JP4126497B2 - Electronic calculation apparatus and calculation display processing program - Google Patents

Description

  The present invention relates to an electronic calculation device and a calculation display processing program for converting an arithmetic result according to an arbitrary arithmetic expression into a mathematical expression and displaying the result.

  In electronic calculators called scientific calculators that have been widely used in general, in addition to the usual four arithmetic calculations, there are various types such as trigonometric functions, inverse trigonometric functions, irrational numbers, power functions, square roots, square roots, etc. Can be calculated.

In such a conventional electronic computing device, for example, when an inverse trigonometric function expression of “sin ⁻¹ 0.5” is input and the calculation is executed, the solution is “0.523598. Is displayed as a real number.

  For example, when a calculation is performed by inputting an expression of a trigonometric function of “cos (6 / π)”, the solution is displayed as a real number consisting of all decimal values such as “0.8660254.

  Further, for example, when an expression including an irrational number of “2 / (√5 + √3)” is input and the calculation is executed, the solution is displayed as a real number consisting of all decimal numbers, such as “0.5040171 ...”.

  As described above, in the conventional electronic calculation device, the calculation formula input as a calculation target is an integer value or a solution regardless of any type of calculation formula such as a trigonometric function, an inverse trigonometric function, or an irrational number. It is displayed as a real number consisting of decimal values.

However, in the learning process of mathematics in universities and high schools, for example, the inverse trigonometric function “sin ⁻¹ 0.5” has a solution of π and a fraction combined with a fraction suitable for the calculation type. For example, the solution of “cos (6 / π)”, which is the trigonometric function, is obtained as a fraction “π / 6”, and a solution of a root and a fraction suitable for the calculation type is a √fraction “√ (3/2”). ) ”, And for example, the solution of“ 2 / (√5 + √3) ”, which is an expression including the irrational number, is learned as a route addition / subtraction formula“ √5-√3 ”suitable for the calculation type. Therefore, especially in educational sites and research institutions that require this kind of calculation, the solution can be an integer or a decimal for any type of calculation formula, as in the case of the conventional electronic computer. If displayed in real format, the result is the same value , Prospects of solution is very attached difficult.

  In view of this, an application has been filed by the same applicant for a device that converts a numerical value in the form of an integer or a decimal number into a specific mathematical expression and displays it.

  The first is an electronic computing device that displays decimal numbers converted to fractions (rational numbers) (see Patent Document 1).

  The second is a calculation device that converts a trigonometric function, a power function, or the like into a π fraction and displays it (see Patent Document 2).

  The third is a square root symbol display control device that converts and displays a real number having a value less than a decimal (decimal part) into a formula for calculating the sum or difference of square roots (see Patent Document 3).

The fourth is a square root symbol display control device that converts a real number having a decimal part into a polynomial including a square root symbol (√) and displays it (see Patent Document 4).
Japanese Patent Laid-Open No. 11-282807 JP 2000-057100 A JP 2003-030159 A JP 2003-203057 A

  However, in the conventional electronic computing device and the square root symbol display control device filed by the same applicant, the respective devices can display in a form converted into the specific formula of the device, for example, certain calculation results Is converted to a fraction (rational number) and displayed, or a certain calculation result is converted to π fraction and displayed. There is a problem that cannot be converted into a form and displayed.

  Therefore, by combining the techniques of the conventional electronic computing device and the square root symbol display control device, it can be considered that the real value of the calculation result is appropriately converted into an optimal type of mathematical form and displayed. In the numerical conversion processing of individual devices, conversion is displayed by performing the most precise calculation processing within the range of digits that can be displayed for a specific type of mathematical formula of the device. In addition to the need for a large processing unit (CPU), for example, in junior high school and high school level education sites, the number of digits in the converted mathematical formula may be too precise, and conversely it is difficult to find a solution prospect Occurs.

  The present invention has been made in view of the above problems. For example, even in a junior and senior high school level education site, it is possible to display a good-looking solution converted into an optimal type of mathematical expression according to the calculation result. An object of the present invention is to provide an electronic calculation apparatus and a calculation display processing program.

An electronic computing device according to claim 1 is an expression input means for inputting an arithmetic expression, an arithmetic means for performing arithmetic processing according to the arithmetic expression input by the expression input means, and numerical data obtained as a result of the arithmetic operation by the arithmetic means. A fractional expression converting means for converting to a number, a digit number determining means for determining whether or not the fractional expression converted by the fractional expression converting means falls within a predetermined number of digits, and the fraction converted by the digit number determining means When it is determined that the mathematical expression falls within a predetermined number of digits, display control means for displaying the calculation result of the arithmetic expression in the display form of the converted fractional expression, and the conversion by the digit number determination means When it is determined that the fractional expression does not fit in a predetermined number of digits, another format display control means for converting and displaying the numerical data of the computation result by the computation means into a mathematical expression including √ or a fractional expression including π, and With And wherein the door.

The electronic computing device according to claim 2 is the electronic computing device according to claim 1, wherein the different format display control means divides the numerical data of the result of computation by the computing means by π and multiplies by 25200. And a display control means for displaying (integer / 25200) π as a calculation result of a fractional expression including π when it is determined that the determination means is an integer. It is characterized by.

  According to this, the calculation result obtained by inputting an arbitrary arithmetic expression is not simply a list of real values, but for example, in an educational field at a junior and senior high school level, each parameter is suppressed within a range of digits with good visibility (a / B) It can be displayed as a display form of the mathematical expression of π or another mathematical expression display form.

According to the electronic computing device according to claim 1 (claim 3) of the present invention (calculated display processing program), the calculation result due to the enter any arithmetic expression, rather than the enumeration of mere real value, for example, teenagers level Can be displayed as a display form of a fractional expression with a good number of digits, a mathematical expression including √, or a numerical expression display form of a fractional expression including π .

  Therefore, for example, even in a junior and senior high school level education site, it is possible to provide an electronic calculation device and a calculation display processing program that can display a solution with a good prospect converted into an optimal type of mathematical expression according to the calculation result.

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

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

  This electronic computing device includes a control unit (CPU) 11 formed of a computer or the like.

  The control unit (CPU) 11 is a calculation device control program stored in advance in the ROM 13 or a calculation read from the external recording medium 18 via the recording medium reading unit 17 in accordance with a key operation signal from the key input unit 12. A device control program or a computer device control program downloaded from a Web server (in this case, a program server) 20 on a communication network (Internet) via a communication unit 19 is started, and the RAM 14 is set as a work (work) memory. The operation of each part of the circuit is controlled as follows.

  The control unit (CPU) 11 is connected to the key input unit 12, ROM 13, recording medium reading unit 17, communication unit 19, and RAM 14, and a liquid crystal display unit 16 through a display drive circuit 15. .

  The key input unit 12 is provided with a data input key 12a composed of various numerical / symbol key groups such as a numerical key, an operator key, and a function key, and instructs setting of selected or input data and execution of calculation. “Execution” key 12b that is operated at the time of operation, “arithmetic input” key 12c for inputting and displaying an arbitrary arithmetic expression, and arithmetic modes such as [DEG] mode and [RAD] mode. “Mode” key 12d operated when switching, cursor keys “↑”, “↓”, “←”, “→” 12e, etc. operated when moving the cursor on the display screen, selecting data, and the like are provided. .

  The ROM 13 stores in advance system program data that controls the entire processing in the electronic circuit of the electronic computing device, and subprograms that control processing in various operation modes such as the calculation display control processing shown in FIGS. Control program data, which is data, is also stored in advance.

  FIG. 2 is a diagram showing a configuration of a data memory provided in the RAM 14 of the electronic computing device.

  The RAM 14 includes a display data memory 14a, an input data memory 14b, an operation result data memory 14c, a code saving memory 14d, an integer part saving memory 14e, a first conversion data [(a / b)] memory 14f, and a second conversion data [ (A + b√c) / d] memory 14g, third conversion data [(a√b ± c√d) / e] memory 14h, fourth conversion data [(a / b) π] memory 14i, variable a memory 14j Various data memories such as a variable e memory 14n and a work memory 14o are provided.

  In the display data memory 14a, display data to be displayed on the liquid crystal display unit 16 in the various operation modes is developed and stored as bitmap pattern data.

  The input data memory 14b stores input data such as a calculation formula input by operating the key input unit 12.

  In the calculation result data memory 14c, the solution of the calculation result corresponding to the calculation expression stored in the input data memory 14b is stored as an integer or decimal real value.

  The code saving memory 14d stores code data extracted and saved from the calculation result of the arithmetic expression stored in the calculation result data memory 14c.

  The integer part saving memory 14e stores the integer part data extracted and saved from the calculation result of the arithmetic expression stored in the arithmetic result data memory 14c.

  In the first conversion data [(a / b)] memory 14f to the fourth conversion data [(a / b) π] memory 14i, solutions of the calculation results of the arithmetic expressions stored in the calculation result data memory 14c are stored. Depending on the value of the solution, it is converted into an optimal type of mathematical expression and stored.

  In the first conversion data [(a / b)] memory 14f, the solution of the calculation result of the arithmetic expression stored in the arithmetic result data memory 14c is converted into a fractional expression (a / b) and stored.

  In the second conversion data [(a + b√c) / d] memory 14g, the solution of the calculation result of the arithmetic expression stored in the calculation result data memory 14c is the square root symbol (√) of (a + b√c) / d. It is converted into a polynomial including it and stored.

  In the third conversion data [(a√b ± c√d) / e] memory 14h, the solution of the calculation result of the arithmetic expression stored in the calculation result data memory 14c is (a√b + c√d) / e. It is converted into a formula for calculating the sum or difference of square roots and stored.

  In the fourth conversion data [(a / b) π] memory 14i, the solution of the calculation result of the arithmetic expression stored in the arithmetic result data memory 14c is converted into a π-partial expression of (a / b) π and stored. Is done.

  In the variable a memory 14j to the variable e memory 14n, when the numerical value of the solution of the calculation result is converted into various types of mathematical expressions, each variable value (a, b, c, Substitution values to be assigned to d and e) are updated and stored.

  In the work memory 14o, various data input / output by the control unit (CPU) 11 accompanying various calculation / control processes are temporarily stored as necessary.

  Next, the calculation display control function by the electronic computer having the above-described configuration will be described.

  FIG. 3 is a flowchart showing the calculation display control process (part 1) of the electronic computer.

  FIG. 4 is a flowchart showing the calculation display control process (part 2) of the electronic computer.

  FIG. 5 is a flowchart showing a calculation display control process (No. 3) of the electronic computer.

  FIG. 6 is a flowchart showing the calculation display control process (No. 4) of the electronic computer.

  FIG. 7 is a diagram showing the input of an arithmetic expression accompanying the arithmetic display control processing of the electronic computer and the display state of the answer.

  In accordance with the operation of the “calculation input” key 12c of the key input unit 12, an arbitrary arithmetic expression is input in response to a user operation using the data input key 12a in a state where an arbitrary arithmetic expression can be input and displayed. When the data is stored in the input data memory 14b, the input data of the arithmetic expression is written in the display data memory 14a and displayed on the display unit 16 (step S1).

  When the “execute” key 12b is operated, calculation processing is executed according to the arithmetic expression stored in the input data memory 14b (step S2), and the numerical data in the real number format of the solution of the calculation result is calculated. While being stored in the result data memory 14c, the real value of the solution is set as a converted value for conversion into an optimal type of mathematical formula corresponding to this (step S3).

  Then, it is first determined whether or not the numerical data (absolute value) of the calculation result set as the converted numerical value is within a certain numerical range (step S4). If it is determined that the numerical value is not within a certain numerical range, that is, the numerical data of the converted numerical value is too large and is not suitable for conversion to a mathematical expression such as a fraction, irrational number, or π fraction (step) S4 (No)), the numerical data of the calculation result is displayed on the display unit 16 as an answer in the form of the numerical data in the real number format without performing the conversion processing to the corresponding mathematical expression (END).

  On the other hand, when it is determined that the numerical data (absolute value) of the calculation result set as the converted numerical value is within a certain numerical value range (step S4 (Yes)), the converted numerical value In preparation for conversion, the minus sign “−” attached to the numerical data is saved (if any) and stored in the code saving memory 14d to be a “positive” value (step S5).

  Then, it is determined whether or not the converted numerical value is an integer (step S6). If it is determined that the converted numerical value is an integer, conversion to a mathematical expression such as a fraction, an irrational number, or a π fraction is not necessary. The converted numerical value, which is an integer, is used as an answer as it is (steps S6 → S7), and the minus sign “−” saved (stored) in the sign saving memory 14d is added (if any) and displayed on the display unit 16 ( Step S55).

  On the other hand, when it is determined that the converted numeric value is not an integer but a real number including a decimal number (step S6 (No)), the integer part of the converted numeric value is saved (if any) and is an integer. The value is stored and held in the copy saving memory 14e, and only the decimal part is set (step S8).

  Then, the converted numeric data having only the decimal part is converted into a fractional value (a / b) and stored in the first converted data memory 14f (step S9).

  Here, the conversion processing by various methods exists in the [decimal → fraction] conversion processing, but the decimal → fraction conversion processing of this embodiment does not require a given number of decimal numbers or digits. Any decimal number is converted into a fraction according to a technique (Japanese Patent Application No. 10-81023) that can be easily converted into a fraction.

  That is, in the fraction conversion process disclosed in this Japanese Patent Application No. 10-81023, each numerator of the minimum irreducible fraction [o / p = 0/1] and the maximum irreducible fraction [q / r = 1/1] , If the middle irreducible fraction [(o + q) / (p + r) = 1/2] obtained by adding the denominators to each other is larger than the decimal number [y] of the converted value, this is replaced with the next larger irreducible fraction [q / r. = 1/2], the same calculation of the medium irreducible fraction and the size determination process with the decimal [y] are repeated with the same small irreducible fraction [o / p = 0/1], and When the medium irreducible fraction is smaller than the decimal [y], this is regarded as the next small irreducible fraction [o / p = 1/2] and the same large irreducible fraction [q / r = 1/1]. The calculation of the medium irreducible fraction and the size determination process with the decimal [y] are repeated in the same manner, and the small irreducible fraction [o / including the decimal [y] is repeated. ] And Daisunde an interval of about fraction [q / r] narrow gradually. Then, when it is determined that the sequentially calculated small irreducible fraction [o / p] or large irreducible fraction [q / r] matches the decimal [y], the determined fraction is converted into the converted fraction [a / b]. ] Is determined.

  By such decimal-to-fraction conversion processing, when the small irreducible fraction [o / p] or the large irreducible fraction [q / r] matches (success) the decimal [y], the decimal value of the converted numerical value becomes a fraction. It is converted into a numerical value (a / b) and stored in the first converted data memory 14f in the RAM 14 (step S9).

  Then, the integer part of the converted numerical value saved in the integer part saving memory 14e in step S8 is read (if any), the fractional part of the converted numerical value is subjected to fractional conversion, and the first converted data memory 14f is converted. Is added to the fraction stored in (step S10).

  Thereby, the first converted data memory 14f in the RAM 14 is in a state in which the fraction-converted fraction corresponding to the numerical data (converted numerical value) of the calculation result stored in the calculation result data memory 14c is stored. It is determined whether or not the value of the integer part of this fraction is “0”, that is, whether or not the fraction has no integer part (step S11).

  Here, when it is determined that the fraction corresponding to the converted numeric value is a fraction (a / b) having no integer part (integer part = 0), the number of digits and the denominator of the numerator a of the fraction Whether the total number of digits of b is 9 digits or less, that is, when displaying this fraction, the total number of fractions with the fraction symbol “/” within 10 digits It is determined whether or not it fits (steps S11 → S12).

  Then, the number of digits obtained by adding the number of digits of the numerator a corresponding to the converted value and the number of digits of the denominator b is 9 digits or less. When this fraction is displayed, the fraction symbol “/” When it is determined that the total number of fractions between the numbers falls within 10 digits, the fraction is answered (step S12 → S13), and the minus sign “ -"Is added (if present) and displayed on the display unit 16 (step S55).

  On the other hand, when it is determined that the integer part of the fraction corresponding to the converted numerical value is a fraction (x and a / b) which is not “0” but “1” or more, the integer part x of the fraction Whether or not the number of digits of numerator a, the number of digits of numerator a, and the number of digits of denominator b is 8 digits or less, that is, the fraction with this integer part (x and a / b) In this case, it is determined whether or not the total number of digits of the fraction between the integer part separator and the fraction symbol “/” falls within 10 digits (steps S11 → S14).

  The number of digits of the integer part x of the fraction corresponding to the converted value, the number of digits of the numerator a, and the number of digits of the denominator b are 8 digits or less, and this fraction is displayed. In this case, when it is determined that the total number of digits of the fraction between the integer part separator and the fraction symbol “/” is within 10 digits, a certain fraction of the integer part is the answer ( In step S14 → S15), the minus sign “−” saved in the sign saving memory 14d is added (if any) and displayed on the display unit 16 (step S55).

  As a result, when the numerical data that is the calculation result is converted to a fraction as a converted numerical value, the number of digits in which the number of digits for the display is set in advance as the maximum number of digits with good visibility (for example, within 10 digits) If this is the case, the converted fraction is displayed as the answer to the calculation result.Therefore, numerical data including decimals is not displayed as a simple list of real values as the calculation result. Can be displayed.

More specifically, as shown in FIG. 7A, for example, when an arithmetic expression “Σ (1 ÷ 3 ^X ): x = 1 to 8” is input and an arithmetic operation is performed, Numerical data “0.4999923721048” as a calculation result with 13 digits as effective digits is calculated. Then, when the numerical data obtained as a result of the calculation is converted into a decimal value and a fraction, the fraction “3280/6561” in which all the digits including the fractional symbol are within 10 digits matches with 13 digits after the decimal point. Since it is acquired as “0.4999923791048”, a fraction “3280/6561” with such a good prospect even at the middle and high school level is displayed on the display unit 16 as an answer.

  In addition, the display of the answer by the fraction (a / b) on the display unit 16 is not limited to, for example, the form of “a / b” as it is displayed in a single column, but the numerator number a is the upper row, the denominator b is the lower row, It is good also as the form of the multistage display according to the textbook which has the fraction sign in the middle.

  On the other hand, when it is determined that the fraction corresponding to the converted numerical value is a fraction (a / b) without an integer part (integer part = 0) (step S11 (Yes)), the numerator of the fraction a If the number of digits and the number of digits in the denominator b are not less than 9 digits and this fraction is displayed, the total number of digits in the fraction with the fraction symbol “/” within 10 digits If it is determined that it does not fall within the range (step S12 (No)), or the fraction corresponding to the converted numeric value is a fraction (x and a / b) whose integer part is not “0” but “1” or more. (Step S11 (No)), the number of digits obtained by adding the number of digits of the integer part x of the fraction, the number of digits of the numerator a, and the number of digits of the denominator b is 8 digits or less. Instead, when displaying this fraction, the integer part separator and the fraction symbol “/” are sandwiched between them. If it is determined that the total number of digits does not fit within 10 digits (step S14 (No)), it is not appropriate to display the numerical data that is the current calculation result in the fraction format, and The process proceeds to a conversion process (steps S16 to S32) of a polynomial including a square root symbol (√) which is a mathematical expression type into a mathematical expression “(a + b√c) / d”.

