Electronic computer and method of controlling the same

This application is based upon and claims the benefit of priority from prior Japanese Patent Application No. 2009-059670, filed Mar. 12, 2009, the entire contents of which are incorporated herein by reference.

1. Field of the Invention

The present invention relates to an electronic computer suitable for a graphical function calculator or the like and a method of controlling the same.

2. Description of the Related Art

Some of the known electronic computers, including scientific electronic calculators, are so-called graphical function calculators which display a graph corresponding to a function expression input by the user. When the user inputs a function expression by operating the input keys and then gives an instruction to draw a graph by operating a specific key, the graphical function calculator draws and displays a graph of the function on the orthogonal coordinate axes.

Some graphical function calculators have a trace function. The trace function is to move a pointer on the function graph according to the key operation and display the coordinate values of the position of the pointer on the graph at the time.

Concerning the graphical function calculator with a trace function, the technique for enabling two trace pointers to be displayed at the same time has been considered (e.g., Jpn. Pat. Appln. KOKAI Publication No. 2001-216273).

Conventional graphical function calculators are incapable of analyzing the relationship between two points on a graph. The same holds true for the technique disclosed in the above patent document. That is, the relationship between two points on a graph was incapable of being analyzed variously.

It is an object of the invention to provide an electronic computer capable of improving the function graph analysis capability by making various analyses of the relationship between two points on a graph and of helping the user gain a better understanding of a basic structure of the graph and a method of controlling the electronic computer.

According to one aspect of the present invention, there is provided an electronic computer comprising: a display unit; a graph display control unit that performs display control of a graph corresponding to a function expression on the display unit; a position specify unit that specifies a plurality of point positions on the graph displayed on the display unit according to a user operation; a pointer display control unit that performs display control of a pointer for each of the plurality of point positions on the display unit specified by the position specify unit; a calculation result display control unit that does a specific calculation on the basis of positional information on a plurality of pointers displayed on the display unit and the function expression of the graph and performs display control of a result of calculation on the display unit; and a pointer movement control unit that performs movement display control on the graph of an arbitrary one of the plurality of pointers displayed on the display unit according to a user operation, wherein the calculation result display control unit does the calculation again, updates the result of calculation, and performs display control of the updated result on the display unit each time the pointer movement control unit performs movement display control of a pointer.

The accompanying drawings, which are incorporated in and constitute a part of the specification, illustrate embodiments of the invention, and together with the general description given above and the detailed description of the embodiments given below, serve to explain the principles of the invention.

FIG. 1 is a block diagram showing the configuration of a functional circuit of a graphical function calculator, an electronic computer according to an embodiment of the invention;

FIG. 2 is a flowchart to explain the process of displaying a graph of a function expression according to the embodiment;

FIG. 3 is a flowchart to explain the process of displaying the graph of the function expression according to the embodiment;

FIG. 4 is a flowchart to explain a subroutine of inter-pointer calculation result display process 1 of FIG. 2 according to the embodiment;

FIG. 5 is a flowchart to explain a subroutine of inter-pointer calculation result display process 2 of FIG. 3 according to the embodiment;

FIG. 6 illustrates a transition state of the display screen in a slope calculation mode according to the embodiment;

FIG. 7 illustrates a transition state of the display screen in a maximum/minimum value calculation mode according to the embodiment;

FIG. 8 illustrates a transition state of the display screen in an integration calculation mode according to the embodiment;

FIG. 9 illustrates a transition state of the display screen in a maximum/minimum differential value calculation mode according to the embodiment;

FIG. 10 illustrates a transition state of the display screen in a continuity/discontinuity determination mode according to the embodiment;

FIG. 11 illustrates a transition state of the display screen in a local maximum/minimum value calculation mode according to the embodiment;

FIG. 12 illustrates a transition state of the display screen for the process of setting the distance-between-pointers in the slope calculation mode according to the embodiment; and

FIG. 13 illustrates a transition state of the display screen for the process of setting an analysis point in the slope calculation mode according to the embodiment.

Hereinafter, referring to the accompanying drawings, embodiments of the invention will be explained in detail.

As shown in FIG. 1 , a graphical function calculator 10 includes a processor 11 .

The processor 11 controls the operation of each part of the circuitry of the graphical function calculator 10 by use of a work storage area 17 (e.g., random access memory [RAM]) according to a system program previously stored in a storage area 12 (e.g., a flash memory), a computer control program read into the storage area 12 from an external storage medium 13 (e.g., a memory card) via a storage medium controller 14 , or a computer control program downloaded into the storage area 12 from a Web server (or a program server) 15 on a communication network N via a communication control unit 16 .

The system program or computer control program previously stored in the storage area 12 is activated in response to a key input signal from an input unit 18 .

Connected to the processor 11 are the storage area 12 , the storage medium controller 14 , the communication control unit 16 , the work storage area 17 , the input unit 18 , and a display unit 19 .

The storage area 12 stores a computer control program which supervises the entire operation of the graphical function calculator 10 , a mathematical operation program 12 a which performs arithmetic processing according to various function expressions arbitrarily input by the user, a graphing program 12 b which causes the display unit 19 to display various function expressions used by the mathematical operation program 12 a in the form of graphs, a multipoint trace program 12 c which is for displaying a plurality of pointers that move while tracing a function expression graph displayed on the display unit 19 , and a inter-points analysis program 12 d which is for making analyses by various calculations in each of the intervals sectionalized by the plurality of pointers.

The input unit 18 is provided with function keys 18 a which are operated to specify functions in various compute modes provided on the graphical function calculator 10 , alphanumeric keys 18 b which are operated to input various numbers, characters, and others used in function expressions, a confirmation key 18 c which is operated to specify the confirmation of input data or the execution of mathematical operations, cursor keys 18 d , “↑,” “↓,” “←,” “→,” which are operated to move and display cursor C or the input position of an item on the display screen or specify the movement of a pointer on the displayed graph, a touch panel 18 e composed of a transparent electrode layer integrally formed on the display unit 19 , and others.

As for a temporary effective function which is not set in the function keys 18 a , a function name to specify the execution of the function or a symbol or the like corresponding to the function name may be displayed on the display unit 19 in the form of a rectangular button. The function can be executed by pressing the display position of the button on the touch panel 18 e.

The display unit 19 is composed of, for example, a Liquid Crystal Display (LCD) that provides a dot-matrix display with a backlight. The display unit 19 displays an input function expression, a graph of the function expression with the orthogonal coordinate axes, and a plurality of pointers on the graph.

