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Initial revision

   realprecision = 38 significant digits
   echo = 1 (on)
? apol=x^3+5*x+1
x^3 + 5*x + 1
? changevar(x+y,[z,t])
y + z
? deriv((x+y)^5,y)
5*x^4 + 20*y*x^3 + 30*y^2*x^2 + 20*y^3*x + 5*y^4
? ((x+y)^5)'
5*x^4 + 20*y*x^3 + 30*y^2*x^2 + 20*y^3*x + 5*y^4
? dz=vector(30,k,1);dd=vector(30,k,k==1);dm=dirdiv(dd,dz)
[1, -1, -1, 0, -1, 1, -1, 0, 0, 1, -1, 0, -1, 1, 1, 0, -1, 0, -1, 0, 1, 1, -
1, 0, 0, 1, 0, 0, -1, -1]
? direuler(s=1,40,1+s*X+s^2*X)
[1, 6, 12, 0, 30, 72, 56, 0, 0, 180, 132, 0, 182, 336, 360, 0, 306, 0, 380, 
0, 672, 792, 552, 0, 0, 1092, 0, 0, 870, 2160, 992, 0, 1584, 1836, 1680, 0, 
1406, 2280, 2184, 0]
? dirmul(abs(dm),dz)
[1, 2, 2, 2, 2, 4, 2, 2, 2, 4, 2, 4, 2, 4, 4, 2, 2, 4, 2, 4, 4, 4, 2, 4, 2, 
4, 2, 4, 2, 8]
? zz=yy;yy=xx;eval(zz)
xx
? factorpadic(apol,7,8)

[(1 + O(7^8))*x + (6 + 2*7^2 + 2*7^3 + 3*7^4 + 2*7^5 + 6*7^6 + O(7^8)) 1]

[(1 + O(7^8))*x^2 + (1 + 6*7 + 4*7^2 + 4*7^3 + 3*7^4 + 4*7^5 + 6*7^7 + O(7^8
))*x + (6 + 5*7 + 3*7^2 + 6*7^3 + 7^4 + 3*7^5 + 2*7^6 + 5*7^7 + O(7^8)) 1]

? factorpadic(apol,7,8,1)

[(1 + O(7^8))*x + (6 + 2*7^2 + 2*7^3 + 3*7^4 + 2*7^5 + 6*7^6 + O(7^8)) 1]

[(1 + O(7^8))*x^2 + (1 + 6*7 + 4*7^2 + 4*7^3 + 3*7^4 + 4*7^5 + 6*7^7 + O(7^8
))*x + (6 + 5*7 + 3*7^2 + 6*7^3 + 7^4 + 3*7^5 + 2*7^6 + 5*7^7 + O(7^8)) 1]