  In the conversion process to the mathematical expression “(a + b√c) / d”, first, the four variables a, b, c, d stored in the variable a memory 14j to the variable d memory 14m in the RAM 14 are sequentially set to “1”. It is set, and “1” is assigned to each of the four variables a, b, c, d constituting the mathematical expression (steps S16 to S19).

  Then, the equation “(a + b√c) / d” is calculated in a state where “1” is assigned to all the four variables a, b, c, d (step S20). It is determined whether or not the value matches the converted value (step S21).

  Here, when it is determined that the value of the calculation result of the mathematical expression “(a + b√c) / d” corresponding to the four variable substitution values (a to d = 1) this time does not match the converted value, The substitution values of the variables a, b, c, and d are sequentially changed and set for all combinations within a preset range of good number of lines (for example, one digit (range 1 to 9): n = 9). (Steps S23 to S30) Each time the variable substitution value change setting is made, it is determined whether or not the value of the calculation result of the formula “(a + b√c) / d” matches the converted value (Steps S20 and S21). .

  Then, the value of the calculation result of the formula “(a + b√c) / d” and the converted value when a certain value in the predetermined range (1 to 9) is substituted into the four variables a, b, c, d. Is determined to match (step S21 (Yes)), the formula “(a + b√c) / d” into which the substitution values of the variables a, b, c, d at that time are substituted is the answer. Is stored in the second conversion data memory 14g (step S32), and a minus sign “−” (if any) saved in the sign saving memory 14d is added and displayed on the display unit 16 (step S55). ).

  As a result, when the numerical data that is the calculation result is converted as a converted numerical value into a polynomial expression “(a + b√c) / d” including a square root symbol (√), each variable value (a, b) in the expression is converted. , C, d) are in the range of numbers with good visibility in advance (for example, 1 digit (range of 1 to 9)), and match the converted numerical value, each variable value (a, b, c) , D) is substituted and the conversion formula “(a + b√c) / d” is displayed as the answer to the calculation result, so that the numerical data including decimals is displayed as a simple array of real values as the calculation result of an arbitrary arithmetic expression. Instead, it can be displayed as a polynomial expression “(a + b√c) / d” including a square root symbol (√) in which each variable is stored as a good number of digits.

Specifically, as shown in FIG. 7 (B), for example, when the operation expression "(√3 + √2) ^2" formed by enter an expression including a square root sign (√) computed running, a significant digits 13 Numerical data “9.889974855566” of the calculation result as a digit is calculated. Then, when the numerical data obtained as a result of the conversion is converted into a converted numerical value into a polynomial expression “(a + b√c) / d” including a square root symbol (√), the variables a, b, c, and d all have one digit. The value “9.8897944855566” in which the mathematical expression “5 + 2√6” (= (5 + 2√6) / 1) when a = 5, b = 2, c = 6, and d = 1, which are within the same range, is matched in the same 13 digits. Therefore, a polynomial expression “5 + 2√6” including a square root symbol (√) that has a good visibility even at the middle and high school level is displayed on the display unit 16 as an answer.

  In addition, the display of the answer by the mathematical expression “(a + b√c) / d” on the display unit 16 is not limited to, for example, the form of “(a + b√c) / d” as it is in a single row display, A multi-level display format according to a textbook with the denominator part d at the bottom and the fractional symbol at the middle is also possible.

  On the other hand, all combinations of the substituted values of the four variables a, b, c, and d are within a preset range of good visibility (for example, one digit (range 1 to 9): n = 9). When it is determined that the value of any of the calculation results of the mathematical expression “(a + b√c) / d” sequentially changed with respect to is not equal to the converted numerical value (step S29 (No)), It is not appropriate to display the numerical data as the calculation result of the input arithmetic expression in the form of a polynomial expression “(a + b√c) / d” including a square root symbol (√). The process proceeds to a conversion process (steps S33 to S52) to a formula for calculating the sum or difference “(a√b ± c√d) / e”.

  In the conversion process to the mathematical expression “(a√b ± c√d) / e”, first, five variables a, b, c, d, e stored in the variable a memory 14j to the variable e memory 14n in the RAM 14 are stored. Are sequentially set to “1”, and “1” is substituted for all of the five variables a, b, c, d, and e constituting the mathematical expression (steps S33 to S37).

