MATLAB: What does “~” mean in symbolic expression

pretty()symbolicSymbolic Math Toolbox

After I made my computation with symbolic math toolbox, I get a quite long formula. So by using command "pretty", I get a prettyprinted formula, which is the thing I like most about this toolbox. However there is something I don't get it.

        [//a1~ %4   b1~ %3\       /  a1~ %3   b1~ %2\    \

        [||------ - ------| a1~ + |- ------ + ------| b1~| y1
        [\\  %1       %1  /       \    %1       %1  /    /

        [----------------------------------------------------
        [                        p1~
           //a1~ %4   b1~ %3\       /  a1~ %3   b1~ %2\    \
           ||------ - ------| a2~ + |- ------ + ------| b2~| y2
           \\  %1       %1  /       \    %1       %1  /    /
         + ----------------------------------------------------
                                   p2~
           //a1~ %4   b1~ %3\       /  a1~ %3   b1~ %2\    \        ]
           ||------ - ------| a3~ + |- ------ + ------| b3~| y3     ]
           \\  %1       %1  /       \    %1       %1  /    /        ]
         + ---------------------------------------------------- - y1]
                                   p3~                              ]
%1 := a1~  p3~ b2~  + a1~  p2~ b3~  + a2~  p3~ b1~  + a2~  p1~ b3~
              2        2      2        2
         + a3~  p2~ b1~  + a3~  p1~ b2~  - 2 a1~ b1~ p3~ a2~ b2~
         - 2 a1~ b1~ p2~ a3~ b3~ - 2 a2~ b2~ p1~ a3~ b3~
           2              2              2
 %2 := a1~  p2~ p3~ + a2~  p1~ p3~ + a3~  p1~ p2~
 %3 := a1~ b1~ p2~ p3~ + a2~ b2~ p1~ p3~ + a3~ b3~ p1~ p2~
           2              2              2
 %4 := b1~  p2~ p3~ + b2~  p1~ p3~ + b3~  p1~ p2~

What does "~" stand for?

Best Answer

I do not know if it is used in MuPAD (it might be), but in Maple, the ~ immediately after a name indicates that the name has assumptions associated with it, usually assumptions added by the user. For example, an assumption that it is real, or integer valued, or in a particular range.

