y = x ² ” is input, and the state of the corresponding number book sticky note MP30 is further dependent on the second column of the fifth row of the number sticky note MP30. The state where the numerical value “1” is newly input as the value of the variable y is illustrated.

When the input numerical value is confirmed from this display state, the processor 11 sends the input function expression “x = y ² ”, the input numerical value “1”, and the numerical value in the column on the dependent variable x side to the server 20. The determination result that the input is confirmed is transmitted (step C107).

In the server 20 that has received the input function formula, the input numerical value, and the determination result that the column for which the input of the numerical value has been determined is on the dependent variable side, according to the processing described with reference to FIG. Then, the processor 21 executes a solution processing for outputting a mathematical expression that is a result of solving the received functional expression (x = y ² ) with the independent variable y that is not on the side on which the numerical input is confirmed (step S106).

  In this case, the processor 21 determines in step S201 in FIG. 3 that the type of the received function expression is not y = f (x) (No in step S201), and the received function expression in step S203. It is determined that the type is x = g (y) (Yes in step S203), and the received function formula (x = g (y)) is changed to the independent variable (y) that is not the side on which the numerical value is input. The solution processing for outputting the mathematical expression that is the result solved in step S204 is executed (step S204).

  In the solution finding process in step S204, the processor 21 obtains the mathematical expression “y = √ (x), −√ (x)” as a solution (Yes in step S205), and the mathematical expression obtained as the solution is converted into a functional expression. Since the independent variable and the variable unrelated to the dependent variable are not included (Yes in step S206), the processor 21 advances the processing to step S207.

  In the solution solving process in step S204, the processor 21 obtains two equations “y = √ (x), −√ (x)” as solutions, and therefore in step S207, the processor 21 does not have one solution equation. It is determined that there is no error (No in step S207), and symbol data for executing error notation is returned to the communication device 10 (step S209). In step S209, the two independent variables y, which are the results of numerical calculation obtained by substituting the value “1” of the dependent variable x into the above two mathematical formulas “y = √ (x), −√ (x)”. The values “−1, 1” may be returned to the communication device 10. Thus, the process of FIG. 3 is completed.

  In the communication apparatus 10 that has received the reply of the symbol data in error notation from the server 20, in the same row corresponding to the dependent variable x column that has received the numerical input in the number table sticky note MP30 displayed on the display output unit 16. The error notation symbol received from the server 20 is displayed at the position of the independent variable y column (the first column of the fifth row).

  FIG. 11 is a display example of symbols for error notation. In FIG. 11, a triangular error symbol ES with an exclamation mark placed in the center is displayed in the input field of the first column of the fifth row in the number table sticky note MP30. Further, the error reason symbol “ERROR” EPU, which has a larger display area than the error symbol ES, is displayed together to express the error more easily. It is sufficient that at least one of the error symbol ES and the error reason symbol EPU is displayed.

  In step C108, the communication device 10 determines that the value “1” of the dependent variable x determined to be input in step C107 and the value “1,” of the independent variable y received in step S209, as shown in FIG. Based on “−1”, two points corresponding to the two coordinates (1, 1) and (1, −1) may be plotted in the graph area in the graph tag MP20 being displayed on the display output unit 16. Further, these two points are blinked in the graph sticky note MP20, or in the number table sticky note MP30, the input fields corresponding to the two points (the first column and the second column in the fifth row) are set to two points in the graph area. May be displayed in the same color, or may be blinked or reversed. Thereby, for example, when a plurality of points are blinking in the graph sticky note MP20 during the error display, the error is displayed because the numerical value obtained as a solution is not only one. It can be reported visually and clearly.

(Modification 1)
Even when error notation is performed as described above, as shown in FIG. 3, the type of the received function expression is not y = f (x), but the type of the received function expression is x = g (y). If it is determined that there is no solution (No in step S203), if it is determined that the solution formula has not been obtained (No in step S205), if it is determined that the equation obtained as a solution is a periodic function (No in step S206) ), And when there are not only one mathematical formula for the obtained solution but a plurality of formulas (No in step S207), the same error notation is not performed, but the error notation is determined according to the contents of those errors. It is also possible to display them separately.

