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Currently expressions like

DChange[T1[x, 0], x/S@t == ξ, x, ξ, T1[x, t]]

can't be handled very well, see this post for more information. Haven't think out a solution at the moment.

– xzczd Nov 12 '16 at 13:12

Here is an example that DChange can't handle very well currently:

DChange[
  0 == r'[t]^2 + r[t]^2 u'[t]^2 - 2 \[Kappa]^2/r[t] - h
, {r'[t] == R'[u] u'[t], r[t] == R[u], u'[t] == c/R[u]^2}
]

One way I can think out to fix this is to use //. i.e.

DChange[expr_, functions : {(_[___] == _) ..}
] := expr //. Replace[functions, (f_[vars__] == body_) :> (f -> Function[{vars}, body]), {1}]

– xzczd Mar 7 '16 at 13:02

Currently DChange can't handle Piecewise function very well, here's an example. Can't think out a solution though, it's actually because of the limitation of Solve.

– xzczd Aug 5 '16 at 4:03

Maybe an assumption option should be added to DChange because Solve isn't influenced by Assuming and this sometimes makes writing transformation rule a bit painful.

– xzczd Oct 24 '16 at 1:30

The simple examples provided on StackOverflow using built-in transformations do not work (in Mathematica 12.2).

DChange[D[f[x, y], x, x] + D[f[x, y], y, y] == 0, 
     "Cartesian" -> "Polar", {x, y}, {r, th}, f[x, y]]

Generate a series of error messages starting with

Solve::nsmet: This system cannot be solved with the methods available to Solve.

DChange::ambTrans: Transformation rule is ambiguous. The first of found solutions is used:

    r==Sqrt[x^2+y^2]
    th==ArcTan[x,y]

Please add appropriate assumptions if this solution does not meet your expectations.
...

Perhaps a warning message should be generated when Solve finds more than one solution e.g.

"The provided transformation rule is ambiguous, only one of the possible transformations is applied".

See this question for more information.

– xzczd Oct 9 '16 at 12:09

It's quite likely this is just a syntax/implementation on my side, and so apologies if I'm wasting your time.

I'm trying to do a change of variable in the following equations:

eq = x''[t] == -((g R^2)/(R + x[t])^2);
ic1 = x'[0] == v0;
ic2 = x[0] == 0;

Change of variable:

u=x/xc
s=t/tc

Code:
DChange[{eq, ic1, ic2}, {u == x/xc, s == t/tc}, {x, t}, {u, s}, x[t]]

Output:
{u''[s]/tc^2 == -((g R^2)/(R + u[s])^2), v0 == u'[0]/tc, u[0]==0}

Expected Output:
{xc u''[s]/tc^2 == -((g R^2)/(R + xc u[s])^2), v0 == xc u'[0]/tc, u[0]==0}

The characteristic value xc doesn't appear in any of the equations, and I can't figure out why.