Is there a way, or if not, how could one define a function which takes an equation in any form (for example as given by FullSimplify):
$$(A+X_0) x+By=3x$$
and rearranges it in the more compact and tidy form:
$$(A+X_0-3) x+By=0$$
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4 ClearAll[a, b, c, d, x, y] expr = a x + b y + c x == d x; You can use any of
Collect[(expr /. Equal -> Subtract) == 0, x] Collect[Subtract @@ expr == 0, x] FullSimplify[(expr /. Equal -> Subtract) ] == 0 FullSimplify[Subtract @@ expr] == 0 to get
(* (a + c - d) x + b y == 0 *) Alternatively, use a custom ComplexityFunction that makes non-zero expressions on the right-hand-side of == more expensive:
cf[e_] := 100 Count[e, Equal[_, Except[0, _]], {0, Infinity}] + LeafCount[e] FullSimplify[expr, ComplexityFunction -> cf] (* (a + c - d) x + b y == 0 *) Update: In versions 11.3+, you can use the function SubtractSides:
FullSimplify /@ SubtractSides[expr] (a + c - d) x + b y == 0
- $\begingroup$ A very nice solution, that is with the complexity function. $\endgroup$Alexei Boulbitch– Alexei Boulbitch2015-03-03 13:40:47 +00:00Commented Mar 3, 2015 at 13:40
- $\begingroup$ @kglr Hi! In v11.3 and wolframcloud,
FullSimplify / @ SubtractSides[expr]can not run. Syntax: "FullSimplify cannotbe followedby@SubtractSide $\{$ expr']. $\endgroup$lotus2019– lotus20192022-03-24 01:25:10 +00:00Commented Mar 24, 2022 at 1:25 - $\begingroup$ Thank you @lotus2019; the typo is fixed. $\endgroup$kglr– kglr2022-03-24 02:17:08 +00:00Commented Mar 24, 2022 at 2:17
- $\begingroup$ @kglr My pleasure. $\endgroup$lotus2019– lotus20192022-03-24 02:25:07 +00:00Commented Mar 24, 2022 at 2:25