Evaluating expressions by applying corresponding rules stored in another list

Question

I have a list of expressions:

{x,x^2,x^3}

and a list of rules

{x->1,x->2,x->3}

How can I get {1,4,27} by applying the rule to the expression in the corresponding location?

Answer 1

MapThread[ReplaceAll,{{x,x^2,x^3},{x->1,x->2,x->3}}]

Answer 2

I would use MapThread as it is the function designed for this purpose; but here is another solution step by step:

flist = {x, x^2, x^3}
rules = {x -> 1, x -> 2, x -> 3}
Transpose@{flist, rules}

{{x, x -> 1}, {x^2, x -> 2}, {x^3, x -> 3}}

Applying ReplaceAll to each sublist:

ReplaceAll @@@ Transpose@{flist, rules}

{1, 4, 27}

---

Not immediately relevant, but you can try the following variations:

x^# /. x -> # & /@ Range[3]
#^# & /@ Range[3]
Array[#^# &, 3]
Table[i^i, {i, 3}]

Answer 3

We define the following lists:

list = {x, x^2, x^3};
rules = {x -> 1, x -> 2, x -> 3};

And then we can run

0. Map

i[{ii_, iii_}] := ii /. iii;

• $\#_1$

The following:

Map[i, Transpose@{list, rules}]

and

• $\#_2$

equivalently

Map[i, Thread@{list, rules}]

1. Inner + ReplaceAll

Inner[ReplaceAll, list, rules, List]

2. Using Thread

ReplaceAll @@@ Thread[{list, rules}]

3. Why not Table

Table[list[[i]] /. rules[[i]], {i, Length@rules}]

4. What on earth are these @#%^&*?!

fnctn = #1 /. #2 & @@@ Transpose@({##}) &;
fnctn[list, rules]

5. MapIndexed served well

MapIndexed[#^# &, Range@Length@list]

6. Last + Map

Last /@ Power[List @@@ rules, Range[Length@rules]]

7. While also works

Module[{return = {}, i = 1, end = Length@list},
 While[i <= end,
  AppendTo[return, list[[i]] /. rules[[i]]]; i++]; return]

8. Using For because...why not?

Module[{return = {}}, For[
  i = 1, i <= Length@list, i++,
  AppendTo[return, list[[i]] /. rules[[i]]]];
 return]

9. After a lot of trial and error --- see again these weird @#%^&*?! stuff

smthng = {#1 /. #4, #2 /. #5, #3 /. #6} & @@ (## & @@@ {##}) &;
smthng[list, rules]

10. Something fancier using GeneralUtilities

Taking from the relevant code from said post, we have:

Needs@"GeneralUtilities`"
Module[{hold},
  SetAttributes[hold, HoldAll];
oneTimeRules[rules_] :=
Normal@Merge[rules, ListIterator] /. Rule -> RuleDelayed /. 
     i_GeneralUtilities`Iterator :> 
      With[{r = Read[i]}, hold[r, r =!= IteratorExhausted]] /. 
    hold -> Condition;
];

and then

Replace[list, oneTimeRules@rules, Length@rules]

11. Another fancy approach based on Michael E2's answer. This serves as a clarifying comment. Grab the relevant code that is needed

SetAttributes[useRepeated, Listable];
useRepeated[(Rule | RuleDelayed)[pat_, repl_], n_ : 1] :=
  Module[{used = 0},
   pat :> repl /; used++ < n
   ];
useOnce[r_] := useRepeated[r];

and then use

Replace[list, useOnce@rules, Length@rules]

or equivalently

ReplaceAll[list, useOnce@rules]

Note: if one uses Replace and the default value of the command -which is set to 1- the above does not work. So some minor caution is needed.

12. Laborious stuff, but works

• $\#_1$

The following:

(Transpose[{list, Values@rules}] /. {x, i_} -> {i, i} /. {x^2, 
  i_} :> {i^2, i} /. {x^3, i_} :> {i^3, i})[[All, 1]]

and

• $\#_2$

equivalently

(Thread[{list, Values@rules}] /. {x, i_} -> {i, i} /. {x^2, 
  i_} :> {i^2, i} /. {x^3, i_} :> {i^3, i})[[All, 1]]

---

---

All of the above give

Answer 4

a = {x, x^2, x^3};

b = {x -> 1, x -> 2, x -> 3};

Two more possibilities:

Diagonal[a /. List /@ b]

{1, 4, 27}

ReplacePart[a, i_ :> (a[[i]] /. b[[i]])]

{1, 4, 27}

Answer 5

list = {x, x^2, x^3};

rules = {x -> 1, x -> 2, x -> 3};

---

Using SubsetMap:

SubsetMap[Diagonal@*Function[x, #] &@list, Values@#, Values@#] &@rules

{1, 4, 27}

Or using Outer:

Diagonal@Outer[ReplaceAll, list, rules]

{1, 4, 27}