### Related

##### reverse-sort

eq1:[10,2,55,4,5];

eq2:[5,6,7,8,9];

eq1: sort(eq1);

Calculate

##### reverse

reverse([1,2,3]);

Calculate

##### reverse-sort

eq1:[10,2,55,4,5];

eq2:[5,6,7,8,9];

sort(eq1);

Calculate

##### reverse-rreduce

f(x,y):=x+10*y;

rreduce(f,reverse([1,...

Calculate

##### reverse-sort

eq1:[10,2,55,4,5];

eq2:[5,6,7,8,9];

eq1 = sort(eq1);

Calculate

##### reverse-rreduce

f(x,y):=x+10*y;

rreduce(f,reverse([1,...

Calculate

##### reverse

ans : [vasemmalle,oik...

ans[1];

reverse(ans)[1];

Calculate

? reverse;

Calculate

##### reverse-rreduce

rreduce(f,reverse([1,...

Calculate

##### reverse-rreduce

f(x,y):=x+10*y;

rreduce(f,reverse([13...

Calculate

### reverse

Run Example
```(%i1)umrechnung:[];
(%o1)                                 []
(%i2) basis:8;
(%o2)                                  8
(%i3) x[0]:119.0625;
(%o3)                              119.0625
(%i4) x[n]:=block(q:[floor(x[n-1]/basis),mod(x[n-1],basis)],umrechnung:append(umrechnung,[q[2]]),x[n-1]: q[1]);
x
n - 1
(%o4) x  := block(q : [floor(------), mod(x     , basis)],
n                     basis         n - 1
umrechnung : append(umrechnung, [q ]), x      : q )
2     n - 1    1
(%i5) makelist(x[i],i,1,4);
(%o5)                            [14, 1, 0, 0]
(%i6) hexzahl:reverse(umrechnung);
(%o6)                          [0, 1, 6, 7.0625]
(%i7) konverter(x):=if x=10 then "A"else if x=11 then "B"else if x=12 then "C"else if x=13then "D"else if x=14 then "E"else if x=15 then "F"else x;
(%o7) konverter(x) := if x = 10 then "A"
else (if x = 11 then "B" else (if x = 12 then "C"
else (if x = 13 then "D" else (if x = 14 then "E"
else (if x = 15 then "F" else x)))))
(%i8) map(konverter,hexzahl);
(%o8)                          [0, 1, 6, 7.0625]
(%i9) var1:hexzahl[1]*1000+hexzahl[2]*100+hexzahl[3]*10+hexzahl[4];
(%o9)                              167.0625
(%i10) ```
Run Example
```list:makelist([(2*cos(K*%pi/180))/(1+sin(K*%pi/180)^2), (2*sin(2*K*%pi/180))/(1+sin(K*%pi/180)^2)], K,0,90),numer;
(%o1) [[2.0, 0.0], [1.999086495572986, 0.069777740048049],
[1.996350149723932, 0.13934323093466], [1.991803415750492, 0.20848587282253],
[1.985466886890097, 0.27699833753036], [1.977369056636273, 0.34467813763474],
[1.967545990457508, 0.41132911758191], [1.956040915892139, 0.47676284418676],
[1.942903739570119, 0.54079987660576], [1.92819050100733, 0.60327089904147],
[1.911962773997082, 0.6640177029432], [1.894287027067722, 0.72289400917923],
[1.875233954780797, 0.7797661244347], [1.854877791620735, 0.83451342980821],
[1.833295619896932, 0.88702870312007], [1.810566682475158, 0.93721827970532],
[1.786771710318286, 0.9850020593615], [1.761992273792645, 1.030313369594093],
[1.73631016553473, 1.073098697312419], [1.709806821422873, 1.113317302657804],
[1.682562784906746, 1.150940729696483],
[1.654657218657697, 1.185952229301377],
[1.626167466252909, 1.218346109713575],
[1.597168665428064, 1.248127030060829],
[1.567733413351858, 1.275309251569001], [1.53793148340974, 1.299915860389839],
[1.507829592145564, 1.321977974942715], [1.47749121430444, 1.341533949485725],
[1.446976443348512, 1.358628584346392],
[1.416341894375991, 1.373312351902803],
[1.385640646055102, 1.385640646055102],
[1.354922217978753, 1.395673061601276],
[1.324232579740697, 1.403472708659658],
[1.293614188016984, 1.409105566086636],
[1.263106047994089, 1.412639876738551],
[1.232743795604104, 1.414145586432928], [1.20255979719505, 1.413693827582156],
[1.172583263469013, 1.411356447704616],
[1.142840374751538, 1.407205582362521],
[1.113354414903281, 1.401313271527991],
[1.084145911440892, 1.393751117933051],
[1.055232779691837, 1.384589985607161], [1.02663046906144, 1.37389973653912],
[0.99835210973562, 1.361749003209251], [0.97040865837589, 1.348204994613396],
[0.94280904158206, 1.333333333333333], [0.91556029610043, 1.31719792118976],
[0.88866770494101, 1.299860831036038], [0.86213492873513, 1.281382222305664],
[0.8359641318153, 1.261820278007241], [0.81015610263275, 1.241231160961487],
[0.7847103682451, 1.219668987190177], [0.75962530270863, 1.197185814492324],
[0.73489822929675, 1.173831644374521], [0.7105255165406, 1.149654435636771],
[0.68650266815002, 1.124700128049873], [0.66282440692408, 1.099012674693147],
[0.63948475280237, 1.072634081650408], [0.61647709524095, 1.04560445388626],
[0.59379426012242, 1.017962046243082], [0.57142857142857, 0.98974331861079],
[0.54937190791716, 0.96098299442624], [0.52761575505288, 0.93171412175677],
[0.50615125244685, 0.90196813631252], [0.48496923706011, 0.87177492581575],
[0.46406028242428, 0.8411628952311], [0.443414734129, 0.8101590324307],
[0.42302274181927, 0.7787889739308], [0.40287428793874, 0.74707707039378],
[0.38295921344651, 0.71504645164085], [0.36326724072583, 0.68271909096664],
[0.34378799389328, 0.65011586858824], [0.32451101670725, 0.61725663409798],
[0.30542578826422, 0.58416026782167], [0.28652173666157, 0.55084474101299],
[0.26778825079542, 0.51732717484014], [0.24921469045277, 0.48362389814304],
[0.23079039484775, 0.44975050395923], [0.21250468974289, 0.41572190483338],
[0.19434689328808, 0.38155238694037], [0.17630632070204, 0.34725566306484],
[0.15837228791343, 0.31284492449094], [0.1405341142725, 0.27833289186587],
[0.12278112443725, 0.24373186510878], [0.10510264953304, 0.20905377244364],
[0.087488027678901, 0.17431021864045], [0.069926603969868, 0.13951253255419],
[0.052407730000057, 0.104671814055], [0.034920763008395, 0.069798980446196],
[0.017455064725736, 0.034904812469666],
[6.123233995736766E-17, 1.2246467991473532E-16]]
(%i2) lista:reverse(list);
(%o2) [[6.123233995736766E-17, 1.2246467991473532E-16],
[0.017455064725736, 0.034904812469666],
[0.034920763008395, 0.069798980446196], [0.052407730000057, 0.104671814055],
[0.069926603969868, 0.13951253255419], [0.087488027678901, 0.17431021864045],
[0.10510264953304, 0.20905377244364], [0.12278112443725, 0.24373186510878],
[0.1405341142725, 0.27833289186587], [0.15837228791343, 0.31284492449094],
[0.17630632070204, 0.34725566306484], [0.19434689328808, 0.38155238694037],
[0.21250468974289, 0.41572190483338], [0.23079039484775, 0.44975050395923],
[0.24921469045277, 0.48362389814304], [0.26778825079542, 0.51732717484014],
[0.28652173666157, 0.55084474101299], [0.30542578826422, 0.58416026782167],
[0.32451101670725, 0.61725663409798], [0.34378799389328, 0.65011586858824],
[0.36326724072583, 0.68271909096664], [0.38295921344651, 0.71504645164085],
[0.40287428793874, 0.74707707039378], [0.42302274181927, 0.7787889739308],
[0.443414734129, 0.8101590324307], [0.46406028242428, 0.8411628952311],
[0.48496923706011, 0.87177492581575], [0.50615125244685, 0.90196813631252],
[0.52761575505288, 0.93171412175677], [0.54937190791716, 0.96098299442624],
[0.57142857142857, 0.98974331861079], [0.59379426012242, 1.017962046243082],
[0.61647709524095, 1.04560445388626], [0.63948475280237, 1.072634081650408],
[0.66282440692408, 1.099012674693147], [0.68650266815002, 1.124700128049873],
[0.7105255165406, 1.149654435636771], [0.73489822929675, 1.173831644374521],
[0.75962530270863, 1.197185814492324], [0.7847103682451, 1.219668987190177],
[0.81015610263275, 1.241231160961487], [0.8359641318153, 1.261820278007241],
[0.86213492873513, 1.281382222305664], [0.88866770494101, 1.299860831036038],
[0.91556029610043, 1.31719792118976], [0.94280904158206, 1.333333333333333],
[0.97040865837589, 1.348204994613396], [0.99835210973562, 1.361749003209251],
[1.02663046906144, 1.37389973653912], [1.055232779691837, 1.384589985607161],
[1.084145911440892, 1.393751117933051],
[1.113354414903281, 1.401313271527991],
[1.142840374751538, 1.407205582362521],
[1.172583263469013, 1.411356447704616], [1.20255979719505, 1.413693827582156],
[1.232743795604104, 1.414145586432928],
[1.263106047994089, 1.412639876738551],
[1.293614188016984, 1.409105566086636],
[1.324232579740697, 1.403472708659658],
[1.354922217978753, 1.395673061601276],
[1.385640646055102, 1.385640646055102],
[1.416341894375991, 1.373312351902803],
[1.446976443348512, 1.358628584346392], [1.47749121430444, 1.341533949485725],
[1.507829592145564, 1.321977974942715], [1.53793148340974, 1.299915860389839],
[1.567733413351858, 1.275309251569001],
[1.597168665428064, 1.248127030060829],
[1.626167466252909, 1.218346109713575],
[1.654657218657697, 1.185952229301377],
[1.682562784906746, 1.150940729696483],
[1.709806821422873, 1.113317302657804], [1.73631016553473, 1.073098697312419],
[1.761992273792645, 1.030313369594093], [1.786771710318286, 0.9850020593615],
[1.810566682475158, 0.93721827970532], [1.833295619896932, 0.88702870312007],
[1.854877791620735, 0.83451342980821], [1.875233954780797, 0.7797661244347],
[1.894287027067722, 0.72289400917923], [1.911962773997082, 0.6640177029432],
[1.92819050100733, 0.60327089904147], [1.942903739570119, 0.54079987660576],
[1.956040915892139, 0.47676284418676], [1.967545990457508, 0.41132911758191],
[1.977369056636273, 0.34467813763474], [1.985466886890097, 0.27699833753036],
[1.991803415750492, 0.20848587282253], [1.996350149723932, 0.13934323093466],
[1.999086495572986, 0.069777740048049], [2.0, 0.0]]
(%i3) lista[1][1];
(%o3)                        6.123233995736766E-17
(%i4) sum((lista[i-1][2] + lista[i][2])/2 * (lista[i][1] - lista[i-1][1]), i, 2, length(lista)-1);
(%o4)                          1.999576611738301
(%i5) ```
Run Example
```:lisp (defun walk-tree (fun tree)  (subst-if t            (constantly nil)            tree            :key fun));

WALK-TREE
(%i1) :lisp (defun intersperse (obj ls)  (do ((ls1 (reverse (cdr ls)) (cdr ls1))       (ls2 nil (cons obj (cons (car ls1) ls2))))      ((not ls1) (cons (car ls) ls2))));

INTERSPERSE
(%i1) :lisp (defun pre2in (expr)        (cond ((atom expr) expr)              ((listp expr) (intersperse (car expr) (cdr expr)))              (t (pre2in (cdr expr)))));

PRE2IN
(%i1) :lisp (walk-tree 'print '(* 2 2 2));

(* 2 2 2)
*
(2 2 2)
2
(2 2)
2
(2)
2
NIL
(* 2 2 2)
(%i1) ```

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