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1980 MAPLE http://www.maplesoft.com

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1984

SINGULAR http://www.mathematik.uni-kl.de/pub/~zca/Singular

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1988

SMP, MATHEMATICA http://www.wolfram.com

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1989 -

MuPAD http://www.mupad.de http://www.sciface.com

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1991 -

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LiE http://www.mathlabo.univ-poitiers.fr/~maavl/LiE

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1992 MACAULAY 2 http://www.math.uiuc.edu/Macaulay2

1980s - 2000

PARI ftp://megrez.math.u-bordeaux.fr/pub/pari

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program fibonacciimplicitnone! VariablesINTEGER4::f,f1, f2,i! Bodyoffibonaccif1= 1; f2 =1; i= 3; f =f1+f2;Do WhileHMod Hf, 100L = 0Lf1= f2; f2 =f; f= f1+f2; i= i+1EndDoPrint,f,iendprogramfibonacci

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8284360270132553400 522Pressanykeytocontinue

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f1= 1;f2= 1;i= 3;f =f1+f2;While@Mod@f, 100D 0,f1= f2;f2= f;f= f1+f2;++iD;

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In[1]:= 30!2^26+20^20Out[1]= 108810175621190533915703125

In[2]:= 30!H2^301LOut[2]= 382760259469251166863360000000

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In[1]:= A= 881, 2, 3

In[2]:= Expand@HxyL Hx+yL^3DOut[2]= x4+ 2x3y 2xy3 y4

3) pi - ,

In[3]:= Solve@x^2-5 x +60, xDOut[3]= 88x 2>

In[6]:= Solve@8x1-x2+2*x3+x4-2,

-2*x1+x2-3*x3-5 *x44,

x1-x2+x3+6 *x40,

2*x1+3*x2+5 *x3-7 *x4 1

In[7]:= Solve@8x1+x2- x3+x5 1,

-x1-x2+2*x3-x4+x5 ==2,

2*x1+2*x2-3*x3 +3*x4 +x5 0,

x1+x2-3*x4+2*x53

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In[8]:= A= 881, 1, 1

5) pi ,

In[11]:= LimitASin@xDx

,x 0EOut[11]= 1

In[12]:= LimitA!!!!!!!!!1+x !!!!!!!!!1x

x,x 0E

Out[12]= 1

In[13]:= LimitA!!!!!!!!!!!!!!!!!!!x26 x+9x3

, x 3, Direction 1EOut[13]= 1

In[14]:= LimitA!!!!!!!!!!!!!!!!!!!x26 x+9x3

, x 3, Direction 1EOut[14]= 1

6) pi pi ,

In[15]:= SumA 1k2, 8k, 1, Infinity

9) pi ,

In[23]:= DSolve@y@xD==a y@xD+ y@xD, y, xD

Out[23]= ::y FunctionB8x>

In[24]:= DSolve@8y@xD==-z@xD, z@xD==-y@xD

In[25]:= RSolve@8F@n+2D F@n+1D +F@nD, F@1D 1, F@2D 1>

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pi . In[1]:= N@Pi,100D

Out[1]= 3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117068

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(XY plots, XYZ plots, polar plots, log plots ..) pi format pi .

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In[1]:= PlotAx25 x+6, 8x, 1, 5

In[2]:= ParametricPlot@8Cos@tD, Sin@tD

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In[6]:= Table@8x, x^2

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7) In[13]:= Plot3DAE0.2 "#############x2+y2 CosA!!!!!!!!!!!!!x2+y2 E, 8x, 9 Pi2,9 Pi2

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In[8]:= diffAx33 x2+6 x2, xEOut[8]= 6 6x+ 3x2

In[9]:= diffAx33 x2 +6 x2x21

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Out[9]= H1+x2L H6 6x+ 3x2L 2xH2+ 6x 3x2 +x3L

H1+ x2L2

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In[1]:= i = 1;While@PrimeQ@2Prime@iD- 1D,++iD

Print@i, "th prime=", Prime@iDD5th prime=11

p=11 pi . In[4]:= FactorIntegerA2111E

Out[4]= 8823, 1

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In[1]:= A={{1,x1,x1^2},{1,x2,x2^2},{1,x3,x3^2}};

In[2]:= Factor[Det[A]]

Out[2]= -((x1 - x2) (x1 - x3) (x2 - x3))

In[3]:= A={{1,x1,x1^2,x1^3},{1,x2,x2^2,x2^3},{1,x3,x3^2,x3^3},{1,x4,x4^2,x4^3}};

In[4]:= Factor[Det[A]]

Out[4]= (x1 - x2) (x1 - x3) (x2 - x3) (x1 - x4) (x2 - x4) (x3 - x4)

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[1] K. O. Geddes, S.R. Czapor and G. Labahn, 1995, Algorithms for Computer Algebra, Kluwer Academic Publisher. [2] J. Grabmeier, E. Kaltofen and V. Weispfenning, 2003, Computer Algebra Handbook, Springer-Verlag, Berlin, Heidelberg, New York. [3] N. P. Karampetakis and A.I. Vardulakis, 2006, Special issue on the use of computer algebra systems for computer aided control system design, International Journal of Control, Vol.79, Issue 11, pp.1313-1320. [4] R. Mankiewicz, 2002, , . [5] . , 1999, , pi. [6] .. pi, . . pi, 2004, Mathematica, . [7] The MacTutor History of Mathematics archive, http://www-groups.dcs.st-and.ac.uk/~history/ .