JP2000122981A - Calculating device and storage medium - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a computer which can improve the precision of an integration operation and can calculate an integration value on a function to be integrated, which cannot be expression-processed and to provide a storage medium. SOLUTION: In a calculating device which does not execute an expression processing integration, a primitive function corresponding to a prescribed function to be integrated is stored in ROM. At the time of executing an integration operation on an expression, a CPU first executes the integration operation in accordance with an integration program of higher priority based on the primitive function out of a numerical analysis integration program or the integration program based on the primitive function both stored in a ROM. When the execution of the operation by the operation method is impossible, the integration operation is executed next in accordance with the numerical analysis integration program of lower priority. The operation method during the execution is displayed so that it can be identified and an obtained integration value is displayed on a display means.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to the execution of mathematical operations, and more particularly, to a computing device and a storage medium suitable for obtaining an operation result with high operation accuracy.

[0002]

2. Description of the Related Art Conventionally, software executed by a computer performs a function operation on an input mathematical expression, displays a solution, displays a graph based on the input mathematical expression, and displays the integral range. Devices having a function of changing colors and display patterns for display have been developed.

Further, a scientific calculator having a function operation function is
It is used for education sites and for technical calculations of engineers. The scientific calculator has various built-in function calculation programs, and can perform a function calculation based on an input mathematical expression.

In the above-mentioned software and scientific calculator, when an input mathematical expression is a character expression including a character, an operation is performed while leaving the character included in the character expression, and a solution including the character is obtained and displayed. For example, in the case of an integration operation by this mathematical processing, an indefinite integral of a given mathematical expression can be displayed by a mathematical expression including characters.

FIG. 6 is a diagram showing an example of a display when an integrated value is calculated based on a conventional integration method based on mathematical processing.

As shown in FIG. 6A, "1 / x" is input as an integrand, "1" is input as a lower limit of an integration range, and "5" is input as an upper limit in a predetermined format. When the integration operation is executed, the operation result shown in FIG.
(B) As shown in the middle stage, the indefinite integral “logx” of the integrand “1 / x” is displayed by a mathematical expression including the variable “x”, and then the variable “x” of the indefinite integral “logx” is displayed. From the value obtained by substituting the upper limit value “5” of the integration range, the lower limit value “1”
Is subtracted, and the calculation result “log5” is displayed as an integral value as shown in the lower part of FIG. 6B.

As described above, in the integration method using mathematical processing, the integral value is calculated and displayed by substituting the upper and lower limits of the integration range into the indefinite integration obtained by mathematical processing and calculating the difference.

In the case where the conventional software or scientific calculator calculates the integral value based on the integration method by numerical analysis, the integral range of the integrand included in the input mathematical expression is finely divided by a predetermined step size. Then, an integral value is calculated by obtaining the sum of the areas of the divided sections within the integral range.

FIG. 7 is a graph showing an integrand in which an integration range is finely divided at the time of an integration operation by numerical analysis. In the integration operation by the numerical analysis, as shown in FIG. 7A, the integration range of the integrand is divided into sections P1 to Pn, and the respective areas from the sections P1 to Pn are obtained. It is calculated and used as an integral value. The integrated value calculated based on the integration method by such numerical analysis is numerically displayed, for example, as “4.9999999998”.

[0010]

However, there are problems in the integration method by the above-described mathematical processing and the integration method by the numerical analysis, respectively.

First, in the integration method based on numerical analysis, as described above, since the sum of the areas of the respective sections obtained by dividing the integration range is calculated, as shown in FIG. The calculation accuracy of the integrand having a large portion is reduced. Therefore, the reliability of the integral value obtained by the numerical analysis for the integrand including infinity or infinity in such an integration range is low, and the user is required to perform the integration operation when performing the integration operation. It is necessary to carefully consider the integration range and the like. Therefore, for example, in the field of education, it is difficult for students who will learn integral to use.

In addition, in the integration method using mathematical processing, an integral value cannot be calculated for an integrand that cannot perform indefinite integration by mathematical processing. For example, when the integrand is a function “y =「 | x | dx ”including an absolute value,
The indefinite integral cannot be obtained by mathematical processing, and an integral value cannot be calculated for such an integrand. In an actual educational setting, since the integral of such a mathematical expression is also learned, if the integral value cannot be calculated for an integrand that cannot perform an indefinite integral operation by mathematical processing,
There is also a problem that the practicality of the computing device is significantly reduced.

