67
votes
26
votes
23
votes
Accepted
Find the rate of change at a point on a polynomial
Mathematica, 6 bytes
#'@#2&
(Beat THAT, MATL and 05AB1E)
The first argument must be a polynomial, with # as its variable ...
- 13.8k
14
votes
Pi == 3.2
Python + scipy, 92 bytes
from scipy.integrate import*
lambda p:2/p*quad(lambda x:(x/x**p+(1-x)**(1-p))**(1/p),0,1)[0]
Formula is from this math.SE question.
- 39.1k
13
votes
13
votes
The Lehmer-Comtet sequence
Haskell, 77 75 bytes, no differentiation builtins
x@(a:b)&y@(c:d)=a*c:zipWith(+)(b&y)(x&d)
s=1:s&(1:scanl(*)1[-1,-2..])
(s!!)
Try it online!
How ...
- 39.8k
12
votes
Derivative of a product
Python, 54 bytes
lambda s:((l:=len(s))*(l*"'"+-~l*(s+"+")))[-~l*~l::-l]
Attempt This Online!
Python, 56 bytes
lambda s:((l:=-~len(s))*(l*(s+"+")+-~l*"'")...
- 16.7k
11
votes
Pi == 3.2
MATL, 31 bytes
0:1e-3:1lyG^-lG/^v!d|G^!slG/^sE
Try it online! Or verify all test cases.
Explanation
This generates the x,y coordinates of one quarter of the ...
- 105k
11
votes
Compute Dickman
Python, 141 bytes
g=lambda x,p=[1]+[0]*99,I=2,z=0,i=0:x<1and sum(a*(1-x)**~-(i:=i+1)for a in p)or g(x-1,[p[0]-sum(A:=[(z:=(z+w)/I)/(i:=i+1)for w in p])]+A,I+1)
...
- 78.2k
10
votes
Write a Sine-Deriving Machine
Python, 42 bytes
from math import*
lambda x,n:sin(x+pi/2*n)
Uses the fact that differentiating shifts the function by pi/2 ...
- 146k
10
votes
Pi == 3.2
Wolfram Language (Mathematica), 49 46 45 bytes
3 bytes saved thanks to alephalpha.
1 byte saved thanks to att.
\!\(2N@∫\_0\%1\@+++(a^-#-1)^(1-#)\%#a\)&
Try it ...
- 18k
10
votes
The Pedant's Cosine
Mathematica, 49 41 39 31 bytes
Sum[(-#^2)^k/(2k)!,{k,0,#2-1}]&
Old, more "fun" version: (39 bytes)
...
- 7,592
10
votes
The Pedant's Cosine
MATL, 14 bytes
U_iqE:2ep/YpsQ
Try it online! Or verify all test cases.
Explanation with example
All numbers have double precision (this is the default).
Consider ...
- 105k
10
votes
Approximate definite integrals using Riemann sums
R, 69 65 63 57 bytes
function(a,b,n,k,f,w=(b-a)/n)sum(sapply(a+w*(1:n-k),f))*w
Try it online!
Takes k=FALSE for right-hand ...
- 28.8k
10
votes
Derivative of a product
C (clang), 69 64 59 bytes
-10 thanks to @Noodle9 and @ceilingcat
l;f(char*a){for(l=0;a[l];)printf("+%.*s'%s"+!l,++l,a,a+l);}
Try it online!
- 3,230
9
votes
9
votes
Accepted
Definite integral of polynomial functions
Jelly, \$\frac {30} 7 = 4.29\$
÷J$ŻUḅI
Try it online!
Takes the polynomial as a list of coefficients in little-endian format (i.e. the example is ...
- 50.1k
8
votes
Find the rate of change at a point on a polynomial
MATL, 8 6 bytes
yq^**s
Input is: array of exponents, number, array of coefficients.
Try it online! Or verify all test cases: 1, 2 3, 4, 5.
Explanation
Consider ...
- 105k
8
votes
The Pedant's Cosine
Jelly, 22 bytes
-*ð×ø⁹*⁸²ð÷ø⁸Ḥ!
⁸R’Ç€S
This is a full program which takes n as the first argument and x as the second.
Explanation:
...
- 16.3k
8
votes
Solve a separable differential equation
Python 2, 123 122 bytes
def f(p,P):R=[[[a/-~b,b+1]for a,b in F]for F in P];a,b=map(lambda F,x:sum(a*x**b for a,b in F),R,p);R[1]+=[a-b,0],;print R
Try it online!
...
- 8,393
8
votes
8
votes
Derivative of a product
Python, 47 bytes
lambda s:"+".join(s.replace(c,c+"'")for c in s)
Attempt This Online!
How it works:
...
- 505
7
votes
Find the rate of change at a point on a polynomial
Julia, 45 42 40 37 bytes
f(p,x)=sum(i->prod(i)x^abs(i[2]-1),p)
This is a function that acceps a vector of tuples and a number and returns a number. The ...
- 24.7k
7
votes
The Pedant's Cosine
Python, 54 bytes
f=lambda x,n,t=1,p=1:n and t+f(x,n-1,-t*x*x/p/-~p,p+2)
If using Python 2, be sure to pass x as a float, not an integer, but I my understanding ...
- 174k
7
votes
The Lehmer-Comtet sequence
Mathematica, 19 bytes
D[x^x,{x,#-1}]/.x->1&
-18 bytes from @Not a tree
- 24.9k
7
votes
Polynomial Laplace transform
Haskell, 25 bytes
zipWith(*)$scanl(*)1[1..]
Try it online!
Pretty straightforward: Generates the list of factorials ...
- 146k
6
votes
Solve the Laplace equation
Matlab, 84, 81.2 79.1 bytes = 113 - 30%
function u=l(f,N,a,b);A=toeplitz([2,-1,(3:N)*0]);A([1,2,end-[1,0]])=eye(2);u=[a,f((1:N-2)/N)*(N-1)^2,b]/A;plot(u)
Note ...
- 43.9k
6
votes
6
votes
Pi == 3.2
PARI/GP, 48 43 bytes
It's easy after @orlp has found the formula, and @alephalpha's version saves 5 bytes:
p->2*intnum(u=0,1,(1+(u^-p-1)^(1-p))^(1/p))
To add ...
- 7,130
Only top scored, non community-wiki answers of a minimum length are eligible