(*^
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:[font = input; initialization; preserveAspect]
*)
Exercise 0.1
a)
(*
:[font = input; initialization; preserveAspect; startGroup]
*)
s=Sum[2n+1,{n,0,19}]
(*
:[font = output; output; inactive; preserveAspect; endGroup]
400
;[o]
400
:[font = input; initialization; preserveAspect; startGroup]
*)
p=Product[2n+1,{n,0,19}]
(*
:[font = output; output; inactive; preserveAspect; endGroup]
319830986772877770815625
;[o]
319830986772877770815625
:[font = input; initialization; preserveAspect]
*)
b)
(*
:[font = input; initialization; preserveAspect; startGroup]
*)
s/p
(*
:[font = output; output; inactive; preserveAspect; endGroup]
16/12793239470915110832625
;[o]
          16
-----------------------
12793239470915110832625
:[font = input; initialization; preserveAspect; startGroup]
*)
p^s
(*
:[font = output; output; inactive; preserveAspect; endGroup]
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  0625
:[font = input; initialization; preserveAspect]
*)
c)
(*
:[font = input; initialization; preserveAspect; startGroup]
*)
s^p
(*
:[font = output; output; inactive; preserveAspect; endGroup]
$Aborted
;[o]
$Aborted
:[font = input; initialization; preserveAspect]
*)
(There would be many billions of pages of result, and
 time spent accordingly)
(*
:[font = input; initialization; preserveAspect]
*)
d)
(*
:[font = input; initialization; preserveAspect]
*)
Clear[s,p]
(*
:[font = input; initialization; preserveAspect]
*)
Exercise 0.2
(*
:[font = input; initialization; preserveAspect; startGroup]
*)
D[1/(x^2+1)^2,x]
(*
:[font = output; output; inactive; preserveAspect; endGroup]
(-4*x)/(1 + x^2)^3
;[o]
  -4 x
---------
      2 3
(1 + x )
:[font = input; initialization; preserveAspect; startGroup]
*)
Integrate[1/(x^2+1)^2,x]
(*
:[font = output; output; inactive; preserveAspect; endGroup]
x/(2*(1 + x^2)) + ArcTan[x]/2
;[o]
    x        ArcTan[x]
---------- + ---------
        2        2
2 (1 + x )
:[font = input; initialization; preserveAspect]
*)
Exercise 0.3
(*
:[font = input; initialization; preserveAspect; startGroup]
*)
Plot[1/(x^2+1)^2,{x,-5,5}]
(*
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:[font = output; output; inactive; preserveAspect; endGroup]
Graphics["<<>>"]
;[o]
-Graphics-
:[font = input; initialization; preserveAspect]
*)
Exercise 0.4
(*
:[font = input; initialization; preserveAspect; startGroup]
*)
For [n=0,
     n!<=10^n,
     n=n+1,
     Print[n," ",n!," ",10^n]
    ]
(*
:[font = print; inactive; preserveAspect; endGroup]
0 1 1
1 1 10
2 2 100
3 6 1000
4 24 10000
5 120 100000
6 720 1000000
7 5040 10000000
8 40320 100000000
9 362880 1000000000
10 3628800 10000000000
11 39916800 100000000000
12 479001600 1000000000000
13 6227020800 10000000000000
14 87178291200 100000000000000
15 1307674368000 1000000000000000
16 20922789888000 10000000000000000
17 355687428096000 100000000000000000
18 6402373705728000 1000000000000000000
19 121645100408832000 10000000000000000000
20 2432902008176640000 100000000000000000000
21 51090942171709440000 1000000000000000000000
22 1124000727777607680000 10000000000000000000000
23 25852016738884976640000 100000000000000000000000
24 620448401733239439360000 1000000000000000000000000
:[font = input; initialization; preserveAspect; startGroup]
*)
Print[n," ",n!," ",10^n]
(*
:[font = print; inactive; preserveAspect; endGroup]
25 15511210043330985984000000 10000000000000000000000000
:[font = input; initialization; preserveAspect]
*)
Exercise 0.5
(*
:[font = input; initialization; preserveAspect; startGroup]
*)
Do[Print[n," ",Gamma[n]," ",(n-1)!],{n,1,50}]
(*
:[font = print; inactive; preserveAspect; endGroup]
1 1 1
2 1 1
3 2 2
4 6 6
5 24 24
6 120 120
7 720 720
8 5040 5040
9 40320 40320
10 362880 362880
11 3628800 3628800
12 39916800 39916800
13 479001600 479001600
14 6227020800 6227020800
15 87178291200 87178291200
16 1307674368000 1307674368000
17 20922789888000 20922789888000
18 355687428096000 355687428096000
19 6402373705728000 6402373705728000
20 121645100408832000 121645100408832000
21 2432902008176640000 2432902008176640000
22 51090942171709440000 51090942171709440000
23 1124000727777607680000 1124000727777607680000
24 25852016738884976640000 25852016738884976640000
25 620448401733239439360000 620448401733239439360000
26 15511210043330985984000000 15511210043330985984000000
27 403291461126605635584000000 403291461126605635584000000
28 10888869450418352160768000000 
 
  10888869450418352160768000000
29 304888344611713860501504000000 
 
  304888344611713860501504000000
30 8841761993739701954543616000000 
 
  8841761993739701954543616000000
31 265252859812191058636308480000000 
 
  265252859812191058636308480000000
32 8222838654177922817725562880000000 
 
  8222838654177922817725562880000000
33 263130836933693530167218012160000000 
 
  263130836933693530167218012160000000
34 8683317618811886495518194401280000000 
 
  8683317618811886495518194401280000000
35 295232799039604140847618609643520000000 
 
  295232799039604140847618609643520000000
36 10333147966386144929666651337523200000000 
 
  10333147966386144929666651337523200000000
37 371993326789901217467999448150835200000000 
 
  371993326789901217467999448150835200000000
38 13763753091226345046315979581580902400000000 
 
  13763753091226345046315979581580902400000000
39 523022617466601111760007224100074291200000000 
 
  523022617466601111760007224100074291200000000
40 20397882081197443358640281739902897356800000000 
 
  20397882081197443358640281739902897356800000000
41 815915283247897734345611269596115894272000000000 
 
  815915283247897734345611269596115894272000000000
42 33452526613163807108170062053440751665152000000000 
 
  33452526613163807108170062053440751665152000000000
43 1405006117752879898543142606244511569936384000000000 
 
  1405006117752879898543142606244511569936384000000000
44 60415263063373835637355132068513997507264512000000000 
 
  60415263063373835637355132068513997507264512000000000
45 2658271574788448768043625811014615890319638528000000000 
 
  2658271574788448768043625811014615890319638528000000000
46 119622220865480194561963161495657715064383733760000000000 
 
  119622220865480194561963161495657715064383733760000000000
47 5502622159812088949850305428800254892961651752960000000000
 
   5502622159812088949850305428800254892961651752960000000000
48 258623241511168180642964355153611979969197632389120000000\
 
   000 25862324151116818064296435515361197996919763238912000\
 
   0000000
49 124139155925360726708622890473733750385214863546777600000\
 
   00000 124139155925360726708622890473733750385214863546777\
 
   60000000000
50 608281864034267560872252163321295376887552831379210240000\
 
   000000 60828186403426756087225216332129537688755283137921\
 
   0240000000000
:[font = input; initialization; preserveAspect]
*)
Exercise 0.6
a)
(*
:[font = input; initialization; preserveAspect; startGroup]
*)
fact=20!
(*
:[font = output; output; inactive; preserveAspect; endGroup]
2432902008176640000
;[o]
2432902008176640000
:[font = input; initialization; preserveAspect]
*)
b)
(*
:[font = input; initialization; preserveAspect; startGroup]
*)
time=(10^9*365+10^9/4)*24*60*60
(*
:[font = output; output; inactive; preserveAspect; endGroup]
31557600000000000
;[o]
31557600000000000
:[font = input; initialization; preserveAspect]
*)
c)
(*
:[font = input; initialization; preserveAspect; startGroup]
*)
fact/time
(*
:[font = output; output; inactive; preserveAspect; endGroup]
2933186256/38046875
;[o]
2933186256
----------
 38046875
:[font = input; initialization; preserveAspect]
*)
d)
(*
:[font = input; initialization; preserveAspect]
*)
fact=.
(*
:[font = input; initialization; preserveAspect]
*)
Clear[time]
(*
:[font = input; initialization; preserveAspect]
*)
Exercise 0.7
(*
:[font = input; initialization; preserveAspect; startGroup]
*)
Function[x,x^3-3x+1124][{-1234,-123,-12,0,12,123,1234}]
(*
:[font = output; output; inactive; preserveAspect; endGroup]
{-1879076078, -1859374, -568, 1124, 2816, 1861622, 
 