Further, in order to execute the mathematical processing, a complicated algorithm of the mathematical processing, an expensive and high-performance LSI
(Large Scale Integration), large-capacity ROM (Rea
d Only Memory) and the like, which increases the production cost, and as a result, it is difficult to provide an inexpensive product.

[0014] Accordingly, an object of the present invention is to solve the above-mentioned problems by improving the accuracy of the integral operation and calculating an integral value even for an integrand that cannot perform mathematical processing, and The purpose is to provide a storage medium.

[0015]

The present invention has the following features in order to achieve the above object. Reference numerals and the like assigned to each element are reference numerals and the like in the drawings described later.

According to the first aspect of the present invention, there is provided a display means (4 in FIG. 1) for displaying the execution results of mathematical expressions and calculations, and a mathematical expression storage means (6 in FIG. 1; S101 in FIG. 2) for storing mathematical expressions. 4, an operation method storage unit (7 in FIG. 1) storing a plurality of operation methods relating to the same operation in association with priorities, and an operation on the expression stored in the expression storage unit. Is performed, the operation is executed by the operation method with a higher priority among the operation methods stored in the operation method storage means. If execution of the operation by the operation method is not possible, the priority is sequentially reduced. An operation means (2 in FIG. 1; S103, S104 in FIG. 2,
S107 to S109, S111, S112, S2 in FIG.
04 to S209, S211 and S212), a mathematical expression stored in the mathematical expression storage unit, and a mathematical expression display control unit (2 in FIG. 1; S106 and S11 in FIG.
0, S210 in FIG. 4).

According to the computing device of the first aspect,
When performing an operation on a mathematical expression stored in the mathematical expression storage means storing the mathematical expression, a plurality of arithmetic methods relating to the same operation are stored in the arithmetic method storage means storing the arithmetic methods in association with the priorities. The operation is executed by the operation method with the higher priority among the operation methods that are present, and when the operation by the operation method cannot be executed, the operation is sequentially executed by the operation method with the lower priority. The stored mathematical formulas and the results of the calculations performed by the calculation means are displayed on the display means.

Therefore, when there are a plurality of calculation methods for the same calculation, the priorities are stored in association with the respective calculation methods, and the respective calculation methods are executed in accordance with the priorities. Even if analysis is not performed, calculation accuracy is high and efficient calculation processing can be performed.

According to a second aspect of the present invention, in the computing device of the first aspect, the identification display control means (FIG. 1) for displaying the arithmetic method executed by the arithmetic means on the display means in an identifiable manner. 1 of 2; S104 and S in FIG.
111, S204 and S211 in FIG. 4).

According to the second aspect of the present invention, in addition to the effect of the first aspect, each operation method during execution of the operation is identifiably displayed. It can be easily confirmed whether or not it is being executed.

Further, as in the third aspect of the present invention, in the computing device according to the first or second aspect, the arithmetic method storage means has a high priority for an integration method based on a mathematical formula and a high priority for an integration method based on a numerical analysis. It is effective to store as a low priority.

According to the third aspect of the present invention, in addition to the effects of the first or second aspect of the present invention, the integrand whose arithmetic precision is reduced in the numerical analysis integration,
For example, even if the integrand contains an infinite or infinitesimal value within the integration range, if it is possible to perform mathematical formula integration, first perform an integral operation by mathematical formula integration to obtain an indefinite integral and calculate the integral value. Therefore, the integrated value can be calculated with high calculation accuracy, and the reliability of the calculation device can be improved. Furthermore, since indefinite integrals and integral values can be displayed by displaying mathematical formulas, for example, in an educational setting, learning can be performed while confirming indefinite integrals obtained from the integrand, thereby improving the practicality of the computing device. Becomes possible.

In addition, even for mathematical expressions including an integrand that cannot be integrated by mathematical processing, numerical analysis integration can be performed to obtain an integrated value by a numerical value. Therefore, it is possible to increase the types of integrands that can be integrated. it can.