Next, the operation of the embodiment will be explained.

In the embodiment, explanation will be given about a case where any one of “the slope calculation mode,” “the maximum/minimum value calculation mode,” “the integration calculation mode,” “the maximum/minimum differential value calculation mode,” “the continuity/discontinuity determination mode,” and “the local maximum/minimum value calculation mode” is selected for the function displayed in graphical form and calculations are done between a plurality of points.

FIGS. 2 and 3 are flowcharts to mainly explain the process of displaying a graph when a function expression is input. A detailed explanation of the processes not directly related to the embodiment will not be given, provided that other suitable processes are performed.

First, it is determined whether a key operation has been performed to specify graphing for the input function expression (step S 101 ).

If a key operation to specify a process other than graphing has been performed, an explanation of it will be omitted, provided another suitable operation is performed.

If it has been determined in step S 101 that a key operation to specify graphing has been performed, the graphing program 12 b causes the display unit 19 to draw and display a graph under graphing conditions set at the time (step S 102 ). The graphing conditions are such that, for example, an x-coordinate binary value representing a range of the graph on the x-axis and a y-coordinate binary value representing a range of the graph on the y-axis are input and set in advance.

After it has been determined that an analysis point for analyzing the vicinity of a specific point on the graph have not been set (step S 103 ), it is determined whether an operation to add a first trace pointer which moves on the graph has been performed (step S 104 ).

If an operation other than the operation of setting the addition of a trace pointer has been performed, an explanation of it will be omitted, provided another suitable operation is performed.

If it has been determined in step S 104 that an operation to add the first trace pointer has been performed, the multipoint trace program 12 c causes the display unit 19 to display not only the first trace pointer at a point on the graph, such as a position corresponding to the midpoint of the x-coordinate in the display range, but also the x-coordinate value and the y-coordinate value of the position (step S 105 ).

Thereafter, it is further determined whether an operation to add a second trace pointer which moves over the graph has been performed (step S 106 ).

If an operation other than the operation of setting the addition of a trace pointer has been performed, an explanation of it will be omitted, provided another suitable operation is performed.

On the other hand, if it has been determined in step S 106 that an operation to add the second trace pointer has been performed, the multipoint trace program 12 c displays not only the second trace pointer at a point on the graph on the display unit 19 , for example, at a position shifted one graduation from the first trace pointer in the positive direction of the x-axis, but also the x- and y-coordinate values of the position (step S 107 ).

Since the two trace pointers have been positioned on the graph on the display unit 19 , a first process is performed (step S 108 ). In the first process, the inter-points analysis program 12 d carries out an operation between two points in the preset calculation mode and the result of the calculation is displayed together with the graph.

The details of the inter-pointer calculation result display process 1 will be described later.

In a state where the result of calculation is displayed, it is further determined whether operations to add a third and later trace pointers have been performed (step S 109 ).

If it has been determined that operations to add a third and later trace pointers have been performed, control returns to step S 107 and the multipoint trace program 12 c causes the display unit 19 to display not only the trace pointer at one other point on the graph but also the x- and y-coordinate values of the one other point.

Then, the inter-points analysis program 12 d performs a first process in response to the added trace pointer (step S 108 ). In the first process, the inter-points analysis program 12 d carries out an operation between the third and later pointers in the preset calculation mode and displays the result of calculation together with the graph.

In this way, each time one of the third and later trace pointers is added, the processes in steps S 109 , S 107 , and S 108 are performed repeatedly and the result of the distance-between-pointers calculations on the basis of the added trace pointer are displayed sequentially.

If it has been determined in step S 109 that an operation to add a trace pointer has not been performed any more, it is determined whether the distance between the trace pointers already input at the time is set (step S 110 ).

Here, if it has been determined that the distance between the trace pointers is not set, it is determined whether a key operation to specify the movement of any one of the plurality of trace pointers has been performed (step S 112 ).

If it has been determined that a key operation to specify the movement has not been performed, it is determined whether an operation to terminate the operation at the graphical function calculator 10 and shut down the power supply has been performed (step S 114 ).

If it has been determined that an operation to shut down the power supply has not been performed, control returns to the process in step S 112 . In this way, the processes in steps S 112 and S 114 are performed repeatedly, thereby waiting for either a key operation to specify the movement of a trace pointer or a key operation to terminate the operation and shut down the power supply to be performed.

Then, if a key operation to terminate the operation and shut down the power supply has been performed, it is determined in step S 114 that the key operation has been performed and the power supply is shut down as requested by the operation, which terminates the processes of FIGS. 2 and 3 .

If it has been determined in step S 112 that a key operation to specify the movement of a trace pointer has been performed, the multipoint trace program 12 c moves the specified trace pointer on the graph according to the operation of the cursor keys (“←” and “→” keys) 18 d on the input unit 18 and displays the x- and y-coordinate values after the movement of the pointer (step S 113 ).

Thereafter, control is passed to the processes in step S 108 and forward and a first process is carried out. In the first process, the inter-points analysis program 12 d carries out a new operation between trace pointers on the basis of the trace pointer moved on the graph and displays the result of calculation together with the graph.

Next, the first process in step S 108 in each calculation mode will be explained in detail.

In FIG. 4 , it is determined whether the calculation mode set at the time is the slope calculation mode in which a slope between points is calculated (step S 201 ).

If it has been determined that the slope calculation mode has been set, an increment in each of the x- and y-coordinates between two adjacent trace pointers and a slope between the two points are calculated (step S 202 ).

Then, the display unit 19 is caused to display the results of calculation together with the graph (step S 203 ), which terminates the subroutine and returns control to the main routine of FIG. 2 .

FIG. 6 shows an example of the transition of the screen on the display unit 19 when the slope calculation mode has been set. As shown in FIG. 6 (A), when the function expression “Y 1 =X 2 ” is input and then the confirmation key 18 c on the input unit 18 is operated, a graph corresponding to the function expression is displayed together with the function expression “Y=X 2 ” on the display unit 19 , as shown in FIG. 6 (B).

In the display state of FIG. 6 (B), when a trace pointer display operation is carried out, trace pointer P 1 for the first point is displayed in the position of the origin, the intersection of the x- and y-axes. At this time, the coordinate values of trace pointer P 1 are displayed as “(X 1 , Y 1 )=(0, 0)” together with the graph.

