JPH10171786A - System for editing mathematical expression - Google Patents

Abstract

PROBLEM TO BE SOLVED: To display a mathematical expression in a general mathematically natural format in a mathematical expression edition system for displaying the mathematical expression on a screen by using an electronic computer. SOLUTION: This mathematical expression edition system is provided with a mathematical expression editing means 12 for deciding a desired mathematical expression from a mathematical symbol arbitrarily selected from a mathematical symbol table 15 in which plural mathematical symbols are stored and numeric values and characters inputted from an inputting means 13, and a mathematical expression processing means 18 which converts mathematical expression data prepared by a prescribed format into mathematical expression data displayed in a general mathematical format and outputs the data. The editing means 12 transmits the mathematical expression data prepared following the prescribed format by analyzing the decided mathematical expression and a signal for requesting the calculating and graph-preparing processing of the mathematical expression indicated by the mathematical expression data according to the request of an operator to the mathematical expression processing means 18, receives the output from the mathematical expression processing means 18, and displays the output at the prescribed position of a document edition area in the general mathematically natural notation format.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a mathematical expression editing system which can display a complicated mathematical expression in a general mathematically natural notation using an electronic computer.

[0002]

2. Description of the Related Art Conventionally, using a computer such as a personal computer, a mathematical formula unique to a mathematical expression such as a fraction, an integral formula, a differential formula or a power is described in a formula editing area (formula editing window) on a screen. The mathematical expression editing system assigns one line to each of a dividing line in a fraction, an integral symbol (∫), and a numerical value for expressing an integral section thereof. In addition, currently available document editing applications (for example, MS-Word
(Registered Trademark)), the mathematical symbol can be selected from a menu with a mouse and dragged to a document editing area on the screen to create a mathematical formula.

Further, by using a personal computer and a graphic application, symbols, character expressions, and the like relating to mathematical formulas are individually created as graphic format data, and they are arranged close to each other.
2. Description of the Related Art A method of describing a mathematical expression as if it were written in a mathematically natural manner has been widely used. In addition, some mathematical processing software (Mathem of Wolfram Research, USA)
Atica (registered trademark)) is capable of analyzing mathematical expressions described in such a mathematically natural form, analyzing input according to a certain format, and outputting graphic data.

[0004]

However, in the case where a mathematical expression unique to mathematics including a secant in the above-mentioned fraction, an integral symbol and a numerical value for representing the integral interval thereof, etc. is displayed on the screen, in principle, One line had to be assigned to the symbol. For example,

[0005]

(Equation 1)

[0006] In order to make the description, one line is required for each of the integration intervals a and b, one line is required for the integral symbol and the character expression, and one line is required for the exponent "2", for a total of four lines. It is said. Therefore, the notation in this case is

[0007]

(Equation 2)

[0008] Since mathematical notation is not at all satisfactory, there is a drawback that a person learning mathematics (hereinafter referred to as a learner) is impaired.

The mathematical expression description function of the document editing application can be said to be user-friendly in terms of operability. However, since the mathematical expression is described line by line in the same manner as described above, mathematical notation is sufficient. There was a drawback that it could not be obtained. When formulas are created as data in a graphic format, according to the example of the above-described integral formulas, ∫, a, b,
There is a drawback in that each of x, 2, and dx is created as graphic data, and it is necessary to arrange them appropriately by operating a mouse. In addition, when using the above-mentioned mathematical formula processing software, since the desired mathematical formula has to be described once based on the software's own esoteric description language, an educational institution that creates a mathematical teaching material using a document editing application Teachers and developers of teaching material development had to master their description language, which was a major obstacle in creating mathematical teaching materials.

