Hi, I need to find the Taylor coefficient of order 7 in the variable "x4" of the following function:
var('x1 x2 x3 x4 w1 w2 w3 w4 w5 w5 w6');
g= 1/4((w1^2w3^2x1^4x2^6x3^8 + 2(w1^2w3^2x1^4x2^6 + w1^2w3x1^3x2^5)x3^7 + (w1^2w3^2x1^4x2^6 + 2w1^2w3x1^3x2^5 + 2w1^2x1^2x2^4)x3^6)x4^6 + 2((w1^2w3^2x1^4x2^6 + (w1^2w3^2x1^4 + (2w1^2w3 + w1w3^2)x1^3)x2^5)x3^7 + 2(w1^2w3^2x1^4x2^6 + (w1^2w3^2x1^4 + (3w1^2w3 + w1w3^2)x1^3)x2^5 + (w1^2w3x1^3 + (w1^2 + w1w3)x1^2)x2^4)x3^6 + (w1^2w3^2x1^4x2^6 + (w1^2w3^2x1^4 + (4w1^2w3 + w1w3^2)x1^3)x2^5 + 2(w1^2w3x1^3 + (2w1^2 + w1w3)x1^2)x2^4 + 2(w1^2x1^2 + w1x1)x2^3)x3^5)x4^5 + ((w1^2w3^2x1^4x2^6 + 2(w1^2w3^2x1^4 + (3w1^2w3 + 2w1w3^2)x1^3)x2^5 + (w1^2w3^2x1^4 + 2(3w1^2w3 + 2w1w3^2)x1^3 + 2(3w1^2 + 6w1w3 + w3^2)x1^2)x2^4)x3^6 + 2(w1^2w3^2x1^4x2^6 + (2w1^2w3^2x1^4 + (7w1^2w3 + 4w1w3^2)x1^3)x2^5 + (w1^2w3^2x1^4 + 4(2w1^2w3 + w1w3^2)x1^3 + (9w1^2 + 16w1w3 + 2w3^2)x1^2)x2^4 + (w1^2w3x1^3 + (3w1^2 + 4w1w3)x1^2 + 2(3w1 + w3)x1)x2^3)x3^5 + (w1^2w3^2x1^4x2^6 + 2(w1^2w3^2x1^4 + 2(2w1^2w3 + w1w3^2)x1^3)x2^5 + (w1^2w3^2x1^4 + 2(5w1^2w3 + 2w1w3^2)x1^3 + 2(7w1^2 + 10w1w3 + w3^2)x1^2)x2^4 + 2(w1^2w3x1^3 + (5w1^2 + 4w1w3)x1^2 + 2(5w1 + w3)x1)x2^3 + 2(w1^2x1^2 + 4w1x1 + 2)x2^2)x3^4)x4^4 + 2(((w1^2w3 + w1w3^2)x1^3x2^5 + (2(w1^2w3 + w1w3^2)x1^3 + (3w1^2 + 10w1w3 + 2w3^2)x1^2)x2^4 + ((w1^2w3 + w1w3^2)x1^3 + (3w1^2 + 10w1w3 + 2w3^2)x1^2 + 4(3w1 + 2w3)x1)x2^3)x3^5 + (2(w1^2w3 + w1w3^2)x1^3x2^5 + (4(w1^2w3 + w1w3^2)x1^3 + (7w1^2 + 22w1w3 + 4w3^2)x1^2)x2^4 + 2((w1^2w3 + w1w3^2)x1^3 + 2(2w1^2 + 6w1w3 + w3^2)x1^2 + (17w1 + 10w3)x1)x2^3 + ((w1^2 + 2w1w3)x1^2 + 2(5w1 + 2w3)x1 + 8)x2^2)x3^4 + ((w1^2w3 + w1w3^2)x1^3x2^5 + 2((w1^2w3 + w1w3^2)x1^3 + (2w1^2 + 6w1w3 + w3^2)x1^2)x2^4 + ((w1^2w3 + w1w3^2)x1^3 + (5w1^2 + 14w1w3 + 2w3^2)x1^2 + 12(2w1 + w3)x1)x2^3 + ((w1^2 + 2w1w3)x1^2 + 2(7w1 + 2w3)x1 + 12)x2^2 + 2(w1x1 + 2)x2)x3^3)x4^3 + 24(x2^2 + 2x2 + 1)x3^2 + 2(((w1^2 + 4w1w3 + w3^2)x1^2x2^4 + 2((w1^2 + 4w1w3 + w3^2)x1^2 + (8w1 + 7w3)x1)x2^3 + ((w1^2 + 4w1w3 + w3^2)x1^2 + 2(8w1 + 7w3)x1 + 20)x2^2)x3^4 + 2((w1^2 + 4w1w3 + w3^2)x1^2x2^4 + (2(w1^2 + 4w1w3 + w3^2)x1^2 + 3(6w1 + 5w3)x1)x2^3 + ((w1^2 + 4w1w3 + w3^2)x1^2 + 4(5w1 + 4w3)x1 + 27)x2^2 + ((2w1 + w3)x1 + 7)x2)x3^3 + ((w1^2 + 4w1w3 + w3^2)x1^2x2^4 + 2((w1^2 + 4w1w3 + w3^2)x1^2 + 2(5w1 + 4w3)x1)x2^3 + ((w1^2 + 4w1w3 + w3^2)x1^2 + 6(4w1 + 3w3)x1 + 36)x2^2 + 2((2w1 + w3)x1 + 9)x2 + 2)x3^2)x4^2 + 24x2^2 + 48(x2^2 + 2x2 + 1)x3 + 12(((w1 + w3)x1x2^3 + (2(w1 + w3)x1 + 5)x2^2 + ((w1 + w3)x1 + 5)x2)x3^3 + (2(w1 + w3)x1x2^3 + (4(w1 + w3)x1 + 11)x2^2 + 2((w1 + w3)x1 + 6)x2 + 1)x3^2 + ((w1 + w3)x1x2^3 + 2((w1 + w3)x1 + 3)x2^2 + ((w1 + w3)x1 + 7)x2 + 1)x3)x4 + 48x2 + 24)e^(-w2x1x2x3x4)/((x2^3x3^6e^(w5x1x2) + 3x2^3x3^5e^(w5x1x2) + 3x2^3x3^4e^(w5x1x2) + x2^3x3^3e^(w5x1x2))x4^3e^(w6x1x2x3) + 3((x2^3 + x2^2)x3^5e^(w5x1x2) + 3(x2^3 + x2^2)x3^4e^(w5x1x2) + 3(x2^3 + x2^2)x3^3e^(w5x1x2) + (x2^3 + x2^2)x3^2e^(w5x1x2))x4^2e^(w6x1x2x3) + 3((x2^3 + 2x2^2 + x2)x3^4e^(w5x1x2) + 3(x2^3 + 2x2^2 + x2)x3^3e^(w5x1x2) + 3(x2^3 + 2x2^2 + x2)x3^2e^(w5x1x2) + (x2^3 + 2x2^2 + x2)x3e^(w5x1x2))x4e^(w6x1x2x3) + ((x2^3 + 3x2^2 + 3x2 + 1)x3^3e^(w5x1x2) + 3(x2^3 + 3x2^2 + 3x2 + 1)x3^2e^(w5x1x2) + 3(x2^3 + 3x2^2 + 3x2 + 1)x3e^(w5x1x2) + (x2^3 + 3x2^2 + 3x2 + 1)e^(w5x1x2))e^(w6x1x2*x3))
For this we used the command:
taylor(g,x4,0,7)
Then, this return:
RuntimeError: ECL says: THROW: The catch RAT-ERR is undefined. During handling of the above exception, another exception occurred: ...... TypeError: ECL says: THROW: The catch RAT-ERR is undefined.
However, if I compute taylor(g,x4,0,3) returns its expansion without problems, but in order > 3, returns error.
Can anybody say me why don't returns its taylor expansion in order beyond 3?