Here, when a trace pointer display operation is further carried out, trace pointer P 2 for a second point is displayed in a position shifted a specific distance, for example, only 2, from trace pointer P 1 in the positive direction of the x-axis, as shown in FIG. 6 (D). At this time, the coordinate values of trace pointer P 2 are displayed as “(X 2 , Y 2 )=(2, 4)” together with the graph.

With that, since the smallest plurality of trace pointers (or two trace pointers) have been specified, an increment of dX=2 in the x-direction, an increment of dY=4 in the y-direction, a slope of dY/dX=2, and a slope of dX/dY=0.5 are determined by calculations in step S 202 and the results of calculation are displayed together with the graph.

Here, as for the slope between two trace pointers, a slope of dY/dX with respect to an increment in the x-direction and a slope of dX/dY with respect to an increment in the y-direction are calculated. One of the two slopes is the reciprocal of the other unless both of the two slopes are not zero.

In the display state shown in FIG. 6 (D), with trace pointer P 2 selected by, for example, the cursor keys 18 d , the confirmation key 18 c is operated to determine the selection of trace pointer P 2 and then “←” key or “→” key in the cursor keys 18 d is operated to move trace pointer P 2 arbitrarily on the graph.

FIG. 6 (E) shows a state where trace pointer P 2 is moved to the coordinate position (4, 14) by operating, for example, “→” key in the cursor keys 18 d . In FIG. 6 (E), “(X 2 , Y 2 )=(4, 16)” is shown as the coordinate position. In addition, an increment of dX=4 in the x-coordinate, an increment of dY=16 in the y-coordinate, a slope of dY/dX=4, and a slope of dX/dY=0.25 are calculated and the results are displayed together with the graph.

As described above, each time an arbitrary trace pointer P is selected and moved, an increment in the x-coordinate, an increment in the y-coordinate, and a slope between trace pointers are updated and displayed.

In the state shown in FIG. 6 (E), trace pointers for the third and later points can be specified. For example, in a state where the third trace pointer (P 3 ) is displayed in a position greater in the x-direction than the coordinate position of trace pointer P 2 , an increment in the x-coordinate, an increment in the y-coordinate, and a slope between trace pointer P 1 and trace pointer P 2 , and an increment in the x-coordinate, an increment in the y-coordinate, and a slope between trace pointer P 2 and trace pointer P 3 are displayed as the results of calculation.

As described above, in the slope calculation mode, an increment in the x-coordinate and an increment in the y-coordinate between two trace pointers P 1 and P 2 and the slope between two points are calculated and the results of calculation are displayed together with the graph.

Accordingly, a slope liable to be visually misunderstood, depending on the setting of the display range, can be understood easily by displaying various numeric values together with the graph.

In addition, since the positions of two trace pointes can be easily changed and set by moving trace pointers, the way the slope is changed by the position setting of trace pointers can be understood easily.

In step S 201 of FIG. 4 , if it has been determined that the set calculation mode is not the slope calculation mode, it is determined whether the set calculation mode is the maximum/minimum value calculation mode in which the maximum and minimum values between points is found (step S 204 ).

If it has been determined that the maximum/minimum value calculation mode has been set, the maximum and minimum values which Y between two adjacent trace pointers can take are calculated (step S 205 ) and the results of calculation are displayed together with the graph on the display unit 19 (step S 203 ), which completes the subroutine and returns control to the main routine of FIG. 2 .

FIG. 7 shows an example of the transition of the screen on the display unit 19 when the maximum/minimum value calculation mode has been set. As shown in FIG. 7 (A), when the function expression “Y 1 =X 2 ” is input and then the confirmation key 18 c on the input unit 18 is operated, a graph corresponding to the function expression is displayed together with the function expression “Y=X 2 ” on the display unit 19 , as shown in FIG. 7 (B).

In the display state of FIG. 7 (B), when a trace pointer display operation is carried out, trace pointer P 1 for the first point is displayed in the position of the origin, the intersection of the x- and y-axes. At this time, the coordinate values of trace pointer P 1 are displayed as “(X 1 , Y 1 )=(0, 0)” together with the graph.

Here, when a trace pointer display operation is further carried out, trace pointer P 2 for the second point is displayed in a position shifted a specific distance, for example, only 2, from trace pointer P 1 in the positive direction of the x-axis, as shown in FIG. 7 (D). At this time, the coordinate values of trace pointer P 2 are displayed as “(X 2 , Y 2 )=(2, 4).”

With that, since the smallest plurality of trace pointers (or two trace pointers) have been specified, the following are calculated and displayed together with the graph:

f ( X )=4 [X= 2]  Maximum value MAX

f ( x )=0 [X= 0]  Minimum value MIN

At the same time, a y-coordinate range of “0≦Y≦4” between two trace pointers is displayed in the upper part of the y-axis and an x-coordinate range of “0≦X≦2” is displayed above the right end of the x-axis.

In the display state shown in FIG. 7 (D), with trace pointer P 1 selected by, for example, the cursor keys 18 d , the confirmation key 18 c is operated to determine the selection of trace pointer P 1 and then “←” key or “→” key in the cursor keys 18 d is operated to move trace pointer P 1 arbitrarily on the graph.

Similarly, with trace pointer SP 2 selected by the cursor keys 18 d , the confirmation key 18 c is operated to determine the selection of trace pointer P 2 and then “←” key or “→” key in the cursor keys 18 d is operated to move trace pointer P 2 arbitrarily on the graph.

FIG. 7 (E) shows a state where trace pointer P 1 is moved to the coordinate position (−2, 4) by operating, for example, “→” key in the cursor keys 18 d and trace pointer P 2 is moved to the coordinate position (5, 25) by operating “→” key in the cursor keys 18 d.

Here, the coordinate position is displayed as “(X 1 , Y 1 )=(−2, 4)” “(X 2 , Y 2 )=(5, 25).” At the same time, the following maximum and minimum values are calculated and displayed together with the graph:

f ( X )=25 [X= 5]  Maximum value MAX

f ( X )=0 [X= 0]  Minimum value MIN

As described above, each time an arbitrary trace pointer P is selected and moved, the maximum and minimum values which Y between trace pointers will possibly take are updated and displayed.

In the state shown in FIG. 7 (E), trace pointers for the third and later points can be specified. For example, in a state where trace pointer (P 3 ) for the third point is displayed in a position greater in the x-direction than the coordinate position of trace pointer P 2 , the maximum and minimum values between trace pointer P 1 and trace pointer P 2 and the maximum and minimum values between trace pointer P 2 and trace pointer P 3 are displayed as the results of calculation.