Further, as in the invention according to claim 4, in the computing device according to claim 1 or 2, the primitive function storage means (primary function storage means shown in FIG. 1) for storing primitive functions corresponding to a predetermined integrand. 7), wherein the calculation method storage means stores the integration method based on the primitive function as high priority and the integration method based on the numerical analysis as low priority, and the calculation means stores the integration method based on the primitive function. When performing the operation in, the primitive function corresponding to the integrand included in the mathematical expression stored in the mathematical expression storage means is extracted from the primitive function storage means, and the mathematical expression is calculated based on the extracted primitive function. It is effective to perform the operation on.

According to the fourth aspect of the present invention, in addition to the effects of the first or second aspect, the integrand which cannot calculate a highly accurate integrated value by integration by numerical analysis. As for the function, it is possible to calculate a highly accurate integral value, and the reliability of the calculation device 1 can be improved. Further, since the integration by the mathematical processing is not performed, it is not necessary to provide an expensive, high-performance LSI and a large-capacity ROM required for performing the mathematical processing integration, thereby reducing the production cost and the product price. Therefore, it can be widely used among educational sites or engineers performing technical calculations.

[0026]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS [First Embodiment] FIGS.
Referring to FIG. 3, computing device 1 according to the first embodiment of the present invention
Will be described in detail.

First, the configuration will be described. FIG. 1 is a block diagram showing a configuration of a computing device 1 to which the present invention has been applied. In FIG. 1, a computing device 1 includes a CPU (Central
ssing Unit) 2, input unit 3, display unit 4, display drive circuit 5, RAM (Random Access Memory) 6, ROM 7,
It comprises a storage device 8 and a storage medium 9.

The CPU 2 reads a predetermined program from the ROM 7 or the storage device 8 based on an instruction input through the input unit 3 and temporarily stores the read program in the RAM 6, executes various processes based on the program, and executes a computing device. Centralized control of each unit. That is, the CPU 2 executes various processes based on the read predetermined program, stores the processing results in a work area in the RAM 6, and
The image is displayed on the display unit 4 via the display drive circuit 5. Also,
The processing result is stored in the storage medium 9 via the storage device 8 based on an instruction input via the input unit 3.

The CPU 2 stores the mathematical expression input from the input unit 3 in the RAM 6 and, when executing an operation based on the mathematical expression, stores the mathematical expression described later stored in the ROM 7 in association with the execution priority. The display unit 4 refers to the execution priority of the processing integration program or the numerical analysis integration program described later, executes an integration operation based on the integration program having a high priority, and displays a symbol for identifying an integration method during execution of the operation. If the integration value cannot be obtained by the executed integration method, the integration method of the next priority is executed, and a symbol for identifying the integration method being executed is displayed in the same manner. Thereafter, when the integrated value is calculated, the calculated integrated value is stored in the RAM 6 and the display unit 4
To be displayed.

That is, in the first embodiment, the arithmetic unit 1 stores the numerical processing integration program as the high priority and the numerical analysis integration program as the low priority in the ROM 7, and the CPU 2 executes the integration operation. At this time, the mathematical processing integration program is executed first according to this priority,
Performs mathematical processing on the input integrand, calculates the indefinite integral of the integrand, calculates the integral value, and performs numerical analysis integration only when the integral value cannot be obtained by the integration operation using the mathematical processing. Execute the program and obtain the integral value by numerical analysis integration.

The input unit 3 includes a keyboard including character input keys, numeric input keys, up / down / left / right keys, and various function keys, and outputs a press signal of the pressed key to the CPU 2.

The display unit 4 is an LCD (Liquid Crystal D)
isplay) and performs various displays based on the drive signal input from the display drive circuit 5. Display drive circuit 5
Generates a drive signal based on display data input from the CPU 2 and controls display of the display unit 4.

The RAM 6 has a work area for temporarily storing designated application programs, input instructions, input data, processing results, and the like.

The ROM 7 stores a basic program corresponding to the computer 1. That is, it stores an initial display menu program to be executed when the power of the computing device 1 is turned on, a basic program which does not need to be rewritten such as various function operation programs, and further associates the priority with the executed priority with the mathematical processing integration. A program and a numerical analysis integration program are stored.

The storage device 8 has a storage medium 9 for storing programs, data, and the like, and the storage medium 9 is constituted by a magnetic or optical storage medium or a semiconductor memory. The storage medium 9 is fixedly provided in the storage device 8 or is detachably mounted. The storage medium 9 is processed by various processing programs corresponding to the computing device 1 and each processing program. Data and the like are stored.

The program, data, and the like stored in the storage medium 9 may be configured to be received and stored from another device connected via a communication line or the like. The storage medium 9 is stored in another connected device.
May be provided so that programs, data, and the like stored in the storage medium 9 are used via a communication line.

Next, the operation will be described. FIG. 2 is a flowchart showing a flow of the integration operation executed by the calculation device 1 in the first embodiment.

The computing device 1 stores in the ROM 7 a program capable of selecting various menus via the input unit 3. When a function operation menu is selected by a key operation of the input unit 3, the CPU 2 starts processing. Then, a predetermined program is read from the ROM 7, and a mathematical expression input screen for inputting a mathematical expression including an integrand to be calculated and an integral range is displayed on the display unit 4 via the display driving circuit 5. And
Via the input unit 3 to a mathematical expression input screen in a predetermined format
When a mathematical expression as shown in (a) is input, the mathematical expression input on the mathematical expression input screen is secured on the work area of the RAM 6 (step S101).

When an execution instruction is input by a key operation of the input unit 3 (step S102), the CPU 2 reads out the mathematical processing integration program stored in the ROM 7 with a high priority, and thereafter reads the mathematical processing integration program. Therefore, the mathematical formula integration is executed (step S10).
3). That is, in the mathematical processing integration, the CPU 2 determines the format of the integrand f (x) included in the mathematical expression according to the mathematical processing integration program, and determines the coefficient, constant, and variable “x” included in the integrand f (x). Is changed under a predetermined condition (formula transformation based on the formula of integration, etc.), and the indefinite integral F (x) is obtained in a form in which the variable “x” is left in the mathematical expression. During the execution of the mathematical processing integration, for example, as shown in FIG. 3A, the lighting symbol 20 of the mathematical processing integration is lit on the display screen of the display unit 4, and the “sym” symbol 21 of the mathematical processing integration is further displayed.
Is displayed (step S104).

If it is possible to obtain the indefinite integral F (x) by executing the mathematical formula integration (step S105; Yes), then the obtained indefinite integral F (x)
Is stored in the work area of the RAM 6 and the display unit 4
(Step S106).

Then, the upper limit value max of the input integration range is substituted for the variable “x” of the indefinite integral F (x) (F (x = m
ax)) (Step S107), similarly, the indefinite integral F (x)
Is substituted for the lower limit value min of the input integration range (F (x = min)) (step S108).
(X = max) -F (x = min) is calculated, and the result is set as an integral value (step S109), and the integrated value is displayed on the display unit 4 (step S110).

If it is not possible to obtain the indefinite integral F (x) by executing the mathematical formula integration (step S105; No), the CPU 2 executes the numerical analysis integration program stored in the ROM 7. Is read, the lighting symbol 30 for numerical analysis and numerical analysis is lit on the display screen of the display unit 4, and the “ana” symbol 31 for numerical analysis integration is displayed (step S111) (see FIG. 3C). Thereafter, numerical analysis integration is performed on the mathematical expression stored in the RAM 6 (step S112).

That is, in the numerical analysis integration, the range from the upper limit value to the lower limit value of the integration range is finely divided by a predetermined interval.
An area (f (x) × step width) of each of the divided sections is calculated, and an integrated value is obtained by obtaining a sum of the calculated areas. Thereafter, the obtained integral value is stored in the RAM 6 and displayed on the display unit 4 (step S11).
0).

FIG. 3 is a diagram showing mathematical formulas and the like displayed on the display unit 4 in the first embodiment.

As shown in FIG. 3A, an integrand f1 (x) and an integration range "0≤x≤5" are displayed on a mathematical expression input screen.
The following equation (1) is input.

[0046]

(Equation 1)

Here, the integrand f1 (x) is expressed by the following equation (2).

[0048]

(Equation 2)

Thereafter, when an execution instruction is input by operating the key of the input unit 3, the CPU 2 reads out a high-priority mathematical processing integration program from the ROM 7, and thereafter,
Numerical processing integration is performed on the integrand f1 (x) to obtain an indefinite integral F1 (x) as shown in the following equation (3).

[0050]

(Equation 3)

At this time, a lighted symbol 2 is displayed on a part of the display screen as a symbol during the execution of mathematical formula integration on the display screen.
0 and a “sym” symbol 21 are displayed.

As shown in FIG. 3B, the indefinite integral F1 of the integrand f1 (x) obtained by the mathematical processing integration
(x) is displayed on the display unit 4, and the CPU 2 further proceeds with the calculation, and adds the upper limit value “5” and the lower limit value “0” to the indefinite integral F1 (x).
Is substituted, and the difference is obtained as an integral value. In this example, the integral value is calculated as “125/3”, and the CPU 2 displays the calculated integral value on the display unit 4.

When the indefinite integration of the integrand f1 (x) by mathematical processing cannot be obtained, the CPU 2 reads out a low priority numerical analysis processing program from the ROM 7, and as shown in FIG. Next, a lighting symbol 30 and an “ana” symbol 31 are displayed on a part of the display screen as symbols during execution of numerical analysis integration. afterwards,
When the integrated value is obtained by numerical analysis integration, the integrated value “41.6666667” is displayed.

As described above, the calculation device 1 according to the first embodiment sets the numerical processing integration program to high priority and the numerical analysis integration program to low priority.
OM7, and the CPU 2 first calculates an indefinite integral by mathematical processing integration to calculate an integral value according to the priority.
Performs numerical analysis integration only when a mathematical expression for which indefinite integration cannot be obtained is input. In addition to displaying the obtained integral value, symbols 20 and 21 of the numerical processing integration are displayed when performing the numerical processing integration, and symbols 30 and 31 of the numerical analysis integration are displayed when performing the numerical analysis integration.

Therefore, even if the integrand whose arithmetic precision is reduced in the numerical analysis integration, for example, the integrand including an infinite or infinite small value in the integration range, the mathematical processing integration can be performed. First, an integral operation is performed by mathematical formula integration, and an indefinite integral is calculated to calculate an integral value. Therefore, the integral value can be calculated with high operation accuracy, and the reliability of the calculation device 1 can be improved. In addition, since indefinite integrals and integral values can be displayed by displaying mathematical formulas,
For example, in the field of education, learning can be performed while confirming the indefinite integral obtained from the integrand, and the practicality of the computing device 1 can be improved.

Even when a mathematical expression including an integrand that cannot be integrated by mathematical formula processing is input, numerical analysis integration can be performed thereafter to obtain an integrated value by a numerical value. Can be reduced, and the types of integrands that can be integrated can be increased. Further, since a symbol indicating each operation method is displayed during the execution of the operation, it is possible to easily confirm by which operation method the operation is being executed.

[Second Embodiment] Next, referring to FIG. 4 and FIG. 5, a primitive function corresponding to a predetermined integrand is stored in a ROM 7, and the primitive is stored without a mathematical processing integration program. The computing device 1 that stores an integration program based on a function as a high priority and a numerical analysis integration program as a low priority will be described.

In such a computing device 1, the CPU 2
When a formula is input from the input unit 3, the formula is stored in a RAM.
6, and determines whether or not a primitive function corresponding to the integrand function included in the stored mathematical expression is stored in the ROM 7. If the primitive function is stored, integration based on the primitive function described later is performed. It is executed according to an integration program based on primitive functions stored in the ROM 7.

That is, in integration based on primitive functions, R
A primitive function corresponding to the integrand function included in the mathematical expression stored in the AM 6 is extracted from the primitive function stored in the ROM 7 and stored in the work area of the RAM 6, and the coefficients and constants included in the primitive function are further extracted. And a coefficient and a constant of the integrand included in the mathematical expression stored in the RAM 6 are compared and correspond to each other to generate an indefinite integral corresponding to the integrand included in the mathematical expression stored in the RAM 6. Then, the upper limit value and the lower limit value of the integration range are substituted for the generated variable of the indefinite integration, and the difference between them is calculated to be the integrated value.

When the primitive function corresponding to the integrand function included in the mathematical expression stored in the RAM 6 is not stored in the ROM 7, the CPU 2 reads out the numerical analysis integration program stored in the ROM 7 as having a low priority. Perform numerical analysis integration to obtain an integral value.

The ROM 7 stores a basic program corresponding to the computer 1 as described in the first embodiment. That is, an initial display menu program and various function calculation programs to be executed when the power of the computing device 1 is turned on are stored. In addition, a plurality of primitive functions corresponding to the integrand, which is recognized in advance as being difficult to achieve accuracy in the numerical analysis integration, are stored, and an integration program based on this primitive function is set as a high priority, and a numerical analysis integration program is set as a low priority. I remember.

Next, the operation will be described. FIG. 4 is a flowchart illustrating a flow of the integration operation executed by the calculation device 1 in the second embodiment.

First, a mathematical expression input screen is displayed on the display unit 4 in the same manner as in the above-described first embodiment.
When a mathematical expression including an integrand and an integral range as shown in FIG.
2 stores the mathematical expression input to the mathematical expression input screen in the work area of the RAM 6 (step S201).

When an execution instruction is input by operating a key of the input unit 3 (step S202), the CPU 2
It is determined whether or not there is a primitive function G (x) corresponding to the integrand f (x) included in the mathematical expression among the primitive functions stored in the ROM 7 in advance (step S203). If the primitive function G (x) corresponding to the integrand f (x) is stored in the ROM 7 (step S203; Yes), the primitive function G (x) is extracted from the ROM 7 and stored in the work area of the RAM 6. Store.

The CPU 2 sets the ROM 7 with high priority.
The integration program based on the primitive function stored in is stored in the RAM 6 and then integrated based on the primitive function according to the integration program based on the primitive function. At this time, the lighting symbol 40 and the "sac" symbol 41 are displayed as symbols for which integration based on the primitive function is being performed (step S204).

In the integration based on the primitive function, the CPU 2
Integrand f included in the formula stored in RAM 6
Recognize the coefficient or constant of (x) (step S205), compare the extracted coefficient or constant of the primitive function G (x) with the coefficient or constant of the integrand f (x). And an indefinite integral F (x) corresponding to the integrand f (x) is generated (step S206).

Thereafter, a value obtained by substituting the upper limit value max of the integration range into the generated indefinite integral F (x) is defined as Q1 (step S207), and then the lower limit value m of the integration range is substituted for the indefinite integral F (x).
The value obtained by substituting "in" is set as Q2 (step S208), and then the difference (Q1-Q2) between Q1 and Q2 is calculated and set as an integral value (step S209), and the obtained integral value is displayed on the display unit 4 (step S209). Step S210).

Further, in the judgment of step S203,
A primitive function G (x) corresponding to the integrand f (x) is stored in the ROM 7
If it is determined that they are not stored in
03; No), the CPU 2 reads the numerical analysis integration program stored in the ROM 7, turns on the lighting symbol 30 of the numerical analysis integration on the display screen of the display unit 4, and further displays the “ana” symbol 31 of the numerical analysis integration. It is displayed (step S211), and thereafter, numerical analysis integration is executed to obtain an integral value (step S212), and the obtained integral value is displayed on the display unit 4 (step S210).

FIG. 5 shows a ROM in which an integration program based on primitive functions is set as a high priority and a numerical analysis integration is set as a low priority.
FIG. 9 is a diagram showing an example of a display in an integral operation when the data is stored in a memory 7;

FIG. 5A is a diagram in which the following equation (4) including the integrand f2 (x) and the integration range "-1.ltoreq.x.ltoreq.1" is input.

[0071]

(Equation 4)

In equation (4), the integrand f2 (x)
Is the following equation (5).

[0073]

(Equation 5)

When equation (4) is input and an execution instruction is input by key operation of the input unit 3, the CPU 2 determines the integrand function f2 (x) corresponding to the integrand function f2 (x) included in the equation (4). g (x) is determined, and it is determined whether or not the primitive function G (x) previously associated with the integrand g (x) is stored in the ROM 7. Integrand f2 (x) shown in this example
Corresponds to the integrand g (x) shown in the following equation (6).

[0075]

(Equation 6)

Further, the integrand g (x) is associated with a primitive function G (x) shown in the following equation (7).

[0077]

(Equation 7)

The CPU 2 extracts this primitive function G (x) as a primitive function corresponding to the integrand f2 (x), and
Secure in the work area No. 6. Further, the CPU 2 reads an integration program based on the primitive function from the ROM 7 and
As shown in FIG. 5A, the lighting symbol 40 of the integration based on the primitive function is lit on the display unit 4, and the "sac" symbol 41 is displayed.

The CPU 2 compares the characters a, b, and c indicating the coefficients and constants of the integrand g (x) with the coefficients and constants of the integrand f2 (x), and adds the characters a, b, and c to the characters a, b, and c. Set the corresponding numerical value. In this case, "a = 1", "b = 2",
By setting “c = 2”, these coefficients and constants are set to the coefficients and constants of the extracted primitive function G (x), and the indefinite integral F2 (x) expressed by the following equation (8) is obtained. Generate.

[0080]

(Equation 8)

Thereafter, the value “2log3” obtained by substituting the upper limit value max = 1 of the integration range into the variable “x” of the generated indefinite integral F2 (x) is defined as Q1, and the variable “x” is integrated. The value "0" obtained by substituting the lower limit value min = -1 of the range is Q
2 and then calculate the difference (Q1-Q2) between Q1 and Q2 to obtain "2log3".
It is displayed on the display unit 4 as shown in FIG.

If the primitive function G (x) corresponding to the integrand f2 (x) is not stored in the ROM 7, the numerical analysis integration program is read out from the ROM 7 and
As shown in (c), the lighting symbol 30 and the “ana” symbol 31 of the numerical analysis integration are displayed, and then the numerical analysis integration is performed, and the numerical integration value “0.954242” is displayed.
509 ”is calculated and displayed on the display unit 4.

As described above, the primitive function corresponding to the integrand, which has been recognized in advance as being difficult to achieve accuracy in the numerical analysis integration, is stored in the ROM 7, and the integration program based on this primitive function has a high priority. In the computing device 1 in which the numerical analysis integration program is stored in the ROM 7 as a low priority, the CPU 2 extracts the primitive function corresponding to the integrand function included in the input mathematical expression, if the primitive function exists in the ROM 7. Then, the integration based on the primitive function is performed according to the integration program based on the primitive function, and if the corresponding primitive function is not stored in advance,
The numerical analysis integration is executed according to the numerical analysis integration program to calculate and display the integrated value.

Therefore, it is possible to calculate a highly accurate integral value even for an integrand for which it is not possible to calculate a highly accurate integrated value by integration by numerical analysis, thereby improving the reliability of the calculation device 1. Can be. In addition, since integration by mathematical processing is not performed, it is not necessary to provide an expensive, high-performance LSI and a large-capacity ROM required for performing mathematical processing integration, thereby lowering production costs and lowering product prices. Since it is possible to make it available, it can be widely used among educational sites or engineers performing technical calculations.

In the examples shown in the first and second embodiments, the integral operation has been described as an example. However, if there are a plurality of operation methods for the same operation other than the integral operation, each of By storing the calculation method and the priority in association with each other and executing each calculation method according to the priority, the calculation accuracy is high without analyzing the mathematical expression in advance,
Efficient arithmetic processing can be performed,
By displaying symbols for the operation being performed,
It is possible to easily confirm the operation method being executed.

[0086]

According to the first and fifth aspects of the present invention, when there are a plurality of operation methods for the same operation, a priority is stored in association with each operation method, and each operation method is stored in accordance with the priority. By executing the calculation method, it is possible to execute the calculation processing with high calculation accuracy and high efficiency without performing the analysis of the mathematical expression in advance.

According to the second aspect of the invention, in addition to the effect of the first aspect, a symbol indicating each operation method is displayed during execution of the operation, so that the operation can be executed by any operation method. Can be easily confirmed.

According to the third aspect of the present invention, in addition to the effects of the first or second aspect of the present invention, the integrand whose arithmetic precision is low in numerical analysis integration, for example, infinite in the integration range. Even if the integrand includes an infinitesimal value, if the mathematical integration can be performed, the integration operation is first performed by the mathematical integration, and the indefinite integral is calculated to calculate the integrated value. The integration value can be calculated, and the reliability of the calculation device 1 can be improved. Furthermore, since indefinite integrals and integral values can be displayed by displaying mathematical formulas, for example, in an educational setting, learning can be performed while confirming indefinite integrals obtained from the integrand, thereby improving the practicality of the computing device. Becomes possible.