  FIG. 12 is a flowchart showing the processing contents in the case of executing the inverse function calculation processing in accordance with the determination of the numerical value input into the numerical table, which is executed on the server 20 side instead of the processing of FIG.

  Initially, the processor 21 first determines whether the column for which the input of numerical values is determined is on the independent variable side or the dependent variable side (step S300). If the column in which the numerical value is confirmed is not on the dependent variable side, that is, if it is on the independent variable side (No in step S300), the received function expression is not on the side on which the numerical value input is confirmed. Since there is no need to solve with the dependent variable, the processor 21 directly obtains the result of numerical calculation by substituting the received numerical value into the received function expression, and returns the calculated result to the communication device 10 (step S308).

  In step S300, if it is determined that the column for which the numerical value input is confirmed is on the dependent variable side (Yes in step S300), the received function expression is solved with the independent variable that is not on the numerical value input side. Since it is necessary, the processor 21 next determines whether or not the type of the received function expression is y = f (x) (step S301).

  When it is determined that the type of the received function expression is y = f (x) (Yes in step S301), the processor 21 determines the input of the numerical value for the received function expression (y = f (x)). The solution calculation process is performed to output a mathematical expression that is the result of solving with the independent variable (x) that is not the processed side (step S302).

  Further, when it is determined in step S301 that the type of the received function expression is not y = f (x) (No in step S301), the processor 21 determines that the type of the received function expression is x = g (y ) Is determined (step S303).

  When it is determined that the type of the received function expression is x = g (y) (Yes in step S303), the processor 21 confirms the input of numerical values for the received function expression (x = g (y)). A solution processing for outputting a mathematical expression which is a result of solving with the independent variable (y) which is not the other side is executed (step S304).

  After executing the processes in steps S302 and S304, the processor 21 determines whether or not a mathematical expression obtained by solving the function expression with variables is obtained as a solution (step S305).

  If it is determined that a mathematical expression as a solution has been obtained (Yes in step S305), the processor 21 determines whether the mathematical expression obtained as a solution is not a periodic function (step S306).

  If it is determined that the mathematical formula obtained as a solution is not a periodic function (Yes in step S306), the processor 21 further determines whether there is only one mathematical formula for the solution (step S307).

If it is determined that there is only one mathematical formula for the solution (Yes in step S307), the processor 21 substitutes the numerical value received in step S106 into the mathematical formula for the obtained solution, and an independent variable that is the result of the numerical calculation. Is returned to the communication device 10 (step S308).
This completes the processing of FIG.

  If it is determined in step S303 that the type of the received function expression is not y = f (x) and the type of the received function expression is not x = g (y) (No in step S303), the processor 21 cannot perform the numerical calculation as performed in step S308, and returns symbol data of error notation indicating that the received function is not supported to the communication device 10 (step S309).

  In the communication device 10 that has received the symbol data in error notation as a result of the inverse function calculation processing from the server 20, the column on the dependent variable side that has received a numerical value in the number table tag MP30 displayed on the display output unit 16 The symbol of the error notation received from the server 20 is displayed in the input column of the column on the independent variable side in the same row as (Step C108).

  In step S309, the server 20 transmits only data indicating that the received function is not supported, and in step C108, the communication apparatus 10 previously stores a symbol of error notation corresponding to the received data in the storage 13. It may be selected from a plurality of stored error notation symbols and displayed.

  Furthermore, when it is determined in step S305 that the mathematical expression obtained by solving the function expression with the variables has not been obtained as a solution (No in step S305), the processor 21 displays the error notation symbol “No Solution”. Data is returned to the communication device 10 (step S310).

  In the communication device 10 that has received the symbol data in error notation as a result of the inverse function calculation processing from the server 20, the column on the dependent variable side that has received a numerical value in the number table tag MP30 displayed on the display output unit 16 The symbol of the error notation received from the server 20 is displayed in the input column of the column on the independent variable side in the same row as (Step C108).

  If it is determined in step S306 that the mathematical formula obtained as a solution is a periodic function (No in step S306), the processor 21 determines based on the periodic function obtained as a solution and the range of the graph area at that time. Then, a process for obtaining all numerical solutions (coordinate values) existing within the range of the graph area is executed, and numerical values indicating all the obtained numerical solutions are returned to the communication device 10 (step S311).

  Each time the range of the graph area is changed based on a user operation, the communication device 10 transmits data indicating the changed range of the graph area to the server 20, and the server 20 changes the range of the graph area. The data indicating the range of the graph area stored in the large-capacity storage 23 may be updated each time the data indicating is received.

  In the communication device 10 that has received the numerical data as a result of the inverse function calculation processing from the server 20, the same row as the column on the dependent variable side that has received the numerical input in the number table tag MP30 displayed on the display output unit 16 The numerical value received from the server 20 is displayed in the input column of the column on the independent variable side (step C108). When it cannot be displayed in the input field of the number table sticky note MP30, only a part thereof may be displayed, and all numerical values may be displayed according to the user operation for selecting the corresponding input field.

  In step C108, as shown in FIG. 11, the communication device 10 displays the display output unit 16 based on the value of the dependent variable whose input is confirmed in step C107 and the value of the independent variable received in step S209. One or more points corresponding to one or more coordinates may be plotted in the graph area in the graph sticky note MP20 being displayed. Also, as described above, one or more points in the graph sticky note MP20 are blinked, and in the number table sticky note MP30, the input field corresponding to one or more points is the same as one or more points in the graph area. It may be displayed in color, blinking, or reversed.

  Furthermore, in step S307, when it is determined that there are not only one solution formula but a plurality of formulas (No in step S307), the processor 21 calculates a plurality of formulas based on the plurality of formulas obtained as solutions. A process for obtaining a numerical solution (coordinate value) corresponding to each is executed, and numerical values indicating the obtained numerical solutions are returned to the communication device 10 (step S312).

  In the communication device 10 that has received a plurality of numerical data as a result of the inverse function calculation processing from the server 20, the column on the dependent variable side that has received the numerical input in the number table sticky note MP30 displayed on the display output unit 16 and A plurality of numerical values received from the server 20 are displayed in the input column of the column on the independent variable side of the same row (step C108).

  When it cannot be displayed in the input column of the number table sticky note MP30, only a part of it is displayed, and other numerical values are also displayed together with a predetermined symbol, etc. While there is a user operation to select an input field, all numerical values may be temporarily displayed using a wider range than the input field.

  In this way, when a plurality of answers are obtained, or by performing error notation that is distinguished according to the content of the error, the understanding of the inverse function operation can be further deepened.

(Modification 2)
When the server 20 receives the request from the communication device 10 and creates the numerical table data, the server 20 solves the function expression with an arbitrary variable based on the function expression including the specified independent function and dependent variable. And execute the solution processing to obtain the inverse function, and determine whether or not an error will occur by the solution processing, and if it is determined that an error will be generated by this error determination, the error type is further calculated in advance. Also good.

Hereinafter, Modification 2 will be described.
FIG. 13 shows, instead of FIG. 2, graph drawing and numerical table creation from function expression input executed between the communication device 10 as the client device and the server 20 as the server device based on the web application. FIG. 11 is a sequence diagram showing a flow of processing up to execution of an inverse function on a created numerical table.

  In the communication device 10, after the graph drawing / number table creation application is launched, the menu list display MD is displayed at an arbitrary position on the screen of the display output unit 16 by, for example, a double tap operation or a right click operation of the mouse. Is displayed (step C501), the function formula icon is selected and designated (step C502).

  In the communication apparatus 10, when the mathematical formula tag icon is operated, the menu list display MD is hidden and the mathematical formula tag MP 10 is displayed on the display output unit 16 instead.

