the section "Controlling the Form of Solutions" in ?solve,details refers to a single equation or it is not clearly dealing with a system of equation. Anyway, this alternative works also:

_EnvExplicit:=true:
solve(sys, [x, y, z, lambda]);

         1/2  1/2       1/2  1/2       1/2  1/2            1/2  1/2
        3    S         3    S         3    S              3    S
  [[x = ---------, y = ---------, z = ---------, lambda = ---------],
            3              3              6                  12

                1/2  1/2         1/2  1/2         1/2  1/2
               3    S           3    S           3    S
        [x = - ---------, y = - ---------, z = - ---------,
                   3                3                6

                    1/2  1/2
                   3    S
        lambda = - ---------]]
                      12

the section "Controlling the Form of Solutions" in ?solve,details refers to a single equation or it is not clearly dealing with a system of equation. Anyway, this alternative works also:

_EnvExplicit:=true:
solve(sys, [x, y, z, lambda]);

         1/2  1/2       1/2  1/2       1/2  1/2            1/2  1/2
        3    S         3    S         3    S              3    S
  [[x = ---------, y = ---------, z = ---------, lambda = ---------],
            3              3              6                  12

                1/2  1/2         1/2  1/2         1/2  1/2
               3    S           3    S           3    S
        [x = - ---------, y = - ---------, z = - ---------,
                   3                3                6

                    1/2  1/2
                   3    S
        lambda = - ---------]]
                      12

What makes me wonder is whether such accumulation of "vectors" is sane: 'vector', 'Vector', 'VectorCalculus:-Vector', etc,etc.

What makes me wonder is whether such accumulation of "vectors" is sane: 'vector', 'Vector', 'VectorCalculus:-Vector', etc,etc.

I want to see the library source code together with its (now hidden) comments.

OK, let us consider mechanics. The International System (SI) is based on three independent magnitudes (length, mass and time). But this is not the only kind of system of units.

In Relativistic Physics, for instance, it is usual to set c=1, with c the speed of light (3*10^8 m/s aprox). This is  convenient as you avoid writing so many factors c around. But this choice of units, ie this constraint, makes only two magnitudes independent as length and time units become "interchangeable".  Eg you can measure distance in seconds or years. And the same with mass and energy (or linear momentum). Then, you can add them and this is what it is done all the time.

And for General Relativity, that deals with gravitation, it becomes convenient to set  both c=1 and G=1, with G the Newton gravitational constant. Then, you get a system with just a single independent unit. Eg mass and length have the same unit. As this is so usual and convenient, most papers in this field (included mine ones) are written in these units.

Similarly, in Quantum Physics it is usual to set hbar=1, with h the Planck constant and hbar=h/(2*Pi). And in Relativistic Quantum Field Theory, as you may guess, people set both hbar=1 and c=1.

Then, the system of units, as other conventions, is largely arbitrary and its choice depends on convenience.

OK, let us consider mechanics. The International System (SI) is based on three independent magnitudes (length, mass and time). But this is not the only kind of system of units.

In Relativistic Physics, for instance, it is usual to set c=1, with c the speed of light (3*10^8 m/s aprox). This is  convenient as you avoid writing so many factors c around. But this choice of units, ie this constraint, makes only two magnitudes independent as length and time units become "interchangeable".  Eg you can measure distance in seconds or years. And the same with mass and energy (or linear momentum). Then, you can add them and this is what it is done all the time.

And for General Relativity, that deals with gravitation, it becomes convenient to set  both c=1 and G=1, with G the Newton gravitational constant. Then, you get a system with just a single independent unit. Eg mass and length have the same unit. As this is so usual and convenient, most papers in this field (included mine ones) are written in these units.

Similarly, in Quantum Physics it is usual to set hbar=1, with h the Planck constant and hbar=h/(2*Pi). And in Relativistic Quantum Field Theory, as you may guess, people set both hbar=1 and c=1.

Then, the system of units, as other conventions, is largely arbitrary and its choice depends on convenience.

May be that the "best PC" for numerical intensive calculations is not the best for large symbolic calculations.

to clarify what it is intended. But anyway, if Ohm=1, H=F=s.

to clarify what it is intended. But anyway, if Ohm=1, H=F=s.

In the SI system of units say, R*C has units of time (second). Symbolically [RC]=[R][C]=T, and [L/R]=[L]/[R]=T also. Now, in a system of units with [R]=1, [L]=[C]=T.

In the SI system of units say, R*C has units of time (second). Symbolically [RC]=[R][C]=T, and [L/R]=[L]/[R]=T also. Now, in a system of units with [R]=1, [L]=[C]=T.

It is stated R = 100 not 100 Ohm. Another typo or units Ohm=1?

It is stated R = 100 not 100 Ohm. Another typo or units Ohm=1?

as 'argument' does not produce the two argument arctan when assumed real:

argument(z) assuming real;



                 2  2       2                3  2            2  2
          R omega  C      (R  omega C + omega  C  L + R omega  C ) I
argument( -------------- + ----------------------------------------)
               2  2    2                      2  2    2
          omega  C  + R                  omega  C  + R

On the other hand, the resistance, capacitance, etc, are positive magnitudes. So the expression in terms of the two argument 'arctan' is unnecessary complicated in this context.