  1879078326}
;[o]
{-1879076078, -1859374, -568, 1124, 2816, 1861622, 
 
  1879078326}
:[font = input; initialization; preserveAspect]
*)
Exercise 0.8
(*
:[font = input; initialization; preserveAspect]
*)
g[x_]:=(x^3-x+2)/(x^5-3x+27)
(*
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Plot[g[x],{x,-10,10}]
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Graphics["<<>>"]
;[o]
-Graphics-
:[font = input; initialization; preserveAspect]
*)
Horizontal asymptote is y=0. For vertical asymptotes:
(*
:[font = input; initialization; preserveAspect; startGroup]
*)
NSolve[x^5-3x+27==0,x]
(*
:[font = output; output; inactive; preserveAspect; endGroup]
{{x -> -2.012815285956232947}, 
 
  {x -> -0.5331314925846921068 - 1.889330489042373766*I}, 
 
  {x -> -0.5331314925846921068 + 1.889330489042373766*I}, 
 
  {x -> 1.539539135562808581 - 1.053827751190630868*I}, 
 
  {x -> 1.539539135562808581 + 1.053827751190630868*I}}
;[o]
{{x -> -2.01282}, {x -> -0.533131 - 1.88933 I}, 
 
  {x -> -0.533131 + 1.88933 I}, {x -> 1.53954 - 1.05383 I}, 
 
  {x -> 1.53954 + 1.05383 I}}
:[font = input; initialization; preserveAspect]
*)
For local minima and maxima:
(*
:[font = input; initialization; preserveAspect; startGroup]
*)
NSolve[D[g[x],x]==0,x]
(*
:[font = output; output; inactive; preserveAspect; endGroup]
{{x -> -1.891761444651819005 - 0.9330052596625121017*I}, 
 
  {x -> -1.891761444651819005 + 0.9330052596625121017*I}, 
 
  {x -> -0.5091658547759141629}, 
 
  {x -> 0.5271774477380448296}, 
 
  {x -> 0.9113181256524544616 - 1.922167516088427118*I}, 
 
  {x -> 0.9113181256524544616 + 1.922167516088427118*I}, 
 
  {x -> 1.942875045036598419}}
;[o]
{{x -> -1.89176 - 0.933005 I}, {x -> -1.89176 + 0.933005 I}, 
 