  From this state, when arbitrary function expressions are input through the input unit 14 of the communication apparatus 10, these inputs are received by the processor 11. When an operation for confirming the input function expression is performed, the confirmed function expression is received by the processor 11, and the input function expression and a graph display area are designated from the communication apparatus 10 to the server 20. Data is transmitted along with an instruction to request creation of graph data (step C503).

  When the server 20 receives the function formula and the graph area data from the communication device 10 together with the request information, the coordinate data string of the plot point positions within the graph area range according to the corresponding function formula is displayed as graph data for graph drawing. (Step S501).

  The server 20 returns the graph data including the created coordinate data sequence of the plot point positions to the communication device 10 as a response to the request from the communication device 10 (step S502).

  In the communication device 10, the processor 11 newly creates a graph tag MP 20 based on the graph data returned from the server 20 and associates it with the mathematical formula tag MP 10 on the display screen of the display output unit 16. The graph tag MP20 is displayed (step C504).

  In the communication apparatus 10, the graph sticky note icon IC 3 and the number table sticky note icon in the menu list display MD are attached to the mathematical formula sticky note MP 10 by further performing a right click operation of the mouse with the pointer positioned on the mathematical formula sticky note MP 10. The same icon as IC4 is displayed.

  Here, when an icon corresponding to the number table sticky note icon IC4 is designated and the mouse is clicked, the input function formula and an instruction to request creation of number table data are transmitted to the server 20 (step C505). ).

  In the server 20, for example, the value of the dependent variable y in the case of the independent variable x = 1, 2, 3, 4, 5 is calculated as an initial value, respectively, and numerical table data in which the independent variable and the dependent variable are associated is created (Step S503).

  Here, the server 20 further executes a solution finding process for outputting a mathematical expression that is a result of solving the functional expression with the independent variable x as described in steps S201 to S207 in FIG. 3 (step S504). In step S504, the server 20 may execute the solution processing for outputting a mathematical expression that is a result of solving the functional expression with the independent variable x as described in steps S301 to S307 and S309 in FIG.

  Furthermore, when there is only one mathematical expression as a result of solving with the independent variable x, the processor 21 temporarily stores the mathematical expression. In addition, except when there is only one mathematical expression that is the result of solving with the independent variable x, that is, the type of the received function expression is not y = f (x), and the type of the received function expression is x = When it is determined that it is not g (y), when it is determined that the mathematical expression of the solution has not been obtained, when it is determined that the mathematical expression obtained as the solution is a periodic function, and when only one mathematical expression of the obtained solution is obtained. If it is determined that there are a plurality of items, information for error notation is returned to the communication device 10 (step S505).

  Note that in step S504, the processor 21 may execute the solution processing for outputting a mathematical expression that is a result of solving the functional expression with the independent variable x as described in steps S301 to S307 in FIG. When there is only one mathematical formula as a result of solving with the above independent variable x, when it is determined that the mathematical formula obtained as a solution is a periodic function, and there are a plurality of mathematical formulas for the obtained solution instead of only one. If it is determined, each mathematical expression is temporarily stored. Further, except for the above case, that is, when it is determined that the type of the received function formula is not y = f (x) and the type of the received function formula is not x = g (y), and If it is determined that the mathematical formula has not been obtained, information for performing error notation including the type of error corresponding to the content may be returned to the communication device 10 in step S505.

  In addition, the server 20 transmits the number table data created in step S503 to the communication device 10 (step S506).

  In the communication device 10, when information for performing error notation is transmitted from the server 20, the information is stored in the main memory 12 (step C506).

  Further, in the communication device 10, when the number table data is received from the server 20, the processor 11 newly creates a number table tag MP 30 based on the obtained number table data, and the mathematical formula tag is displayed on the display screen of the display output unit 16. The created number table tag MP30 is displayed so as to be associated with MP10 and graph tag MP20 (step C507).

  Next, it is determined from the display state of the number table sticky note MP30 whether or not any input field in the column on the dependent variable side in the number table has been selected by a user operation (step C508). When any input column in the dependent variable side column in the numerical table is selected, the processor 11 does not communicate with the server 20 at this point, and the server 20 side performs the processing in the immediately preceding step C506. It is determined whether information for error notation has been received and stored (step C509).

  When information for performing error notation is stored and it is determined that error display is to be performed, the processor 11 reads out the stored error information from the main memory 12 and displays an error display based on the error information. Perform to output unit 16. Specifically, in the numerical table, an exclamation point as shown in FIG. 11, for example, is placed in the center at the position of the other variable column in the same row as the column in which the numerical value is input. The triangular error symbol ES and the error reason symbol “ERROR” EPU having a larger display area than the error symbol ES are displayed together (step C510).

  On the other hand, as a result of the error determination in step C509, if the information for performing the error notation is not stored and it is determined that the error display is not performed, the processor 11 goes to any input column in the numerical table. Wait until the input of the numeric value is confirmed. If it is determined that the input of a numerical value in any of the input fields is confirmed, the input numerical value and the position of the input column are transmitted to the server 20 (step C509).

  In the server 20, the processor 21 calculates the value of the corresponding variable based on the numerical value stored in the immediately preceding step S504 based on the numerical value received from the communication device 10 and the position of the input column. (Step S507).

  Then, the numerical value resulting from the calculation is returned to the communication device 10 (step S508).

  In the communication device 10 that has received the numerical value that is the result of the inverse function calculation process from the server 20, the same row corresponding to the column of the variable that received the numerical value in the number table tag MP 30 displayed on the display output unit 16. The numerical value received from the server 20 is displayed at the position of the other variable column in (Step C510).

  In this way, when the processor 21 on the server 20 side creates data for displaying the number table sticky note MP30, it is calculated in advance whether or not a correct variable can be obtained by the inverse function calculation, and the error is not displayed. In such a case, communication between the communication device 10 and the server 20 can be omitted, and an error display can be immediately executed on the communication device 10 side, so that the responsiveness in the communication device 10 can be improved particularly when an error is displayed. it can.

  As described above in detail, according to the present embodiment, it is possible to perform an inverse function calculation and display the result in an easily understandable manner even when no answer is obtained.

  In particular, in the above-described embodiment, the variable obtained when only one variable that is the result of the inverse function operation is obtained is displayed in the variable part in the numerical table. Since an error is displayed in the variable part in the numerical table, a simple display mode can be realized particularly when the capacity of the area where the numerical table is displayed cannot be set large.

  In addition, in the above embodiment, the number table sticky note MP30 is displayed visually associated with the corresponding mathematical formula sticky note MP10, the graph sticky note MP20 and the link LK, so that the relevance on the display screen can be simplified. Visible.

  In the above embodiment, the operation example on the communication device 10 side is assumed to be an example in which the communication device 10 is configured by, for example, a mobile type PC, and the input unit 14 has a keyboard and a mouse as a pointing device. Although described, it is needless to say that the present invention is not limited to specific operation examples.

  In addition, 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. In addition, the embodiments may be appropriately combined as much as possible, and in that case, the combined effect can be obtained. Further, the above 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, the problem described in the column of the problem to be solved by the invention can be solved, and the effect described in the column of the effect of the invention Can be obtained as an invention.