Further, even for mathematical expressions including integrands that cannot be integrated by mathematical formula processing, numerical analysis integration can be performed to obtain an integral value by a numerical value. Therefore, it is possible to increase the types of integrands that can be integrated. it can.

According to the fourth aspect of the present invention, in addition to the effects of the first or second aspect of the present invention, the integrand whose integral value cannot be calculated with high accuracy by integration by numerical analysis is also determined. It is possible to calculate a highly accurate integrated value, and the reliability of the calculation device 1 can be improved. In addition, since integration by mathematical processing is not performed, an expensive and high-performance LSI required to execute the mathematical processing integration program is used.
In addition, since there is no need to provide a large-capacity ROM, the production cost can be reduced and the price of the product can be reduced, so that it can be widely used in the field of education or engineers performing technical calculations.

[Brief description of the drawings]

FIG. 1 is a block diagram illustrating a configuration of a computing device 1 according to an embodiment of the present invention.

FIG. 2 is a flowchart illustrating a flow of an integration operation performed by a calculation device 1 in the first embodiment.

FIG. 3 is a diagram illustrating an example of a mathematical expression or the like displayed at the time of an integration operation performed in the first embodiment.

FIG. 4 is a flowchart illustrating a flow of an integration operation performed by a calculation device 1 in a second embodiment.

FIG. 5 is a diagram illustrating an example of a mathematical expression or the like displayed at the time of an integration operation performed in a second embodiment.

FIG. 6 is a diagram illustrating a display example of a mathematical expression or the like of a calculation device that performs an integral operation by conventional mathematical processing.

FIG. 7 is a diagram showing a divided integration range of an integrand in an integration operation by a conventional numerical analysis.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 Computing apparatus 2 CPU 3 Input part 4 Display part 5 Display drive circuit 6 RAM 7 ROM 8 Storage device 9 Storage medium

Claims (5)

[Claims] 1. A display means for displaying an execution result of an equation and an operation, an equation storage means for storing an equation, and an operation method for storing a plurality of operation methods relating to the same operation in association with priorities. Storage means, when performing an operation on the mathematical expression stored in the mathematical expression storage means, performing the operation with a higher priority operation method among the operation methods stored in the operation method storage means,
If it is impossible to perform the operation by the operation method, an operation unit that sequentially executes the operation by an operation method with a low priority, an expression stored in the expression storage unit, and an operation performed by the operation unit And a mathematical expression display control means for causing the display means to display an execution result of the calculation. 2. The computing device according to claim 1, further comprising identification display control means for displaying the calculation method executed by said calculation means on the display means so as to be identifiable. 3. The arithmetic method storage means according to claim 1, wherein the integration method based on mathematical processing is stored as a high priority, and the integration method based on a numerical analysis is stored as a low priority.
Or the computing device according to 2. 4. An apparatus according to claim 1, further comprising a primitive function storing means for storing a primitive function corresponding to a predetermined integrand function, wherein said arithmetic method storing means is configured to integrate the primitive method based on the primitive function with high priority and numerical analysis. The arithmetic means stores the method as a low priority, and when performing the arithmetic operation by the integration method based on the primitive function, the primitive corresponding to the integrand included in the mathematical expression stored in the mathematical expression storage means. 3. The computing device according to claim 1, wherein a function is extracted from the primitive function storage unit, and an operation on the mathematical expression is performed based on the extracted primitive function. 5. A storage medium storing a computer-executable program, wherein: a computer-executable program code for storing a mathematical expression; and a computer-executable program code for executing an operation on the stored mathematical expression. A plurality of calculation methods relating to the calculation are stored in association with the priority, and the calculation is performed by the calculation method having a higher priority among the calculation methods stored in the calculation method storage means. If it is not possible, a computer code that can be executed by a computer for executing an operation in an operation method having a sequentially lower priority, and a computer for displaying the stored mathematical formula and an execution result of the executed operation are provided. A storage medium storing an executable program code and a program including: