Japanese (“ú–{Œê”Å)

LastUpdate 6/22/2024


@My first encounter with computers was during a university lecture. It was a lecture on how to write a programing language called "Fortran". I remember punching holes in a peace of paper tape and letting a big computer read the program I created.
@In my first year as a teacher , I encountered a computer called "NEC-PC9801" at the school where I worked. As a strage medium , I inserted a 5-inch floppy disk , which I think is quite large , into the main unit.
@By the way , the strage medium of the personal computer I purchased for home use was a casstte tape. It wasn't just for personal computers. It was for cassette tape recorders that are still around today for listening to and memorizing music. The boot program is also included in this cassette tape , and it takes about 5 minutes for the computer to start up.
@At that time , computers were machines for numerical processing and could not process mathematical formulas. However , computers now calculate not only numbers , but also formulas. If you use formula manipulation software , "organize formulas" , "expand" , "factorize" , "solve linear equation" , "solve quadratic equations" , "solve cubic equations" , "solve quartic equations" , " differentiate" , and "Integration" is easy for you to do.
@Three-dimensional graphs can be easily drawn using Maxima. By dragging the graph , you can freely change the viewing direction of the graph.
@Typical formula manipulation software includes (1) "Mathematica" , (2) "Maple" , and (3) "Maxima". While (1) , (2) are expensive , ranging from 200,000 yen to 300,000 yen , (3) "Maxima" is free software, so it is free.
@In addition , the source code of "Maxima "is open to the public (open source) , and all kinds of people around the world volunteer to participate in its development. "Maxima" is written in a programming language called "LISP".
@In addition , "wxMaxima 0.8.7"was used for the following examples.


No Table of contens
1 @Graph of a 3D Explicit Function (Part 1)
2 @Graph of a 3D Implicit Function (Part 1)
3 @Graph of a 3D Parameters (Part 1)
4 @Graph of a 2D Explicit Function (Part 1)
5 @Graph of a 2D Implicit Function (Part 1)
6 @Graph of a 2D Parameters (Part 1)
7 @Graph of a 3D Implicit Function (Part 2)
8 @Graph of a 2D Explicit Function (Part 2)
9 @Graph of a 2D Parameters (Part 2)
10 @Graph of a 3D Explicit Function (Part 2)
11 @Graph of a 3D Parameters (Part 2)
12 @Graph of a 2D Explicit Function (Part 3)
13 @Graph of a 2D Parameters (Part 3)
14 @Graph of a 3D Explicit Function (Part 3)
15 @Graph of a 3D Parameters (Part 3)@
16 @Rotating Body
17 @Approximation of Expressions by Taylor Expansion
18 @Euler's Formal Proof
19 @Others
20 @Download and Install
21 @Running "‚l‚‚˜‚‰‚‚"
22 @About Sample Data

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To table of contents
@yExample 1z@Draw a graph of a 3D explicit function. mMexican hatn

m‚PnFunction expression
@@@@@i|‚RƒÎ…‚˜…‚RƒÎji|‚RƒÎ…‚™…‚RƒÎj

m‚QnInput formula
@plot3d(sin(sqrt(x^2+y^2))/sqrt(x^2+y^2),[x,-3*%pi,3*%pi],[y,-3*%pi,3*%pi],[plot_format,gnuplot],[grid,50,50]);

m‚RnDrawing result
@@@@@
ƒHow to draw a graph„
@As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time.
@

@yExample 2z@Draw a graph of a 3D explicit function. mCaldera shapen

m‚PnFunction expression
@@@@@i|‚Q…‚˜…‚Qji|‚Q…‚™…‚Qj

m‚QnInput formula
@@@plot3d(exp(-(x^2+y^2)/2)*(x^2+y^2)/(2*%pi),[x,-2,2],[y,-2,2],[plot_format,gnuplot],[grid,50,50]);

m‚RnDrawing result
@@@@@
ƒHow to draw a graph„
@ As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time.
@

@yExample 3z@Draw a graph of a 3D explicit function. mA slightly sunken saddle shapen

m‚PnFunction expression
@@@@@i|‚Q…‚˜…‚Qji|‚Q…‚™…‚Qj

m‚QnInput formula
@@@plot3d(3*exp(-(x^2+y^2))*(2*x^2+y^2),[x,-2,2],[y,-2,2],[plot_format,gnuplot],[grid,50,50]);

m‚RnDrawing result
@@@@@
ƒHow to draw a graph„
@ As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time.
@

To table of contents
@yExample 4z@Draw a wireframe graph of a 3D implicit function. mSpheren

m‚PnFunction expression
@@@@i|‚P…‚˜…‚Pji|‚P…‚™…‚Pji|‚P…‚š…‚Pj

m‚QnInput formula
@@@draw3d(implicit(x^2+y^2+z^2=1,x,-1,1,y,-1,1,z,-1,1));

m‚RnDrawing result
@@@@@
ƒHow to draw a graph„
@First , input "load(draw)" and press the Shift key and Enter key at the same time to load the package.
@Next , as in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time.
@

@yExample 5z@Draw a graph of a 3D implicit function with hidden surface processing. mSpheren

m‚PnFunction expression
@@@@i|‚P…‚˜…‚Pji|‚P…‚™…‚Pji|‚P…‚š…‚Pj

m‚QnInput formula
@@@draw3d(enhanced3d=true,implicit(x^2+y^2+z^2=1,x,-1,1,y,-1,1,z,-1,1));

m‚RnDrawing result
@@@@@
ƒHow to draw a graph„
@First , input "load(draw)" and press the Shift key and Enter key at the same time to load the package.
@Next , as in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time.
@

@yExample 6z Draw a graph of a 3D implicit function with hidden surface processing. mHollow drumn

m‚PnFunction expression
@@@@i|‚Q…‚˜…‚Qji|‚Q…‚™…‚Qji|‚Q…‚š…‚Qj

m‚QnInput formula
@@@draw3d(enhanced3d=true,implicit(x^2+y^2-z^2=1,x,-2,2,y,-2,2,z,-2,2));

m‚RnDrawing result
@@@@@
ƒHow to draw a graph„
@First , input "load(draw)" and press the Shift key and Enter key at the same time to load the package.
@Next , as in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time.
@

@yExample 7z Draw a graph of a 3D implicit function with hidden surface processing. mSewer pipe jointn

m‚PnFunction expression
@@@@i|‚P…‚˜…‚Pji|‚P…‚™…‚Pji|‚P…‚š…‚Pj

m‚QnInput formula
@@@draw3d(enhanced3d=true,implicit((x^2-1)^2+(y^2-1)^2+(z^2-1)^2=1.5, x,-1,1,y,-1,1,z,-1,1));

m‚RnDrawing result
@@@@@
ƒHow to draw a graph„
@First , input "load(draw)" and press the Shift key and Enter key at the same time to load the package.
@Next , as in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time.
@

@yExample 8z@Draw a graph of a 3D implicit function with hidden surface processing. ma cell with nucleus in the centern

m‚PnFunction expression
@@@‚ƒ‚‚“(‚˜{ƒÓ‚™){‚ƒ‚‚“(‚˜|ƒÓ‚™) {‚ƒ‚‚“(‚™{ƒÓ‚š){‚ƒ‚‚“(‚™|ƒÓ‚š){‚ƒ‚‚“(‚š{ƒÓ‚˜){‚ƒ‚‚“(‚š|ƒÓ‚˜)‚Q
@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@iHowever , ƒÓ represents the golden ratio.j
m‚QnInput formula
@@@draw3d(enhanced3d=true,implicit(cos(x+%phi*y)+cos(x-%phi*y)+cos(y+%phi*z)
@@@@@@@@@@@@@@@@@+cos(y-%phi*z)+cos(z+%phi*x)+cos(z-%phi*x)=2,x,-4,4,y,-4,4,z,-4,4));
m‚RnDrawing result
@@@@@
ƒHow to draw a graph„
@First , input "load(draw)" and press the Shift key and Enter key at the same time to load the package.
@Next , as in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time.
@

To table of contents
@yExample 9z@Draw a graph of a 3D parameter. mSpheren

m‚PnFunction expression
@@@‚˜‚ƒ‚‚“‚“E‚ƒ‚‚“‚”
@@@‚™‚ƒ‚‚“‚“E‚“‚‰‚Ž‚”
@@@‚š‚“‚‰‚Ž‚“@@@@@@@@i‚O…‚“…‚QƒÎj i‚O…‚”…ƒÎj
m‚QnInput formula
@@@plot3d([cos(s)*cos(t),cos(s)*sin(t),sin(s)],[s,0,2*%pi],[t,0,%pi]);

m‚RnDrawing result
@@@@@
ƒHow to draw a graph„
@As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time.
@

@yExample 10z@Draw a graph of a 3D parameter. mDonut shapeitorusjn

m‚PnFunction expression
@@@‚˜(‚T{‚Q‚ƒ‚‚“‚“)‚ƒ‚‚“‚”
@@@‚™(‚T{‚Q‚ƒ‚‚“‚“)‚“‚‰‚Ž‚”
@@@‚š‚Q‚“‚‰‚Ž‚“ @@@@@@@@@@@i‚O…‚“…‚QƒÎj i‚O…‚”…‚QƒÎj

m‚QnInput formula
@@@plot3d([(5+2*cos(s))*cos(t),(5+2*cos(s))*sin(t),2*sin(s)],[s,0,2*%pi],[t,0,2*%pi]);

m‚RnDrawing result
@@@@@
ƒHow to draw a graph„
@ As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time.
@

@yExample 11z@Draw a graph of a 3D parameter mSpring typen

m‚PnFunction expression
@@@‚˜(‚T{‚ƒ‚‚“‚“)‚ƒ‚‚“‚”
@@@‚™(‚T{‚ƒ‚‚“‚“)‚“‚‰‚Ž‚”
@@@‚š‚“‚‰‚Ž‚“{‚OD‚U‚” @@@@@i‚O…‚“…‚QƒÎj i‚O…‚”…‚VƒÎj

m‚QnInput formula
@@@plot3d([(5+cos(s))*cos(t),(5+cos(s))*sin(t),sin(s)+0.6*t],[s,0,2*%pi],[t,0,7*%pi]);

m‚RnDrawing result
@@@@@
ƒHow to draw a graph„
@As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time.
@

@yExample 12z@Draw a graph of a 3D parameter. mMobius stripn

m‚PnFunction expression
@@@
@@@
@@@@@@@@@@@@@@@@@@i|ƒÎ…‚“…ƒÎj i|‚P…‚”…‚Pj

m‚QnInput formula
@@@plot3d([cos(s)*(3+t*cos(s/2)),sin(s)*(3+t*cos(s/2)),t*sin(s/2)],[s,0-%pi,%pi],[t,-1,1]);

m‚RnDrawing result
@@@@@
ƒHow to draw a graph„
@As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time.
@

@yExample 13z@Draw a graph of a 3D parameter. mKlein's jarn

m‚PnFunction expression
@@@
@@@
@@@
@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@i|ƒÎ…‚“…ƒÎj i|ƒÎ…‚”…ƒÎj

m‚QnInput formula
@@@plot3d([5*cos(s)*(cos(s/2)*cos(t)+sin(s/2)*sin(2*t)+3)-10,
@@@@-5*sin(s)*(cos(s/2)*cos(t)+sin(s/2)*sin(2*t)+3.0),5*(-sin(s/2)*cos(t)+cos(s/2)*sin(2*t))],
@@@@@[s,-%pi,%pi],[t,-%pi,%pi]);

m‚RnDrawing result
@@@@@
ƒHow to draw a graph„
@As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time.
@

To table of contents
@yExample14z@Draw a graph of a 2D explicit function. mQuadratic functionn

m‚PnFunction expression
@@@@i|‚Q…‚˜…‚Qj

m‚QnInput formula
@@@ plot2d(3*x^2-1,[x,-2,2]);

m‚RnDrawing result
@@@@@
ƒHow to draw a graph„
@As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time.
@

@yExample 15z@Draw a graph of a 2D explicit function. mExpotentialETrigonometric functionn

m‚PnFunction expression
@@@@@i‚O…‚˜…‚Q‚Oj

m‚QnInput formula
@@@ plot2d(exp(x)*sin(7*x),[x,0,20]);

m‚RnDrawing result
@@@@@
ƒHow to draw a graph„
@As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time.
@

@yExample 16z@Draw a graph of a 2D explicit function. mDraw multiple graphs simultaneouslyn

m‚PnFunction expression
@@@@@‚™‚“‚‰‚Ž‚˜A‚™‚“‚‰‚Ž‚Q‚˜A‚™‚“‚‰‚Ž‚R‚˜@@@i‚O…‚˜…‚QƒÎj

m‚QnInput formula
@@@ plot2d([sin(x),sin(2*x),sin(3*x)],[x,0,2*%pi]);

m‚RnDrawing result
@@@@@
ƒHow to draw a graph„
@As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time.
@

Table of contents
@yExample 17z@Draw a graph of a 2D implicit function. mCirclen

m‚PnFunction expression
@@@@

m‚QnInput formula
@@@ implicit_plot(x^2+y^2=1,[x,-2,2],[y,-2,2]);

m‚RnDrawing result
@@@@@
ƒHow to draw a graph„
@First , input "load(implicitplot)" and press the Shift key and Enter key at the same time to load the package.
@Next , as in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time.
@

@yExample 18z@Draw a graph of a 2D implicit function. mFour leaf clovern

m‚PnFunction expression
@@@@
@@@

m‚QnInput formula
@@@ implicit_plot((x^2+y^2)^4-(x^2-y^2)^2=0,[x,-2,2],[y,-2,2]);

m‚RnDrawing result
@@@@@
ƒHow to draw a graph„
@First , input "load(implicitplot)" and press the Shift key and Enter key at the same time to load the package.
@Next , as in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time.
@

@yExample 19z@Draw a graph of a 2D implicit function. mCircle and Four leaf clovern

m‚PnFunction expression
@@@@
@@@@@

m‚QnInput formula
@@@ plot2d([x^2+y^2=1,(x^2+y^2)^4-(x^2-y^2)^2=0],[x,-2,2],[y,-2,2]);

m‚RnDrawing result
@@@@@
ƒHow to draw a graph„
@First , input "load(implicitplot)" and press the Shift key and Enter key at the same time to load the package.
@Next , as in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time.
@

To table of contents
@yExample 20z@Draw a graph of a 2D parameter. m‡ shapen

m‚PnFunction expression
@@@@‚˜‚ƒ‚‚“‚”
@@@@‚™‚“‚‰‚Ž‚Q‚” @i‚O…‚”…‚QƒÎj ‚P‚O‚O divisions

m‚QnInput formula
@@@ plot2d([parametric,cos(t),sin(2*t)],[t,0,2*%pi],[nticks,100]);

m‚RnDrawing result
@@@@@
ƒHow to draw a graph„
@As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time.
@

@yExample 21z@Draw a graph of a 2D parameter. mChrysanthemum petal shapen

m‚PnFunction expression
@@@@‚˜‚S‚“‚‰‚Ž‚S‚”‚ƒ‚‚“‚”
@@@@‚™‚S‚“‚‰‚Ž‚S‚”‚“‚‰‚Ž‚” @i‚O…‚”…‚QƒÎj@ ‚S‚O‚O divisions

m‚QnInput formula
@@@ plot2d([parametric,4*sin(4*t)*cos(t),4*sin(4*t)*sin(t)],[t,0,2*%pi],[nticks,400]);

m‚RnDrawing result
@@@@@
ƒHow to draw a graph„
@As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time.
@

@yExample 22z@Draw a graph of a 2D parameter. mSwirl shapen

m‚PnFunction expression
@@@@‚˜‚”‚ƒ‚‚“‚”@@@@ @(500 divisions)
@@@@‚™‚”‚“‚‰‚Ž‚” @@@@@

m‚QnInput formula
@@@ plot2d([parametric,t*cos(t),t*sin(t)],[t,0,35*%pi/2],[nticks,500]);

m‚RnDrawing result
@@@@@
ƒHow to draw a graph„
@As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time.
@

@yExample 23z@Draw a graph of a 2D parameter. mHeart shapen

m‚PnFunction expression
@@@@‚˜(‚P{‚ƒ‚‚“‚”)‚ƒ‚‚“‚”
@@@@‚™(‚P{‚ƒ‚‚“‚”)‚“‚‰‚Ž‚” @@i‚O…‚”…‚QƒÎj@ ‚P‚O‚O divisions

m‚QnInput formula
@@@ plot2d([parametric,(1+cos(t))*cos(t),(1+cos(t))*sin(t)],[t,0,2*%pi],[nticks,100]);

m‚RnDrawing result
@@@@@
ƒHow to draw a graph„
@As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time.
@

To table of contents
@yExample 24z@Draw a wireframe graph of a 3D implicit function. mellipsoidn

m‚PnFunction expression
@@@

m‚QnInput formula
@@@draw3d(implicit(x^2/1^2+y^2/2^2+z^2/3^2=1,x,-1,1,y,-2,2,z,-3,3));
@@@
m‚RnDrawing result
@@@@@
ƒHow to draw a graph„
@First , input "load(draw)" and press the Shift key and Enter key at the same time to load the package.
@Next , as in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time.
@

@yExample 25z@Draw a wireframe graph of a 3D implicit function. mSingle leaf hyperbolan

m‚PnFunction expression
@@@

m‚QnInput formula
@@@draw3d(implicit(x^2/1^2+y^2/2^2-z^2/3^2=1,x,-7,7,y,-7,7,z,-7,7));
@@@
m‚RnDrawing result
@@@@@
ƒHow to draw a graph„
@First , input "load(draw)" and press the Shift key and Enter key at the same time to load the package.
@Next , as in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time.
@

@yExample 26z@Draw a wireframe graph of a 3D implicit function. mBilobal hyperbolan

m‚PnFunction expression
@@@

m‚QnInput formula
@@@draw3d(implicit(x^2/1^2-y^2/2^2-z^2/3^2=1,x,-2,2,y,-4,4,z,-8,8));
@@@
m‚RnDrawing result
@@@@@
ƒHow to draw a graph„
@First , input "load(draw)" and press the Shift key and Enter key at the same time to load the package.
@Next , as in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time.
@

@yExample 27z@Draw a wireframe graph of a 3D implicit function. mElliptical paraboloidn

m‚PnFunction expression
@@@

m‚QnInput formula
@@@draw3d(implicit(x^2/1^2+y^2/2^2=1/20*z,x,-1,1,y,-2,2,z,0,20));
@@@
m‚RnDrawing result
@@@@@
ƒHow to draw a graph„
@First , input "load(draw)" and press the Shift key and Enter key at the same time to load the package.
@Next , as in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time.
@

@yExample 28z@Draw a wireframe graph of a 3D implicit function. mHyperbolic paraboloidn

m‚PnFunction expression
@@@

m‚QnInput formula
@@@draw3d(implicit(x^2/1^2-y^2/2^2=1/2*z,x,-2,2,y,-3,3,z,-4,4));
@@@
m‚RnDrawing result
@@@@@
ƒHow to draw a graph„
@First , input "load(draw)" and press the Shift key and Enter key at the same time to load the package.
@Next , as in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time.
@

@yExample 29z@Draw a wireframe graph of a 3D implicit function. mElliptical cylindern

m‚PnFunction expression
@@@

m‚QnInput formula
@@@draw3d(implicit(x^2/1^2+y^2/2^2=1,x,-2,2,y,-2,2,z,-10,10));
@@@
m‚RnDrawing result
@@@@@
ƒHow to draw a graph„
@First , input "load(draw)" and press the Shift key and Enter key at the same time to load the package.
@Next , as in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time.
@

@yExample 30z@Draw a wireframe graph of a 3D implicit function. mHyperbolic columnn

m‚PnFunction expression
@@@

m‚QnInput formula
@@@draw3d(implicit(x^2/2^2-y^2/3^2=1,x,-10,10,y,-10,10,z,-20,20));
@@@
m‚RnDrawing result
@@@@@
ƒHow to draw a graph„
@First , input "load(draw)" and press the Shift key and Enter key at the same time to load the package.
@Next , as in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time.
@

@yExample 31z@Draw a wireframe graph of a 3D implicit function. mParabolic columnn

m‚PnFunction expression
@@@

m‚QnInput formula
@@@draw3d(implicit(x^2=y,x,-5,5,y,0,25,z,-20,20));
@@@
m‚RnDrawing result
@@@@@
ƒHow to draw a graph„
@First , input "load(draw)" and press the Shift key and Enter key at the same time to load the package.
@Next , as in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time.
@

To table of contents
@yExample 32z@Draw a graph of a 2D explicit function. mMake it easier to see by specifying the range of y valuesn

m‚PnFunction expression
@@@

m‚QnInput formula
@@@plot2d((x^3+2*x^2-4*x-3)/(x+1),[x,-3,3],[y,-10,10]);
@@@
m‚RnDrawing result
@@@@@
ƒHow to draw a graph„
@As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time.
@

@yExample 33z@Draw a graph of a 2D explicit function. mDisplay multiple graphs simultaneouslyn

m‚PnFunction expression
@@@

m‚QnInput formula
@@@plot2d([exp(-2*x),exp(x),1],[x,-2,2],[y,0,10]);
@@@
m‚RnDrawing result
@@@@@
ƒHow to draw a graph„
@As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time.
@

@yExample 34z@Draw a graph of a 2D explicit function. mFind the number of real solutions to an equationn

m‚PnEquation
@@@

m‚QnInput formula
@@@plot2d([x/8,cos(x)],[x,-15,15],[y,-2,2]);
@@@
m‚RnDrawing result
@@@@@
ƒHow to draw a graph„
@As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time.
@Since there are 5 intersections , we know that the equation has 5 real solutions.
@

To table of contents
@yExample 35z@Draw a graph of a 2D parameter. mSpecify the number of divisionsn

m‚PnFunction expression
@@@@@‚O…‚”…‚QƒÎ

m‚QnInput formula
@@@plot2d([parametric,3*cos(t)+cos(13*t),3*sin(t)+sin(13*t)],[t,0,2*%pi],[nticks,300]);
@@@
m‚RnDrawing result
@@@@@
ƒHow to draw a graph„
@As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time.
@

@yExample 36z@Draw a graph of a 2D parameter. mLissajous curven

m‚PnFunction expression
@@@@@

m‚QnInput formula
@@@plot2d([parametric,cos(7*t),sin(4*t)],[t,0,2*%pi],[nticks,300]);
@@@
m‚RnDrawing result
@@@@@
ƒHow to draw a graph„
@As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time.
@

@yExample 37z@Draw a graph of a 2D parameter. mBernoulli's lemniscate curven

m‚PnFunction expression
@@@@@

m‚QnInput formula
@@@plot2d([parametric,cos(t)/(1+sin(t)^2),sin(t)*cos(t)/(1+sin(t)^2)],[t,0,2*%pi],[nticks,300]);
@@@
m‚RnDrawing result
@@@@@
ƒHow to draw a graph„
@As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time.
@

To table of contents
@yExample 38z@Draw a graph of a 3D explicit function. mDo not specify the number of devisionsn

m‚PnFunction expression
@@@@@

m‚QnInput formula
@@@plot3d(exp(-sqrt(x^2+y^2)/2)*cos(%pi*sqrt(x^2+y^2)),[x,-4,4],[y,-4,4]);
@@@
m‚RnDrawing result
@@@@@
ƒHow to draw a graph„
@As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time.
@

@yExample 39z@Draw a graph of a 3D explicit function. mShark minimal surfacen

m‚PnFunction expression
@@@@@

m‚QnInput formula
@@@plot3d(log(cos(x)/cos(y)),[x,-%pi/2,%pi/2],[y,-%pi/2,%pi/2]);
@@@
m‚RnDrawing result
@@@@@
ƒHow to draw a graph„
@As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time.
@

@yExample 40z@Draw a graph of a 3D explicit function. mDefine and draw a functionn

m‚PnFunction expression
@@@@@ @@@i‚Oƒ‚˜…‚QC‚Oƒ‚™…‚Qj

m‚QnInput formula
@@@u(a,x,y,p,q,r):=a*(p*x^(-r)+q*y^(-r))^(-1/r);
@@@plot3d(u(2,x,y,2,3,2),[x,0.01,2],[y,0.01,2]);
@@@
m‚RnDrawing result
@@@@@
ƒHow to draw a graph„
@First , enter the first line of the above input express in half-width , and press the Shift key and Enter key at the same time.
@Next , enter the second line in half-width and press the Shift key and Enter key at the same time.
@

To table of contents
@yExample 41z@Draw a graph of a 3D parameter. mTorusn

m‚PnFunction expression
@@@@
@@@ @‚O…‚“…‚QƒÎA‚O…‚”…‚QƒÎ

m‚QnInput formula
@@@plot3d([cos(s)*(3+cos(t)),sin(s)*(3+cos(t)),sin(t)],[s,0,2*%pi],[t,0,2*%pi]);
@@@
m‚RnDrawing result
@@@@@
ƒHow to draw a graph„
@As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time.
@

@yExample 42z@Draw a graph of a 3D parameter. mAsteroidal spheren

m‚PnFunction expression
@@@@
@@@ @‚O…‚“…‚QƒÎA‚O…‚”…‚QƒÎ

m‚QnInput formula
@@@plot3d([cos(s)^3*cos(t)^3,sin(s)^3*cos(t)^3,sin(t)^3],[s,0,2*%pi],[t,0,2*%pi]);
@@@
m‚RnDrawing result
@@@@@
ƒHow to draw a graph„
@As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time.
@

@yExample 43z@Draw a graph of a 3D parameter. mHenneberg Minimal Surfacen

m‚PnFunction expression
@@@@
@@@@
@@@@
@@@ @‚OD‚R…‚“…‚OD‚X@A@‚O…‚”…‚QƒÎ

m‚QnInput formula
@@@plot3d([2*sinh(s)*cos(t)-(2/3)*sinh(3*s)*cos(3*t),2*sinh(s)*sin(t)-(2/3)*sinh(3*s)
@@@@@@@@@@@@@@@@@@*sin(3*t),2*cosh(2*s)*cos(2*t)],[s,0.3,0.9],[t,0,2*%pi],[grid,4,72]);

m‚RnDrawing result
@@@@@
ƒHow to draw a graph„
@As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time.
@

To table of contents
@yExample 44z@Draw a graph of a 2D explicit function. mMake it easier to see by specifying the range of y-axis valuesn

m‚PnFunction expression
@@@@

m‚QnInput formula
@@@plot2d(1/(x-1)+1,[x,-5,5],[y,-5,5]);

m‚RnDrawing result
@@@@@
ƒHow to draw a graph„
@As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time.
@

@yExample 45z@Draw a graph of a 2D explicit function. mCompare with the Taylor expansion graph of the approximation formulan

m‚PnFunction expression
@@@@

m‚QnInput formula
@@@plot2d([cos(x),1-x^2/2+x^4/24-x^6/720,1-x^2/2+x^4/24-x^6/720+x^8/40320,
@@@@@@@@1-x^2/2+x^4/24-x^6/720+x^8/40320-x^10/3628800],[x,-2*%pi,2*%pi],[y,-5,5]);

m‚RnDrawing result
@@@@@
ƒHow to draw a graph„
@As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time.
@

@yExample 46z@Draw a graph of a 2D explicit function. mFind a number of real solutions to an equationn

m‚PnEquation
@@@@

m‚QnInput formula
@@@plot2d([exp(x),3-x^2],[x,-2,2],[y,-1,4]);

m‚RnDrawing result
@@@@@
ƒHow to draw a graph„
@As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time.
@Since there are two points of intersection , we know that the equation has two real solutions.
@

To table of contents
@yExample 47z@Draw a graph of a 2D parameter. mCircleFDon't specify the number of divisionsn

m‚PnFunction expression
@@@@@@@‚O…‚”…‚QƒÎ

m‚QnInput formula
@@@ plot2d([parametric,cos(t),sin(t)],[t,0,2*%pi]);

m‚RnDrawing result
@@@@@
ƒHow to draw a graph„
@As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time.
@

@yExample 48z@Draw a graph of a 2D parameter. mCircleFspecify 15 divisionsn

m‚PnFunction expression
@@@@@@@‚O…‚”…‚QƒÎ

m‚QnInput formula
@@@ plot2d([parametric,cos(t),sin(t)],[t,0,2*%pi],[nticks,15]);

m‚RnDrawing result
@@@@@
ƒHow to draw a graph„
@As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time.
@

@yExample 49z@Draw a graph of a 2D parameter. mCircleFspecify 100 divisionsn

m‚PnFunction expression
@@@@@@@‚O…‚”…‚QƒÎ

m‚QnInput formula
@@@ plot2d([parametric,cos(t),sin(t)],[t,0,2*%pi],[nticks,100]);

m‚RnDrawing result
@@@@@
ƒHow to draw a graph„
@As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time.
@

To table of contents
@yExample 50z@Draw a graph of a 3D explicit function. mDo not specify the number of divisionsn

m‚PnFunction expression
@@@@

m‚QnInput formula
@@@ plot3d(x^3-3*x*y^2,[x,-1,1],[y,-1,1]);

m‚RnDrawing result
@@@@@
ƒHow to draw a graph„
@As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time.
@

@yExample 51z@Draw a graph of a 3D explicit function. mDon't specify the number of divisionsn

m‚PnFunction expression
@@@@@@@@@|‚P…‚˜…‚PA|‚P…‚™…‚P

m‚QnInput formula
@@@ plot3d((x^2*y)/(x^4+y^2),[x,-1,1],[y,-1,1]);

m‚RnDrawing result
@@@@@
ƒHow to draw a graph„
@As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time.
@

@yExample 52z@Draw a graph of a 3D explicit function. mSpecify the number of divisionsn

m‚PnFunction expression
@@@@@@@@@|‚P…‚˜…‚PA|‚P…‚™…‚P

m‚QnInput formula
@@@ plot3d((x^2*y)/(x^4+y^2),[x,-1,1],[y,-1,1],[grid,100,100]);

m‚RnDrawing result
@@@@@
ƒHow to draw a graph„
@As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time.
@

To table of contents
@yExample 53z@Draw a graph of a 3D parameter. mSpherical surfaceFSpecify the number of divisionn

m‚PnFunction expression
@@@@
@@@@@‚O…‚“…‚QƒÎA‚O…‚”…‚QƒÎ

m‚QnInput formula
@@@ plot3d([cos(s)*cos(t),cos(s)*sin(t),sin(s)],[s,0,2*%pi],[t,0,2*%pi],[grid,50,50]);

m‚RnDrawing result
@@@@@
ƒHow to draw a graph„
@As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time.
@

@yExample 54z@Draw a graph of a 3D parameter. mAmazing shapes and equationsn

m‚PnFunction expression
@@@@
@@@@@@@@@@@@@@
@@@@
@@@@@@@@@@@@@@
@@@@

@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@‚O…‚•…‚QƒÎA‚O…‚–…‚QƒÎ

m‚QnInput formula
@@@ plot3d([3*cos(u)+5*cos(3*u)+(3*(cos(u)+5*cos(3*u))*cos(v))/(2*sqrt(234+90*cos(2*u)))
@@@ -(3*cos(6*u)*(sin(u)+5*sin(3*u))*sin(v))/(2*sqrt(13+5*cos(2*u))*sqrt(22+5*cos(2*u)
@@@ +9*cos(12*u))),3*sin(u)+5*sin(3*u)+(3*cos(v)*(sin(u)+5*sin(3*u)))/(2*sqrt(234+90*cos
@@ @(2*u)))+(3*(5*cos(3*u)+cos(5*u)+cos(7*u)+5*cos(9*u))*sin(v))/(4*sqrt(13+5*cos(2*u))
@@@ *sqrt(22+5*cos(2*u)+9*cos(12*u))),3*sin(6*u)-(sqrt(13+5*cos(2*u))*sin(v))/(2*sqrt
@@ @(22+5*cos(2*u)+9*cos(12*u)))],[u,0,2*%pi],[v,0,2*%pi],[grid,80,8]);

m‚RnDrawing result
@@@@@
ƒHow to draw a graph„
@As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time.
@

To table of contents
@yExample 55z@Draw a graph of a 3D parameter. mRotating body 1n

m‚PnRotating body
@@@@A solid created by rotating the part enclosed by parabola y=x^2 , x=-3 , x=3 , the x-axis around the x-axis.

m‚QnInput formula
@@@ plot3d([t,t^2*cos(s),t^2*sin(s)],[t,-3,3],[s,0,2*%pi]);

m‚RnDrawing result
@@@@@
ƒHow to draw a graph„
@As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time.
@

@yExample 56z@Draw a graph of a 3D parameter. mRotating body 2n

m‚PnRotating body
@@@@A solid created by rotating the part enclosed by parabola x=ã‚™ , y=0 , y=9 , the y-axis around the y-axis.

m‚QnInput formula
@@@ plot3d([sqrt(t)*cos(s),t,sqrt(t)*sin(s)],[t,0,9],[s,0,2*%pi]);

m‚RnDrawing result
@@@@@
ƒHow to draw a graph„
@As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time.
@

@yExample 57z@Draw a graph of a 3D parameter. mRotating body 3n

m‚PnRotating body
@@@@A solid created by rotating the part enclosed by parabola y=x^2-2 , x=-3 , x=3 , the x-axis around the x-axis.

m‚QnInput formula
@@@ plot3d([t,(t^2-2)*cos(s),(t^2-2)*sin(s)],[t,-3,3],[s,0,2*%pi]);

m‚RnDrawing result
@@@@@
ƒHow to draw a graph„
@As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time.
@

@yExample 58z@Draw a graph of a 3D parameter. mRotating body 4n

m‚PnRotating body
@@@@A solid created by rotating the part enclosed by parabola y=x^2+2 , x=-3 , x=3 , the x-axis around the x-axis.

m‚QnInput formula
@@@ plot3d([t,(t^2+2)*cos(s),(t^2+2)*sin(s)],[t,-2,2],[s,0,2*%pi]);

m‚RnDrawing result
@@@@@
ƒHow to draw a graph„
@As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time.
@

@yExample 59z@Draw a graph of a 3D parameter. mRotating body 5n

m‚PnRotating body
@@@@A solid created by rotating circle: x^2+y^2=4 around the x-axis.

m‚QnInput formula
@@@ plot3d([t,sqrt(4-t^2)*cos(s),sqrt(4-t^2)*sin(s)],[t,-2,2],[s,0,2*%pi]);

m‚RnDrawing result
@@@@@
ƒHow to draw a graph„
@As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time.
@

To table of contents
@yExample 60z@Approximation of expressions by Taylor Expansion m‚™‚“‚‰‚Ž‚˜n

m‚PnInput expression for Taylor Expansion of sinx
@@@@taylor(sin(x),x,0,12);

m‚QnDeployment result
@@@

m‚RnAn input expression that draws the graph of ‚™‚“‚‰‚Ž‚˜ and its approximation
@@@plot2d([sin(x),x-x^3/6+x^5/120-x^7/5040+x^9/362880-x^11/39916800],[x,-10,10],[y,-1.2,1.2]);

m‚SnDrawing result
@@@@@
ƒHow to draw a graph„
@ As in the input formula in [3] above , enter all in half-width and press the Shift key and Enter key at the same time.
@

@yExample 61z@Approximation of expressions by Taylor Expansion m‚™‚ƒ‚‚“‚˜n

m‚PnInput expression for Taylor Expansion of cosx
@@@@taylor(cos(x),x,0,12);

m‚QnDeployment result
@@@

m‚RnAn input expression that draws the graph of ‚™‚ƒ‚‚“‚˜ and its aaproximation
@@@plot2d([cos(x),1-x^2/2+x^4/24-x^6/720+x^8/40320-x^10/3628800+x^12/479001600]
@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@,[x,-10,10],[y,-1.2,1.2]);

m‚SnDrawing result
@@@@@
ƒHow to draw a graph„
@ As in the input formula in [3] above , enter all in half-width and press the Shift key and Enter key at the same time.
@

@yExample 62z@Approximation of expressions by Taylor Expansion

m‚PnInut expression for Taylor Expansion of e^x
@@@@taylor(exp(x),x,0,6);

m‚QnDeployment result
@@@ 1+x+x^2/2+x^3/6+x^4/24+x^5/120+...

m‚Rn An input expression that draws the graph of and its approximation
@@@@plot2d([exp(x),1+x+x^2/2+x^3/6+x^4/24+x^5/120],[x,-3,3],[y,0,5]);

m‚SnDrawing result
@@@@@
ƒHow to draw a graph„
@ As in the input formula in [3] above , enter all in half-width and press the Shift key and Enter key at the same time.
@

To table of contents
@yExample 63z@Prove Euler's formula

m‚PnInput expression for Taylor Expansion of ‚“‚‰‚Ž‚˜
@@@@taylor(‚“‚‰‚Ž(x),x,0,12);

m‚QnTaylor Expansion result of ‚“‚‰‚Ž‚˜
@@@ @@@@@@@@@|||‡@

m‚RnInput expression for Taylor Expansion of cos‚˜
@@@@taylor(cos(x),x,0,12);

m‚SnTaylor Expansion result of cos‚˜
@@@@@@@|||‡A

m‚TnInput expression for Taylor Expansion of@
@@@@taylor(exp(%i*x),x,0,12);

m‚UnTaylor Expansion result of@
@@@
@@@@|||‡B

@@@Above , from ‡@ , ‡A , ‡B
@@@@@
@@@@@@@@@@@@@@@@@@@
@@@@@@@@ ‚ƒ‚‚“‚˜ { ‚‰‚“‚‰‚Ž‚˜

@@@Therefore , ‚ƒ‚‚“‚˜ { ‚‰‚“‚‰‚Ž‚˜

ƒHow to display the expansion formula„
@ As in the input formulas in [1] , [3] , [5] above , enter all in half-width and press the Shift key and Enter key at the same time.
@




To table of contents
@yProblem 1z@How many digits is 2^30 in integer ? However , ‚Œ‚‚‡(10C2)0.3010.
@This problem always comes up in common logarithms.
@If you teach in the order of ‡@¨‡A¨‡B¨‡C below , you can make the number of digits more specific.
‡@Display 2^30 , 2^50 , 2^100 , 3^30 , 3^50 , and 3^100 computed by ‚l‚‚˜‚‰‚‚ and count the number of digits.
‡ATeach how to find the number of digits by using common rogarithms.
‡BFind the number of digits in 2^30 , 2^50 , 2^100 , 3^30 , 3^50 , and 3^100 using common logarithms and
comfirm that it matches the number of digits you just counted.
‡CTouching on how to count large numbers.

Below are the results caluculated by Maxima.
@2^301073741824
@2^501125899906842624
@2^1001267650600228229401496703205376
@3^30205891132094649
@3^50717897987691852588770249
@3^100515377520732011331036461129765621272702107522001

ƒHow to use "‚l‚‚˜‚‰‚‚"„
@For example , to calculate 2^30
@Enter 2^30@in half-width , and press the Shift key and Enter key at the same time.

@yProblem 2z@Expand i‚{‚‚j^3@and@i‚{‚‚{‚ƒj^2@
@Expanding i‚{‚‚j^3@or@i‚{‚‚{‚ƒj^2@doesn't surprise you much.
@I wondered if it would be possible to have a class that surprises and impresses students by having Maxima calculate and display the expansion of i‚{‚‚j^50 and i‚{‚‚{‚ƒj^20 in the introduction of the expansion of equations.

Below is the result of expansion by Maxima
@@i‚{‚‚j^50
@b^50+50*a*b^49+1225*a^2*b^48+19600*a^3*b^47+230300*a^4*b^46+2118760*a^5*b^45
@@+15890700*a^6*b^44+99884400*a^7*b^43+536878650*a^8*b^42+2505433700*a^9*b^41
@@+10272278170*a^10*b^40+37353738800*a^11*b^39+121399651100*a^12*b^38
@@+354860518600*a^13*b^37+937845656300*a^14*b^36+2250829575120*a^15*b^35
@@+4923689695575*a^16*b^34+9847379391150*a^17*b^33+18053528883775*a^18*b^32
@@+30405943383200*a^19*b^31+47129212243960*a^20*b^30+67327446062800*a^21*b^29
@@+88749815264600*a^22*b^28+108043253365600*a^23*b^27+121548660036300*a^24*b^26
@@+126410606437752*a^25*b^25+121548660036300*a^26*b^24+108043253365600*a^27*b^23
@@+88749815264600*a^28*b^22+67327446062800*a^29*b^21+47129212243960*a^30*b^20
@@+30405943383200*a^31*b^19+18053528883775*a^32*b^18+9847379391150*a^33*b^17
@@+4923689695575*a^34*b^16+2250829575120*a^35*b^15+937845656300*a^36*b^14
@@+354860518600*a^37*b^13+121399651100*a^38*b^12+37353738800*a^39*b^11
@@+10272278170*a^40*b^10+2505433700*a^41*b^9+536878650*a^42*b^8+99884400*a^43*b^7
@@+15890700*a^44*b^6+2118760*a^45*b^5+230300*a^46*b^4+19600*a^47*b^3+1225*a^48*b^2
@@+50*a^49*b+a^50

@@i‚{‚‚{‚ƒj^20
@c^20+20*b*c^19+20*a*c^19+190*b^2*c^18+380*a*b*c^18+190*a^2*c^18+1140*b^3*c^17
@@+3420*a*b^2*c^17+3420*a^2*b*c^17+1140*a^3*c^17+4845*b^4*c^16+19380*a*b^3*c^16
@@+29070*a^2*b^2*c^16+19380*a^3*b*c^16+4845*a^4*c^16+15504*b^5*c^15+77520*a*b^4*c^15
@@+155040*a^2*b^3*c^15+155040*a^3*b^2*c^15+77520*a^4*b*c^15+15504*a^5*c^15
@@+38760*b^6*c^14+232560*a*b^5*c^14+581400*a^2*b^4*c^14+775200*a^3*b^3*c^14
@@+581400*a^4*b^2*c^14+232560*a^5*b*c^14+38760*a^6*c^14+77520*b^7*c^13
@@+542640*a*b^6*c^13+1627920*a^2*b^5*c^13+2713200*a^3*b^4*c^13+2713200*a^4*b^3*c^13
@@+1627920*a^5*b^2*c^13+542640*a^6*b*c^13+77520*a^7*c^13+125970*b^8*c^12
@@+1007760*a*b^7*c^12+3527160*a^2*b^6*c^12+7054320*a^3*b^5*c^12
@@+8817900*a^4*b^4*c^12+7054320*a^5*b^3*c^12+3527160*a^6*b^2*c^12
@@+1007760*a^7*b*c^12+125970*a^8*c^12+167960*b^9*c^11+1511640*a*b^8*c^11
@@+6046560*a^2*b^7*c^11+14108640*a^3*b^6*c^11+21162960*a^4*b^5*c^11
@@+21162960*a^5*b^4*c^11+14108640*a^6*b^3*c^11+6046560*a^7*b^2*c^11
@@+1511640*a^8*b*c^11+167960*a^9*c^11+184756*b^10*c^10+1847560*a*b^9*c^10
@@+8314020*a^2*b^8*c^10+22170720*a^3*b^7*c^10+38798760*a^4*b^6*c^10
@@+46558512*a^5*b^5*c^10+38798760*a^6*b^4*c^10+22170720*a^7*b^3*c^10
@@+8314020*a^8*b^2*c^10+1847560*a^9*b*c^10+184756*a^10*c^10+167960*b^11*c^9
@@+1847560*a*b^10*c^9+9237800*a^2*b^9*c^9+27713400*a^3*b^8*c^9
@@+55426800*a^4*b^7*c^9+77597520*a^5*b^6*c^9+77597520*a^6*b^5*c^9
@@+55426800*a^7*b^4*c^9+27713400*a^8*b^3*c^9+9237800*a^9*b^2*c^9
@@+1847560*a^10*b*c^9+167960*a^11*c^9+125970*b^12*c^8+1511640*a*b^11*c^8
@@+8314020*a^2*b^10*c^8+27713400*a^3*b^9*c^8+62355150*a^4*b^8*c^8
@@+99768240*a^5*b^7*c^8+116396280*a^6*b^6*c^8+99768240*a^7*b^5*c^8
@@+62355150*a^8*b^4*c^8+27713400*a^9*b^3*c^8+8314020*a^10*b^2*c^8
@@+1511640*a^11*b*c^8+125970*a^12*c^8+77520*b^13*c^7+1007760*a*b^12*c^7
@@+6046560*a^2*b^11*c^7+22170720*a^3*b^10*c^7+55426800*a^4*b^9*c^7
@@+99768240*a^5*b^8*c^7+133024320*a^6*b^7*c^7+133024320*a^7*b^6*c^7
@@+99768240*a^8*b^5*c^7+55426800*a^9*b^4*c^7+22170720*a^10*b^3*c^7
@@+6046560*a^11*b^2*c^7+1007760*a^12*b*c^7+77520*a^13*c^7+38760*b^14*c^6
@@+542640*a*b^13*c^6+3527160*a^2*b^12*c^6+14108640*a^3*b^11*c^6
@@+38798760*a^4*b^10*c^6+77597520*a^5*b^9*c^6+116396280*a^6*b^8*c^6
@@+133024320*a^7*b^7*c^6+116396280*a^8*b^6*c^6+77597520*a^9*b^5*c^6
@@+38798760*a^10*b^4*c^6+14108640*a^11*b^3*c^6+3527160*a^12*b^2*c^6
@@+542640*a^13*b*c^6+38760*a^14*c^6+15504*b^15*c^5+232560*a*b^14*c^5
@@+1627920*a^2*b^13*c^5+7054320*a^3*b^12*c^5+21162960*a^4*b^11*c^5
@@+46558512*a^5*b^10*c^5+77597520*a^6*b^9*c^5+99768240*a^7*b^8*c^5
@@+99768240*a^8*b^7*c^5+77597520*a^9*b^6*c^5+46558512*a^10*b^5*c^5
@@+21162960*a^11*b^4*c^5+7054320*a^12*b^3*c^5+1627920*a^13*b^2*c^5
@@+232560*a^14*b*c^5+15504*a^15*c^5+4845*b^16*c^4+77520*a*b^15*c^4
@@+581400*a^2*b^14*c^4+2713200*a^3*b^13*c^4+8817900*a^4*b^12*c^4
@@+21162960*a^5*b^11*c^4+38798760*a^6*b^10*c^4+55426800*a^7*b^9*c^4
@@+62355150*a^8*b^8*c^4+55426800*a^9*b^7*c^4+38798760*a^10*b^6*c^4
@@+21162960*a^11*b^5*c^4+8817900*a^12*b^4*c^4+2713200*a^13*b^3*c^4
@@+581400*a^14*b^2*c^4+77520*a^15*b*c^4+4845*a^16*c^4+1140*b^17*c^3
@@+19380*a*b^16*c^3+155040*a^2*b^15*c^3+775200*a^3*b^14*c^3
@@+2713200*a^4*b^13*c^3+7054320*a^5*b^12*c^3+14108640*a^6*b^11*c^3
@@+22170720*a^7*b^10*c^3+27713400*a^8*b^9*c^3+27713400*a^9*b^8*c^3
@@+22170720*a^10*b^7*c^3+14108640*a^11*b^6*c^3+7054320*a^12*b^5*c^3
@@+2713200*a^13*b^4*c^3+775200*a^14*b^3*c^3+155040*a^15*b^2*c^3
@@+19380*a^16*b*c^3+1140*a^17*c^3+190*b^18*c^2+3420*a*b^17*c^2
@@+29070*a^2*b^16*c^2+155040*a^3*b^15*c^2+581400*a^4*b^14*c^2
@@+1627920*a^5*b^13*c^2+3527160*a^6*b^12*c^2+6046560*a^7*b^11*c^2
@@+8314020*a^8*b^10*c^2+9237800*a^9*b^9*c^2+8314020*a^10*b^8*c^2
@@+6046560*a^11*b^7*c^2+3527160*a^12*b^6*c^2+1627920*a^13*b^5*c^2
@@+581400*a^14*b^4*c^2+155040*a^15*b^3*c^2+29070*a^16*b^2*c^2
@@+3420*a^17*b*c^2+190*a^18*c^2+20*b^19*c+380*a*b^18*c+3420*a^2*b^17*c
@@+19380*a^3*b^16*c+77520*a^4*b^15*c+232560*a^5*b^14*c+542640*a^6*b^13*c
@@+1007760*a^7*b^12*c+1511640*a^8*b^11*c+1847560*a^9*b^10*c
@@+1847560*a^10*b^9*c+1511640*a^11*b^8*c+1007760*a^12*b^7*c
@@+542640*a^13*b^6*c+232560*a^14*b^5*c+77520*a^15*b^4*c+19380*a^16*b^3*c
@@+3420*a^17*b^2*c+380*a^18*b*c+20*a^19*c+b^20+20*a*b^19+190*a^2*b^18
@@+1140*a^3*b^17+4845*a^4*b^16+15504*a^5*b^15+38760*a^6*b^14
@@+77520*a^7*b^13+125970*a^8*b^12+167960*a^9*b^11+184756*a^10*b^10
@@+167960*a^11*b^9+125970*a^12*b^8+77520*a^13*b^7+38760*a^14*b^6
@@+15504*a^15*b^5+4845*a^16*b^4+1140*a^17*b^3+190*a^18*b^2+20*a^19*b+a^20

ƒHow to use "Maxima"„
@For example , when expanding (a+b)^50
@Enter expand((a+b)^50)@in half-width , and press the Shift key and Enter key at the same time.

@yProblem 3z@Solve the higher equation ‚˜^3{‚Q‚˜^2{‚Q‚˜{‚P‚O.
@The high-level equation handled in high school is a form that can be solved by using factor decomposition or the like , or can be solved as x^2=t or the like.
@Solve the cubic equation ax^3+bx^2+cx+d=0 in "Maxima". Then the formula of the cubic equation is displayed. Will the students be surprised and impressed ?
@Also , if you solve the cubic equation ‚˜^3|‚U‚˜|‚P‚O‚O@, and the quartic equation ‚˜^4{‚R‚˜^3|‚P‚W‚˜^2{‚U‚˜|‚T‚O@using Maxima and display them , the complexity of the solution should surprise the students.

ƒHow to use "‚l‚‚˜‚‰‚‚"„
@For example , when solving ax^3+bx^2+cx+d=0
@Enter solve(‚*‚˜^3{‚‚*‚˜^2{‚ƒ*‚˜{‚„‚O,x)@in half-width , press the Shift key and Enter key at the same time.
@The result of letting "Maxima"@solve a cubic equation ‚‚˜^3{‚‚‚˜^2{‚ƒ‚˜{‚„‚O
@The result of letting "Maxima" solve a cubic equation @‚˜^3|‚U‚˜|‚P‚O‚O

@yProblem 4z@Factor ‚‚‚|‚{‚‚|‚P
@This is a problem of cleaning up and factoring for one character.
@If we let Maxima solve more complex factorizations and display them , I wondered if it would be possible to create a class that surprises and impresses the students.
@Students would be surprised if@(‚{‚‚{‚ƒ)(‚‚‚ƒ{‚ƒ‚{‚‚‚)|‚‚‚‚ƒ , (‚‚|‚ƒ)^3{(‚ƒ|‚)^3{(‚|‚‚)^3 , ‚^3{‚‚^3{‚ƒ^3|‚R‚‚‚‚ƒ , and (‚‚{‚ƒ)(‚ƒ{‚)(‚{‚‚){‚‚‚‚ƒ were factored instantly , using Maxima displayed.

Below is the result of following with "Maxima"
@(a+b+c)(bc+ca+ab)-abc = (b+a)(c+a)(c+b)
@(b-c)^3+(c-a)^3+(a-b)^3 = 3(b-a)(c-a)(c-b)
@a^3+b^3+c^3-3*a*b*c = (c+b+a)(c^2-b*c-a*c+b^2-a*b+a^2)
@(b+c)(c+a)(a+b)+abc = (c+b+a)(bc+ac+ab)

ƒHow to use "Maxima"„
@For example , when factoring (a+b+c)(bc+ca+ab)-abc
@
@Enter factor((a+b+c)*(b*c+c*a+a*b)-a*b*c)@in half-width , and press the Shift key and Enter key at the same time.

@yProblem 5z@Differentiate (‚˜{‚V‚˜^2)^(1/3).@
@I wonder if I could create a class that surprise and impress students by searching for more complex expressions in workbooks and using "Maxima" to differentiate them and display them.

Below is the result of differentiating with "Maxima"
@{(‚˜{‚V‚˜^2)^(1/3)}f = (14*x+1)/(3*(7*x^2+x)^(2/3))

ƒHow to use "‚l‚‚˜‚‰‚‚"„
@For example , when differentiating (‚˜{‚V‚˜^2)^(1/3)
@Enter diff((x+7*x^2)^(1/3), x)@in half-width , and press the Shift key and Enter key at the same time.

@yProblem 6z@Integrate ã(‚P{‚T‚˜)@
@I wonder if I could create a class that surprises and impresses by searching for more complex expressions in workbooks and using "Maxima" to integrate them and display them.

Below is the result of integrating with "Maxima".
çã(‚P{‚T‚˜)‚„‚˜ = (2*(5*x+1)^(3/2))/15

ƒHow to use "‚l‚‚˜‚‰‚‚"„
@For example , when integrating@ã(‚P{‚T‚˜)
@Enter integrate(sqrt(1+5*x) , x)@in half-width , and press the Shift key and Enter key at the same time.




@To table of contents
@Formula manipulation software "Maxima" @Formula manipulation software "wx‚l‚‚˜‚‰‚‚"

@Click on the formula manipulation software "‚—‚˜‚l‚‚˜‚‰‚‚" above to open Maxima's official website.
@Click Download on the left menue of this wxMaxima official site.
@Next , click Sourceforge download page.
@And , click Maxima Windows.
@Furthermore , click 5.26.0-Windows.
@
Then , ckick maxima-5.26.0.exe to download "maxima 5.26.0.exe".
@Double-click "
maxima-5.26.0.exe" downloaded to launch the Maxima installer.
@After that , follow the instructions on the screen to install. However , 5.26.0 in "maxima-5.26.0.exe" represents the version. (2/12/2012)




@To table of contents

@Since the icon of "wxMaxima" is created on the desktop , double-click it to start "Maxima".





@To table of contents

@You can download a Maxima data file "MSample.wxm" containing all the sample programs shown on this website.
@Click the data file "MSamp.lzh" and save it to your desktop or other location.
@Unzip the downloaded file "MSamp.lzh" , put the cursor on the input expression you want to excute , and press the Shift key and Enter key at the same time to excute it. Of course , "Maxima" must be installed before that.

Data file "MSamp.wxm"





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yReferencesz
The first formula manipulation software@Written by Kaoru Takeuchi@from Kodansha

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