Hereinafter, the invention described in the scope of claims of the present application will be appended.
[Claim 1]
A data processing method executed by a control unit of a data processing system,
Display a numerical table showing the relationship between the independent variable and the dependent variable associated by the function expression on the display screen of the display unit,
Based on the inverse function of the functional formula obtained by executing the solution processing based on the functional formula, and the numerical value input to the display area of the dependent variable in the numerical table displayed on the display screen of the display unit If only one numerical solution is obtained, in response to accepting the numerical value input operation, the one numerical solution is notified,
If the calculated numerical solution is not only one, an error is notified in response to accepting an operation to the display area of the dependent variable in the numerical table.
A data processing method.
[Claim 2]
The inverse function of the function formula obtained by executing the solution processing based on the function formula in response to accepting an operation on the display area of the dependent variable in the numerical table is a periodic function. Based on the information shown, inform all numerical solutions within the default or set coordinate range,
The data processing method according to claim 1, further comprising:
[Claim 3]
There is not only one inverse function of the function formula obtained by executing the solution processing based on the function formula in response to an operation on the display area of the dependent variable in the numerical table. Informing a plurality of numerical solutions according to a plurality of inverse functions based on the information indicating
The data processing method of Claim 1 or 2 including this.
[Claim 4]
Display the graph based on the functional expression on the display screen of the display unit,
Identifying and displaying a portion of the graph corresponding to the one or more numerical solutions to be notified;
The data processing method according to any one of claims 1 to 3, further comprising:
[Claim 5]
A data processing method executed by a control unit of a data processing system,
Display a numerical table showing the relationship between the independent variable and the dependent variable associated by the function expression on the display screen of the display unit,
In response to receiving an operation on the display area of the dependent variable in the numerical table displayed on the display screen of the display unit, an inverse function of the function expression is obtained by executing a solution processing based on the function expression. Informing that the inverse function of the functional expression could not be obtained based on the information indicating that it was not obtained,
A data processing method.
[Claim 6]
A data processing system comprising a control unit,
The controller is
Display a numerical table showing the relationship between the independent variable and the dependent variable associated by the function expression on the display screen of the display unit,
Based on the inverse function of the functional formula obtained by executing the solution processing based on the functional formula, and the numerical value input to the display area of the dependent variable in the numerical table displayed on the display screen of the display unit If only one numerical solution is obtained, in response to accepting the numerical value input operation, the one numerical solution is notified,
If the calculated numerical solution is not only one, an error is notified in response to accepting an operation to the display area of the dependent variable in the numerical table.
Including data processing system.
[Claim 7]
A data processing system comprising one or more control units,
The one or more control units are:
Display a numerical table showing the relationship between the independent variable and the dependent variable associated by the function expression on the display screen of the display unit,
In response to receiving an operation on the display area of the dependent variable in the numerical table displayed on the display screen of the display unit, an inverse function of the function expression is obtained by executing a solution processing based on the function expression. Informing that the inverse function of the functional expression could not be obtained based on the information indicating that it was not obtained,
Including data processing system.
[Claim 8]
A computer program readable by a control unit of a data processing system,
By the control unit of the data processing system,
Display a numerical table showing the relationship between the independent variable and the dependent variable associated by the function expression on the display screen of the display unit,
Based on the inverse function of the functional formula obtained by executing the solution processing based on the functional formula, and the numerical value input to the display area of the dependent variable in the numerical table displayed on the display screen of the display unit If only one numerical solution is obtained in response to the input operation of the numerical value, the one numerical solution is notified,
If the obtained numerical solution is not only one, in response to accepting an operation to the display area of the dependent variable in the numerical table, an error is notified,
Computer program.
[Claim 9]
A computer program readable by a control unit of a data processing system,
By the control unit of the data processing system,
Display a numerical table showing the relationship between the independent variable and the dependent variable associated by the function expression on the display screen of the display unit,
In response to receiving an operation on the display area of the dependent variable in the numerical table displayed on the display screen of the display unit, an inverse function of the function expression is obtained by executing a solution processing based on the function expression. Based on the information indicating that it was not obtained, it is informed that the inverse function of the functional expression could not be obtained.
Computer program.

1 ... System,
10: Communication device,
11 ... Processor,
12 ... Main memory,
13 ... Storage,
14 ... input part,
15 ... communication section,
16 ... display output part,
17 ... System bus,
20 ... server,
21 ... Processor,
22 ... main memory,
23 ... Mass storage,
24 ... communication section,
25 ... System bus,
IC1 ... Operation sticky note icon,
IC2: Formula sticky note icon,
IC3 ... graph sticky note icon,
IC4 ... Number table sticky note icon,
IC5: Geometric sticky note icon,
IC6 ... memo sticky note icon,
LK ... link,
MD ... Menu list display,
MP10: Formula sticky notes,
MP20 ... graph sticky notes,
MP30 ... Number table sticky notes,
N ... Network,
PT ... Pointer

