Created
November 8, 2019 15:09
-
-
Save robinhouston/0bd2a04521333b0025c23f1e819d9eca to your computer and use it in GitHub Desktop.
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
sage: var("x1, x2, y") | |
....: f = exp(x1 + x2) / (1 - (1+x1)*(1+x2)*y) | |
....: | |
....: for (c, i) in f.taylor(x1, 0, 5).coefficients(): | |
....: fac1 = factorial(i) | |
....: for (d, j) in c.taylor(x2, 0, 5).coefficients(): | |
....: fac = fac1 * factorial(j) | |
....: for (e, k) in d.taylor(y, 0, 5).coefficients(): | |
....: print(i, j, k, e * fac) | |
....: | |
(x1, x2, y) | |
(0, 0, 0, 1) | |
(0, 0, 1, 1) | |
(0, 0, 2, 1) | |
(0, 0, 3, 1) | |
(0, 0, 4, 1) | |
(0, 0, 5, 1) | |
(0, 1, 0, 1) | |
(0, 1, 1, 2) | |
(0, 1, 2, 3) | |
(0, 1, 3, 4) | |
(0, 1, 4, 5) | |
(0, 1, 5, 6) | |
(0, 2, 0, 1) | |
(0, 2, 1, 3) | |
(0, 2, 2, 7) | |
(0, 2, 3, 13) | |
(0, 2, 4, 21) | |
(0, 2, 5, 31) | |
(0, 3, 0, 1) | |
(0, 3, 1, 4) | |
(0, 3, 2, 13) | |
(0, 3, 3, 34) | |
(0, 3, 4, 73) | |
(0, 3, 5, 136) | |
(0, 4, 0, 1) | |
(0, 4, 1, 5) | |
(0, 4, 2, 21) | |
(0, 4, 3, 73) | |
(0, 4, 4, 209) | |
(0, 4, 5, 501) | |
(0, 5, 0, 1) | |
(0, 5, 1, 6) | |
(0, 5, 2, 31) | |
(0, 5, 3, 136) | |
(0, 5, 4, 501) | |
(0, 5, 5, 1546) | |
(1, 0, 0, 1) | |
(1, 0, 1, 2) | |
(1, 0, 2, 3) | |
(1, 0, 3, 4) | |
(1, 0, 4, 5) | |
(1, 0, 5, 6) | |
(1, 1, 0, 1) | |
(1, 1, 1, 4) | |
(1, 1, 2, 9) | |
(1, 1, 3, 16) | |
(1, 1, 4, 25) | |
(1, 1, 5, 36) | |
(1, 2, 0, 1) | |
(1, 2, 1, 6) | |
(1, 2, 2, 21) | |
(1, 2, 3, 52) | |
(1, 2, 4, 105) | |
(1, 2, 5, 186) | |
(1, 3, 0, 1) | |
(1, 3, 1, 8) | |
(1, 3, 2, 39) | |
(1, 3, 3, 136) | |
(1, 3, 4, 365) | |
(1, 3, 5, 816) | |
(1, 4, 0, 1) | |
(1, 4, 1, 10) | |
(1, 4, 2, 63) | |
(1, 4, 3, 292) | |
(1, 4, 4, 1045) | |
(1, 4, 5, 3006) | |
(1, 5, 0, 1) | |
(1, 5, 1, 12) | |
(1, 5, 2, 93) | |
(1, 5, 3, 544) | |
(1, 5, 4, 2505) | |
(1, 5, 5, 9276) | |
(2, 0, 0, 1) | |
(2, 0, 1, 3) | |
(2, 0, 2, 7) | |
(2, 0, 3, 13) | |
(2, 0, 4, 21) | |
(2, 0, 5, 31) | |
(2, 1, 0, 1) | |
(2, 1, 1, 6) | |
(2, 1, 2, 21) | |
(2, 1, 3, 52) | |
(2, 1, 4, 105) | |
(2, 1, 5, 186) | |
(2, 2, 0, 1) | |
(2, 2, 1, 9) | |
(2, 2, 2, 49) | |
(2, 2, 3, 169) | |
(2, 2, 4, 441) | |
(2, 2, 5, 961) | |
(2, 3, 0, 1) | |
(2, 3, 1, 12) | |
(2, 3, 2, 91) | |
(2, 3, 3, 442) | |
(2, 3, 4, 1533) | |
(2, 3, 5, 4216) | |
(2, 4, 0, 1) | |
