Changes between Initial Version and Version 1 of Ticket #11934


Ignore:
Timestamp:
10/18/11 02:45:45 (11 years ago)
Author:
kcrisman
Comment:

Can you be more specific about the invalidity? I think the plot errors are because of the imaginary pieces. Remember, these simplifications are not supposed to be 100 percent valid at all times; especially with roots there are branch issues, unfortunately. The f in question is pretty long - any sense as to where it might simplify in an unusual way?

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  • Ticket #11934 – Description

    initial v1  
    11I ran into this today with a real function. Sorry I don't have a shorter test case. The attached file should show a simplification which, as far as I can tell, is invalid.
     2
     3{{{
     4sage: f = QQ(0.25)*(sqrt(2) - 2)*(x + 1)*x**3 - QQ(3)/QQ(8)*(sqrt(2) - 2)*(x + 1)*x**2 - QQ(0.25)*(sqrt(2) - 2)*(2*(3*sqrt(2) - 2)*x**2 - 2*(sqrt(2) - 1)*x + sqrt(-8*(4*sqrt(2) - 7)*x**4 + 16*(3*sqrt(2) - 5)*x**3 - 8*(2*sqrt(2) - 3)*x - 4*x**2 + 4) - 4*sqrt(2) + 2)*x**3/(sqrt(2)*x**2 + sqrt(2)*x - 2*sqrt(2)) - 1/24*(x + 1)**3*(x**3 - 3*x + 2) + QQ(3)/QQ(8)*(sqrt(2) - 2)*(2*(3*sqrt(2) - 2)*x**2 - 2*(sqrt(2) - 1)*x + sqrt(-8*(4*sqrt(2) - 7)*x**4 + 16*(3*sqrt(2) - 5)*x**3 - 8*(2*sqrt(2) - 3)*x - 4*x**2 + 4) - 4*sqrt(2) + 2)*x**2/(sqrt(2)*x**2 + sqrt(2)*x - 2*sqrt(2)) - QQ(1)/QQ(16)*(x + 1)**2*(2*(sqrt(2) - 3)*x**3 - (3*sqrt(2) - 8)*x**2 + 2*x + sqrt(2) - 4) + QQ(1)/QQ(8)*(x + 1)*sqrt(2) + QQ(1)/QQ(96)*(x**3 - 3*x + 2)*(2*(3*sqrt(2) - 2)*x**2 - 2*(sqrt(2) - 1)*x + sqrt(-8*(4*sqrt(2) - 7)*x**4 + 16*(3*sqrt(2) - 5)*x**3 - 8*(2*sqrt(2) - 3)*x - 4*x**2 + 4) - 4*sqrt(2) + 2)**3/(sqrt(2)*x**2 + sqrt(2)*x - 2*sqrt(2))**3 + 1/32*(2*(3*sqrt(2) - 2)*x**2 - 2*(sqrt(2) - 1)*x + sqrt(-8*(4*sqrt(2) - 7)*x**4 + 16*(3*sqrt(2) - 5)*x**3 - 8*(2*sqrt(2) - 3)*x - 4*x**2 + 4) - 4*sqrt(2) + 2)**2*(2*(sqrt(2) - 3)*x**3 - (3*sqrt(2) - 8)*x**2 + 2*x + sqrt(2) - 4)/(sqrt(2)*x**2 + sqrt(2)*x - 2*sqrt(2))**2 - QQ(0.25)*x - QQ(1)/QQ(8)*(2*(3*sqrt(2) - 2)*x**2 - 2*(sqrt(2) - 1)*x + sqrt(-8*(4*sqrt(2) - 7)*x**4 + 16*(3*sqrt(2) - 5)*x**3 - 8*(2*sqrt(2) - 3)*x - 4*x**2 + 4) - 4*sqrt(2) + 2)*sqrt(2)/(sqrt(2)*x**2 + sqrt(2)*x - 2*sqrt(2)) + QQ(0.25)*(2*(3*sqrt(2) - 2)*x**2 - 2*(sqrt(2) - 1)*x + sqrt(-8*(4*sqrt(2) - 7)*x**4 + 16*(3*sqrt(2) - 5)*x**3 - 8*(2*sqrt(2) - 3)*x - 4*x**2 + 4) - 4*sqrt(2) + 2)/(sqrt(2)*x**2 + sqrt(2)*x - 2*sqrt(2)) - QQ(0.25)
     5sage: f.full_simplify()
     6-1/24*(sqrt(2)*x^8 - 2*(sqrt(2) - 3)*x^7 - (14*sqrt(2) - 15)*x^6 + 10*(9*sqrt(2) - 13)*x^5 - (93*sqrt(2) - 128)*x^4 - 4*(9*sqrt(2) - 14)*x^3 + (58*sqrt(2) - 77)*x^2 + 4*(sqrt(2) - 2)*x - sqrt(2*(4*sqrt(2) - 7)*x^2 + 4*(sqrt(2) - 2)*x - 1)*((16*I*sqrt(2) - 28*I)*x^4 + (-24*I*sqrt(2) + 40*I)*x^3 + (8*I*sqrt(2) - 12*I)*x + 2*I*x^2 - 2*I) - 8*sqrt(2) + 10)/(sqrt(2)*x^2 + 4*sqrt(2)*x + 4*sqrt(2))
     7}}}