As described above, in the maximum/minimum value calculation mode, since the maximum and minimum values between two trace pointers are calculated and the results of calculation are displayed together with the graph, the range the graph will possibly take can be understood easily.

In step S 204 of FIG. 4 , if it has been determined that the set calculation mode is not the maximum/minimum value calculation mode, it is determined whether the set calculation mode is the integration calculation mode in which an integration value between points is found (step S 206 ).

If it has been determined that the integration calculation mode has been set, an integration value between two adjacent trace pointers is calculated (step S 207 ) and the result of calculation is displayed together with the graph on the display unit 19 (step S 203 ), which completes the subroutine and returns control to the main routine of FIG. 2 .

FIG. 8 shows an example of the transition of the screen on the display unit 19 when the integration calculation mode has been set. As shown in FIG. 8 (A), when the function expression “Y 1 =X 2 ” is input and then the confirmation key 18 c on the input unit 18 is operated, a graph corresponding to the function expression is displayed together with the function expression “Y=X 2 ” on the display unit 19 , as shown in FIG. 8 (B).

In the display state of FIG. 8 (B), when a trace pointer display operation is carried out, trace pointer P 1 for the first point is displayed in the position of the origin, the intersection of the x- and y-axes, as shown in FIG. 8 (C). At this time, the coordinate values of trace pointer P 1 are displayed as “(X 1 , Y 1 )=(0, 0)” together with the graph.

Here, when a trace pointer display operation is further carried out, trace pointer P 2 for the second point is displayed in a position shifted a specific distance, for example, only 2, from trace pointer P 1 in the positive direction of the x-axis, as shown in FIG. 8 (D). At this time, the coordinate values of trace pointer P 2 are displayed as (X 2 , Y 2 )=(2, 4)” together with the graph.

With that, since the smallest plurality of trace pointers (or two trace pointers) have been specified, the integral equation calculated in step S 207 is displayed together with the graph.

∫ 0 2 X 2 dx= 2.6666667

A numeric value of “2.6666667” expressed by the integral equation shows the area of the part sandwiched by the graph between the relevant trace pointers and the x-axis represented by Y=0.

In the display state shown in FIG. 8 (D), with trace pointer P 1 selected by, for example, the cursor keys 18 d , the confirmation key 18 c is operated to determine the selection of trace pointer P 1 and then “←” key or “→” key in the cursor keys 18 d is operated to move trace pointer P 1 arbitrarily on the graph.

Similarly, with trace pointer SP 2 selected by the cursor keys 18 d , the confirmation key 18 c is operated to determine the selection of trace pointer P 2 and then “←” key or “→” key in the cursor keys 18 d is operated to move trace pointer P 2 arbitrarily on the graph.

FIG. 8 (E) shows a state where trace pointer P 1 has been moved to the coordinate position (−2, 4) by operating, for example, “←” key in the cursor keys 18 d and trace pointer P 2 has been moved to the coordinate position (4, 16) by operating “→” key in the cursor keys 18 d.

Here, not only are the coordinate positions displayed as “(X 1 , Y 1 )=(−2, 4)” “(X 2 , Y 2 )=(4, 16)” together with the graph, but also the integration equation is displayed.

∫ −2 4 X 2 dx= 24

As described above, each time an arbitrary trace pointer P is selected and moved, the integration value between trace pointers is updated and displayed.

In the state shown in FIG. 8 (E), trace pointers for the third and later points can be specified. For example, in a state where trace pointer (P 3 ) for the third point is displayed in a position greater in the x-direction than the coordinate position of trace pointer P 2 , the integration value between trace pointer P 1 and trace pointer P 2 and the integration value between trace pointer P 2 and trace pointer P 3 are displayed as the results of calculation.

As described above, in the integration calculation mode, since an integration value between two adjacent trace pointers is calculated and the result of calculation is displayed together with the graph, an accurate area or length of the range displayed on the graph can be understood easily.

In step S 206 of FIG. 4 , if it has been determined that the set calculation mode is not the integration calculation mode, it is determined that the set calculation mode is the maximum/minimum differential value calculation mode in which the maximum and minimum differential values between points is found (step S 208 ).

If it has been determined that the maximum/minimum differential value calculation mode has been set, the maximum and minimum differential values between two adjacent trace pointers are calculated (step S 209 ) and the results of calculation are displayed together with the graph on the display unit 19 (step S 203 ), which completes the subroutine and returns control to the main routine of FIG. 2 .

FIG. 9 shows an example of the transition of the screen on the display unit 19 when the maximum/minimum differential value calculation mode has been set. As shown in FIG. 9 (A), when the function expression “Y 1 =sin X” is input and then the confirmation key 18 c on the input unit 18 is operated, a graph corresponding to the function expression is displayed together with the function expression “Y=sin X” on the display unit 19 , as shown in FIG. 9 (B).

In the display state of FIG. 9 (B), when a trace pointer display operation is carried out, trace pointer P 1 for the first point is displayed in the position of the origin, the intersection of the x- and y-axes. At this time, the coordinate values of trace pointer P 1 are displayed as “(X 1 , Y 1 )=(0, 0)” together with the graph.

Here, when a trace pointer display operation is further carried out, trace pointer P 2 for the second point is displayed in a position shifted a specific distance, for example, only 2, from trace pointer P 1 in the positive direction of the x-axis. At this time, the coordinate values of trace pointer P 2 are displayed as “(X 2 , Y 2 )=(2, 0.91).”

With that, since the smallest plurality of trace pointers (or two trace pointers) have been specified, the following are calculated in step S 209 and displayed together with the graph:

Maximum differential value=1[X=0]

Minimum differential value=−0.4161472 [X= 2]

In the display state shown in FIG. 9 (D), with trace pointer P 2 selected by, for example, the cursor keys 18 d , the confirmation key 18 c is operated to determine the selection of trace pointer P 2 and then “←” key or “→” key in the cursor keys 18 d is operated to move trace pointer P 2 arbitrarily on the graph.

FIG. 9 (E) shows a state where trace pointer P 2 is moved to the coordinate position (4, −0.77) by operating, for example, “→” key in the cursor keys 18 d.

Here, the coordinate positions are displayed as “(X 1 , Y 1 )=(0, 0)” “(X 2 , Y 2 )=(4, 0.77).” At the same time, the following maximum and minimum differential values are calculated and displayed together with the graph:

Maximum differential value=1[X=0]

Minimum differential value=−1 [X= 3.1415927]

As described above, each time an arbitrary trace pointer P is selected and moved, the integration value between trace pointers is updated and displayed.

In the state shown in FIG. 9 (E), trace pointers for the third and later points can be specified. For example, in a state where trace pointer (P 3 ) for the third point is displayed in a position greater in the x-direction than the coordinate position of trace pointer P 2 , the maximum and minimum differential values between trace pointer P 1 and trace pointer P 2 and the maximum and minimum differential values between trace pointer P 2 and trace pointer P 3 are displayed as the results of calculation.

As described above, in the maximum/minimum differential value calculation mode, since the maximum and minimum differential values between two trace pointers are calculated and the results of calculation are displayed together with the graph, the position with the largest slope and the position with the smallest slope can be known easily.

In step S 208 of FIG. 4 , if it has been determined that the set calculation mode is not the maximum/minimum differential value calculation mode, it is determined whether the set calculation mode is the continuity/discontinuity determination mode in which it is determined whether the graph is continuous or discontinuous between points is found (step S 210 ).

If it has been determined that the continuity/discontinuity determination mode has been set, it is determined whether the graph between two adjacent trace pointers is continuous or discontinuous (step S 211 ) and the determination result is displayed together with the graph on the display unit 19 (step S 203 ), which completes the subroutine and returns control to the main routine of FIG. 2 .

FIG. 10 shows an example of the transition of the screen on the display unit 19 when the continuity/discontinuity determination mode has been set. As shown in FIG. 10 (A), when the function expression “Y 1 =tan X” is input and then the confirmation key 18 c on the input unit 18 is operated, a graph corresponding to the function expression is displayed together with the function expression “Y=tan X” on the display unit 19 , as shown in FIG. 10 (B).

In the display state of FIG. 10 (B), when a trace pointer display operation is carried out, trace pointer P 1 for the first point is displayed in the position of the origin, the intersection of the x- and y-axes. At this time, the coordinate values of trace pointer P 1 are displayed as “(X 1 , Y 1 )=(0, 0)” together with the graph.

Here, when a trace pointer display operation is further carried out, trace pointer P 2 for the second point is displayed in a position shifted a specific distance, for example, only 2, from trace pointer P 1 in the positive direction of the x-axis. At this time, the coordinate values of trace pointer P 2 are displayed as “(X 2 , Y 2 )=(2, −2.185).”

With that, since the smallest plurality of trace pointers (or two trace pointers) have been specified, the determination result in step S 211 is displayed as “the interval between P 1 and P 2 is discontinuous” together with the graph.

In the display state shown in FIG. 10 (C), when a trace pointer display operation is further carried out, trace pointer P 3 for the third point is displayed in a position shifted a specific distance, for example, only 2, from trace pointer P 2 in the positive direction of the x-axis. At this time, the coordinate values of trace pointer P 3 are displayed as “(X 3 , Y 3 )=(4, 1.158).”

Since the trace pointers for a total of three points have been specified, the following determination results in step S 211 are displayed together with the graph:

“The interval between P 1 and P 2 is discontinuous and the interval between P 2 and P 3 is continuous”

In the display state shown in FIG. 10 (D), with trace pointer P 2 selected by, for example, the cursor keys 18 d , the confirmation key 18 c is operated to determine the selection of trace pointer P 2 and then “←” key or “→” key in the cursor keys 18 d is operated to move trace pointer P 2 arbitrarily on the graph.

FIG. 10 (E) shows a state where trace pointer P 2 has been moved to the coordinate position (1.2, 2.572).

Here, the coordinate positions are displayed as “(X 1 , Y 1 )=(0, 0)” “(X 2 , Y 2 )=(1.2, 2.572)” “(X 3 , Y 3 )=(4, 1.158). At the same time, the following determination results are displayed together with the graph:

“The interval between P 1 and P 2 is continuous and the interval between P 2 and P 3 is discontinuous”

As described above, each time an arbitrary trace pointer P is selected and moved, the result of determining whether the interval between trace pointers is continuous or discontinuous is updated and displayed.

In the state shown in FIG. 10 (E), trace pointers for the fourth and later points can be specified. For example, in a state where trace pointer (P 4 ) for the fourth point is displayed in a position greater in the x-direction than the coordinate position of trace pointer P 3 , the result of determining whether the interval between trace pointer P 1 and trace pointer P 2 is continuous or discontinuous, the result of determining whether the interval between trace pointer P 2 and trace pointer P 3 is continuous and discontinuous, and the result of determining whether the interval between trace pointer P 3 and trace pointer P 4 is continuous and discontinuous are displayed as the results of calculation.

As described above, in the continuity/discontinuity determination mode, since whether the graph is continuous or discontinuous between two trace pointers with an analysis point at midpoint between the pointers is determined and the determination result is displayed together with the graph, whether the graph is continuous or discontinuous between trace pointers near the analysis point can be easily understood.

In step S 210 of FIG. 4 , if it has been determined that the set calculation mode is not the continuity/discontinuity determination mode, it is determined whether the set calculation mode is the local maximum/minimum value calculation mode in which a local maximum value and a local minimum value between points are found (step S 212 ).

If it has been determined that a calculation mode other than the local maximum/minimum value calculation mode has been set, an explanation of it will be omitted, provided that another suitable operation is performed.

If it has been determined in step S 212 that the local maximum/minimum value calculation mode has been set, a local maximum value and a local minimum value between two adjacent trace pointers are calculated (step S 213 ) and the results of calculation are displayed together with the graph on the display unit 19 (step S 203 ), which completes the subroutine and returns control to the main routine of FIG. 2 .

FIG. 11 shows an example of the transition of the screen on the display unit 19 when the local maximum/minimum value calculation mode has been set. As shown in FIG. 11 (A), when the function expression “Y 1 =X 3 −2X” is input and then the confirmation key 18 c on the input unit 18 is operated, a graph corresponding to the function expression is displayed together with the function expression “Y=X 3 −2X” on the display unit 19 , as shown in FIG. 11 (B).

In the display state of FIG. 11 (B), when a trace pointer display operation is carried out, trace pointer P 1 for the first point is displayed in the position of the origin, the intersection of the x- and y-axes. At this time, the coordinate values of trace pointer P 1 are displayed as “(X 1 , Y 1 )=(0, 0)” together with the graph.

