JP4218223B2 - Scientific calculator and program - Google Patents

Description

[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a scientific calculator including a differential operation means for obtaining a solution of an input differential equation or a simultaneous differential equation , and a program.
[0002]
[Prior art]
Conventionally, various functions have been provided in scientific calculators, pocket computers, and other electronic calculators. For example, a function for obtaining a solution of a differential equation or a simultaneous differential equation (hereinafter referred to as a “differential operation function”). Some have In an electronic calculation apparatus having this function, a differential equation is expressed by using a variable symbol with a subscript indicating a differential rank. A mathematical expression including such a variable symbol with a subscript is called a “graph expression”. For example, in the graph expression 3Y2-3Y1 + 1, “Y2” represents the second derivative of the variable Y, and “Y1” represents the first derivative of the variable Y.
[0003]
In addition to the function of obtaining a differential equation solution, a conventional scientific calculator is also provided with an electronic calculator that further includes a function of defining a composite function (hereinafter referred to as “composite function function”). . Also in this function, a variable symbol with a subscript is used to distinguish a symbol for defining a function from a general variable. For example, when a variable x ² +1 is pre-defined for the variable symbol Y 1 and a monomial 3x is pre-defined for the variable symbol Y 2, according to this function, the graph Y 1 (Y 2) can be expressed as Y 1 and Y 2. This is recognized as a mathematical function of (3x) ² +1.
[0004]
[Problems to be solved by the invention]
However, in the conventional electronic calculation device having both the differential operation function and the synthesis function function, there is a problem that the graph expression representing the differential equation and the graph expression representing the synthesis function are confused for the user. Specifically, for example, as shown in FIG. 6, when a graph expression Y1 (1-Y1) is input in the differential mode, the graph expression is the expression defined in advance for the variable symbol Y1 and the graph expression 1 Whether it is a composite function with -Y1 or the variable symbol Y1 represents the first derivative of the variable Y, it is not clear whether it is a differential equation representing the multiplication of the Y1 and (1-Y1).
[0005]
Therefore, even if the user intends to input a graph expression corresponding to a desired differential equation or simultaneous differential equation in the differential mode, the input graph expression is recognized as representing a composite function in the electronic calculator. As a result, the expected calculation result may not be obtained. In such a case, since an error is not displayed in the electronic calculator, the user may mistakenly recognize that the calculation result is correct.
[0006]
The present invention has been made in view of the above problems, and is an easy-to-use scientific calculator that can avoid recognizing that an equation input as a differential equation by a user is an equation representing a composite function, etc. And to provide a program.
[0007]
[Means for Solving the Problems]
The present invention is a scientific calculator having a differential calculation function and a synthesis function function, wherein a setting means for setting a mode for solving a differential equation, and a differential equation mode set by the setting means, with a numerical subscript An equation input means for inputting a differential equation representing the rank of the number according to a user operation, and whether a parenthesis symbol “(” is input immediately after a subscripted variable symbol included in the differential equation input by the equation input means. A multiplication symbol insertion means for inserting a multiplication symbol between the variable symbol and the parenthesis symbol “(”, and the multiplication symbol when it is determined that the parenthesis symbol “(” is input. And an expression display control means for displaying the differential equation in which the multiplication symbol is inserted by the inserting means.
[0036]
DETAILED DESCRIPTION OF THE INVENTION
FIG. 1 shows a block diagram of a scientific calculator 10 to which the present invention is applied. The scientific calculator 10 includes a central processing unit (CPU) 11, a random access memory (RAM) 12, a read only memory (ROM) 13, a display unit 15, a key input unit 14, and a bus that connects the components. It is configured. The scientific calculator 10 has a differentiation operation function, a synthesis function function, and the like as well as a conventional so-called scientific calculator, but is characterized in that a multiplication symbol insertion program 132 is stored in the ROM 13. Yes.
[0037]
The CPU 11 realizes the function as the scientific calculator 10 by uniformly controlling each component according to a procedure defined in the system program 131 and the like stored in the ROM 13. In particular, the CPU 11 further expands a multiplication symbol insertion program 132 stored in the ROM 13 in response to a press signal of the EXE key 145 in the work area 125 in the RAM 12, and performs a multiplication symbol insertion process (described later) based on the expanded program. 4).
[0038]
The RAM 12 has a first-order to higher-order differential equation or simultaneous differential equation (hereinafter referred to as “differential equation etc.”) input by the user temporarily stored therein. A differential equation storage area 122 for storing applied differential equations, an initial condition storage area 123 for storing initial conditions input by the user, a work area 125 for developing various programs read from the ROM 13, and the like. Although it does not, it has a function definition area for predefining functions for variable symbols.
[0039]
The ROM 13 stores a system program 131, a multiplication symbol insertion program 132, an application program 133, and the like.
The system program 131 is a program for causing the CPU 11 to realize the overall basic functions of the scientific calculator 10.
The multiplication symbol insertion program 132 is a program for causing the CPU 11 to realize multiplication symbol insertion processing.
[0040]
The application program 133 is a program for causing the CPU 11 to realize a function as a well-known so-called scientific calculator. For example, a differential operation program for obtaining a numerical solution such as a differential equation, a graph obtained by plotting the obtained numerical solution A graph drawing program for drawing a function, a synthesis function program for obtaining a synthesis function of functions defined in advance in variable symbols, or a function defined in advance and a specified monomial or polynomial.
[0041]
The key input unit 14 is a function key including an F1 key 141a, an F2 key 141b, an F3 key 141c, an F4 key 141d, an F5 key 141e, and an F6 key 141f, an alphabetic key 142 for inputting variable symbols, initial conditions, Numeric key 143 for inputting subscripts, four arithmetic symbol input key 144 for inputting four arithmetic symbols, EXE key (determining key) 145 for determining the input differential equation, etc. The function selection key 146 is used to specify various functions, and a pressing signal corresponding to the key pressed by the user is output to the CPU 11.
[0042]
The display unit 15 is configured by a liquid crystal display (LCD) and displays various designated menu screens, graphs, and the like under the control of the CPU 11.
[0043]
Hereinafter, the operation of the scientific calculator 10 will be described. FIG. 2 shows a flowchart for explaining the overall operation of the scientific calculator 10 in the differential calculation function, and FIG. 3 shows a display mode of the display unit 15 in the differential calculation function. First, when the CPU 11 detects that the differential calculation function is selected based on the pressing signal of the function selection key 146, the CPU 11 displays the differential equation top menu 31 (see FIG. 3) on the display unit 15 (step S20).
[0044]
In this state, when the CPU 11 detects the pressing signal of the F1 key 141a, the CPU 11 shifts to a mode for solving the first-order differential equation (1st Order Equation) (step S21), and when detecting the pressing signal of the F2 key 141b, the second-order differential. The mode shifts to the mode for solving the equation (2nd Order Lin Eq) (step S22). When the pressing signal of the F3 key 141c is detected, the mode shifts to the mode for solving the higher order differential equation (Nst Order Equation) (step S23), and the F4 key 141d. When a press signal is detected, the mode shifts to a mode for solving simultaneous differential equations (1st Order System) (step S24), and when a press signal of the F5 key is detected, the mode returns to the current mode (the last set mode) (step S25). .
[0045]
Here, since the processing in each of these modes is substantially the same, a mode for solving a higher-order differential equation (Nst Order Equation) and a mode for solving simultaneous differential equations (1st Order System) will be particularly described.
[0046]
First, a mode for solving higher-order differential equations will be described.
When the CPU 11 detects a pressing signal of the F3 key 141c and shifts to a mode for solving a higher-order differential equation (Nst Order Equation), it waits for the user to set a graph output list (step S231). When the CPU 11 detects that the graph output list has been set based on the pressing signal of the F3 key 141c, the higher order menu screen 32 for inputting the higher order differential equations and the initial conditions of the differential equations (see FIG. 3). Is displayed on the display unit 15. The user inputs a desired higher-order differential equation and initial conditions on the higher-order menu screen 32 (step S232).
[0047]
In this process, the CPU 11 stores the input differential equation in the input buffer area 121 in the RAM 12, and stores the input initial condition in the initial condition storage area 123 (step S233).
However, when the CPU 11 detects a press signal of the F2 key 141b in this state, the CPU 11 rewrites the differential equation stored in the input buffer area 121 into a simultaneous differential equation (step S234). Then, the CPU 11 switches from the mode for solving the higher order differential equations to the mode for solving the simultaneous differential equations, and changes the higher order menu screen 32 displayed on the display unit 15 to the simultaneous menu screen 35 to be described later. The simultaneous differential equation is displayed on 35. Next, the process proceeds to step S243 described later.
[0048]
Specifically, on the higher-order menu screen 32 shown in FIG. 3, a differential equation (graph equation) y (3) = Y1 (1−Y1) is input by the user, and the differential equation is stored in the input buffer area 121. However, at this stage, the graph expression is a composite function of the expression defined in advance in the variable symbol Y1 and the graph expression 1-Y1, or the variable symbol Y1 is the variable Y. It represents the first derivative, and it is not clear whether the differential equation represents the multiplication of Y1 and (1-Y1).
[0049]
Next, when the CPU 11 detects a press signal of the EXE key 145, the CPU 11 executes a multiplication symbol insertion process, which will be described later, so that “x” as a multiplication symbol is set between Y1 and (1-Y1) in the input buffer 121. insert. Then, the CPU 11 stores the differential equation after the multiplication symbol is inserted in the differential equation storage area 122 and redisplays the differential equation on the display unit 15 (step S236). Thereby, the higher floor menu screen 32 of the display unit 15 is changed to the higher floor menu screen 33. On the higher-order menu screen 33 after the transition, a multiplication symbol “x” 331 is inserted between Y1 and (1-Y1) and displayed.
[0050]
Next, when detecting the depression signal of the F6 key 141c, the CPU 11 performs numerical solution of the differential equation in the differential equation storage area 121 for the initial condition in the initial condition storage area 123 based on the execution of the calculation routine of the differential calculation program. (Step S237), and the obtained numerical solution is temporarily stored in the work area 125.
[0051]
Next, the CPU 11 displays the graph / output list screen 34 (see FIG. 3) on the display unit 15 by drawing the numerical solution temporarily stored in the work area 125 based on the execution of the graph drawing program (step S238). .
Next, the CPU 11 displays the differential equation top menu screen 31 on the display unit 15 again. Thereby, the process returns to step S20 again. When the CPU 11 detects a press signal of the F5 key 141e in the state returning to step S20, the CPU 11 proceeds to a mode for solving a higher-order differential equation that is the current mode, that is, step S23.
[0052]
Next, a mode for solving simultaneous differential equations will be described.
When the CPU 11 detects the pressing signal of the F4 key 141d and shifts to the mode for solving the simultaneous differential equations, it waits for the user to set the graph output list (step S241). When the CPU 11 detects that the graph output list is set based on the pressing signal of the F3 key 141c, the CPU 11 displays a simultaneous menu screen 35 for inputting the simultaneous differential equations and the initial conditions of the simultaneous differential equations on the display unit 15. Display. The user inputs a desired simultaneous differential equation and initial conditions on the simultaneous menu screen 35 (step S242).
[0053]
Next, the CPU 11 stores the simultaneous differential equation rewritten from the higher-order differential equation in step S234 or the simultaneous differential equation input by the user in step S242 in the input buffer area 121 in the RAM 12, and the initial condition to be input is initialized. Store in the condition storage area 123 (step S243).
[0054]
In the simultaneous menu screen 35 shown in FIG. 3, the differential equation input in step S233 is rewritten into two simultaneous differential equations (graph equations) y1 ′ = Y2 and y2 ″ = Y2 (1-Y2). , It is assumed that each differential equation is stored in the input buffer area 121. At this stage, the latter graph equation is expressed in advance by a variable symbol Y2 and a graph equation 1-Y2. Or the variable symbol Y2 represents the second derivative of the variable Y, and it is not clear whether it is a differential equation representing the multiplication of Y2 and (1-Y2).
[0055]
Next, when the CPU 11 detects a press signal of the EXE key 145, the CPU 11 executes a multiplication symbol insertion process to be described later, thereby setting “x” as a multiplication symbol between Y2 and (1-Y2) in the input buffer 121. insert. Then, the CPU 11 stores the differential equation after the multiplication symbol is inserted in the differential equation storage area 122 and redisplays the differential equation on the display unit 15 (step S245). As a result, the simultaneous menu screen 35 of the display unit 15 transitions to the simultaneous menu screen 36. In the simultaneous menu screen 36 after the transition, a multiplication symbol 361 is inserted between Y2 and (1-Y2).
[0056]
Next, when the CPU 11 detects the pressing signal of the F6 key 141c, the numerical value of the simultaneous differential equation in the differential equation storage area 121 is determined for the initial condition in the initial condition storage area 123 based on the execution of the calculation routine of the differential calculation program. A solution is obtained (step S246), and the obtained numerical solution is temporarily stored in the work area 125.
[0057]
Next, the CPU 11 displays the graph / output list screen 37 on the display unit 15 by drawing the numerical solution temporarily stored in the work area 125 based on the execution of the graph drawing program (step S247).
Next, the CPU 11 displays the differential equation top menu screen 31 on the display unit 15 again. Thereby, the process returns to step S20 again. When the CPU 11 detects a press signal of the F5 key 141e in the state returned to step S20, the CPU 11 proceeds to a mode for solving simultaneous differential equations, which is the current mode, that is, step S241.
[0058]
Hereinafter, the multiplication symbol insertion process will be described with reference to the flowchart shown in FIG. First, the CPU 11 refers to the differential equation or the like stored in the input buffer area 121 of the RAM 12 one character at a time, and immediately after the variable symbol Yn (n represents a subscript), a symbol “(” indicating a parenthesis is adjacent. When a location (address) is searched (step S41), and a location adjacent to the symbol “(” representing parentheses immediately after the variable symbol Yn is detected (step S41; YES), a multiplication symbol is added to the location. “X” is inserted (step S42).
[0059]
Next, the CPU 11 stores a character string such as a differential equation in which a multiplication symbol is inserted at the detected location in the input buffer area in the differential equation storage area 122 (step S43). Thereby, when the CPU 11 reads the differential equation or the like again, it can be recognized that the variable symbol Yn is a variable multiplied by a polynomial or a monomial expression enclosed in parentheses.
[0060]
On the other hand, when there is no portion where the symbol “(” adjacent to the variable symbol Yn is adjacent (step S41; NO), the character string such as the differential equation stored in the input buffer area 121 is directly used as the differential equation. Save in the storage area (step S43).
[0061]
Next, the CPU 11 reads the differential equation and the like stored in the differential equation storage area 122 and performs control to redisplay it on the display unit 15 (step S44). As a result, the display unit 15 displays a differential equation or the like in which a multiplication symbol “x” is inserted at a location adjacent to the variable symbol Yn immediately after the symbol “(” representing a parenthesis.
[0062]
According to the scientific calculator described above, the following effects can be obtained.
(1) In the differential equation or the like input by the user, when the CPU 11 finds a location (address) adjacent to the symbol “(” representing the parenthesis immediately after the variable symbol Yn, the variable symbol Yn is This is a case where a function is defined in advance in the RAM 12 for the variable symbol Yn because the numerical solution of the input expression is obtained by recognizing that it is a variable multiplied by the polynomial or monomial expression enclosed in In addition, it is possible to avoid that an expression input by the user as a differential equation or a simultaneous differential equation is recognized as a composite function or the like and is calculated.
[0063]
(2) In the differential equation or the like input by the user, when the CPU 11 finds a location (address) adjacent to the symbol “(” indicating the parenthesis immediately after the variable symbol Yn, the multiplication symbol “ Since “” is inserted and the differential equation or the like after the multiplication symbol is inserted is redisplayed on the display unit 15, the user can add a polynomial in which the variable symbol Yn in the formula entered by the user is enclosed in parentheses by the scientific calculator or You can know that it is recognized as a variable that can be multiplied by a monomial.
[0064]
The preferred embodiment of the present invention has been described above, but the technical idea of the present invention is not limited to this. For example, in the multiplication symbol insertion process, the multiplication symbol “x” is inserted in the adjacent part of the variable symbol Yn and the symbol “(” indicating the parenthesis. However, as shown in FIG. By inserting, it may be expressed that the variable is multiplied by the variable symbol Yn.
[0065]
In this case, when the parenthesis is inserted, if it becomes a double parenthesis like “((Yn))”, the insertion of the parenthesis is avoided, and the variable symbol Yn is assigned to the composite function. You may make it recognize that it is.
In addition, the detailed configuration and operation of the scientific calculator 10 can be changed as appropriate without departing from the spirit of the present invention.
In this embodiment, the case where the present invention is applied to a scientific calculator is described as an example. However, the present invention is not limited to a scientific calculator, and various electronic devices such as a pocket computer and other electronic calculators or personal computers are described. You may make it apply to an apparatus.
[0066]
【The invention's effect】
According to the present invention, in a differential equation mode, when a differential equation representing a differential rank with a numerical subscript is input according to a user operation, immediately after a subscripted variable symbol included in the input differential equation. It is determined whether or not the parenthesis symbol “(” is input. When it is determined that the parenthesis symbol “(” is input, a multiplication symbol is inserted between the variable symbol and the parenthesis symbol “(”. Therefore, even if a function is defined in advance for the variable symbol, the expression entered by the user as a differential equation or a simultaneous differential equation is recognized as representing a composite function, etc. Can be avoided.
[Brief description of the drawings]
FIG. 1 is a block diagram showing an internal configuration of a scientific calculator according to an embodiment.
2 is a flowchart showing an overall operation in a differential operation function of the scientific calculator shown in FIG.
FIG. 3 is a diagram schematically showing a display mode in the differential operation function of the scientific calculator shown in FIG. 1;
4 is a flowchart for explaining multiplication symbol insertion processing in the scientific calculator shown in FIG. 1. FIG.
FIG. 5 is a diagram for explaining a modified example of multiplication symbol insertion processing;
FIG. 6 is a diagram showing a display mode of a scientific calculator in the prior art.
[Explanation of symbols]
10. Scientific calculator (equation processor)
11 CPU (calculation symbol insertion means, formula display control means, solution display control means)
14 Input section (input means)
132 Multiplication Symbol Insertion Program

Claims (5)

A scientific calculator having a differential operation function and a synthesis function function,
  Setting means for setting a mode for solving the differential equation;
In the differential equation mode set by the setting unit, an equation input unit that inputs a differential equation representing a differential rank with a numerical subscript according to a user operation;
It is determined whether or not the parenthesis symbol “(” is input immediately after the subscripted variable symbol included in the differential equation input by this equation input means, and it is determined that the parenthesis symbol “(” is input. A multiplication symbol insertion means for inserting a multiplication symbol between the variable symbol and the parenthesis symbol "(";
  Expression display control means for displaying the differential equation in which the multiplication symbol is inserted by the multiplication symbol insertion means;
A scientific calculator characterized by comprising. The multiplication symbol insertion means determines whether a parenthesis symbol “(” is input immediately after the subscripted variable symbol in response to the EXE key being operated after the differential equation is input by the equation input means. The scientific calculator according to claim 1, wherein a multiplication symbol is inserted. The scientific calculator according to claim 2, wherein the differential equation is a higher-order differential equation. The scientific calculator according to claim 2, wherein the differential equation is a simultaneous differential equation. A computer operating as a scientific calculator having a differential operation function and a composite function function,
  Setting means for setting the mode for solving the differential equation;
In the differential equation mode set by the setting unit, an equation input unit that inputs a differential equation representing a differential rank by a numerical subscript according to a user operation;
It is determined whether or not the parenthesis symbol “(” is input immediately after the subscripted variable symbol included in the differential equation input by this equation input means, and it is determined that the parenthesis symbol “(” is input. A multiplication symbol insertion means for inserting a multiplication symbol between the variable symbol and the parenthesis symbol “(”,
  A program for functioning as an expression display control means for displaying a differential equation in which a multiplication symbol is inserted by the multiplication symbol insertion means.

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