  {x -> -0.509166}, {x -> 0.527177}, 
 
  {x -> 0.911318 - 1.92217 I}, {x -> 0.911318 + 1.92217 I}, 
 
  {x -> 1.94288}}
:[font = input; initialization; preserveAspect]
*)
Exercise 0.9
(*
:[font = input; initialization; preserveAspect; startGroup]
*)
Plot3D[4Sin[4x]+10Cos[y],{x,-Pi,Pi},{y,-Pi,Pi}]
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.916 .966 .793 r
.37657 .63479 .4001 .62667 .43804 .57687 .41546 .58385 Metetra
.54 .924 .817 r
.41546 .58385 .43804 .57687 .47519 .55616 .45334 .56272 Metetra
.719 .236 .098 r
.45334 .56272 .47519 .55616 .51248 .58808 .49101 .5955 Metetra
.496 .899 .779 r
.49101 .5955 .51248 .58808 .55089 .56691 .5302 .57388 Metetra
.909 .98 .775 r
.5302 .57388 .55089 .56691 .58903 .51617 .56931 .52196 Metetra
.521 0 0 r
.56931 .52196 .58903 .51617 .62896 .53133 .60984 .53755 Metetra
.521 0 0 r
.60984 .53755 .62896 .53133 .6702 .54697 .65173 .55367 Metetra
.894 .988 .749 r
.65173 .55367 .6702 .54697 .70879 .49495 .69131 .5004 Metetra
.483 .891 .768 r
.69131 .5004 .70879 .49495 .74911 .47279 .7325 .47774 Metetra
.659 .119 0 r
.7325 .47774 .74911 .47279 .79443 .5046 .77853 .51043 Metetra
.433 .858 .723 r
.77853 .51043 .79443 .5046 .83622 .48189 .82125 .4872 Metetra
.864 .985 .707 r
.82125 .4872 .83622 .48189 .87496 .42885 .861 .43286 Metetra
.414 0 0 r
.861 .43286 .87496 .42885 .92192 .44336 .90886 .44779 Metetra
.601 .105 .048 r
.31588 .62938 .34109 .61823 .37657 .63479 .3518 .64652 Metetra
.907 .981 .779 r
.3518 .64652 .37657 .63479 .41546 .58385 .39174 .59431 Metetra
.441 .861 .72 r
.39174 .59431 .41546 .58385 .45334 .56272 .43041 .57273 Metetra
.718 .25 .138 r
.43041 .57273 .45334 .56272 .49101 .5955 .46849 .60652 Metetra
.39 .824 .671 r
.46849 .60652 .49101 .5955 .5302 .57388 .50853 .58442 Metetra
.891 .989 .752 r
.50853 .58442 .5302 .57388 .56931 .52196 .5487 .53119 Metetra
.545 .008 0 r
.5487 .53119 .56931 .52196 .60984 .53755 .58989 .54732 Metetra
.545 .008 0 r
.58989 .54732 .60984 .53755 .65173 .55367 .63248 .56401 Metetra
.864 .987 .714 r
.63248 .56401 .65173 .55367 .69131 .5004 .67315 .50935 Metetra
.375 .813 .657 r
.67315 .50935 .69131 .5004 .7325 .47774 .71529 .48617 Metetra
.669 .147 0 r
.71529 .48617 .7325 .47774 .77853 .51043 .7621 .51989 Metetra
.7621 .51989 .77853 .51043 .82125 .4872 .80585 .49611 Metetra
.817 .969 .656 r
.80585 .49611 .82125 .4872 .861 .43286 .84669 .44033 Metetra
.459 0 0 r
.84669 .44033 .861 .43286 .90886 .44779 .89555 .45579 Metetra
.592 .076 0 r
.2897 .63782 .31588 .62938 .3518 .64652 .32603 .65549 Metetra
.916 .966 .793 r
.32603 .65549 .3518 .64652 .39174 .59431 .36702 .60203 Metetra
.537 .923 .815 r
.36702 .60203 .39174 .59431 .43041 .57273 .40648 .57998 Metetra
.72 .237 .099 r
.40648 .57998 .43041 .57273 .46849 .60652 .44493 .61474 Metetra
.493 .897 .777 r
.44493 .61474 .46849 .60652 .50853 .58442 .48582 .59215 Metetra
.909 .98 .775 r
.48582 .59215 .50853 .58442 .5487 .53119 .52707 .53761 Metetra
.523 0 0 r
.52707 .53761 .5487 .53119 .58989 .54732 .56888 .55425 Metetra
.523 0 0 r
.56888 .55425 .58989 .54732 .63248 .56401 .61215 .57147 Metetra
.894 .988 .749 r
.61215 .57147 .63248 .56401 .67315 .50935 .65393 .51543 Metetra
.48 .889 .766 r
.65393 .51543 .67315 .50935 .71529 .48617 .69701 .49171 Metetra
.66 .121 0 r
.69701 .49171 .71529 .48617 .7621 .51989 .74457 .52641 Metetra
.43 .856 .72 r
.74457 .52641 .7621 .51989 .80585 .49611 .78933 .50206 Metetra
.864 .985 .706 r
.78933 .50206 .80585 .49611 .84669 .44033 .8313 .44484 Metetra
.416 0 0 r
.8313 .44484 .84669 .44033 .89555 .45579 .88113 .46077 Metetra
.537 0 0 r
.26303 .63735 .2897 .63782 .32603 .65549 .29966 .65539 Metetra
.912 .907 .804 r
.29966 .65539 .32603 .65549 .36702 .60203 .34165 .60081 Metetra