Here, when a trace pointer display operation is further carried out, trace pointer P 2 for the second point is displayed in a position shifted a specific distance, for example, only 2, from trace pointer P 1 in the positive direction of the x-axis, as shown in FIG. 11 (D). At this time, the coordinate values of trace pointer P 2 are displayed as “(X 2 , Y 2 )=(2, 4).”

With that, since the smallest plurality of trace pointers (or two trace pointers) have been specified, the following are calculated in step S 213 and displayed together with the graph:

none  Local maximum value

( x,y )=(0.816,−1.089)  Local minimum value

In the display state shown in FIG. 11 (D), for example, with trace pointer P 1 for the first point selected by the cursor keys 18 d , the confirmation key 18 c is operated to determine the selection of trace pointer P 1 and then “←” key or “→” key in the cursor keys 18 d is operated to move trace pointer P 1 arbitrarily on the graph.

Similarly, with trace pointer SP 2 for the second point selected by the cursor keys 18 d , the confirmation key 18 c is operated to determine the selection of trace pointer P 2 and then “←” key or “→” key in the cursor keys 18 d is operated to move trace pointer P 2 arbitrarily on the graph.

FIG. 11 (E) shows a state where trace pointer P 1 for the first point has been moved to the coordinate position (−1, 0.672) by operating, for example, “←” key in the cursor keys 18 d.

Here, the coordinate position is displayed as “(X 1 , Y 1 )=(−1, 0.672).” At the same time, the following local maximum and minimum values are calculated and displayed together with the graph:

( x,y )=(−0.816,1.089)  Local maximum value

( x,y )=(0.816,−1.089)  Local minimum value

As described above, each time an arbitrary trace pointer P is selected and moved, the local maximum and minimum values between trace pointers are updated and displayed.

In the state shown in FIG. 11 (E), trace pointers for the third and later points can be specified. For example, in a state where trace pointer (P 3 ) for the third point is displayed, the local maximum and minimum values between trace pointer P 1 and trace pointer P 2 and the local maximum and minimum values between trace pointer P 2 and trace pointer P 3 are displayed as the results of calculation.

As described above, in the local maximum/minimum value calculation mode, it is determined whether there are a local maximum value and a local minimum value between two trace pointers. When there is at least one of a local maximum value and a local minimum value, its value is calculated and the result of calculation is displayed together with the graph. Therefore, when the graph takes at least one of a local maximum value and a local minimum value, its coordinate position can easily understood.

If it has been determined in step S 110 of FIG. 2 that the distance between the trace pointers input at the time is set, the individual trace pointers are rearranged on the graph so that the distance may be equal to the distance in the x-axis direction previously set by the multipoint trace program 12 c and, from this point on, setting is done so that the distance in the x-axis direction between the individual trace pointers may always be constant (step S 111 ).

FIG. 12 shows an example of the transition of the screen on the display unit 19 concerning the setting of trace pointer interval when the slope calculation mode has been set. As shown in FIG. 12 (A), when the function expression “Y 1 =X 2 ” is input and then the confirmation key 18 c on the input unit 18 is operated, a graph corresponding to the function expression is displayed together with the function expression “Y=X 2 ” on the display unit 19 , as shown in FIG. 12 (B).

In the display state of FIG. 12 (B), when the operation of displaying trace pointers for the first and second points is performed in sequence repeatedly, trace pointer P 1 for the first point is displayed in the position of the origin, the intersection of the x- and y-axes, and trace pointer P 2 for the second point is displayed in a position shifted a specific distance, for example, only 2, from trace pointer P 1 in the positive direction of the x-axis, as shown in FIG. 12 (C).

At this time, the coordinate values of trace pointer P 1 are displayed as “(X 1 , Y 1 )=(0, 0)” and the coordinate values of trace pointer P 2 are displayed as “(X 2 , Y 2 )=(2, 4).”

With that, since the trace pointers for the two points have been specified, an increment of dX=2 in the x-direction, an increment of dY=4 in the y-direction, and slope of dY/dX=2, and a slope of dX/dY=0.5 are calculated and the results of calculation are displayed with the graph.

In the display state shown in FIG. 12 (C), for example, with trace pointer P 1 for the first point selected by the cursor keys 18 d , the confirmation key 18 c is operated twice, which passes control to a state where the distance between trace pointers is set.

FIG. 12 (D) illustrates a trace pointer distance setting window WS displayed almost in the center of the display unit 19 . In the window WS, the following is displayed:

Set a distance between pointers

X direction [1]

↑: increase/↓: decrease/“Confirm”

The default distance “1” is highlighted. On the basis of the distance at the time, the value is updated and set by operating “↑” key or “↓” key in the cursor keys 18 d and the confirmation key 18 c is operated to complete the setting.

With the distance between trace pointers being set to “1,” when the setting has been completed, the graph display on the display unit 19 changes as shown in FIG. 12 (E) as a result of the setting.

In FIG. 12 (E), trace pointer P 1 of the specified first point moves on the graph automatically so that the distance from trance pointer P 2 for the second point may be equal to the set value “1.” At this time, the coordinate values of trace pointer P 1 are “(X 1 , Y 1 )=(1, 1), the coordinate values of trace pointer P 2 are “(X 2 , Y 2 )=(2, 4), an increment in the x-direction is dX=2, an increment in the y-direction is dX=4, and slopes are “dY/dX=3” and “dX/dY=⅓” These equations are displayed together with the graph.

As described above, when an arbitrary trace pointer is selected and moved, the distance from another trace pointer is input and set, which makes it possible to know the slope or the like between two pointes a desired distance apart without a complicated moving operation of trace pointers.

In the state of FIG. 12 (E), it is possible to specify trace pointers for the third and later points or set the position of each of the trace pointers at a specific distance from an adjacent trace pointer.

This holds true for various cases excluding a case where the slope calculation mode has been set in FIG. 12 . That is, it is possible to set the distance between trace pointers arbitrary in any one of the maximum/minimum value calculation mode, integration calculation mode, maximum/minimum differential value calculation mode, continuity/discontinuity determination mode, and local maximum/minimum value calculation mode.

If it has been determined in step S 103 of FIG. 2 that an analysis point for analyzing the vicinity of a specific position on the graph has been set, the position of a point to be analyzed by the graphing program 12 b and its coordinate value are displayed on the graph on the display unit 19 (step S 115 ).

Then, trace pointers for two points, which are each equally spaced from the displayed analysis point in the positive and negative directions along the x-axis, for example, X∓0.5 from the analysis point, are displayed on the graph as a pair of pointers with the analysis point at midpoint between the pointers (step S 16 ).

After the analysis point has been set, a second process is performed (step S 117 ). In the second process, calculations between two points forming a pair are done by the inter-points analysis program 12 d in the preset calculation mode and the results of calculation are displayed together with the graph.

The details of the distance-between-multipoint calculation result display process 2 will be described later.

In a state where the results of calculation are displayed, it is determined whether a key operation to specify the movement of one of the two trace pointers has been performed (step S 118 ).

If it has been determined that a key operation to specify the movement has not been performed, it is determined whether an operation to terminate the operation of the graphical function calculator 10 and shut down the power supply has been performed (step S 120 ).

If the power shutdown operation has not been performed, control returns to step S 118 . Then, the processes in steps S 118 and S 120 are carried out repeatedly, thereby waiting for either a key operation to specify the movement of the trace pointer or a key operation to terminate the operation and shut down the power supply to be performed.

Then, if a key operation to terminate the operation and shut down the power supply has been performed, it is determined in step S 120 that the key operation has been performed and the power supply is shut down as requested by the operation, which completes the processes of FIGS. 2 and 3 .

If it has been determined in step S 118 that a key operation to specify the movement of the trace pointer has been performed, the specified trace pointer is moved on the graph by the multipoint trace program 12 c according to the operation of the cursor keys (“←” and “→” keys) 18 d on the input unit 18 and, at the same time, the other of the pair of trace pointers is also moved so that the distance from the analysis point in the x-direction may be the same, interlocking with the positional relationship between the moved trace pointer and the analysis point (step S 119 ).

Thereafter, control proceeds to the process in step S 117 and a second process is performed. In the second process, the inter-points analysis program 12 d does calculations between two trace pointers on the basis of the trace pointer whose position has been moved on the graph and the results of calculation are displayed together with the graph.

Next, the second process in step S 117 in each of the calculation modes will be explained in detail.

FIG. 5 shows a subroutine to explain the details of the second process related to the calculations between trace pointers and the display of the results of calculation in step S 117 .

At the beginning of the process, it is determined whether the calculation mode set at the time is the slope calculation mode in which a slope between points is calculated (step S 301 ).

If it has been determined that the slope calculation mode has been set, a differential value at the analysis point, an increment in each of the x- and y-coordinates between two trace pointers, and a slope between the two points are calculated (step S 302 ).

Then, the display unit 19 is caused to display the result of calculation together with the graph (step S 303 ), which terminates the subroutine and returns control to the main routine of FIG. 3 .

FIG. 13 shows an example of the transition of the screen on the display unit 19 when the slope calculation mode has been set. As shown in FIG. 13 (A), when the function expression “Y 1 =X 2 ” is input and then the confirmation key 18 c on the input unit 18 is operated, a graph corresponding to the function expression is displayed together with the function expression “Y=X 2 ” on the display unit 19 , as shown in FIG. 13 (B).

In the display state of FIG. 13 (B), when an analysis point setting operation is carried out, the coordinates of the position of a point to be analyzed and a differential value at the position of the point are displayed, as shown in FIG. 13 (C).

In FIG. 13 (C), the coordinate position (2, 4) is the position of analysis point A and the differential value at that position is 4 (differential value=4).

Here, when a trace pointer display operation is further carried out, a pair of trace pointers P 1 , P 2 whose x-coordinate values are ∓0.5 with respect to analysis point A is displayed on the graph, as shown in FIG. 13 (D). At this time, the coordinate values of trace pointers P 1 , P 2 are displayed as “(X 1 , Y 1 )=(1.5, 2.25) “(X 2 , Y 2 )=(2.5, 6.25)” together with the graph.

With that, since a pair of trace pointers P 1 , P 2 whose coordinate values are equally spaced from analysis point A at midpoint between the pointers have been specified, an increment of dX=1 in the x-direction, an increment of dY=4 in the y-direction, a slope of dY/dX=4, and a slope of dX/dY=0.25 are calculated and the results of calculation are displayed together with the graph.

Here, as for the slope between two trace pointers P 1 and P 2 , a slope of dY/dX with respect to an increment in the x-direction and a slope of dX/dY with respect to an increment in the y-direction are determined. One of the two slopes is the reciprocal of the other unless both of them are not zero.

In the display state shown in FIG. 13 (D), with trace pointer SP 1 selected by, for example, the cursor keys 18 d , the confirmation key 18 c is operated to determine the selection of trace pointer P 1 and then “←” key or “→” key in the cursor keys 18 d is operated to move trace pointer P 1 arbitrarily on the graph.

FIG. 13 (E) shows a state where trace pointer P 1 has been moved to the coordinate position (1.7, 2.89) by operating, for example, “→” key in the cursor keys 18 d.

The position of trace pointer P 2 moves automatically, interlocking with the movement of trace pointer P 1 . Since the distance between trace pointer P 1 and the analysis point on the x-axis is 0.3, trace pointer P 2 moves automatically to the coordinates (2.3, 5.29) to keep the equal distance in the x-axis direction.

After the movement of trace pointers P 1 , P 2 , an increment of dX=0.6 in the x-direction, an increment of dY=2.4 in the y-direction, a slope of dY/dX=4, and a slope of dY/dX=0.25 are calculated and the results of calculation are displayed together with the graph.

Each time one of the pair of trace pointers P 1 , P 2 is selected and moved, the other of the pair of trace pointers P 1 , P 2 moves, interlocking with the former. The increment in the x-coordinate, the increment in the y-coordinate, and the slope between trace pointers P 1 and P 2 making a pair are updated and displayed.

As described above, in the slope calculation mode, a differential value at analysis point A, an increment in each of the x- and y-coordinates between two trace pointers P 1 and P 2 with the analysis point at mid-point between them, and a slope between two points are calculated and the results of calculation are displayed together with the graph.

Accordingly, a slope liable to be visually misunderstood, depending on the setting of the display range, can be understood easily by displaying various numeric values together with the graph.

In addition, since the distance between two trace pointes with the analysis point at midpoint between them can be easily changed and set by the moving operation of trace pointers, the way the slope is changed by the setting of a range centering on the analysis point can be understood easily.

In step S 301 of FIG. 5 , if it has been determined that the set calculation mode is not the slope calculation mode, it is determined whether the set calculation mode is the maximum/minimum value calculation mode in which the maximum and minimum values between points is found (step S 304 ).

If it has been determined that the maximum/minimum value calculation mode has been set, the maximum and minimum values between two adjacent trace pointers are calculated (step S 305 ) and the results of calculation are displayed together with the graph on the display unit 19 (step S 303 ), which completes the subroutine and returns control to the main routine of FIG. 3 .

As described above, in the maximum/minimum value calculation mode, since the maximum and minimum values between two trace pointers are calculated and the results of calculation are displayed together with the graph, the range which the graph will possibly take can be understood easily.

In step S 304 of FIG. 5 , if it has been determined that the set calculation mode is not the maximum/minimum value calculation mode, it is determined whether the set calculation mode is the integration calculation mode in which an integration value between points is found (step S 306 ).

If it has been determined that the integration calculation mode has been set, an integration value between two adjacent trace pointers is calculated (step S 307 ) and the result of calculation is displayed together with the graph on the display unit 19 (step S 303 ), which completes the subroutine and returns control to the main routine of FIG. 3 .

As described above, in the integration calculation mode, since an integration value between two trace pointers is calculated and the result of calculation is displayed together with the graph, an accurate area or length of the range displayed on the graph can be understood easily.

In step S 306 of FIG. 5 , if it has been determined that the set calculation mode is not the integration calculation mode, it is determined whether the set calculation mode is the maximum/minimum differential value calculation mode in which the maximum and minimum differential values between points is found (step S 308 ).

If it has been determined that the maximum/minimum differential value calculation mode has been set, not only a differential value at the analysis point but also the maximum and minimum differential values between two adjacent trace pointers are calculated (step S 309 ) and the results of calculation are displayed together with the graph on the display unit 19 (step S 303 ), which completes the subroutine and returns control to the main routine of FIG. 3 .

As described above, in the maximum/minimum differential value calculation mode, since not only a differential value at the analysis point but also the maximum and minimum differential values between two trace pointers with the analysis point at midpoint between them are calculated and the results of calculation are displayed together with the graph, the position with the maximum slope and the position with the minimum slope in the range with the analysis point at midpoint on the graph can be easily known.

In step S 308 of FIG. 5 , if it has been determined that the set calculation mode is not the maximum/minimum differential value calculation mode, it is determined whether the set calculation mode is the continuity/discontinuity determination mode in which it is determined whether the graph is continuous or discontinuous between points is found (step S 310 ).

If it has been determined that the continuity/discontinuity determination mode has been set, it is determined whether the graph is continuous or discontinuous between two adjacent trace pointers (step S 311 ) and the determination result is displayed together with the graph on the display unit 19 (step S 303 ), which completes the subroutine and returns control to the main routine of FIG. 3 .

As described above, in the continuity/discontinuity determination mode, since it is determined whether the graph is continuous or discontinuous between two trace pointers with the analysis point at midpoint between them and the determination result is displayed together with the graph, whether the graph is continuous or discontinuous between trace pointers near the analysis point can be understood easily.

In step S 310 of FIG. 5 , if it has been determined that the set calculation mode is not the continuity/discontinuity determination mode, it is determined whether the set calculation mode is the local maximum/minimum value calculation mode in which a local maximum value and a local minimum value between two trace pointers are found (step S 312 ).

If a calculation mode other than the local maximum/minimum value calculation mode has been set, an explanation of it will be omitted in the embodiment, provided that another suitable process is performed.

In step S 312 , if it has been determined that the local maximum/minimum value calculation mode has been set, a local maximum value and a local minimum value between two adjacent trace pointers are calculated (step S 313 ) and the results of calculation are displayed together with the graph on the display unit 19 (step S 303 ), which completes the subroutine and returns control to the main routine of FIG. 3 .

As described above, in the local maximum/minimum value calculation mode, it is determined whether there are a local maximum value and a local minimum value between two trace pointers and, if at least one of a local maximum value and a local minimum value exists, the value of it is calculated and the result of calculation is displayed together with the graph. Therefore, when the graph takes at least one of a local maximum value and a local minimum value, its coordinate position can be known easily.

As the process in each of the calculation modes has been explained, the set calculation mode is performed in a state where the analysis point is displayed in the process of FIG. 5 , thereby displaying the contents of the calculation together with the graph in each of the calculation modes, particularly including the position of an arbitrary point to be analyzed, which enables the user to gain a better understanding of the graph.

As described above, with the embodiment, it is possible to improve the capability of analyzing a function graph and deepen the level of understanding of a basic structure of a graph of a function expression by making various analyses of the relationship between two points on a graph.

While in the embodiment, the calculation mode is set in advance and a graph of the input function expression is displayed, the invention is not limited to this. For instance, after a graph of the input function expression is displayed and then trace pointers are displayed on the graph, each of the calculation modes may be selected and set. In that case, the selected calculation mode can be changed in a state where the graph of the function expression is displayed, which contributes to a better understanding of the graph of the function expression.

Furthermore, not only is the position of a trace pointer on the graph moved by moving the trace pointer displayed temporarily on the graph with the cursor keys 18 d , but also the x-coordinate value may be input directly with the alphanumeric keys 18 b . In that case, it is conceivable that, for example, infinity can be input.

The methods of operating in the mathematical operation modes on the graphical function calculator 10 described in the embodiment, including the process shown in the flowchart of FIG. 3 , the subroutine of inter-pointer calculation result display process 1 shown in FIG. 4 , and the subroutine of inter-pointer calculation result display process 2 shown in FIG. 5 , can be stored in an external storage medium 13 , such as a memory card (e.g., a ROM card or a RAM card), a magnetic disk (e.g., a floppy disk or a hard disk), an optical disk (e.g., a CD-ROM or a DVD), or a semiconductor memory, in the form of programs the computer can execute. Then, the mediums can be delivered.

The computer 11 of the graphical function calculator 10 reads the program stored in the external storage medium 13 into a storage unit 12 or work unit 17 . The computer is controlled by the read-in program, thereby realizing the functions explained in the embodiment, which enables the same processes in the aforementioned methods to be carried out.

Furthermore, the data of the programs which realize the above methods can be transferred in the form of program code through a communication network (public line) N. The program data can be loaded into the computer 11 of the graphical function calculator 10 by the communication control unit 16 connected to the communication network N, thereby realizing the aforementioned functions.

Furthermore, the program data can be loaded into a personal computer, thereby realizing the aforementioned functions.

Additional advantages and modifications will readily occur to those skilled in the art. Therefore, the invention in its broader aspects is not limited to the specific details and representative embodiments shown and described herein. Accordingly, various modifications may be made without departing from the spirit or scope of the general inventive concept as defined by the appended claims and their equivalents.