? intformal(sin(x),x)
1/2*x^2 - 1/24*x^4 + 1/720*x^6 - 1/40320*x^8 + 1/3628800*x^10 - 1/479001600*
x^12 + 1/87178291200*x^14 - 1/20922789888000*x^16 + O(x^17)
? intformal((-x^2-2*a*x+8*a)/(x^4-14*x^3+(2*a+49)*x^2-14*a*x+a^2),x)
(x + a)/(x^2 - 7*x + a)
? newtonpoly(x^4+3*x^3+27*x^2+9*x+81,3)
[2, 2/3, 2/3, 2/3]
? padicappr(apol,1+O(7^8))
[1 + 6*7 + 4*7^2 + 4*7^3 + 3*7^4 + 4*7^5 + 6*7^7 + O(7^8)]
? padicappr(x^3+5*x+1,Mod(x*(1+O(7^8)),x^2+x-1))
[Mod((1 + 3*7 + 3*7^2 + 4*7^3 + 4*7^4 + 4*7^5 + 2*7^6 + 3*7^7 + O(7^8))*x + 
(2*7 + 6*7^2 + 6*7^3 + 3*7^4 + 3*7^5 + 4*7^6 + 5*7^7 + O(7^8)), x^2 + x - 1)
]~
? Pol(sin(x),x)
-1/1307674368000*x^15 + 1/6227020800*x^13 - 1/39916800*x^11 + 1/362880*x^9 -
 1/5040*x^7 + 1/120*x^5 - 1/6*x^3 + x
? Pol([1,2,3,4,5],x)
x^4 + 2*x^3 + 3*x^2 + 4*x + 5
? Polrev([1,2,3,4,5],x)
5*x^4 + 4*x^3 + 3*x^2 + 2*x + 1
? polcoeff(sin(x),7)
-1/5040
? polcyclo(105)
x^48 + x^47 + x^46 - x^43 - x^42 - 2*x^41 - x^40 - x^39 + x^36 + x^35 + x^34
 + x^33 + x^32 + x^31 - x^28 - x^26 - x^24 - x^22 - x^20 + x^17 + x^16 + x^1
5 + x^14 + x^13 + x^12 - x^9 - x^8 - 2*x^7 - x^6 - x^5 + x^2 + x + 1
? pcy=polcyclo(405)
x^216 - x^189 + x^135 - x^108 + x^81 - x^27 + 1
? pcy*pcy
x^432 - 2*x^405 + x^378 + 2*x^351 - 4*x^324 + 4*x^297 - x^270 - 4*x^243 + 7*
x^216 - 4*x^189 - x^162 + 4*x^135 - 4*x^108 + 2*x^81 + x^54 - 2*x^27 + 1
? poldegree(x^3/(x-1))
2
? poldisc(x^3+4*x+12)
-4144
? poldiscreduced(x^3+4*x+12)
[1036, 4, 1]
? polinterpolate([0,2,3],[0,4,9],5)
25
? polisirreducible(x^5+3*x^3+5*x^2+15)
0
? pollegendre(10)
46189/256*x^10 - 109395/256*x^8 + 45045/128*x^6 - 15015/128*x^4 + 3465/256*x
^2 - 63/256
? zpol=0.3+pollegendre(10)
46189/256*x^10 - 109395/256*x^8 + 45045/128*x^6 - 15015/128*x^4 + 3465/256*x
^2 + 0.053906249999999999999999999999999999999
? polrecip(3*x^7-5*x^3+6*x-9)
-9*x^7 + 6*x^6 - 5*x^4 + 3
? polresultant(x^3-1,x^3+1)
8
? polresultant(x^3-1.,x^3+1.,,1)
8.0000000000000000000000000000000000000
? polroots(x^5-5*x^2-5*x-5)
[2.0509134529831982130058170163696514536 + 0.E-38*I, -0.67063790319207539268
663382582902335603 + 0.84813118358634026680538906224199030917*I, -0.67063790
319207539268663382582902335603 - 0.84813118358634026680538906224199030917*I,
 -0.35481882329952371381627468235580237077 + 1.39980287391035466982975228340
62081964*I, -0.35481882329952371381627468235580237077 - 1.399802873910354669
8297522834062081964*I]~
? polroots(x^4-1000000000000000000000,1)
[-177827.94100389228012254211951926848447 + 0.E-38*I, 177827.941003892280122
54211951926848447 + 0.E-38*I, 6.6530622500127354998594589316364200753 E-111 
+ 177827.94100389228012254211951926848447*I, 6.65306225001273549985945893163
64200753 E-111 - 177827.94100389228012254211951926848447*I]~
? polrootsmod(x^16-1,41)
[Mod(1, 41), Mod(3, 41), Mod(9, 41), Mod(14, 41), Mod(27, 41), Mod(32, 41), 
Mod(38, 41), Mod(40, 41)]~
? polrootspadic(x^4+1,41,6)
[3 + 22*41 + 27*41^2 + 15*41^3 + 27*41^4 + 33*41^5 + O(41^6), 14 + 20*41 + 2
5*41^2 + 24*41^3 + 4*41^4 + 18*41^5 + O(41^6), 27 + 20*41 + 15*41^2 + 16*41^
3 + 36*41^4 + 22*41^5 + O(41^6), 38 + 18*41 + 13*41^2 + 25*41^3 + 13*41^4 + 
7*41^5 + O(41^6)]~
? polsturm(zpol)
4
? polsturm(zpol,0.91,1)
1
? polsylvestermatrix(a2*x^2+a1*x+a0,b1*x+b0)

[a2 b1 0]

[a1 b0 b1]

[a0 0 b0]

? polsym(x^17-1,17)
[17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 17]~
? poltchebi(10)
512*x^10 - 1280*x^8 + 1120*x^6 - 400*x^4 + 50*x^2 - 1
? polzagier(6,3)
4608*x^6 - 13824*x^5 + 46144/3*x^4 - 23168/3*x^3 + 5032/3*x^2 - 120*x + 1
? serconvol(sin(x),x*cos(x))
x + 1/12*x^3 + 1/2880*x^5 + 1/3628800*x^7 + 1/14631321600*x^9 + 1/1448500838
40000*x^11 + 1/2982752926433280000*x^13 + 1/114000816848279961600000*x^15 + 
O(x^16)
? serlaplace(x*exp(x*y)/(exp(x)-1))
1 + (y - 1/2)*x + (y^2 - y + 1/6)*x^2 + (y^3 - 3/2*y^2 + 1/2*y)*x^3 + (y^4 -
 2*y^3 + y^2 - 1/30)*x^4 + (y^5 - 5/2*y^4 + 5/3*y^3 - 1/6*y)*x^5 + (y^6 - 3*
y^5 + 5/2*y^4 - 1/2*y^2 + 1/42)*x^6 + (y^7 - 7/2*y^6 + 7/2*y^5 - 7/6*y^3 + 1
/6*y)*x^7 + (y^8 - 4*y^7 + 14/3*y^6 - 7/3*y^4 + 2/3*y^2 - 1/30)*x^8 + (y^9 -
 9/2*y^8 + 6*y^7 - 21/5*y^5 + 2*y^3 - 3/10*y)*x^9 + (y^10 - 5*y^9 + 15/2*y^8
 - 7*y^6 + 5*y^4 - 3/2*y^2 + 5/66)*x^10 + (y^11 - 11/2*y^10 + 55/6*y^9 - 11*
y^7 + 11*y^5 - 11/2*y^3 + 5/6*y)*x^11 + (y^12 - 6*y^11 + 11*y^10 - 33/2*y^8 
+ 22*y^6 - 33/2*y^4 + 5*y^2 - 691/2730)*x^12 + (y^13 - 13/2*y^12 + 13*y^11 -
 143/6*y^9 + 286/7*y^7 - 429/10*y^5 + 65/3*y^3 - 691/210*y)*x^13 + (y^14 - 7
*y^13 + 91/6*y^12 - 1001/30*y^10 + 143/2*y^8 - 1001/10*y^6 + 455/6*y^4 - 691
/30*y^2 + 7/6)*x^14 + O(x^15)
? serreverse(tan(x))
x - 1/3*x^3 + 1/5*x^5 - 1/7*x^7 + 1/9*x^9 - 1/11*x^11 + 1/13*x^13 - 1/15*x^1
5 + O(x^16)
? subst(sin(x),x,y)
y - 1/6*y^3 + 1/120*y^5 - 1/5040*y^7 + 1/362880*y^9 - 1/39916800*y^11 + 1/62
27020800*y^13 - 1/1307674368000*y^15 + O(y^16)
? subst(sin(x),x,x+x^2)
x + x^2 - 1/6*x^3 - 1/2*x^4 - 59/120*x^5 - 1/8*x^6 + 419/5040*x^7 + 59/720*x
^8 + 13609/362880*x^9 + 19/13440*x^10 - 273241/39916800*x^11 - 14281/3628800
*x^12 - 6495059/6227020800*x^13 + 69301/479001600*x^14 + 26537089/1188794880
00*x^15 + O(x^16)
? taylor(y/(x-y),y)
(O(y^16)*x^15 + y*x^14 + y^2*x^13 + y^3*x^12 + y^4*x^11 + y^5*x^10 + y^6*x^9
 + y^7*x^8 + y^8*x^7 + y^9*x^6 + y^10*x^5 + y^11*x^4 + y^12*x^3 + y^13*x^2 +
 y^14*x + y^15)/x^15
? variable(name^4-other)
name
? getheap
[61, 7110]
? print("Total time spent: ",gettime);
Total time spent: 260
? \q