Related Solutions

MATLAB: Warning: Explicit integral could not be found

-(4/3) * (R12^4 * (B2^2 + A2^2) * A2 * (-(3/8) * exp(6 * B2 * L) + (-(3/16) * R12^4 + L * B2 * R12^2 + 3/8) * exp(2 * B2 * L) + (3/16) * R12^4 * exp(-2 * B2 * L)) * cos(2 * S12 + 2 * A2 * L) - (1/2) * R12^2 * (B2^2 + A2^2) * A2 * ((L * B2 * R12^2 + 1/8 - (3/8) * R12^4) * exp(4 * B2 * L) - (1/8) * exp(8 * B2 * L) + (3/8) * R12^4) * cos(4 * S12 + 4 * A2 * L) + (1/16) * R12^4 * A2 * (B2^2 + A2^2) * ( - exp(6 * B2 * L) + exp(2 * B2 * L)) * cos(6 * S12 + 6 * A2 * L) + (1/16) * B2 * (B2^2 + A2^2) * (R12^4 * exp(4 * B2 * L) + exp(8 * B2 * L)) * sin(2 * S12 + 4 * A2 * L) + (1/2) * R12 * B2^2 * A2 * ((R12^2 + 1/2) * exp(6 * B2 * L) + R12^4 * exp(2 * B2 * L)) * cos(3 * S12 + 2 * A2 * L) - (1/2) * ((R12^4 + R12^2) * exp(4 * B2 * L) + (1/2) * exp(8 * B2 * L)) * R12 * B2^2 * A2 * cos(4 * A2 * L + 3 * S12) + (1/2) * ((-R12^2 + 1/2) * exp(6 * B2 * L) + R12^4 * exp(2 * B2 * L)) * R12 * B2 * A2^2 * sin(3 * S12 + 2 * A2 * L) - (1/2) * R12 * ((R12^4 - R12^2) * exp(4 * B2 * L) + (1/2) * exp(8 * B2 * L)) * B2 * A2^2 * sin(4 * A2 * L + 3 * S12) + (1/16) * exp(6 * B2 * L) * B2 * R12^2 * (B2^2 + A2^2) * sin(4 * S12 + 2 * A2 * L) - (1/16) * exp(6 * B2 * L) * B2 * R12^2 * (B2^2 + A2^2) * sin(4 * S12 + 6 * A2 * L) - (1/4) * R12^3 * B2^2 * A2 * cos(5 * S12 + 4 * A2 * L) * exp(4 * B2 * L) + (1/4) * R12^3 * B2^2 * A2 * cos(6 * A2 * L + 5 * S12) * exp(6 * B2 * L) - (1/4) * R12^3 * A2^2 * B2 * sin(5 * S12 + 4 * A2 * L) * exp(4 * B2 * L) + (1/4) * R12^3 * A2^2 * B2 * sin(6 * A2 * L + 5 * S12) * exp(6 * B2 * L) + (1/4) * ((4 * R12^2 + 2) * exp(6 * B2 * L) + R12^4 * exp(2 * B2 * L) * (R12^2 + 3)) * R12 * B2^2 * A2 * cos(S12 + 2 * A2 * L) + (1/4) * ((4 * R12^2 - 2) * exp(6 * B2 * L) + R12^4 * exp(2 * B2 * L) * (-3 + R12^2)) * R12 * B2 * A2^2 * sin(S12 + 2 * A2 * L) - (1/2) * ((1/8) * R12^2 * B2 * (B2^2 + A2^2) * sin(2 * S12) + A2 * ((2 * R12 * B2^2 + (3/2) * B2^2 * R12^3) * cos(S12) - (3/2) * R12 * B2 * A2 * (R12^2 - 4/3) * sin(S12) + (B2^2 + A2^2) * (-(1/2) * R12^4 + 3/16 + L * B2 * R12^2))) * R12^2 * exp(4 * B2 * L) - (1/8) * sin(2 * A2 * L) * B2 * R12^2 * (B2^2 + A2^2) * exp(6 * B2 * L) + (-(1/16) * B2 * (B2^2 + A2^2) * sin(2 * S12) + (1/4) * (-2 * R12 * B2^2 * cos(S12) + 2 * A2 * R12 * sin(S12) * B2 + (B2 * L + (3/8) * R12^2) * (B2^2 + A2^2)) * A2) * exp(8 * B2 * L) - (1/4) * ((1/8) * R12^4 * (B2^2 + A2^2) * exp(-4 * B2 * L) + R12 * B2^2 * cos(S12) + A2 * R12 * sin(S12) * B2 + (L * B2 * R12^2 + 1 - (1/8) * R12^4) * (B2^2 + A2^2)) * R12^6 * A2) * R12^2 / ((R12^2 * (R12^8 * exp(2 * B2 * L) + 3 * R12^4 * exp(6 * B2 * L) + exp(10 * B2 * L)) * cos(2 * S12 + 2 * A2 * L) + (-R12^4 * exp(8 * B2 * L) - R12^8 * exp(4 * B2 * L)) * cos(4 * S12 + 4 * A2 * L) - (3/2) * R12^8 * exp(4 * B2 * L) - (1/6) * exp(12 * B2 * L) - (3/2) * R12^4 * exp(8 * B2 * L) - (1/6) * R12^12 + (1/3) * R12^6 * exp(6 * B2 * L) * cos(6 * S12 + 6 * A2 * L)) * B2 * (B2^2 + A2^2) * A2)

Note: If you substitute in the constants that you show, then the expression becomes very very sensitive to the exact value of L when you are near L = 0, especially in the slightly negative L range. This instability continues even if you do symbolic calculations with 256 digits precision.

MATLAB: Explicit root of symbolic equations

syms d1 d2 d3 d4 d5 d6 h11 h12 h13 h14 h21 h22 h23 h24 h41 h42...
    h45 h46 h51 h52 h55 h56 h61 h62 h65 h66
eq1 = h11*d1+h12*d2+h13*d3+h14*d4 == 0;
eq2 = h21*d1+h22*d2+h23*d3+h23*d4 == 0;
eq3 = d1+d2+d3+d4-d5-d6 == 0;
eq4 = h41*d1+h42*d2-h41*d3-h42*d4-h45*d5-h46*d6 == 0;
eq5 = h51*d1+h52*d2+h51*d3+h52*d4-h55*d5-h56*d6 == 0;
eq6 = h61*d1+h62*d2-h61*d3-h62*d4-h65*d5-h66*d6 == 0;
% Solve for d1...d6
sol_d1 = isolate(eq1,d1)
sol_d2 = isolate(eq2,d2)
sol_d3 = isolate(eq3,d3)
sol_d4 = isolate(eq4,d4)
sol_d5 = isolate(eq5,d5)
sol_d6 = isolate(eq6,d6)

gives:

sol_d1 =
 
d1 == -(d2*h12 + d3*h13 + d4*h14)/h11
 
 
sol_d2 =
 
d2 == -(d1*h21 + d3*h23 + d4*h23)/h22
 
 
sol_d3 =
 
d3 == d5 - d2 - d4 - d1 + d6
 
 
sol_d4 =
 
d4 == -(d3*h41 - d2*h42 - d1*h41 + d5*h45 + d6*h46)/h42
 
 
sol_d5 =
 
d5 == (d1*h51 + d2*h52 + d3*h51 + d4*h52 - d6*h56)/h55
 
 
sol_d6 =
 
d6 == -(d3*h61 - d2*h62 - d1*h61 + d4*h62 + d5*h65)/h66

This is what you wanted to get?

Best Answer

Related Solutions

MATLAB: Warning: Explicit integral could not be found

MATLAB: Explicit root of symbolic equations

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