(2, 4, 1, 15) | |
(2, 4, 2, 147) | |
(2, 4, 3, 949) | |
(2, 4, 4, 4389) | |
(2, 4, 5, 15531) | |
(2, 5, 0, 1) | |
(2, 5, 1, 18) | |
(2, 5, 2, 217) | |
(2, 5, 3, 1768) | |
(2, 5, 4, 10521) | |
(2, 5, 5, 47926) | |
(3, 0, 0, 1) | |
(3, 0, 1, 4) | |
(3, 0, 2, 13) | |
(3, 0, 3, 34) | |
(3, 0, 4, 73) | |
(3, 0, 5, 136) | |
(3, 1, 0, 1) | |
(3, 1, 1, 8) | |
(3, 1, 2, 39) | |
(3, 1, 3, 136) | |
(3, 1, 4, 365) | |
(3, 1, 5, 816) | |
(3, 2, 0, 1) | |
(3, 2, 1, 12) | |
(3, 2, 2, 91) | |
(3, 2, 3, 442) | |
(3, 2, 4, 1533) | |
(3, 2, 5, 4216) | |
(3, 3, 0, 1) | |
(3, 3, 1, 16) | |
(3, 3, 2, 169) | |
(3, 3, 3, 1156) | |
(3, 3, 4, 5329) | |
(3, 3, 5, 18496) | |
(3, 4, 0, 1) | |
(3, 4, 1, 20) | |
(3, 4, 2, 273) | |
(3, 4, 3, 2482) | |
(3, 4, 4, 15257) | |
(3, 4, 5, 68136) | |
(3, 5, 0, 1) | |
(3, 5, 1, 24) | |
(3, 5, 2, 403) | |
(3, 5, 3, 4624) | |
(3, 5, 4, 36573) | |
(3, 5, 5, 210256) | |
(4, 0, 0, 1) | |
(4, 0, 1, 5) | |
(4, 0, 2, 21) | |
(4, 0, 3, 73) | |
(4, 0, 4, 209) | |
(4, 0, 5, 501) | |
(4, 1, 0, 1) | |
(4, 1, 1, 10) | |
(4, 1, 2, 63) | |
(4, 1, 3, 292) | |
(4, 1, 4, 1045) | |
(4, 1, 5, 3006) | |
(4, 2, 0, 1) | |
(4, 2, 1, 15) | |
(4, 2, 2, 147) | |
(4, 2, 3, 949) | |
(4, 2, 4, 4389) | |
(4, 2, 5, 15531) | |
(4, 3, 0, 1) | |
(4, 3, 1, 20) | |
(4, 3, 2, 273) | |
(4, 3, 3, 2482) | |
(4, 3, 4, 15257) | |
(4, 3, 5, 68136) | |
(4, 4, 0, 1) | |
(4, 4, 1, 25) | |
(4, 4, 2, 441) | |
(4, 4, 3, 5329) | |
(4, 4, 4, 43681) | |
(4, 4, 5, 251001) | |
(4, 5, 0, 1) | |
(4, 5, 1, 30) | |
(4, 5, 2, 651) | |
(4, 5, 3, 9928) | |
(4, 5, 4, 104709) | |
(4, 5, 5, 774546) | |
(5, 0, 0, 1) | |
(5, 0, 1, 6) | |
(5, 0, 2, 31) | |
(5, 0, 3, 136) | |
(5, 0, 4, 501) | |
(5, 0, 5, 1546) | |
(5, 1, 0, 1) | |
(5, 1, 1, 12) | |
(5, 1, 2, 93) | |
(5, 1, 3, 544) | |
(5, 1, 4, 2505) | |
(5, 1, 5, 9276) | |
(5, 2, 0, 1) | |
(5, 2, 1, 18) | |
(5, 2, 2, 217) | |
(5, 2, 3, 1768) | |
(5, 2, 4, 10521) | |
(5, 2, 5, 47926) | |
(5, 3, 0, 1) | |
(5, 3, 1, 24) | |
(5, 3, 2, 403) | |
(5, 3, 3, 4624) | |
(5, 3, 4, 36573) | |
(5, 3, 5, 210256) | |
(5, 4, 0, 1) | |
(5, 4, 1, 30) | |
(5, 4, 2, 651) | |
(5, 4, 3, 9928) | |
(5, 4, 4, 104709) | |
(5, 4, 5, 774546) | |
(5, 5, 0, 1) | |
(5, 5, 1, 36) | |
(5, 5, 2, 961) | |
(5, 5, 3, 18496) | |
(5, 5, 4, 251001) | |
(5, 5, 5, 2390116) |
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment