Abstract:
An electronic apparatus includes: a display device; and a processor configured to: display a graph corresponding to a function formula on the display device, wherein a coefficient of a term included in the function formula comprises a variable; determine a numeric value range of numeric values which are to be inputted to the variable, based on a degree of the term and a display state of the graph; generate an operation receiver for allowing a user to variably specify a numeric value within the determined numeric value range; display the operation receiver on the display device. When a numeric value is specified within the numeric value range through the operation receiver, the processor displays a graph corresponding to a function formula in which the specified numeric value is inputted to the variable on the display device.

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
       [0001]    This application claims priority from Japanese Patent Application No. 2013-122774, filed on Jun. 11, 2013, the entire contents of which are hereby incorporated by reference. 
       BACKGROUND 
       [0002]    1. Technical Field 
         [0003]    The present invention relates to an electronic apparatus having a graph display function for displaying a graph corresponding to a function formula, a graph display method, and a computer readable medium having a graph display program stored thereon. 
         [0004]    2. Description of the Related Art 
         [0005]    In the background art, when a user inputs a function formula y=f(x) in a scientific electronic calculator (graph scientific electronic calculator) having a graph display function, a graph corresponding to the inputted function formula is displayed on a display of the scientific electronic calculator. 
         [0006]    Here, the user may want to see the change of the shape of the graph when a coefficient of a term in the function formula is varied. In such a case, the graph scientific electronic calculator is conceived as follows. That is, when the user inputs, for example, a formula of a quadratic function y=AX 2 +X+1 in the graph scientific electronic calculator, a special screen for setting values of a coefficient A of the formula y=AX 2 +X+1 is displayed to allow the user to input a start value (Start), an end value (End) and a pitch (Pitch) of the coefficient A on the special screen. When the values of the coefficient A which vary are set thus, graphs of the function formula in accordance with the values of the coefficient A are displayed successively on a display of the graph scientific electronic calculator (for example, see JP-A-09-282475). 
         [0007]    In order to display the graphs in which the values of the coefficient included in the function formula are varied in the related-art graph scientific electronic calculator, the special screen for setting the values of the coefficient needs to be displayed once and an operation for setting the respective values needs to be performed. For this sake, a troublesome operation is necessary. 
         [0008]    In addition, whenever the values and the pitch of the coefficient which have been set once are to be changed on the special screen, the screen needs to be displayed again and the values and the pitch of the coefficient need to be set again. For this sake, there is a problem that it takes much time and labor. 
       SUMMARY 
       [0009]    One of illustrative aspects of the present invention is to provide an electronic apparatus and a graph display method in which a value of a coefficient can be varied easily when the coefficient included in a function formula is set as a variable, and a computer readable medium having a graph display program stored thereon. 
         [0010]    According to one or more aspects of the present invention, an electronic apparatus includes: a display device; and a processor configured to: display a graph corresponding to a function formula on the display device, wherein a coefficient of a term included in the function formula comprises a variable; determine a numeric value range of numeric values which are to be inputted to the variable, based on a degree of the term and a display state of the graph; generate an operation receiver for allowing a user to variably specify a numeric value within the determined numeric value range; display the operation receiver on the display device. When a numeric value is specified within the numeric value range through the operation receiver, the processor displays a graph corresponding to a function formula in which the specified numeric value is inputted to the variable on the display device. 
         [0011]    According to the invention, an operation receiver called slider for receiving a value of a coefficient included in a function formula can be displayed so that a user can display a graph corresponding to the function formula while varying the coefficient easily. 
     
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         [0012]      FIG. 1  is a front view of the external appearance of a graph scientific electronic calculator  10  as an embodiment of an electronic apparatus according to the invention; 
           [0013]      FIG. 2  is a block diagram showing the circuit configuration of the graph scientific electronic calculator  10 ; 
           [0014]      FIG. 3  is a view showing the contents of table data stored in a slider pattern table  15   f  of the graph scientific electronic calculator  10 ; 
           [0015]      FIG. 4  is a flow chart showing a graph display process of the graph scientific electronic calculator  10 ; 
           [0016]      FIG. 5  is a flow chart showing a slider generation process of the graph scientific electronic calculator  10 ; 
           [0017]      FIG. 6  is a flow chart showing a slider operation process of the graph scientific electronic calculator  10 ; 
           [0018]      FIG. 7  is a view showing an operation to change a slider of the graph scientific electronic calculator  10 ; and 
           [0019]      FIG. 8  is a view showing the change of the display of a graph  y  in response to the slider operation. 