.705 .959 .947 r
.34165 .60081 .36702 .60203 .40648 .57998 .38181 .57829 Metetra
.712 .188 0 r
.38181 .57829 .40648 .57998 .44493 .61474 .42052 .61376 Metetra
.687 .962 .941 r
.42052 .61376 .44493 .61474 .48582 .59215 .46218 .59068 Metetra
.919 .927 .8 r
.46218 .59068 .48582 .59215 .52707 .53761 .50443 .53498 Metetra
.407 0 0 r
.50443 .53498 .52707 .53761 .56888 .55425 .54675 .55193 Metetra
.407 0 0 r
.54675 .55193 .56888 .55425 .61215 .57147 .59059 .56949 Metetra
.923 .946 .794 r
.59059 .56949 .61215 .57147 .65393 .51543 .63341 .51223 Metetra
.682 .963 .938 r
.63341 .51223 .65393 .51543 .69701 .49171 .67734 .48797 Metetra
.598 .026 0 r
.67734 .48797 .69701 .49171 .74457 .52641 .7255 .52337 Metetra
.659 .963 .927 r
.7255 .52337 .74457 .52641 .78933 .50206 .77119 .49845 Metetra
.922 .966 .78 r
.77119 .49845 .78933 .50206 .8313 .44484 .81421 .43995 Metetra
.23 0 0 r
.81421 .43995 .8313 .44484 .88113 .46077 .86487 .45616 Metetra
0 .28 .664 r
.23643 .62324 .26303 .63735 .29966 .65539 .27323 .64135 Metetra
.877 .817 .786 r
.27323 .64135 .29966 .65539 .34165 .60081 .31607 .58592 Metetra
.749 .843 .921 r
.31607 .58592 .34165 .60081 .38181 .57829 .3568 .56295 Metetra
.612 .061 0 r
.3568 .56295 .38181 .57829 .42052 .61376 .3956 .59868 Metetra
.748 .852 .928 r
.3956 .59868 .42052 .61376 .46218 .59068 .43787 .57512 Metetra
.886 .833 .788 r
.43787 .57512 .46218 .59068 .50443 .53498 .48099 .51853 Metetra
0 .428 .827 r
.48099 .51853 .50443 .53498 .54675 .55193 .52365 .53549 Metetra
0 .428 .827 r
.52365 .53549 .54675 .55193 .59059 .56949 .56785 .55307 Metetra
.896 .849 .79 r
.56785 .55307 .59059 .56949 .63341 .51223 .61157 .49487 Metetra
.747 .855 .93 r
.61157 .49487 .63341 .51223 .67734 .48797 .65619 .47008 Metetra
0 .155 .622 r
.65619 .47008 .67734 .48797 .7255 .52337 .70472 .50569 Metetra
.744 .865 .936 r
.70472 .50569 .7255 .52337 .77119 .49845 .75115 .48022 Metetra
.906 .869 .791 r
.75115 .48022 .77119 .49845 .81421 .43995 .79509 .42074 Metetra
.114 .526 .913 r
.79509 .42074 .81421 .43995 .86487 .45616 .84634 .4369 Metetra
.103 .43 .872 r
.21038 .59348 .23643 .62324 .27323 .64135 .24719 .61129 Metetra
.833 .735 .756 r
.24719 .61129 .27323 .64135 .31607 .58592 .2907 .55533 Metetra
.724 .719 .845 r
.2907 .55533 .31607 .58592 .3568 .56295 .33183 .53193 Metetra
0 .128 .658 r
.33183 .53193 .3568 .56295 .3956 .59868 .37054 .56739 Metetra
.724 .724 .849 r
.37054 .56739 .3956 .59868 .43787 .57512 .41323 .54337 Metetra
.84 .744 .758 r
.41323 .54337 .43787 .57512 .48099 .51853 .45704 .48623 Metetra
.236 .488 .893 r
.45704 .48623 .48099 .51853 .52365 .53549 .49982 .50283 Metetra
.236 .488 .893 r
.49982 .50283 .52365 .53549 .56785 .55307 .54418 .52004 Metetra
.847 .754 .76 r
.54418 .52004 .56785 .55307 .61157 .49487 .5886 .46125 Metetra
.724 .725 .851 r
.5886 .46125 .61157 .49487 .65619 .47008 .6337 .43597 Metetra
0 .295 .792 r
.6337 .43597 .65619 .47008 .70472 .50569 .68234 .47121 Metetra
.724 .73 .855 r
.68234 .47121 .70472 .50569 .75115 .48022 .72929 .44521 Metetra
.856 .767 .762 r
.72929 .44521 .75115 .48022 .79509 .42074 .77395 .38513 Metetra
.329 .523 .893 r
.77395 .38513 .79509 .42074 .84634 .4369 .8255 .40082 Metetra
.286 .435 .836 r
.18512 .54938 .21038 .59348 .24719 .61129 .22179 .56657 Metetra
.798 .678 .731 r
.22179 .56657 .24719 .61129 .2907 .55533 .2658 .51039 Metetra
.698 .642 .791 r
.2658 .51039 .2907 .55533 .33183 .53193 .30715 .48656 Metetra
0 .234 .747 r
.30715 .48656 .33183 .53193 .37054 .56739 .34561 .52125 Metetra
.697 .644 .793 r
.34561 .52125 .37054 .56739 .41323 .54337 .38855 .4968 Metetra
.803 .683 .732 r
.38855 .4968 .41323 .54337 .45704 .48623 .43287 .43943 Metetra
.356 .466 .834 r
.43287 .43943 .45704 .48623 .49982 .50283 .47558 .45531 Metetra
.356 .466 .834 r
.47558 .45531 .49982 .50283 .54418 .52004 .51988 .47179 Metetra
.808 .689 .733 r
.51988 .47179 .54418 .52004 .5886 .46125 .56484 .41277 Metetra
.697 .645 .793 r
.56484 .41277 .5886 .46125 .6337 .43597 .61021 .38701 Metetra
.159 .336 .792 r
.61021 .38701 .6337 .43597 .68234 .47121 .6587 .42134 Metetra
.697 .647 .796 r
.6587 .42134 .68234 .47121 .72929 .44521 .70596 .39484 Metetra
.814 .696 .734 r
.70596 .39484 .72929 .44521 .77395 .38513 .75116 .3345 Metetra
.409 .488 .829 r
.75116 .3345 .77395 .38513 .8255 .40082 .80275 .34936 Metetra
.349 .422 .796 r
.1605 .49527 .18512 .54938 .22179 .56657 .19694 .51159 Metetra
.778 .646 .716 r
.19694 .51159 .22179 .56657 .2658 .51039 .24133 .4554 Metetra
.682 .603 .761 r
.24133 .4554 .2658 .51039 .30715 .48656 .28278 .43119 Metetra
.109 .267 .746 r
.28278 .43119 .30715 .48656 .34561 .52125 .32087 .46475 Metetra
.681 .604 .763 r
.32087 .46475 .34561 .52125 .38855 .4968 .36393 .43988 Metetra
.782 .65 .716 r
.36393 .43988 .38855 .4968 .43287 .43943 .40863 .3825 Metetra
.399 .447 .795 r
.40863 .3825 .43287 .43943 .47558 .45531 .45114 .39743 Metetra
.399 .447 .795 r
.45114 .39743 .47558 .45531 .51988 .47179 .49524 .41292 Metetra
.785 .653 .717 r
.49524 .41292 .51988 .47179 .56484 .41277 .54059 .3539 Metetra
.681 .604 .763 r
.54059 .3539 .56484 .41277 .61021 .38701 .58611 .32769 Metetra
.238 .344 .77 r
.58611 .32769 .61021 .38701 .6587 .42134 .63427 .36071 Metetra
.68 .605 .764 r
.63427 .36071 .6587 .42134 .70596 .39484 .68168 .33374 Metetra
.79 .657 .717 r
.68168 .33374 .70596 .39484 .75116 .3345 .72729 .27341 Metetra
.437 .466 .792 r
.72729 .27341 .75116 .3345 .80275 .34936 .77873 .28716 Metetra
.364 .417 .783 r
.13603 .43731 .1605 .49527 .19694 .51159 .1722 .45268 Metetra
.772 .636 .711 r
.1722 .45268 .19694 .51159 .24133 .4554 .21691 .39657 Metetra
.677 .591 .752 r
.21691 .39657 .24133 .4554 .28278 .43119 .25843 .37196 Metetra
.142 .274 .741 r
.25843 .37196 .28278 .43119 .32087 .46475 .29611 .40425 Metetra
.676 .591 .753 r
.29611 .40425 .32087 .46475 .36393 .43988 .33923 .37896 Metetra
.775 .639 .711 r
.33923 .37896 .36393 .43988 .40863 .3825 .38427 .32167 Metetra
.409 .441 .782 r
.38427 .32167 .40863 .3825 .45114 .39743 .42653 .33555 Metetra
.409 .441 .782 r
.42653 .33555 .45114 .39743 .49524 .41292 .47037 .34995 Metetra
.778 .642 .711 r
.47037 .34995 .49524 .41292 .54059 .3539 .51608 .29101 Metetra
.676 .591 .753 r
.51608 .29101 .54059 .3539 .58611 .32769 .56168 .26436 Metetra
.259 .344 .761 r
.56168 .26436 .58611 .32769 .63427 .36071 .60945 .29593 Metetra
.675 .592 .755 r
.60945 .29593 .63427 .36071 .68168 .33374 .65695 .26847 Metetra
.782 .645 .711 r
.65695 .26847 .68168 .33374 .72729 .27341 .70293 .20825 Metetra
.445 .459 .78 r
.70293 .20825 .72729 .27341 .77873 .28716 .75413 .22079 Metetra
.35 .422 .796 r
.11092 .38206 .13603 .43731 .1722 .45268 .14683 .39654 Metetra
.778 .646 .716 r
.14683 .39654 .1722 .45268 .21691 .39657 .19193 .34042 Metetra
.682 .603 .761 r
.19193 .34042 .21691 .39657 .25843 .37196 .23355 .3154 Metetra
.11 .268 .746 r
.23355 .3154 .25843 .37196 .29611 .40425 .27084 .34651 Metetra
.681 .604 .762 r
.27084 .34651 .29611 .40425 .33923 .37896 .31408 .32079 Metetra
.782 .649 .716 r
.31408 .32079 .33923 .37896 .38427 .32167 .35952 .26351 Metetra
.399 .447 .794 r
.35952 .26351 .38427 .32167 .42653 .33555 .40155 .27638 Metetra
.399 .447 .794 r
.40155 .27638 .42653 .33555 .47037 .34995 .44518 .28975 Metetra
.785 .653 .717 r
.44518 .28975 .47037 .34995 .51608 .29101 .4913 .23082 Metetra
.681 .604 .763 r
.4913 .23082 .51608 .29101 .56168 .26436 .53703 .2037 Metetra
.239 .344 .77 r
.53703 .2037 .56168 .26436 .60945 .29593 .58446 .2339 Metetra
.68 .605 .764 r
.58446 .2339 .60945 .29593 .65695 .26847 .63211 .20595 Metetra
.79 .657 .717 r
.63211 .20595 .65695 .26847 .70293 .20825 .67851 .14574 Metetra
.438 .466 .791 r
.67851 .14574 .70293 .20825 .75413 .22079 .72955 .15712 Metetra
.298 .44 .836 r
.08422 .33514 .11092 .38206 .14683 .39654 .11996 .34889 Metetra
.797 .677 .731 r
.11996 .34889 .14683 .39654 .19193 .34042 .16559 .29256 Metetra
.698 .642 .789 r
.16559 .29256 .19193 .34042 .23355 .3154 .20744 .2671 Metetra
.002 .246 .753 r
.20744 .2671 .23355 .3154 .27084 .34651 .24442 .2973 Metetra
.698 .643 .792 r
.24442 .2973 .27084 .34651 .31408 .32079 .28791 .27111 Metetra
.802 .682 .732 r
.28791 .27111 .31408 .32079 .35952 .26351 .33389 .2136 Metetra
.365 .47 .834 r
.33389 .2136 .35952 .26351 .40155 .27638 .37583 .22566 Metetra
.365 .47 .834 r
.37583 .22566 .40155 .27638 .44518 .28975 .41936 .23818 Metetra
.807 .688 .733 r
.41936 .23818 .44518 .28975 .4913 .23082 .46605 .17901 Metetra
.697 .644 .792 r
.46605 .17901 .4913 .23082 .53703 .2037 .51207 .15137 Metetra
.173 .343 .794 r
.51207 .15137 .53703 .2037 .58446 .2339 .55929 .18051 Metetra
.697 .646 .795 r
.55929 .18051 .58446 .2339 .63211 .20595 .60725 .15201 Metetra
.813 .695 .734 r
.60725 .15201 .63211 .20595 .67851 .14574 .65424 .09156 Metetra
.416 .49 .828 r
.65424 .09156 .67851 .14574 .72955 .15712 .70527 .10197 Metetra
.172 .462 .886 r
.05502 .3003 .08422 .33514 .11996 .34889 .09071 .3136 Metetra
.828 .729 .755 r
.09071 .3136 .11996 .34889 .16559 .29256 .13709 .25673 Metetra
.724 .712 .838 r
.13709 .25673 .16559 .29256 .20744 .2671 .17935 .23075 Metetra
0 .185 .71 r
.17935 .23075 .20744 .2671 .24442 .2973 .21614 .26047 Metetra
.724 .716 .842 r
.21614 .26047 .24442 .2973 .28791 .27111 .26007 .23373 Metetra
.835 .738 .757 r
.26007 .23373 .28791 .27111 .33389 .2136 .30683 .17566 Metetra
.284 .507 .895 r
.30683 .17566 .33389 .2136 .37583 .22566 .34882 .18717 Metetra
.284 .507 .895 r
.34882 .18717 .37583 .22566 .41936 .23818 .39244 .19912 Metetra
.842 .747 .759 r
.39244 .19912 .41936 .23818 .46605 .17901 .43994 .13937 Metetra
.724 .717 .843 r
.43994 .13937 .46605 .17901 .51207 .15137 .48646 .11113 Metetra
.033 .331 .814 r
.48646 .11113 .51207 .15137 .55929 .18051 .53369 .13962 Metetra
.724 .722 .848 r
.53369 .13962 .55929 .18051 .60725 .15201 .58221 .11049 Metetra
.85 .759 .761 r
.58221 .11049 .60725 .15201 .65424 .09156 .63002 .04943 Metetra
.364 .534 .89 r
.63002 .04943 .65424 .09156 .70527 .10197 .68131 .05914 Metetra
P
p
.002 w
.67932 .02494 m
.94594 .43277 L
s
.94594 .43277 m
.97506 .64585 L
s
.97506 .64585 m
.69286 .25814 L
s
.69286 .25814 m
.67932 .02494 L
s
.06024 .26735 m
.02494 .49015 L
s
.02494 .49015 m
.69286 .25814 L
s
.69286 .25814 m
.67932 .02494 L
s
.67932 .02494 m
.06024 .26735 L
s
P
p
p
.002 w
.06024 .26735 m
.67932 .02494 L
s
P
p
.002 w
.16191 .22754 m
.16631 .23196 L
s
P
[(-2)] .15311 .2187 .99496 1 Mshowa
p
.002 w
.35089 .15354 m
.35496 .15826 L
s
P
[(0)] .34275 .1441 .86223 1 Mshowa
p
.002 w
.55515 .07356 m
.55883 .07859 L
s
P
[(2)] .54781 .06348 .7295 1 Mshowa
p
.001 w
.19857 .21319 m
.20117 .21587 L
s
P
p
.001 w
.23578 .19861 m
.23834 .20134 L
s
P
p
.001 w
.27356 .18382 m
.27609 .18658 L
s
P
p
.001 w
.31193 .1688 m
.31441 .17159 L
s
P
p
.001 w
.39046 .13804 m
.39286 .14091 L
s
P
p
.001 w
.43066 .1223 m
.43301 .12521 L
s
P
p
.001 w
.4715 .10631 m
.4738 .10926 L
s
P
p
.001 w
.51299 .09007 m
.51525 .09305 L
s
P
p
.001 w
.1258 .24168 m
.12847 .2443 L
s
P
p
.001 w
.09021 .25561 m
.09292 .25819 L
s
P
p
.001 w
.598 .05678 m
.60015 .05984 L
s
P
p
.001 w
.64156 .03972 m
.64365 .04282 L
s
P
P
% End of Graphics
MathPictureEnd

:[font = output; output; inactive; preserveAspect; endGroup]
SurfaceGraphics["<<>>"]
;[o]
-SurfaceGraphics-
:[font = input; initialization; preserveAspect]
*)
Exercise 0.10
(*
:[font = input; initialization; preserveAspect; startGroup]
*)
Unprotect[Sum]
(*
:[font = output; output; inactive; preserveAspect; endGroup]
{"Sum"}
;[o]
{Sum}
:[font = input; initialization; preserveAspect; startGroup]
*)
Sum=Product
(*
:[font = output; output; inactive; preserveAspect; endGroup]
Product
;[o]
Product
:[font = input; initialization; preserveAspect; startGroup]
*)
Sum[i,{i,0,50}]
(*
:[font = output; output; inactive; preserveAspect; endGroup]
0
;[o]
0
:[font = input; initialization; preserveAspect]
*)
As expected, we got the product.
(*
:[font = input; initialization; preserveAspect]
*)
Clear[Sum]
(*
:[font = input; initialization; preserveAspect]
*)
Now Sum got its default functionality back:
(*
:[font = input; initialization; preserveAspect; startGroup]
*)
Sum[i,{i,0,50}]
(*
:[font = output; output; inactive; preserveAspect; endGroup]
1275
;[o]
1275
^*)