Claims (9)

A data processing method executed by a control unit of a data processing system,
Display a numerical table showing the relationship between the independent variable and the dependent variable associated by the function expression on the display screen of the display unit,
Based on the inverse function of the functional formula obtained by executing the solution processing based on the functional formula, and the numerical value input to the display area of the dependent variable in the numerical table displayed on the display screen of the display unit If only one numerical solution is obtained, in response to accepting the numerical value input operation, the one numerical solution is notified,
If the calculated numerical solution is not only one, an error is notified in response to accepting an operation to the display area of the dependent variable in the numerical table.
A data processing method. The inverse function of the function formula obtained by executing the solution processing based on the function formula in response to accepting an operation on the display area of the dependent variable in the numerical table is a periodic function. Based on the information shown, inform all numerical solutions within the default or set coordinate range,
The data processing method according to claim 1, further comprising: There is not only one inverse function of the function formula obtained by executing the solution processing based on the function formula in response to an operation on the display area of the dependent variable in the numerical table. Informing a plurality of numerical solutions according to a plurality of inverse functions based on the information indicating
The data processing method of Claim 1 or 2 including this. Display the graph based on the functional expression on the display screen of the display unit,
Identifying and displaying a portion of the graph corresponding to the one or more numerical solutions to be notified;
The data processing method according to any one of claims 1 to 3, further comprising: A data processing method executed by a control unit of a data processing system,
Display a numerical table showing the relationship between the independent variable and the dependent variable associated by the function expression on the display screen of the display unit,
In response to receiving an operation on the display area of the dependent variable in the numerical table displayed on the display screen of the display unit, an inverse function of the function expression is obtained by executing a solution processing based on the function expression. Informing that the inverse function of the functional expression could not be obtained based on the information indicating that it was not obtained,
A data processing method. A data processing system comprising a control unit,
The controller is
Display a numerical table showing the relationship between the independent variable and the dependent variable associated by the function expression on the display screen of the display unit,
Based on the inverse function of the functional formula obtained by executing the solution processing based on the functional formula, and the numerical value input to the display area of the dependent variable in the numerical table displayed on the display screen of the display unit If only one numerical solution is obtained, in response to accepting the numerical value input operation, the one numerical solution is notified,
If the calculated numerical solution is not only one, an error is notified in response to accepting an operation to the display area of the dependent variable in the numerical table.
Including data processing system. A data processing system comprising one or more control units,
The one or more control units are:
Display a numerical table showing the relationship between the independent variable and the dependent variable associated by the function expression on the display screen of the display unit,
In response to receiving an operation on the display area of the dependent variable in the numerical table displayed on the display screen of the display unit, an inverse function of the function expression is obtained by executing a solution processing based on the function expression. Informing that the inverse function of the functional expression could not be obtained based on the information indicating that it was not obtained,
Including data processing system. A computer program readable by a control unit of a data processing system,
By the control unit of the data processing system,
Display a numerical table showing the relationship between the independent variable and the dependent variable associated by the function expression on the display screen of the display unit,
Based on the inverse function of the functional formula obtained by executing the solution processing based on the functional formula, and the numerical value input to the display area of the dependent variable in the numerical table displayed on the display screen of the display unit If only one numerical solution is obtained in response to the input operation of the numerical value, the one numerical solution is notified,
If the obtained numerical solution is not only one, in response to accepting an operation to the display area of the dependent variable in the numerical table, an error is notified,
Computer program. A computer program readable by a control unit of a data processing system,
By the control unit of the data processing system,
Display a numerical table showing the relationship between the independent variable and the dependent variable associated by the function expression on the display screen of the display unit,
In response to receiving an operation on the display area of the dependent variable in the numerical table displayed on the display screen of the display unit, an inverse function of the function expression is obtained by executing a solution processing based on the function expression. Based on the information indicating that it was not obtained, it is informed that the inverse function of the functional expression could not be obtained.
Computer program.