       
    
    
     DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS 
       [0020]    An embodiment of the invention will be described below with reference to the drawings. 
         [0021]      FIG. 1  is a front view of the external appearance of a graph scientific electronic calculator  10  as an embodiment of an electronic apparatus according to the invention. 
         [0022]    This electronic apparatus may be applied to a special graph scientific electronic calculator  10  which will be described below or may be applied to a tablet terminal, a cellular phone, a portable game machine, etc. provided with a display which can display a graph. 
         [0023]    The graph scientific electronic calculator  10  has a function of displaying an inputted function formula and a graph corresponding to the function formula. 
         [0024]    A key input portion  12  and a touch panel display  13  are provided in a body of the graph scientific electronic calculator  10  so that the key input portion  12  covers about an area of a lower half part of the front surface of the body while the touch panel display  13  covers about an area of an upper half part of the same. 
         [0025]    The key input portion  12  is provided with numeric and symbol keys  12   a , function and operator keys  12   b , a [Menu] key  12   c , a [Graph] key  12   d , a [Mdfy] key  12   e , cursor keys  12   f , etc. 
         [0026]    The numeric and symbol keys  12   a  are constituted by a numeric and symbol inputting key group in which various keys such as numeric keys and symbol keys are arrayed. 
         [0027]    The function and operator keys  12   b  are constituted by various functional symbol keys and operator keys such as [+], [−], [×], [÷] and [=] which are operated for inputting a mathematical formula or a function formula. 
         [0028]    The [Menu] key  12   c  is operated for displaying a selection menu of various operation modes such as an arithmetic operation mode for inputting a calculation formula and performing arithmetic processing thereon, a graph mode for drawing a graph of an inputted function formula, and a program mode for installing a desired program and making the program perform calculation processing. 
         [0029]    The [Graph] key  12   d  is operated for drawing a graph based on inputted data. 
         [0030]    The [Mdfy(Modify)] key  12   e  is a key for displaying a slider (operation receiver) SL for varying a value of a coefficient when a graph corresponding to a function formula y=f(x) is displayed in the graph mode. The slider SL is constituted by a long-shaped display body indicating a variable range of numeric values and a knob portion CS provided slidably on the display body. In the slider SL, a numeric value corresponding to the position of the knob portion CS can be specified as a coefficient (see  FIG. 1  and  FIG. 8 ). 
         [0031]    Incidentally, inputting of the [Graph] key  12   d  and the [Mdfy] key  12   e  may be performed by means of icons displayed on the touch panel display  13 . 
         [0032]    The cursor keys ([↑], [.↓], [←] and [→])  12   f  are operated respectively for performing an operation for selecting and sending displayed data, an operation for moving the cursor, etc. 
         [0033]    In addition, the touch panel display  13  is constituted by a transparent touch panel  13   t  pasted on a liquid crystal display screen  13   d  which can perform color display. 
         [0034]      FIG. 2  is a block diagram showing the circuit configuration of the graph scientific electronic calculator  10 . 
         [0035]    The graph scientific electronic calculator  10  has a CPU  11  which is a microcomputer. 
         [0036]    The CPU  11  executes an electronic calculator control program  14   a  stored in advance in a storage device  14  such as a flash ROM using an RAM  15  as a working memory to thereby perform operation for an electronic calculator function, a function graph display function, etc. Incidentally, the electronic calculator control program  14   a  may be read into the storage device  14  from an external recording medium  17  such as a memory card through a recording medium reader  16 , or may be downloaded into the storage device  14  from a Web server (program server) on a communication network (the Internet) through a communication controller  18 . 
         [0037]    The key input portion  12 , the touch panel display  13 , the storage device  14 , the RAM  15 , the recording medium reader  16  and the communication controller  18  which are shown in  FIG. 2  are connected to the CPU  11 . 
         [0038]    The RAM  15  stores various kinds of data required for processing operation of the CPU  11 . A display data storage region  15   a , a touch coordinate data storage region  15   b , a range data storage region  15   c , a mathematical formula data storage region  15   d , a coefficient data storage region  15   e , a slider pattern table  15   f , a slider data storage region  15   g , and a graph data storage region  15   h  are provided in the RAM  15 . 
         [0039]    Data displayed in colors on the screen of the touch panel display  13  are stored in the display data storage region  15   a.    
         [0040]    Coordinate data of a touch position corresponding to a user operation detected by the touch panel display  13  are stored in the touch coordinate data storage region  15   b.    
         [0041]    An X-coordinate range (Xmin to Xmax) and a Y-coordinate range (Ymin to Ymax) which indicate a display range set for a graph screen Gs of the touch panel display  13  are stored in the range data storage region  15   c . Incidentally, since the graph scientific electronic calculator  10  has a zoom function of zooming in on (scaling up) or zooming out on (scaling down) a graph displayed on the graph screen Gs and displaying the zoomed-in or zoomed-out graph, the X-coordinate range (ZXmin to ZXmax) and the Y-coordinate range (ZYmin to ZYmax) after the zooming are also stored. 
         [0042]    Data about a function formula y=f(x) inputted by an operation on the key input portion  12  are stored in the mathematical formula data storage portion  15   d . In the embodiment, a formula of a quadratic function as the function formula is to be processed. 
         [0043]    Data about a coefficient of each term included in the function formula y=f(x) stored in the mathematical formula data storage region  15   d  are stored in the coefficient data storage region  15   e.    
         [0044]    A reference variable range (value width) and variable pitches (step values) for each of a second-degree term, a first-degree term and a constant term of the quadratic function are registered in advance in the slider pattern table  15   f , as data for generating the slider (operation receiver) SL to be displayed together with a graph. 
         [0045]    The variable range (value width) and the variable pitches (step values) are shown in  FIG. 3 . [−2 to 2] and [−2, −1, −0.5, −0.2, −0.1, −0.05, 0, 0.05, 0.1, 0.2, 0.5, 1, 2] are registered respectively as a variable range (value width) and variable pitches (step values) of a coefficient A of a second-degree term of a formula y=AX 2 +BX+C. Here, values at the opposite ends of the variable range are also included as the step values. In addition, [−5 to 5] and [−5, −2, −1, −0.5, −0.2, 0, 0.2, 0.5, 1, 2, 5] are registered respectively as a variable range (value width) and variable pitches (step values) of a coefficient B of a first-degree term of the formula y=AX 2 +BX+C. In addition, [−5 to 5] and [−5, −4, −3, −2, −1, 0, 1, 2, 3, 4, 5] are registered respectively as a variable range (value width) and variable pitches (step values) of a constant term C of the formula y=AX 2 +BX+C. Incidentally, these values are values regarded as appropriate for learning the quadratic formula from the shape of the graph. However, the invention is not limited thereto. Alternatively, these values may fluctuate due to the values of the coordinate ranges or a user may set the values desirably. 
         [0046]    Data about the slider SL to be displayed together with the graph are stored in the slider data storage region  15   g . The data are determined in accordance with the coefficient of each term included in the function formula y=f(x) and stored in the coefficient data storage region  15   e , the X- and Y-coordinate ranges of the graph screen Gs stored in the range data storage region  15   c , and the reference variable range (value width) and the variable pitches (step values) of the coefficient of the term registered in the slider pattern table  15   f.    
         [0047]    Data about a graph generated based on the function formula y=f(x) stored in the mathematical formula data storage region  15   d  and each value of the coefficient of each term included in the function formula y=f(x) are stored in the graph data storage region  15   h.    
         [0048]    When the CPU  11  controls operations of the respective portions of the circuit in accordance with commands of various kinds of processing described in the electronic calculator control program  14   a  and software and hardware cooperate with each other, the graph scientific electronic calculator  10  configured thus can operate to implement various functions which will be described in the following operation description. 
         [0049]    Next, operation of the graph scientific electronic calculator  10  having the aforementioned configuration will be described.  FIG. 4  is a flow chart showing a graph display process of the graph scientific electronic calculator  10 . 
         [0050]      FIG. 5  is a flow chart showing a slider generation process of the graph scientific electronic calculator  10 . 
         [0051]    When a user operates the [Menu] key  12   c  to select a graph mode from a menu screen (not shown), the graph display process shown in  FIG. 4  is started up. In the graph display process, first, a setting screen (not shown) of coordinate ranges for the graph screen Gs is displayed, an X-axis coordinate range (Xmin to Xmax) and a Y-axis coordinate range (Ymin to Ymax) are inputted by the user, stored in the range data storage region  15   c  and set as reference coordinate ranges (Step S 1 ). Incidentally, instead of the coordinate ranges inputted by the user, data of coordinate ranges which have been stored already may be used as the reference coordinate ranges directly. 
         [0052]    Then, the graph screen Gs of the X-Y coordinates in accordance with the set coordinate ranges and a mathematical formula screen Fs are displayed on the touch panel display  13 . 
         [0053]    When a desired function formula y=f(x) is inputted by the user in the mathematical formula screen Fs (Step S 2 ), determination is made as to whether there is a coefficient inputted as a character (other than a number) in any term included in the function formula or not (Step S 3 ). That is, determination is made as to whether any coefficient has been set as a variable or not. 
         [0054]    When, for example, a function formula “y=(A/2)X 2 +X−2” is inputted (Step S 2 ), determination is made as to whether there is a coefficient including a character in each of a second-degree term, a first-degree term and a constant term included in the function formula or not (Step S 3 ). 
         [0055]    Here, when conclusion is made that a character A is included in the second-degree term (Yes in Step S 3 ), a default value (for example, “2”) is inputted to the coefficient A and “A=2” is stored in the coefficient data storage region  15   e  (Step S 4 ). 
         [0056]    Then, data for drawing a graph  y  of the function formula “y=(A/2)X 2 +X−2” in which the coefficient is set to be “A=2” are generated in accordance with the set coordinate ranges and stored in the graph data storage region  15   h  and the graph  y  is displayed on the X-Y coordinates of the graph screen Gs (Step S 5 ). 
         [0057]    Here, when conclusion is made that a character coefficient B is included in the first-degree term of the function formula or when conclusion is made that a character coefficient C is included in the constant term of the function formula (Yes in Step S 3 ), a default value is inputted to the character coefficient B or C and stored in the coefficient data storage region  15   e  (Step S 4 ). Then, data for drawing a corresponding graph  y  are generated and displayed on the graph screen Gs (Step S 5 ). 
         [0058]    Incidentally, when the coefficient of each term included in the function formula y=f(x) inputted on the mathematical formula screen Fs is inputted as a number (constant) (also including “1” which is omitted on the display) (No in Step S 3 ), the graph  y  corresponding the function formula y=f(x) is generated in accordance with the coefficient as it is and displayed on the X-Y coordinates of the graph screen Gs (Step S 5 ). 
         [0059]    Here, when zoom-in (scaling-up) or zoom-out (scaling-down) is specified by the user operating on one of icons arrayed and displayed in an upper portion of the touch panel display  13 , the current reference coordinate ranges (Xmin to Xmax) and (Ymin to Ymax) set for the graph screen Gs are changed in accordance with a magnification factor (α) or a reduction factor (1/α) of the zoom-in or zoom-out so that the zoomed coordinate ranges (ZXmin to ZXmax) and (ZYmin to ZYmax) can be reset. In accordance with this resetting, the graph  y  is displayed in a scaled-up or scaled-down manner. In the case of the zoom-in (scaling-up), the interval of the scale of each coordinate in the graph screen Gs is widened. In the case of the zoom-out (scaling-down), the interval of the same is narrowed. The zoomed coordinate ranges (ZXmin to ZXmax) and (ZYmin to ZYmax) in the state in which the zoom function is active are also stored in the range data storage region  15   c.    
         [0060]    In the state in which the graph  y  has been displayed on the graph screen Gs, the user may operate the [Mdfy] key  12   e  to display the graph  y  in which any coefficient included in the function formula is varied. 
         [0061]    When the [Mdfy] key  12   e  is operated (Yes in Step S 6 ), the flow of processing is shifted to a slider generation process (Step SA). 
         [0062]    The slider generation process will be described with reference to the flow chart of  FIG. 5 . 
         [0063]    First, any term having a character coefficient is specified from the function formula “y=(A/2)X 2 +X−2” (Step A 1 ). Here, conclusion is made that there is a second-degree term “(A/2)X 2 ” having a coefficient “A” (Yes in Step A 2 ). 