  Then, the mathematical expression “(a√b ± c√d) / e” is calculated in a state where “1” is assigned to all the five variables a, b, c, d, and e (step S38). It is determined whether or not the value of the calculation result of this mathematical formula matches the converted numerical value (step S39).

  Here, it is determined that the value of the calculation result of the mathematical expression “(a√b ± c√d) / e” corresponding to the five variable substitution values (a to e = 1) this time does not match the converted value. In this case, the substitution values of the variables a, b, c, d, and e are all within a preset range of good number of lines (for example, one digit (range 1 to 9): n = 9). The combinations are sequentially changed and set (steps S41 to S50), and the value of the calculation result of the formula “(a√b ± c√d) / e” matches the converted numerical value each time the variable substitution value change setting is made. Is determined (steps S38 and S39).

  Then, the calculation result of the formula “(a√b ± c√d) / e” when a certain value within a predetermined range (1 to 9) is assigned to the five variables a, b, c, d, and e. When it is determined that the converted value and the converted numerical value match (step S39 (Yes)), the mathematical expression “(a√) in which the substituted values of the variables a, b, c, d, e at that time are substituted. b ± c√d) / e ”is the answer and stored in the third conversion data memory 14h (step S52), and a minus sign“ − ”(if present) saved in the code saving memory 14d is added. And displayed on the display unit 16 (step S55).

  As a result, when the numerical data as the calculation result is converted as a converted numerical value into a calculation formula “(a√b ± c√d) / e” of the sum of square roots, each variable value (a , B, c, d, e) in the state where the numbers are within the range of digits with good visibility in advance (for example, one digit (range of 1 to 9)), the variable values (a , B, c, d, e), the conversion formula “(a√b ± c√d) / e” is displayed as the answer to the calculation result, so that the numerical data including decimals as the calculation result of an arbitrary arithmetic expression Can be displayed as a formula ((a√b ± c√d) / e) of the sum or difference of the square roots in which each variable is stored as a good number of digits. Become.

  Specifically, as shown in FIG. 7C, for example, when an arithmetic expression “2 ÷ (√5 + √3)” including a square root symbol (√) is input and the arithmetic operation is executed, 13 decimal places are obtained. Numerical data “0.5040171699309” as a calculation result with the digit being an effective digit is calculated. Then, when the numerical data obtained as a result of the conversion is converted into the converted numerical value into the formula “(a√b ± c√d) / e” for the sum or difference of square roots, the variables a, b, c, d, and e In any case, the numerical formula “√5−√3” (= (1√5−1√3) // when a = 1, b = 5, c = 1, d = 3, and e = 1 fit in one digit. Since 1) is obtained as a value “0.5040171699309” that matches with 13 digits after the decimal point, the formula “√5-√3” for calculating the sum or difference of square roots with good visibility even in the middle and high school level is the answer. It is displayed on the display unit 16.

  Note that the display of the answer by the mathematical expression “(a√b ± c√d) / e” on the display unit 16 is not limited to, for example, “(a√b ± c√d) / e” as it is in a single-line display form. The display may be a multi-level display format according to a textbook in which the numerator part a√b ± c√d is the upper stage, the denominator part e is the lower stage, and the fractional symbol is the middle stage.

  On the other hand, the substitution values of the five variables a, b, c, d, e are all set within a preset range of good number of lines (for example, one digit (range of 1 to 9): n = 9). If it is determined that the value of any of the calculation results of the mathematical expression “(a√b ± c√d) / e”, which is sequentially changed with respect to the combination, is not equal to the converted numerical value (step S49 ( No)), it is not appropriate to display the numerical data that is the calculation result of the current input arithmetic expression in the form of the calculation formula “(a√b ± c√d) / e” of the sum or difference of square roots. The process shifts to a conversion process (steps S53 and S54) to the next mathematical expression type π fractional expression “(a / b) π”.

In the conversion process to the π fractional expression “(a / b) π”, it is first determined whether or not the value obtained by dividing the converted numerical value by π and multiplying by 25200 is an integer (step S53).

Then, the to be converted numerical divided by [pi, if the value obtained by multiplying the 25200 is determined to an integer (step S53 (Yes)), based on the integer that is the calculation result, the answer is [pi (integer / 25200) Is stored in the fourth conversion data memory 14i (step S54), and a minus sign “−” (if any) saved in the sign saving memory 14d is added and displayed on the display unit 16 (step S54). S55).

Here, the basis for answering (integer / 25200) π “= (a / b) π” based on an integer obtained by dividing the converted numerical value by π and multiplying by 25200 will be described.

That is, a value expected as the denominator b so as to have a good π fraction when the converted numerical value, which is the calculation result of the input arithmetic expression, is converted into the form of a π fraction of (a / b) π. Is limited to divisors of 1 , 2, to, 9, 360 (considering up to 0.5 degree) and divisors of 400 (considering up to 0.5 grad), taking these least common multiples 25200, If the value divided by π and multiplied by 25200 becomes an integer, it is determined that conversion is possible as π fraction.

Specifically, as shown in FIG. 7D, for example, an inverse trigonometric function expression “2 × tan ⁻¹ (1/3) + tan ⁻¹ (1/7)” in the RAD (radian) mode. When the calculation is executed by inputting “”, numerical data “0.7853981633974” as a result of calculation with 13 decimal places as effective digits is calculated. Then, when the numerical data of the calculation result is converted into a π fractional expression “(a / b) π” as a converted value, the π fractional expression “π / 4” in which the denominator b is within one digit (1 to 9). ”(= (1/4) π) is obtained as a value“ 0.7853981633974 ”that coincides with 13 digits after the decimal point, so that the π-particulate formula“ π / 4 ”with a good outlook even in such a middle and high school level is the answer Is displayed on the display unit 16.

  It should be noted that the display of the answer by the π-fractional expression “(a / b) π” on the display unit 16 is not limited to a single-line display form of “(a / b) π”, for example, as shown in FIG. In addition, it is possible to adopt a multi-level display format according to a textbook with the numerator part a being the upper stage, the denominator part b being the lower stage, the fractional symbol, and π being the middle stage.

  As described above, when the numerical data as the calculation result is converted into the π fractional expression “(a / b) π” as the converted value, the denominator (b) in the fractional expression has a good number of digits in advance. If it matches the converted value in a state that falls within the range (for example, one digit (range 1 to 9)), the π fractional expression “(a / b) π” based on this denominator (b) is calculated. Therefore, numerical data including decimal numbers is not displayed as a simple list of real values as a result of calculation of an arbitrary arithmetic expression, but a π-fractional expression “(a / B) π ”and can be displayed.

On the other hand, if it is determined that the value obtained by dividing the converted numerical value by π and multiplying by 25200 does not become an integer (step S53 (No)), the numerical data that is the calculation result of the current input arithmetic expression is expressed in a fractional format. , Or a polynomial expression “(a + b√c) / d” including a square root symbol (√), or a calculation expression “(a√b ± c√d) / e” of a square root, or a π fraction “( a / b) π ”is not suitable for display, and a minus sign“ − ”saved and held in the sign saving memory 14d as it is with respect to a converted numeric value including a decimal value is included. Attached (if present) is displayed on the display unit 16 as an answer (step S56).

  Therefore, according to the calculation display control function of the electronic computer having the above-described configuration, first, when the numerical data as the calculation result is converted into a fraction as a converted numerical value, the total number of digits for the display is previously estimated. If the converted value matches the converted value within the range of the number of digits set as a good maximum number of digits (for example, within 10 digits), the converted fraction is displayed as the answer to the calculation result. When the converted numerical value is converted into a polynomial expression “(a + b√c) / d” including a square root symbol (√), each variable value (a, b, c, d) in the expression has a good visibility in advance. When the value to be converted matches within a numerical range (for example, one digit (range 1 to 9)), the conversion formula “(a + b) into which each variable value (a, b, c, d) is substituted. √c) / d ”is displayed as the answer to the calculation result. When a numerical value is converted into a formula for calculating the sum or difference of square roots “(a√b ± c√d) / e”, each variable value (a, b, c, d, e) in the formula is predicted in advance. When the converted numeric value matches the converted value within a good range of numbers (for example, one digit (range 1 to 9)), the variable values (a, b, c, d, e) are substituted. When the conversion formula “(a√b ± c√d) / e” is displayed as an answer to the calculation result, and fourth, when the converted numerical value is converted into a π-partial expression “(a / b) π”, If the denominator (b) in the fractional expression coincides with the converted numerical value in a state where the denominator (b) falls within the range of good number of digits (for example, one digit (range of 1 to 9)), this denominator (b ) Based on the π fractional expression “(a / b) π” is displayed as an answer to the calculation result, so that numerical data including a decimal number is simply a real value as a calculation result of an arbitrary arithmetic expression. Calculation of polynomial expression “(a + b√c) / d” or sum or difference of square roots including fractions (a / b) or square root symbols (√) that are not displayed as an enumeration but contained as a good number of digits. The expression “(a√b ± c√d) / e” or the π-fractional expression “(a / b) π” can be displayed.

  Therefore, for example, even in a junior and senior high school level education site, it is possible to display a solution with a good prospect converted into an optimal type of mathematical expression according to the calculation result.