[0010]

Means for Solving the Problems Accordingly, the present inventor has proposed:
Mathematical expression editing means for determining a desired mathematical expression based on mathematical symbols arbitrarily selected from a mathematical symbol table in which a plurality of mathematical symbols are stored and numerical values and characters input from the input means, as a result of earnest research, A mathematical expression processing unit that converts mathematical expression data formed in a predetermined format into mathematical expression data displayed in a general mathematical form and outputs the mathematical expression data, wherein the mathematical expression editing unit converts the determined mathematical expression Transmitting the mathematical formula data formed according to the predetermined format by analysis and a signal requesting a calculation and graphing process of the mathematical formula represented by the mathematical formula data to the mathematical formula processing means in response to an operator's request; And a mathematical expression editing system that receives the output from the document editing device and displays the output at a predetermined position in the document editing area in a general mathematically natural notation mode, so that even complex mathematical expressions Manner can be displayed in a natural notation embodiment is obtained by solving the above problems.

[0011]

DESCRIPTION OF THE PREFERRED EMBODIMENTS The present system enables an operator to easily select a desired mathematical symbol, a power or a fraction from a menu in a mathematical expression editing area displayed on a terminal screen. A mathematical expression having a mathematically natural expression form created by such a method can be described at a predetermined position in a separately opened document editing area. Also,
If necessary, execution of the mathematical expression and graphing processing are requested from the mathematical expression processing means, and the result can be pasted at a predetermined position in the document editing area. Less than,
An embodiment according to the present invention will be described with reference to the drawings.

FIG. 1 is a block diagram of a mathematical expression editing system according to the present invention. A central processing unit 10, preferably a floating point arithmetic means 11 for calculating mathematical expressions, and a mathematical expression editing means 12
Input means 13 such as a mouse and a keyboard; display means 14; a mathematical symbol table 15 in which mathematical symbols are stored and which can be read at all times; 20, a temporary storage means 16 for pasting at a predetermined position, an auxiliary storage means 17 for storing a document file to which the mathematical data is pasted, and a general method of interpreting a character string according to a predetermined format. Mathematical formula processing means 18 for converting mathematical formula data into mathematically natural notation is connected by a bus so as to follow the control of the central processing unit 10.

The central processing unit 10 stores a central processing unit that performs overall processing of the mathematical expression editing system of the present invention, and a program and the like necessary for executing the overall processing.
It includes an OM, a RAM that provides a work area for performing mathematical expression editing and mathematical expression processing, and the like. The floating point arithmetic means 11 is ideally used in the present invention for the purpose of reducing the load on the central processing unit in complicated differential and integral calculations. The mathematical expression editing means 12 provides a mathematical expression editing area 21 for editing a mathematical expression on the display means 14 so that an operator can select a desired mathematical symbol from a menu, and input a necessary numerical value or character from the input means 13. Is provided so that a desired mathematical expression can be easily edited. The mathematical expression created in the mathematical expression editing area 21 cannot be converted into a character string in a description form according to a predetermined format of the mathematical expression processing unit 18 because the mathematical expression in the natural mathematical form is not sufficient as it is. In addition, the character string referred to here is a combination of characters such as numerals, alphabets, and parentheses, asterisks, arithmetic symbols, and the like, which means an integral expression or a differential expression. Or any other mathematical formula.
The input unit 13 drags a keyboard for inputting numerical values and characters related to a desired mathematical expression, and designation of a mathematical symbol related to the desired mathematical expression or designation of a power, etc. from a menu of a mathematical expression editing area 21 displayed on the display unit 14. A mathematical symbol is stored in a mathematical symbol table 15 in advance. The stored mathematical symbols are, for example, symbols required for describing mathematical expressions, such as ∫, +,-, √, ∂, and can be supplemented or deleted as necessary.

The temporary storage means 16 is a RAM,
This is storage means for temporarily storing mathematical data in a general mathematically natural notation format received from the mathematical formula processing means 18 before pasting it at a predetermined position in the document editing area 20. The auxiliary storage unit 17 is a storage unit for permanently storing the text created by the present system, and preferably uses a hard disk drive, a magneto-optical disk drive, a floppy disk drive, or the like. The mathematical formula processing means 18 receives the mathematical formula data composed of a predetermined character string generated by the mathematical formula editing means 12, interprets the mathematical formula data composed of the character string based on a predetermined procedure, and generally mathematically It is output as mathematical data in a simple notation mode. Here, the “general mathematically natural notation” means that the expression is expressed in a form that is not unnatural as a mathematical expression. Specifically, in an integral expression, an integral symbol and an integral interval are expressed. 2
It means that two numbers or characters are written with an optimum distance from each other so as not to be conscious of the line.
In addition, according to a procedure defined in advance as a program, a mathematical expression represented by mathematical data composed of an input character string is calculated based on a request from the mathematical expression editing unit 12, and the calculation result can be output. . Similarly, based on the domain of a mathematical expression represented by the mathematical expression data, the mathematical expression can be regarded as a function and a graphing process can be performed. Note that the mathematical formula processing means 18 may be present in an electronic computer or the like at a location remote from the present system. This is because data can be exchanged by communicating with the formula editing means 12. Therefore, formula editing means 1
2 and the numerical processing means 18 can both have communication means such as a LAN port and a modem port.

[0015]

Next, as an embodiment of the present invention, an embodiment of the mathematical formula editing system in a mathematical learning system will be described. FIG. 2 shows the document editing area 2 displayed on the display unit 14.
7 is a flowchart of a series of operations for inputting a mathematical expression that is a solution to a mathematical problem described in “0”.
The math learning system referred to here means that a math problem prepared in advance is displayed in the document editing area 20 on the display unit 14.
The learner (operator) uses the input means 13 to input a mathematical expression to be answered in the document editing area 20.
, And its validity is determined. That is, the document editing area 20 is an area where a commentary can be displayed like a textbook, a question can be presented like a collection of questions, and an answer can be input like an answer sheet. First,
In S21, the learner clicks the icon displayed on the display unit 14 with the mouse to activate the mathematical expression editing unit 12. By this operation, the program necessary for editing the mathematical formula is read into the RAM of the central processing unit 10 as in S22, and the storage area necessary for the work is secured. Here, the document editing area 20 is already open on the screen of the display means 14, and the mathematical expression editing area 21 is
Opens.

Next, it is assumed that the learner wants to input the integral expression shown in S24 as a solution. The elements required for the formula are ∫, a
, B, x, 2, dx. When the learner selects the integral symbol from the symbol menu, a frame for editing the mathematical formula is displayed. Specifically, as shown in FIG.
When an integral symbol is selected from the menu, a lower limit input frame portion 23 for inputting the lower limit of the integration interval and an upper limit input frame portion 24 for inputting the upper limit are secured below and above the integral symbol, respectively. A mathematical expression input box 22 for inputting a function is also secured on the right side of the integral symbol. “Dx” is input by default. However, it is assumed that “dy”, “dz”, etc. can be input by selecting “dx” from the pop-up menu with the mouse.

Next, in FIG. 6, "x" is input in the alphanumeric input area 25 displayed on the display means 14 in order to input the integrand "x ² " from the keyboard.
Preferably, the input method is performed directly from the mouse and the keyboard of the input means 13, but a virtual keyboard is separately displayed on the display means 14, and a desired numeral is displayed by the mouse.
It is also possible to adopt a method of selecting characters and the like, and to be able to input an arbitrary numerical value, character expression, or function. The learner inputs the character "x" by the above method and selects "power" with the mouse. Here, when the learner inputs the number “2” from the keyboard, “x” is recognized as the base and “2” is recognized as the exponent. Since “2” is input after the selection of “power”, it is slightly superscripted. Next, the learner inputs the upper limit “a” and the lower limit “b” of the integration section in the alphanumeric input area 25 displayed on the display unit 14 as shown in FIG. Here, the lower limit input frame portion 23 is selected with the mouse to enable input, and then the lower limit “a” is input from the keyboard.
Is input to Hereinafter, the upper limit “b” is similarly input to the upper limit input frame section 24. This is another frame portion to clarify that “a, b” is the domain of the mathematical formula shown in the lower frame portion.

Here, in order to make the mathematical expressions input so far into a mathematically general and mathematically natural notation, the learner selects “data” from the menu of the mathematical expression editing area 21 in S25 of FIG. Select "Update" with the mouse. This case is shown in FIG. Subsequent processing jumps to subroutine A of S26. FIG. 3 and FIG. 4 show a process in which the mathematical expression editing means 12 converts the previously created integral expression in S24 into a character string conforming to a predetermined format of the mathematical expression processing means 18.
First, in step S31, the mathematical expression editing unit 12 identifies the integral symbol of the mathematical expression as the header 1, and recognizes that it is a definite integral calculation. In this case, a is identified as the lower limit, b is identified as the upper limit, and the integration variable is identified as x. Next, in S32, the power is identified as the header 2, and the base is recognized as x and the exponent is recognized as 2.

Next, at S33, the formula editing means 12
Generates “Integrate [] based on the recognition in S31 according to a predetermined format of the mathematical formula processing means 18. Hereinafter, S3
4 and “(x) ＾ (2)),” which mean a power based on the recognition of S32, in S35, and S3.
6, “{x, (a), (b)}” meaning an integration variable and an integration interval based on S31, and in S37 and S38,
Generates closing parentheses "@" and "]" to indicate the end of the character string. Finally, the character strings generated so far in S39 are arranged in order and “Integrate [((x) ＾ (2)), ｛x, (a),
(b) Form mathematical formula data consisting of a character string “｝]”. Here, “forming” means that, based on the recognition in S31 and S32, the character strings generated in the character string generation process from S33 to S38 are assembled as a series of character strings in the order of generation on the RAM, It is stored on the RAM of the central processing unit 10. A series of strings formed as described above, "Integrate [((x) ＾
(2)), {x, (a), (b)}] "is transmitted to the mathematical expression processing means 18 in order to provide a general mathematically natural representation. In order to eliminate data loss as much as possible, the transmission method preferably employs a packet communication procedure and also supports the TCP / IP protocol.

Next, in FIG. 4, in S40, it is determined whether or not the learner requests display of the calculation result. If no request is made, the process proceeds to S43, where the formula editing means 12 receives the formula data output from the formula processing means 18. Here, the mathematical expression indicated by the mathematical expression data is a mathematical expression already described in a general mathematically natural manner. When requesting the display of the calculation result, the learner selects “calculation” from the menu of the formula editing area 21 on the screen with the mouse as shown in FIG. In S41, the formula editing means 12 transmits a calculation request signal to the formula processing means 18. The mathematical formula processing means 18 having received the request signal executes the calculation using the built-in function included in the request signal and returns the calculation result to the mathematical formula editing means 12 in S42. Therefore, the formula editing means 12 sets S
At 43, the calculation result is received.

Next, in S44, it is determined in S44 whether or not the learner requests graphing processing. If no request is made, the process proceeds to S47, where the output data formed so far is converted into bitmap data, which is one type of graphic data widely used in personal computers. When requesting a graphing process, the learner selects “Graph” from the menu of the mathematical expression editing area 21 on the screen with a mouse. In S45, the mathematical expression editing unit 12 transmits a graph request signal to the mathematical expression processing unit 18. The mathematical formula processing means 18 which has received the request signal executes the graphing processing using the graphing processing procedure included in S42, and returns the result as graphic format data to the mathematical formula editing means 12. However, if the "graphic format data" is not in the so-called bitmap format, the subsequent processing is passed to the formula editing unit 12, and the formula editing unit 12 performs an operation of converting the data into bitmap format data (S47). reference).

The data thus converted into the bitmap format is transferred to the temporary storage means 16 (S48).
reference). This is a temporary operation for pasting the bitmap format data at a predetermined position in the document editing area 20 opened on the display unit 14. The “predetermined” is an answer column for the math problem displayed in the document display area 20, and refers to a position where the cursor was last. In step S49, the data in the bitmap format, that is, the mathematical expression or numerical value of the answer expressed in a general mathematically natural notation mode or a graph thereof is generated at a predetermined position in the document editing area 20 at the original cursor position. Transfer as data. Then, a calculation result or a graph is displayed at the original cursor position (see S50). This case is shown in FIG. As described above, the input of the answer is completed, so that the flow returns to the original flow in FIG. 2 and the series of answer operations is completed.

In the above embodiment, the mathematical expression editing system in the mathematical learning system has been described. However, the present invention can be applied to the following. (1) A teaching material development system for developing mathematical teaching materials. (2) A document editing system for editing mathematics test questions such as entrance examinations and practice tests.

[0024]

According to the first aspect of the present invention, a desired mathematical expression is obtained by a mathematical symbol arbitrarily selected from a mathematical symbol table 15 storing a plurality of mathematical symbols, and numerical values and characters input from the input means 13. Formula editing means 1 for determining
A mathematical expression editing system comprising: a mathematical expression processing unit 18 for converting mathematical expression data formed in a predetermined format into mathematical expression data displayed in a general mathematical form and outputting the converted mathematical expression data;
The mathematical expression editing means 12 analyzes the determined mathematical expression and generates mathematical expression data formed in accordance with a predetermined format and a signal requesting a calculation and graphing process of the mathematical expression represented by the mathematical expression data in response to an operator's request. A mathematical expression editing system for transmitting to the mathematical expression processing means 18, receiving an output from the mathematical expression processing means 18, and displaying the output at a predetermined position in the document editing area 20 in a general mathematically natural notation mode. By
First, it is possible to easily express a mathematical expression in a general mathematically natural form without having to understand a difficult description language, thereby overcoming the drawback of hindering a learner's understanding. . Secondly, since there is no need to rely on the mathematical description function of the document editing application,
There is an advantage that mathematical formulas with mathematically natural notation can be easily incorporated into a document created by the document editing application, while securing an existing document editing application as a resource. Third, it is necessary to create each of the components of the above-described formulas as data in a graphic format, appropriately arrange them with a mouse, and make small modifications as if they were represented in general mathematically natural notation. Therefore, the time required for editing the mathematical expression is significantly reduced.

According to a second aspect of the present invention, in the first aspect, the output from the numerical formula processing means is a temporary storage means 16.
After being temporarily stored in the document editing area 20, the formula editing system is written in a predetermined position in the document editing area 20.
Since mathematical data in a general mathematically natural notation format can be loaded into another document file via the RAM, there is an advantage that the loading process is performed at high speed.

According to the invention of claim 3, claim 1 or 2
In the above, the mathematical formula editing means 12 is a mathematical formula editing system for transmitting and receiving mathematical formula data to and from the mathematical formula processing means 18 via communication means, so that a plurality of learning terminals including the present system can be used in educational institutions such as schools. There is a great advantage even when is connected to a network such as a LAN.

[Brief description of the drawings]

FIG. 1 is a configuration diagram of the present system.

FIG. 2 is a flowchart of a mathematical expression editing process of the present system.

FIG. 3 is a subroutine of a first half of a mathematical expression editing process of the present system.

FIG. 4 is a subroutine in the latter half of the mathematical expression editing process of the present system.

FIG. 5 is an example of a screen displayed on a display unit.

FIG. 6 shows an example of a screen displayed on a display unit.

FIG. 7 shows a mode of a screen displayed on a display unit.

FIG. 8 is an example of a screen displayed in a text editing area of a display unit immediately after updating data.

FIG. 9 is an example of a screen displayed in a text editing area of the display unit immediately after the calculation processing.

[Explanation of symbols]

 12 Formula editing means 20 Document editing area 15 Mathematical symbol table 18 Formula processing means

Claims (3)

[Claims] A mathematical expression editing means for determining a desired mathematical expression from a mathematical symbol arbitrarily selected from a mathematical symbol table storing a plurality of mathematical symbols and numerical values and characters input from an input means; A mathematical expression processing means for converting mathematical data formed by a format into mathematical data displayed in a general mathematical form and outputting the converted mathematical data, wherein the mathematical expression editing means analyzes the determined mathematical expression. The formula data formed according to the predetermined format and a signal requesting the calculation and graphing of the formula represented by the formula data in response to the request of the operator are transmitted to the formula processing means. A mathematical expression editing system characterized by receiving an output and displaying the output at a predetermined position in a document editing area in a general mathematically natural notation manner. 2. The mathematical expression editing apparatus according to claim 1, wherein the output from the mathematical expression processing means is temporarily stored in a temporary storage means and then written in a predetermined position in a document editing area. system. 3. The mathematical expression editing system according to claim 1, wherein said mathematical expression editing means exchanges mathematical expression data with said mathematical expression processing means via communication means.