         [0064]    Then, variable pitches (step values) [−2, −1, −0.5, −0.2, −0.1, −0.05, 0, 0.05, 0.1, 0.2, 0.5, 1, 2] for a slider SLA corresponding to the second-degree term specified as the term having the character coefficient “A” are read from the slider pattern table  15   f  (see  FIG. 3 ) (Step A 3 ). 
         [0065]    Attention is paid to the second-degree term “(A/2)X 2 ” and the first-degree term “X” included in the function formula “y=(A/2)X 2 +X−2” (Step A 4 ). Next, determination is made as to whether a constant (number) coefficient other than the character is included or not in the specified term having the character coefficient (Step A 5 ). 
         [0066]    Here, conclusion is made that a constant coefficient “½” other than the character “A” is included in the specified second-degree term “(A/2)X 2 ” having the character coefficient “A” (Yes in Step A 5 ). Then, the variable pitches (step values) for the slider SLA read from the slider pattern table  15   f  are multiplied by “2” which is the reciprocal of the coefficient “½” so that the variable pitches (step values) are corrected to [−4, −2, −1, −0.4, −0.2, −0.1, 0, 0.1, 0.2, 0.4, 1, 2, 4] (Step A 6 ). 
         [0067]    When the formula of the quadratic function is graphed, the size of the value of the coefficient of the second-degree term affects the degree of an opening of the graph. That is, when the value is large, the opening is narrow. When the value is small, the opening is wide. The reason why the correction is performed by multiplication by the reciprocal of the constant coefficient is to restore the change of the opening of the graph to its original change to thereby make it easy to understand the change of the shape of the graph, otherwise the originally planned change of the opening of the graph would be different due to the constant. 
         [0068]    Incidentally, when conclusion is made in the steps A 1  and A 2  that there is a first-degree term “BX” having a character coefficient “B”, variable pitches (steps values) [−5, −2, −1, −0.5, −0.2, 0, 0.2, 0.5, 1, 2, 5] for a slider SLB corresponding to the first-degree term are read from the slider pattern table  15   f  (see  FIG. 3 ) (Step A 3 ). Similarly, when conclusion is made that there is a constant term having a character “C”, variable pitches (step values) [−5, −4, −3, −2, −1, 0, 1, 2, 3, 4, 5] for a slider SLC corresponding to the constant term are read from the slider pattern table  15   f  (see  FIG. 3 ) (Step A 3 ). 
         [0069]    When conclusion is made in Steps A 4  and A 5  that a constant (number) coefficient other than the character “B” is included in the first-degree term “BX” (Yes in Step A 5 ), the variable pitches (step values) read from the slider pattern table  15   f  are corrected to be multiplied by the reciprocal of the constant coefficient (Step A 6 ). 
         [0070]    Incidentally, when conclusion is made in the Steps A 1  and A 2  that no term having a character coefficient is included in the inputted function formula “y=f(x)” (No in Step A 2 ), a message indicating that there is no target term whose coefficient can be varied, for example, “there is no coefficient to be varied” is displayed (Step A 2   m ). 
         [0071]    Then, a value Xmax-Xmin is calculated from the values of the reference coordinate range of the X-axis stored in the range data storage region  15   c  in the Step S 1  so that the value Xmax-Xmin is set as a reference value (Step A 7 ). When the current graph screen Gs is zoomed and data for the zoomed coordinate ranges (ZXmin to ZXmax) and (ZYmin to ZYmax) are stored, a value ZXmax-ZXmin is calculated and determination is made as to whether the value ZXmax-ZXmin is larger or smaller than the reference value (Step A 8   a  or A 8   b ). 
         [0072]    Here, when conclusion is made that the value ZXmax-ZXmin is larger than the reference value and the graph screen Gs is in a zoom-out state (scaled down) (Yes in Step A 8   a ), the reduction factor (1/α) of the zoom-out is calculated (Step A 9   a ). 
         [0073]    The data of the variable pitches (step values) for the slider SL in the second-degree term are corrected to be multiplied by the reciprocal (α) of the reduction factor (1/α) so that the width of each of the step values can be increased (Step A 10   a ). 
         [0074]    Here, the variable pitches (step values) [−4, −2, −1, −0.4, −0.2, −0.1, 0, 0.1, 0.2, 0.4, 1, 2, 4] for the slider SLA in the second-degree term, which pitches (step values) have been corrected in the Steps A 5  and A 6  are multiplied by the reciprocal (α) of the reduction factor (1/α). For example, when the reduction factor (1/α) of the graph  y  displayed on the graph screen Gs is “⅓”, the variable pitches (step values) are multiplied by the reciprocal “3” of the reduction factor “⅓” so as to be corrected to [−12, −6, −3, −1.2, −0.6, −0.3, 0, 0.3, 0.6, 1.2, 3, 6, 12]. 
         [0075]    The reason why the correction is performed in accordance with the zoom-out is as follows. That is, when the graph screen Gs is zoomed out (scaled down) to make the display range of the graph  y  wide, the interval of the scale of each coordinate becomes narrow and the change of the graph  y  for each variable pitch (step value) based on the slider SLA becomes small. Therefore, the correction is performed in such a manner that the variable pitches (step values) are multiplied by the reciprocal (α) of the reduction factor (1/α) of the zoom-out so that the variable pitches can be increased. With this correction, the change of the shape of the graph in accordance with the coefficient of the second-degree term varied by the slider SLA can be understood easily. 
         [0076]    In addition, when the character “C” is included in the constant term of the graphed function formula “y=f(x)”, the variable pitches (step values) [−5, −4, −3, −2, −1, 0, 1, 2, 3, 4, 5] for the slider SLC are corrected to be multiplied by the reciprocal (α) of the reduction factor (1/α) for the similar reason to the slider SLA (Step A 10   a ). 
         [0077]    Incidentally, even when the coefficient “B” as a character is included in the first-degree term of the graphed function formula “y=f(x)”, the variable pitches (step values) for the slider SLB are not corrected but left as they are because the zoom-out (scaling-down) of the graph screen Gs has a small influence on the degree with which the graph  y  changes in accordance with the variation of the coefficient of the first-degree term. 
         [0078]    On the other hand, when conclusion is made that the value ZXmax-ZXmin is smaller than the reference value and the graph screen Gs is in a zoom-in state (scaled up) (Yes in Step A 8   b ), a magnification factor (α) of the zoom-in is calculated (Step A 9   b ). 
         [0079]    The data for the slider SLA in the second-degree term are corrected to be multiplied by the reciprocal (1/α) of the magnification factor (α) so that the width of each of the step values can be reduced (Step A 10   b ). 
         [0080]    Here, the variable pitches (step values) [−4, −2, −1, −0.4, −0.2, −0.1, 0, 0.1, 0.2, 0.4, 1, 2, 4] for the slider SLA in the second-degree term, which pitches (step values) have been corrected in the Steps A 5  and A 6 , are multiplied by the reciprocal (1/α) of the magnification factor (α). For example, when the magnification factor (α) of the graph  y  displayed on the graph screen Gs is “2”, the variable pitches (step values) are multiplied by the reciprocal “½” of the magnification factor “2” so as to be corrected to [−2, −1, −0.5, −0.2, −0.1, −0.05, 0, 0.05, 0.1, 0.2, 0.5, 1, 2]. 
         [0081]    The reason why the correction is performed in accordance with the zoom-in is as follows. That is, when the graph screen Gs is zoomed in (scaled up) to make the display range of the graph  y  narrow, the interval of the scale of each coordinate becomes wide and the change of the graph  y  for each variable pitch (step value) based on the slider SLA becomes large. Therefore, the correction is performed in such a manner that the variable pitches (step values) are multiplied by the reciprocal (1/α) of the magnification factor (α) of the zoom-in (scaling-up) so that the variable pitches can be reduced. With this correction, the change of the shape of the graph in accordance with the coefficient of the second-degree term varied by the slider SLA can be understood easily. 
         [0082]    In addition, when the character “C” is included in the constant term of the graphed function formula “y=f(x)”, the variable pitches (step values) [−5, −4, −3, −2, −1, 0, 1, 2, 3, 4, 5] for the slider SLC are corrected to be multiplied by the reciprocal (1/α) of the magnification factor (α) for the similar reason to the slider SLA of the second-degree term (Step A 10   b ). 
         [0083]    Incidentally, even when the coefficient “B” as a character is included in the first-degree term, the variable pitches (step values) for the slider SLB are not corrected but left as they are. 
         [0084]    Thus, variable pitches (step values) for a slider SL for varying the value of the character coefficient are determined for each term included in the function formula y=f(x), and stored in the slider data storage region  15   g  (Step A 11 ). The slider SL having the determined variable pitches (step values) is generated (Step A 12 ) and displayed on the display  13  (Step S 7 ). 
         [0085]    For example, when the function formula “y=(A/2)X 2 +X−2” is inputted and the graph screen Gs is displayed in a zoom-out state (in a scaled-down manner) with a factor (⅓), variable pitches (step values) [−12, −6, −3, −1.2, −0.6, −0.3, 0, 0.3, 0.6, 1.2, 3, 6, 12] for the slider SLA in the second-degree term are determined as a result of the Steps A 1  to A 8   a , A 9   a , and A 10   a  so that the slider SLA having a variable range (value width) [−12 to 12] as shown in  FIG. 1  is displayed above the graph screen Gs (Step S 7 ). 
         [0086]    When the knob portion CS of the slider SLA is slid while touched (Step S 8 ), the value of the coefficient “A” is changed to a value where the knob portion CS is located (Step S 9 ) so that data for drawing a graph  y  of “y=(A/2)X 2 +X−2” using the value of the coefficient “A” are regenerated and displayed on the graph screen Gs again (Step S 10 ). 
         [0087]    Incidentally, when the slider SLB for varying the character coefficient “B” of the first-degree term included in the function formula y=f(x) is generated in the slider generation process (Step SA), and further, when the slider SLC for varying the character “C” of the constant term is generated, the knob portion CS of each of the sliders SLB and SLC is slid while touched (Step S 8 ) so that the value of the character “B” or “C” can be changed (Step S 9 ) and the graph  y  can be displayed again (Step S 10 ). 
         [0088]    Thus, according to the slider generation process involved in the graph display process of the graph scientific electronic calculator  10 , the value of each coefficient included in the graphed function formula can be varied as a proper pitch in a proper range so that the change of the graph can be understood by the user easily. 
         [0089]      FIG. 6  is a flow chart showing a slider operation process of the graph scientific electronic calculator  10 . 
         [0090]    When a touch operation on the slider SLA displayed on the touch panel display  13  is detected (Yes in Step S 81 ), determination is made as to whether the knob portion CS of the slider SLA is directly touched or not (Step S 82   a ). 
         [0091]    Here, when conclusion is made that the knob portion CS is touched (Yes in Step S 82   a ), a position of the knob portion CS from which the touch is released after the knob portion CS is slid is specified (Step S 83   a ). A step position of a coefficient value closest to the specified position is determined (Step S 84   a ). 
         [0092]    On the other hand, when conclusion is made that the knob portion CS is not directly touched but a neighbor portion to the knob portion CS is touched (Yes in Step S 82   b ), the touch position is specified to be on the left side or the right side of the knob portion CS (Step S 83   b ). When the touch position is specified to be the neighbor portion on the left side of the knob portion CS, a step position having a next smaller value to the knob portion CS is determined. On the other hand, when the touch position is specified to be the neighbor portion on the right side of the knob portion CS, a step position having a next larger value to the knob portion CS is determined (Step S 84   b ). 
         [0093]    When the step position corresponding to the user operation is determined thus, the knob portion CS is moved to the step position so that the slider SLA updated thus is displayed (Step S 85 ). 
         [0094]      FIGS. 7A and 7B  are views showing a motion of the graph scientific electronic calculator  10  in response to a slider operation. 
         [0095]    When a neighbor portion on the right side of the knob portion CS in the slider SLA displayed on the touch panel display  13  is touched as specified by an arrow T in the state in which the knob portion CS is located in a position of a coefficient value “−12”, as shown in  FIG. 7(A)  (Steps S 81 , S 82   b  and S 83   b ), a step position of a coefficient value “−6” in the neighbor portion on the right side of the knob portion CS is determined (Step S 84 ). 
         [0096]    Then, the knob portion CS is moved to the determined step position of the coefficient value “−6” so that the slider SLA updated thus is displayed, as shown in  FIG. 7(B)  (Step S 85 ). 
         [0097]      FIGS. 8(A) to 8(H)  are views showing the change of the display of a graph  y  in response to a slider operation in the graph display process of the graph scientific electronic calculator  10 . 
         [0098]    Specific examples shown in  FIGS. 8(A) to 8(H)  show the change of the display of the graph  y  in the case where the graph  y  of the function formula “y=(A/2)X 2 +X−2” is displayed on the graph screen Gs (with a reduction factor of ⅓) and the value of the coefficient “A” is varied successively by the slider SLA. 
         [0099]    That is, as described in the slider generation process (see  FIG. 5 ), the reference variable pitches (step values) for the slider SLA in the second-degree term of the function formula “y=(A/2)X 2 +X−2” are read as [−2, −1, −0.5, −0.2, −0.1, −0.05, 0, 0.05, 0.1, 0.2, 0.5, 1, 2] from the slider pattern table  15   f  (see  FIG. 3 ) (Steps A 1  to A 3 ). 
         [0100]    The read step values are corrected by the reciprocal “2” of the constant coefficient “½” (Steps A 4  to A 6 ) and further corrected by the reciprocal “3” of the reduction factor “⅓” of the graph screen Gs (Steps A 7  and A 8   a  to A 10   a ), so that the step values are changed to [−12, −6, −3, −1.2, −0.6, −0.3, 0, 0.3, 0.6, 1.2, 3, 6, 12] (Step S 11 ). Then, the slider SLA corresponding to the determined variable pitches (step values) is displayed as shown in  FIGS. 8(A) to 8(H) . 
         [0101]    As shown in  FIGS. 8(A) to 8(H) , when the slider SLA is operated to slide while touched by the user, the value of the coefficient “A” is varied successively (Steps S 8  and S 9 ) so that data for drawing the graph  y  are regenerated and displayed again on the graph screen Gs whenever the value of the coefficient “A” is varied (Step S 10 ). 
         [0102]    Incidentally, the respective operation methods performed by the graph scientific electronic calculator  10  as described in the embodiments, that is, the methods of the graph display process shown in the flow chart of  FIG. 4 , the slider generation process shown in the flow chart of  FIG. 5 , the slider operation process shown in the flow chart of  FIG. 6 , etc. can be recorded as a computer-executable program onto a recording medium (recording medium  17 ) such as a memory card (an ROM card, an RAM card, or the like), a magnetic disk (a flexible disk, a hard disk, or the like), an optical disk (a CD-ROM, a DVD, or the like) or a semiconductor memory and distributed. The computer (CPU  11 ) of the electronic calculator ( 10 ) having the graph display function can read the program recorded on the recording medium to execute the same processes based on the aforementioned methods. 
         [0103]    In addition, data of the program for implementing the methods can be transmitted as a form of program codes through a communication network (public line). The computer (CPU  11 ) of the electronic calculator  10  having the graph display function can receive the program through a communication device (the communication controller  18 ) connected to the communication network to execute the same processes based on the aforementioned methods. 
         [0104]    Incidentally, the embodiment of the graph display has been described as a device performing all operations for the graph display process in a special appliance which is the graph scientific electronic calculator  10 . However, the graph display may be formed as a server device of a cloud system. 
         [0105]    That is, in this case, when a desired function formula “y=f(x)” is inputted to the server device by a user from a terminal device such as a tablet terminal having a user interface, the server device generates graph data corresponding to the function formula and outputs the data for displaying the graph to the terminal device so that the data can be displayed on the terminal device. When an instruction [Modify] issued in accordance with a user operation is inputted from the terminal device, the service device generates a slider SL and outputs the slider SL to the terminal device in the same manner as in the embodiment so that the slider SL can be displayed on the terminal device. When a value of a coefficient in accordance with a user operation on the slider SL is inputted from the terminal device, the server device regenerates the graph data in which the value of the coefficient has been changed and outputs the data for displaying the graph to the terminal device so that the data can be displayed on the terminal device. 
         [0106]    In this manner, it is matter of course that even a terminal device having no special function can display a graph  y  corresponding to a function formula inputted by a user as long as the terminal device can gain access to the server device. In addition, a value of a coefficient included in the function formula can be varied as a suitable pitch in a suitable range by the slider SL so that the change of the graph  y  can be understood easily by the user. 
         [0107]    While the present invention has been shown and described with reference to certain exemplary embodiments thereof, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims. It is aimed, therefore, to cover in the appended claim all such changes and modifications as fall within the true spirit and scope of the present invention.