  The methods described in the embodiment, that is, the calculation display control processes (part 1) to (part 4) shown in the flowcharts of FIGS. 3 to 6 are programs that can be executed by a computer. Store and distribute in an external recording medium 18 such as a memory card (ROM card, RAM card, etc.), magnetic disk (floppy (registered trademark) disk, hard disk, etc.), optical disk (CD-ROM, DVD, etc.), semiconductor memory, etc. Can do. Then, the computer reads the program recorded on the external recording medium 18 by the recording medium reading unit 17, and the operation is controlled by the read program, whereby the calculation process of the arbitrary input arithmetic expression described in the above embodiment is performed. It is possible to realize an answer display function in the form of an optimal type of mathematical formula and to execute the same processing by the method described above.

  Further, program data for realizing each of the above methods can be transmitted on a communication network (Internet) N as a program code form, and a computer terminal (program server) connected to the communication network (Internet) N ) The above-mentioned program data can be fetched from 20, and an answer display function in the form of an optimal type of mathematical expression in the calculation processing of the arbitrary input arithmetic expression described above can be realized.

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

  In other words, in the above-described embodiment, the calculation result of the arithmetic processing is used as a converted numerical value, and in each case, a fraction “a / b” within the range of digits with good numerical visibility, or a polynomial expression “( a + b√c) / d ”, or a formula for calculating the sum or difference of square roots“ (a√b ± c√d) / e ”, or a π-partial expression“ (a / b) π ”. Although the procedure of converting and displaying is used, the conversion order and combination of various mathematical formulas are not limited to this. For example, two formulas to a fraction “a / b” or a square root polynomial “(a + b√c) / d” are used. A conversion display function only for a mathematical expression form may be used, or a conversion process may be performed in the order of π-fractional expression → square root expression → fractional expression.

The block diagram which shows the structure of the electronic circuit of the electronic calculator concerning embodiment of this invention. The figure which shows the structure of the data memory with which RAM14 of the said electronic calculation apparatus is equipped. The flowchart which shows the calculation display control process (the 1) of the said electronic computer. The flowchart which shows the calculation display control process (the 2) of the said electronic computer. The flowchart which shows the calculation display control process (the 3) of the said electronic computer. The flowchart which shows the calculation display control process (the 4) of the said electronic computer. The figure which shows the display state of the input of the arithmetic expression accompanying the calculation display control process of the said electronic computer, and the answer.

Explanation of symbols

11: Control unit (CPU)
12 ... Key input part 12a ... Data input key 12b ... "Execution" key 12c ... "Calculation input" key 12d ... "Mode" key 12e ... Cursor key 13 ... ROM
14 ... RAM
14a ... Display data memory 14b ... Input data memory 14c ... Calculation result data memory 14d ... Sign save memory 14e ... Integer save memory 14f ... First conversion data [(a / b)] memory 14g ... Second conversion data [(a + b √c) / d] memory 14h: third conversion data [(a√b ± c√d) / e] memory 14i: fourth conversion data [(a / b) π] memory 14j-14n: variable a memory Variable e memory 14o Work memory 16 Liquid crystal display unit 17 Recording medium reading unit 18 External recording medium 19 Communication unit 20 Web server

Claims (3)

An expression input means for inputting an arithmetic expression;
Arithmetic means for performing arithmetic processing according to the arithmetic expression input by the expression input means;
A fractional expression conversion means for converting numerical data of a calculation result by the calculation means into a fractional expression;
Digit number judgment means for judging whether or not the fractional expression converted by the fractional expression conversion means falls within a predetermined number of digits;
A display control means for displaying a calculation result of the arithmetic expression in a display form of the converted fractional expression when it is determined by the digit number determining means that the converted fractional expression falls within a predetermined number of digits; ,
When it is determined that the converted fractional expression does not fit within a predetermined number of digits by the digit number determining means, it is converted into a numerical expression including √ or a fractional expression including π including the numerical data of the calculation result by the calculating means. Another form display control means to display,
An electronic computing device comprising: The another format display control means includes:
A determination means for determining whether the value obtained by dividing the numerical data of the calculation result by the calculation means by π and multiplying by 25200 is an integer;
Display control means for displaying (integer / 25200) π as a calculation result of a fractional expression including π when the determination means determines that it is an integer;
The electronic computer according to claim 1, further comprising: A calculation display processing program for controlling a computer of an electronic computing device,
The computer,
Arithmetic means for performing arithmetic processing according to the arithmetic expression input by the expression input means;
A fractional expression conversion means for converting numerical data of a calculation result by the calculation means into a fractional expression;
Digit number judgment means for judging whether or not the fractional expression converted by this fractional expression conversion means fits within a predetermined number of digits,
Display control means for displaying the calculation result of the arithmetic expression in the display form of the converted fractional expression when the converted fractional expression is determined to be within a predetermined number of digits by the digit number determining means;
When it is determined by the digit number determining means that the converted fractional expression does not fit in a predetermined number of digits, the numerical data of the calculation result by the calculating means is converted into a mathematical expression including √ or a fractional expression including π. Another form display control means to display,
A computer-readable calculation display processing program designed to function as a computer.

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